Histone proteins are decorated by a variety of protein posttranslational modifications called histone marks that modulate chromatin structure and function, contributing to the cellular gene expression program. This SnapShot summarizes the reported human, mouse, and rat histone marks, including recently identified lysine acylation marks.

In a SnapShot (short magazine feature) in Cell this week, Huang et al. provide this map of sorts, charting the landscape of histone modifications uncovered to date.
The crystal structure of the histone was resolved by Luger et al. in 1997, showing the octamer was held together by various protein-protein interactions (mainly through contacts between H3 and H3 within the (H3-H4)2 tetramer, and H3-H2B contacts between the tetramer and the H2A-H2B dimers. The histone proteins themselves are strongly basic, such that the entire octamer hydrogen bonds and electrostatically interacts with the [negatively charged] DNA phosphate backbone (as well as through non-polar contacts with the sugar groups). The ‘tails’ of the histone proteins contact neighbouring nucleosomes, and thus fine modifications throughout the structure modulate both the protein-protein and protein-DNA interactions (see Ryan 2011 for the full [thesis-length!] tale including a run-down on the Histone Code Hypothesis).
Histone modifiers, such as histone methyltransferases (often simply ‘methylases’) can act locally, globally, or in restricted domains (as for the H3K27me3 modification, i.e. trimethylathion of lysine 27 on histone 3). Recruitment to chromatin induced by protein’s DNA binding domains, other proteins complex members, TFs, RNA Pol and histone mod’s.
Interestingly, this leads to a system of feedback: modifications themselves recruit modifier enzymes to add further modifications.

Just 7 years ago the landscape was looking a whole lot simpler (as pictured by Bhaumik et al.)
The effects of these marks are usually separated (Ruthenburg et al. 2007, Campos & Reinberg 2009) into the
intrinsic single nucleosome changes, e.g. histone variant specific modifications like H2AX),
extrinsic chromatin organisation, i.e. nucleosome/nucleosome interactions; chromatin packaging, electrostatic charge effects such as H4 acetylation
effector-mediated in recruiting other proteins to chromatin, e.g. bromodomains binding acetylated sites, chromo-like royal domains (chromo, tudor, MBT “Malignant Brain Tumour domain” ) and PHD binding methylated sites, and 14-3-3 proteins binding phosphorylated sites; or preventing binding).
If this appears confusing, last month bioinformatician Ewan Birney wrote up a “cheat’s guide to histone modifications”

There are different types of histone protein. And just to be extra confusing, the same type of histone protein is sometimes made by more than one gene. (A lot of histone protein needs to be made during each cell cycle.)
Histone proteins are mainly compact, globular structures, but each one has a floppy peptide region at the start of the protein, which is described as the histone “tail” (somewhat confusingly in my view, as it’s at the start of the protein! Isn’t it more like a “trunk”?).


There is a raging debate about whether histone modifications can be considered to drive chromatin behaviour, or whether chromatin behaviour is simply a consequence of things which are happening nearby on the chromatin (in particular, transcription factor binding) (I am mainly a “consequence” person here). Either way, these modifications are extremely informative about what is going on in any given cell type.

Kouzarides, 2007, is another nice introductory paper for anyone seeking an introduction, but as Ewan’s post and the prior example emphasise 7 years has been a long time in the world of epigenetics research.

There was an interesting paper out earlier in the year under PLOS Genetics, in which the authors sought to “Uncouple Transcription from Covalent Histone Modification”. To summarise,

It is widely accepted that transcriptional regulation of eukaryotic genes is intimately coupled to covalent modifications of the underlying chromatin template, and in certain cases the functional consequences of these modifications have been characterized. Here we present evidence that gene activation in the silent heterochromatin of the yeast Saccharomyces cerevisiae can occur in the context of little, if any, covalent histone modification… Our results indicate that large increases in transcription can be observed in the virtual absence of histone modifications often thought necessary for gene activation.

The experiment that led them to such a conclusion involved an inducible heat shock gene (which would strongly stimulate transcription of genes involved in the heat shock response) under regulation by SIR. Finding this inducible system worked to produce >200-fold transcriptional induction even with neglible levels of histone modifications (H3K4me3, H3K36me3 and H3K79me2) that had been associated with transcription initiation and elongation.
A paper uploaded to BioRxiv 2 days ago describes a computational method to infer the interactions between chromatin modifiers and histone modifications (the feedback mechanism I referred to above), as a “high-confidence backbone of the chromatin-signaling network”.

The interactions between chromatin modifiers and histone modifications are often unknown, are based on the analysis of few genes, or are studied in vitro… Many recovered interactions have literature support; others provide hypotheses about yet unknown interactions. We experimentally verified two of these predicted interactions, leading to a link between H4K20me1 and members of the Polycomb Repressive Complexes 1 and 2.

Computationally, the technique revolves around use of sparse partial correlation networks (algorithms finding conditional probabilities in gene sequencing data, indicating causal influence) over previous methods of Bayesian Network inference and maximum entropy framework [the schematic overview for which is shown below].

Redundant information
Addressing what Birney described as the “raging debate” on histone modification (HM) causality ‒ whether they drive chromatin and chromatin modifier (CM) behaviour or not ‒ the authors write:

This approach accounts for interactions induced by correlations between HMs. Consequently, we prune the so-derived candidate chromatin-signaling network by computing sparse partial correlation networks, which is aimed to identify direct interactions between HMs and CMs accounting for correlations between CMs and HMs.

They describe the HMs and CMs as holding “redundant information” (both should contain information on gene expression, so for a particular gene they should be saying the same thing). Indeed, ~75% of gene expression variance is capable of attribution to HM and CM levels, “good predictive performance”.

If HMs and CMs reflect the same chromatin-signaling network, both should contain redundant information about gene expression such that combining them should yield only a marginal increase in the predictive power. Indeed, using both, CMs and HMs, improves the explained variance in gene expression only by 3% (4%) compared to using only HMs (CMs) at the expense of a higher model complexity (Figure 1C). Thus, these findings support that CMs and HMs jointly constitute a chromatin-signaling network involved in transcription and its regulation.


Their next step in the analysis showed CM levels accurately predict HM levels and vice versa, the accuracy of the prediction being limited by accuracy in expression and biochemical activity measurements. Having found colocalisation of HMs and CMs, they sought to determine likely CM-HM interacting pairs by first simply selecting the CMs most predictive of HMs and then applying sparse partial correlation networks. Exactly why they did so is a little abstract, but central to the work:

There are groups of HMs and CMs that exhibit very high pairwise correlation, suggesting that they are functionally related. However, within these groups no internal structure is visible, rendering an identification of interactions between the group members difficult. As CMs and HMs constitute a chromatin-signaling network, this high correlation is expected due to direct interactions between its components. However, high correlations could also be induced by other factors connecting the respective CM and HM. In general, the identity of these additional factors is not known, but we can account for those factors that are present in the dataset. Thus, we want to recover interactions between CMs and HMs that cannot be “explained away” by other variables in the dataset.
We recovered these interactions by applying a two-step procedure. First, we used a regularized regression technique called “Elastic Net”, where the CMs are used to predict HMs, to select only CMs that are informative for the prediction of a HM.

For a group of say 3 proteins [CMs] associated with a histone modification (e.g. H3K27me3), the Elastic Net method would try and dissect the contributions of each protein - how much more information one provides on the H3K27me3 HM in addition to the info provided by the other 2 chromatin modifiers.

Moreover, in case of groups of strongly correlated CMs the members of these groups tend to remain all in the model or are removed together. This approach accounts for possible interactions induced by correlations within the CMs but does not take into account correlations between the HMs. This indicates that highly correlated HMs might be predicted by similar sets of CMs, while only certain CMs actually interact with specific HMs.
Second, to remedy this situation we used a technique called “Sparse partial correlation networks” (SPCN), where the pairwise rank correlation between a CM and a HM is conditioned on all other variables in the data set. This method takes into account the correlation structure of both, CMs and HMs, and is conservative in proposing interactions. As a consequence, in groups of strongly correlated CMs and/or HMs, interactions may be explained away by individual members of the group. Thus, in the SPCN framework an identified interaction is likely to represent a direct interaction in the sense that it cannot be explained by other variables in the dataset. However, the failure to recover an interaction does not imply the absence of a biologically meaningful interaction. Within the SPCN framework some interactions between CMs and HMs arise from logical dependencies induced by sharing a common target. 
Thus, to recover interactions, we establish first the necessary condition that a CM is consistently highly predictive for an HM level by the Elastic Net approach and in a second step we prune those interactions that may be induced by correlations between the HMs using the SPCN approach. Thus, we focus only on interactions that are recovered by both methods. These interactions may originate from a direct function of the CM in setting, erasing or binding the HM but also from indirect interactions via unobserved CMs.

The important thing to take away from this is that this Elastic Net and SPCN combination is very conservative in its predictions of interactions, i.e. the false positives are minimised at the expense of potential false negatives: valorising specificity over sensitivity.
Sure enough, predicted interactions were backed up in the literature, and a couple of novel ones — H4K20me with CBX2 and EZH2 (components of Polycomb Repressor Complex 1 and 2 respectively) — were verified by the authors themselves upon immunoprecipitation. Interestingly, the finding “may form a mechanistic basis for the maintenance of Polycomb repression through the cell cycle”

The progression of cells through the cell cycle constitutes two challenges for the maintenance of Polycomb-mediated repression: (i) During DNA replication old and newly synthesized nucleosomes are randomly distributed to the daughter strands. This leads to an effective dilution of H3K27me3- bearing nucleosomes by half. (ii) During mitosis HMs, chromatin composition and structure change dramatically, rendering the proper transmission of H3K27me3 difficult.
H4K20me1 is tightly regulated during the cell cycle. It starts accumulating during S-phase and attains high levels during mitosis (37). Given this pattern, H4K20me1 may play an important role in maintaining PRCs at their target sites throughout the replicative and mitotic challenges by recruiting PRCs 1 and 2 to regions with old H3K27me3- and new H4K20me1-bearing nucleosomes.

Compared to the classical kinds of genetic disease (point mutations in a gene leading to a gain or loss of function) histone modification effects clearly present a great deal of complexity.
A little light was shed on the enigmatic complexes last year, when a group of Chinese scientists published cryo-electron microscopy images of the chromatin fibre. The structure produced by Song et al. showed

a histone H1-dependent left-handed twist of repeating tetranucleosomal structural units, within which the four nucleosomes zigzag back and forth with a straight linker DNA.

The veracity of the 30nm fibre in vivo has been challenged; a long-standing debate unresolved by these results. However, even in this garish false colour, they really are stunning.

The chromatin fibre was from the frog Xenopus laevis commonly used in biomedical research, and notably it lacked PTMs of the kind I’ve been discussing above. The paper notes:

Histone modifications and histone variants may also play important roles in the regulation of higher-order chromatin structure via modulating the internucleosomal surface interactions between tetranucleosomal units.

In the same issue in which they were published, Andrew Travers of the MRC-LMB in Cambridge, UK, described how the structures

[resolve] the fundamental issue as to whether the fiber is built from one nucleosome stack — a solenoid — or from two. However, importantly, the new structure differs in one largely unanticipated aspect from most previous models. Instead of the monotonous helix previously imposed by the limitations of the available information, the 30-nm fiber is formed by the tight helical packing of a tetranucleosomal unit. Within this unit, first observed by the crysallization of a tetranucleosome lacking linker histone, the two opposing nucleosome dimers are fully stacked on each other with only a small angular separation.
Between the units, the angular separation is larger and each unit is staggered relative to its nieghbor. The structure agrees well with all other direct measurements but does not exclude the possibility that a nucleosome array may still have the potential to fold into other helical forms.



…modelling of the fiber showed that retention of the tetranucleosome unit necessitated the alternating angular separation of nucleosomes observed by Song et al. However, in a second “idealized” model, some stacking interactions were broken to allow the formation of a more regular structure.
The presence of alternating stacking modes between spatially adjacent nucleosomes implies alternating internucleosomal contacts. In the tetranucleosomal dimer stacks, a major contact is between the exposed surfaces of two H2A-H2B core histone dimers. This interaction is absent in the inter-tetranucleosome contacts, where instead there are contacts between the amino-terminal tail of H4, primarily involving residue Arg-23 [ed: the most basic amino acid] and the acidic patches on the faces of the opposed nucleosomes.
…In the assembled fibers, the bulk of the globular domain of the linker histone is placed asymmetrically with respect to the inward-facing nucleosome dyad so that the principal contacts are at the dyad itself and with each of the entering linker DNA duplexes… The linker histone thus confers polarity on the symmetric core nucleosome in such a way that in the fiber, successive nucleosomes in a stack have opposite polarities, thereby stabilizing coherent stacking in the tetranucleosome unit and helical curvature between these units.
…Although the formation of continuous stacks by nucleosome core particles is well established, their biological relevance has been unclear.

Side note: The paper cited here [published in 2011] contains some pretty poor quality sketches from the early Luger structures (that is, all the way back in 1997), which really underscores the value of Song and colleagues’ work. It does however also contain a type of diagram I’ve never seen for DNA before — a schematic phase diagram of native nucleosome core particles.


Do we expect similar organizations of nucleosome core particles  in the living cell?
In chromosomes, NCPs are connected together by the continuous DNA link. Other components are also present, namely the fifth histone protein H1 and other proteins involved in the functional activity of the genetic material. The living system is therefore of a much higher complexity, with local variations in the concentrations of the multiples components of chromatin. These local heterogeneities offer the possibilities to monitor local changes of short-range interactions between NCPs, via histone tails interactions (the current hypothesis predicts that distinct covalent modifications of the histone tails, such as acetylation, methylation, etc., would determine a code (Jenuwein & Allis 2001). Interestingly, phase transitions can be triggered experimentally using living cells. The whole nucleus already engaged in a process of cell division can be swollen to several times its initial size by changing the ionic conditions, further condensed again by returning to initial ionic conditions to finally complete its cell division process.

Such experiments demonstrate the reversibility of chromatin structural changes upon variations of ionic conditions. Similar reversible phase transitions of unique chromosomes were also obtained experimentally by changing ionic conditions and using micromanipulation techniques (Poirier et al. 2002).
Unfortunately, structural data to understand how chromatin reorganizes during these processes are missing. The ordered phases formed by isolated NCPs in solution can be considered as possible models for the organization of chromatin in vivo. They provide a library of structures that may possibly exist in situ, since they were found under biologically relevant salt and NCP concentration ranges. Telomeric chromatin (a chromatin located at the extremity of chromosomes and playing a crucial role in the control of the lifetime of a given cell; Blackburn 2005) was proposed to be organized in a columnar phase for biochemical reasons, such as the lack of nucleosome positioning and a specific spacing along the DNA (Fajkus & Trifonov 2001). Lamellar structures with a periodicity of about 50 nm were also described in the fish Scyliorhinus sperm cell at a given step of the spermiogenesis process (Gusse & Chevaillier 1978). This organization may remind us of the lamello-columnar phase of NCPs. These and other examples lead us to suspect the possible regular organization of nucleosomes in special types of chromatin, but the structures remain to be analysed carefully, using new available developments of ultrastructural methodology.
More generally, in the classical eukaryotic chromatin, we do not expect the organization of NCPs to extend over long distances, but to be most probably restricted to micro-domains. In the context of the living cell, not only physico-chemical processes but also the activity of numerous enzymes and cofactors would help chromatin to organize in a sophisticated way, following an unknown path in the extremely complex phase diagram of chromatin. We guess that this complexity may offer extremely high possibilities of adaptation of chromatin organization to multiple local constraints.

▚  Huang et al. (2014) Snapshot: Histone Modifications. Cell, 159(2), 458-458.e1
▞  Draker Ryan’s PhD thesis — A Characterization of the Role of Post-translational Modification in Transcriptional Regulation by the Histone Variant H2A.Z. 
▚  Ewan Birney’s Cheat’s guide to histone modifications
▞  Perner et al. (2014) Inference of interactions between chromatin modifiers and histone modifications: from ChIP-Seq data to chromatin-signaling. bioRxiv, doi: 10.1101/010132
▚  Zhang et al. (2014) Uncoupling Transcription from Covalent Histone Modification. PLOS Genetics, 10(4): e1004202
▞  Song et al. (2014) Cryo-EM Study of the Chromatin Fiber Reveals a Double Helix Twisted by Tetranucleosomal Units. Science, 344, 376
▚  Andrew Travers (2014) The 30-nm Fiber Redux. Science, 344, 370
▞  Livolant et al. (2006) Are liquid crystalline properties of nucleosomes involved in chromosome structure and dynamics? Phil. Trans. R. Soc. A, 364, 2615-2633

Histone proteins are decorated by a variety of protein posttranslational modifications called histone marks that modulate chromatin structure and function, contributing to the cellular gene expression program. This SnapShot summarizes the reported human, mouse, and rat histone marks, including recently identified lysine acylation marks.

In a SnapShot (short magazine feature) in Cell this week, Huang et al. provide this map of sorts, charting the landscape of histone modifications uncovered to date.

The crystal structure of the histone was resolved by Luger et al. in 1997, showing the octamer was held together by various protein-protein interactions (mainly through contacts between H3 and H3 within the (H3-H4)2 tetramer, and H3-H2B contacts between the tetramer and the H2A-H2B dimers. The histone proteins themselves are strongly basic, such that the entire octamer hydrogen bonds and electrostatically interacts with the [negatively charged] DNA phosphate backbone (as well as through non-polar contacts with the sugar groups). The ‘tails’ of the histone proteins contact neighbouring nucleosomes, and thus fine modifications throughout the structure modulate both the protein-protein and protein-DNA interactions (see Ryan 2011 for the full [thesis-length!] tale including a run-down on the Histone Code Hypothesis).

Histone modifiers, such as histone methyltransferases (often simply ‘methylases’) can act locally, globally, or in restricted domains (as for the H3K27me3 modification, i.e. trimethylathion of lysine 27 on histone 3). Recruitment to chromatin induced by protein’s DNA binding domains, other proteins complex members, TFs, RNA Pol and histone mod’s.

Interestingly, this leads to a system of feedback: modifications themselves recruit modifier enzymes to add further modifications.

Just 7 years ago the landscape was looking a whole lot simpler (as pictured by Bhaumik et al.)

The effects of these marks are usually separated (Ruthenburg et al. 2007, Campos & Reinberg 2009) into the

  • intrinsic single nucleosome changes, e.g. histone variant specific modifications like H2AX),
  • extrinsic chromatin organisation, i.e. nucleosome/nucleosome interactions; chromatin packaging, electrostatic charge effects such as H4 acetylation
  • effector-mediated in recruiting other proteins to chromatin, e.g. bromodomains binding acetylated sites, chromo-like royal domains (chromo, tudor, MBT “Malignant Brain Tumour domain” ) and PHD binding methylated sites, and 14-3-3 proteins binding phosphorylated sites; or preventing binding).

If this appears confusing, last month bioinformatician Ewan Birney wrote up a “cheat’s guide to histone modifications

There are different types of histone protein. And just to be extra confusing, the same type of histone protein is sometimes made by more than one gene. (A lot of histone protein needs to be made during each cell cycle.)

Histone proteins are mainly compact, globular structures, but each one has a floppy peptide region at the start of the protein, which is described as the histone “tail” (somewhat confusingly in my view, as it’s at the start of the protein! Isn’t it more like a “trunk”?).

There is a raging debate about whether histone modifications can be considered to drive chromatin behaviour, or whether chromatin behaviour is simply a consequence of things which are happening nearby on the chromatin (in particular, transcription factor binding) (I am mainly a “consequence” person here). Either way, these modifications are extremely informative about what is going on in any given cell type.

Kouzarides, 2007, is another nice introductory paper for anyone seeking an introduction, but as Ewan’s post and the prior example emphasise 7 years has been a long time in the world of epigenetics research.

There was an interesting paper out earlier in the year under PLOS Genetics, in which the authors sought to “Uncouple Transcription from Covalent Histone Modification”. To summarise,

It is widely accepted that transcriptional regulation of eukaryotic genes is intimately coupled to covalent modifications of the underlying chromatin template, and in certain cases the functional consequences of these modifications have been characterized. Here we present evidence that gene activation in the silent heterochromatin of the yeast Saccharomyces cerevisiae can occur in the context of little, if any, covalent histone modification… Our results indicate that large increases in transcription can be observed in the virtual absence of histone modifications often thought necessary for gene activation.

The experiment that led them to such a conclusion involved an inducible heat shock gene (which would strongly stimulate transcription of genes involved in the heat shock response) under regulation by SIR. Finding this inducible system worked to produce >200-fold transcriptional induction even with neglible levels of histone modifications (H3K4me3, H3K36me3 and H3K79me2) that had been associated with transcription initiation and elongation.

A paper uploaded to BioRxiv 2 days ago describes a computational method to infer the interactions between chromatin modifiers and histone modifications (the feedback mechanism I referred to above), as a “high-confidence backbone of the chromatin-signaling network”.

The interactions between chromatin modifiers and histone modifications are often unknown, are based on the analysis of few genes, or are studied in vitro… Many recovered interactions have literature support; others provide hypotheses about yet unknown interactions. We experimentally verified two of these predicted interactions, leading to a link between H4K20me1 and members of the Polycomb Repressive Complexes 1 and 2.

Computationally, the technique revolves around use of sparse partial correlation networks (algorithms finding conditional probabilities in gene sequencing data, indicating causal influence) over previous methods of Bayesian Network inference and maximum entropy framework [the schematic overview for which is shown below].

Redundant information

Addressing what Birney described as the “raging debate” on histone modification (HM) causality ‒ whether they drive chromatin and chromatin modifier (CM) behaviour or not ‒ the authors write:

This approach accounts for interactions induced by correlations between HMs. Consequently, we prune the so-derived candidate chromatin-signaling network by computing sparse partial correlation networks, which is aimed to identify direct interactions between HMs and CMs accounting for correlations between CMs and HMs.

They describe the HMs and CMs as holding “redundant information” (both should contain information on gene expression, so for a particular gene they should be saying the same thing). Indeed, ~75% of gene expression variance is capable of attribution to HM and CM levels, “good predictive performance”.

If HMs and CMs reflect the same chromatin-signaling network, both should contain redundant information about gene expression such that combining them should yield only a marginal increase in the predictive power. Indeed, using both, CMs and HMs, improves the explained variance in gene expression only by 3% (4%) compared to using only HMs (CMs) at the expense of a higher model complexity (Figure 1C). Thus, these findings support that CMs and HMs jointly constitute a chromatin-signaling network involved in transcription and its regulation.

Their next step in the analysis showed CM levels accurately predict HM levels and vice versa, the accuracy of the prediction being limited by accuracy in expression and biochemical activity measurements. Having found colocalisation of HMs and CMs, they sought to determine likely CM-HM interacting pairs by first simply selecting the CMs most predictive of HMs and then applying sparse partial correlation networks. Exactly why they did so is a little abstract, but central to the work:

There are groups of HMs and CMs that exhibit very high pairwise correlation, suggesting that they are functionally related. However, within these groups no internal structure is visible, rendering an identification of interactions between the group members difficult. As CMs and HMs constitute a chromatin-signaling network, this high correlation is expected due to direct interactions between its components. However, high correlations could also be induced by other factors connecting the respective CM and HM. In general, the identity of these additional factors is not known, but we can account for those factors that are present in the dataset. Thus, we want to recover interactions between CMs and HMs that cannot be “explained away” by other variables in the dataset.

We recovered these interactions by applying a two-step procedure. First, we used a regularized regression technique called “Elastic Net”, where the CMs are used to predict HMs, to select only CMs that are informative for the prediction of a HM.

For a group of say 3 proteins [CMs] associated with a histone modification (e.g. H3K27me3), the Elastic Net method would try and dissect the contributions of each protein - how much more information one provides on the H3K27me3 HM in addition to the info provided by the other 2 chromatin modifiers.

Moreover, in case of groups of strongly correlated CMs the members of these groups tend to remain all in the model or are removed together. This approach accounts for possible interactions induced by correlations within the CMs but does not take into account correlations between the HMs. This indicates that highly correlated HMs might be predicted by similar sets of CMs, while only certain CMs actually interact with specific HMs.

Second, to remedy this situation we used a technique called “Sparse partial correlation networks” (SPCN), where the pairwise rank correlation between a CM and a HM is conditioned on all other variables in the data set. This method takes into account the correlation structure of both, CMs and HMs, and is conservative in proposing interactions. As a consequence, in groups of strongly correlated CMs and/or HMs, interactions may be explained away by individual members of the group. Thus, in the SPCN framework an identified interaction is likely to represent a direct interaction in the sense that it cannot be explained by other variables in the dataset. However, the failure to recover an interaction does not imply the absence of a biologically meaningful interaction. Within the SPCN framework some interactions between CMs and HMs arise from logical dependencies induced by sharing a common target.

Thus, to recover interactions, we establish first the necessary condition that a CM is consistently highly predictive for an HM level by the Elastic Net approach and in a second step we prune those interactions that may be induced by correlations between the HMs using the SPCN approach. Thus, we focus only on interactions that are recovered by both methods. These interactions may originate from a direct function of the CM in setting, erasing or binding the HM but also from indirect interactions via unobserved CMs.

The important thing to take away from this is that this Elastic Net and SPCN combination is very conservative in its predictions of interactions, i.e. the false positives are minimised at the expense of potential false negatives: valorising specificity over sensitivity.

Sure enough, predicted interactions were backed up in the literature, and a couple of novel ones — H4K20me with CBX2 and EZH2 (components of Polycomb Repressor Complex 1 and 2 respectively) — were verified by the authors themselves upon immunoprecipitation. Interestingly, the finding “may form a mechanistic basis for the maintenance of Polycomb repression through the cell cycle

The progression of cells through the cell cycle constitutes two challenges for the maintenance of Polycomb-mediated repression: (i) During DNA replication old and newly synthesized nucleosomes are randomly distributed to the daughter strands. This leads to an effective dilution of H3K27me3- bearing nucleosomes by half. (ii) During mitosis HMs, chromatin composition and structure change dramatically, rendering the proper transmission of H3K27me3 difficult.

H4K20me1 is tightly regulated during the cell cycle. It starts accumulating during S-phase and attains high levels during mitosis (37). Given this pattern, H4K20me1 may play an important role in maintaining PRCs at their target sites throughout the replicative and mitotic challenges by recruiting PRCs 1 and 2 to regions with old H3K27me3- and new H4K20me1-bearing nucleosomes.

Compared to the classical kinds of genetic disease (point mutations in a gene leading to a gain or loss of function) histone modification effects clearly present a great deal of complexity.

A little light was shed on the enigmatic complexes last year, when a group of Chinese scientists published cryo-electron microscopy images of the chromatin fibre. The structure produced by Song et al. showed

a histone H1-dependent left-handed twist of repeating tetranucleosomal structural units, within which the four nucleosomes zigzag back and forth with a straight linker DNA.

The veracity of the 30nm fibre in vivo has been challenged; a long-standing debate unresolved by these results. However, even in this garish false colour, they really are stunning.



The chromatin fibre was from the frog Xenopus laevis commonly used in biomedical research, and notably it lacked PTMs of the kind I’ve been discussing above. The paper notes:

Histone modifications and histone variants may also play important roles in the regulation of higher-order chromatin structure via modulating the internucleosomal surface interactions between tetranucleosomal units.

In the same issue in which they were published, Andrew Travers of the MRC-LMB in Cambridge, UK, described how the structures

[resolve] the fundamental issue as to whether the fiber is built from one nucleosome stack — a solenoid — or from two. However, importantly, the new structure differs in one largely unanticipated aspect from most previous models. Instead of the monotonous helix previously imposed by the limitations of the available information, the 30-nm fiber is formed by the tight helical packing of a tetranucleosomal unit. Within this unit, first observed by the crysallization of a tetranucleosome lacking linker histone, the two opposing nucleosome dimers are fully stacked on each other with only a small angular separation.

Between the units, the angular separation is larger and each unit is staggered relative to its nieghbor. The structure agrees well with all other direct measurements but does not exclude the possibility that a nucleosome array may still have the potential to fold into other helical forms.

…modelling of the fiber showed that retention of the tetranucleosome unit necessitated the alternating angular separation of nucleosomes observed by Song et al. However, in a second “idealized” model, some stacking interactions were broken to allow the formation of a more regular structure.

The presence of alternating stacking modes between spatially adjacent nucleosomes implies alternating internucleosomal contacts. In the tetranucleosomal dimer stacks, a major contact is between the exposed surfaces of two H2A-H2B core histone dimers. This interaction is absent in the inter-tetranucleosome contacts, where instead there are contacts between the amino-terminal tail of H4, primarily involving residue Arg-23 [ed: the most basic amino acid] and the acidic patches on the faces of the opposed nucleosomes.

…In the assembled fibers, the bulk of the globular domain of the linker histone is placed asymmetrically with respect to the inward-facing nucleosome dyad so that the principal contacts are at the dyad itself and with each of the entering linker DNA duplexes… The linker histone thus confers polarity on the symmetric core nucleosome in such a way that in the fiber, successive nucleosomes in a stack have opposite polarities, thereby stabilizing coherent stacking in the tetranucleosome unit and helical curvature between these units.

…Although the formation of continuous stacks by nucleosome core particles is well established, their biological relevance has been unclear.

Side note: The paper cited here [published in 2011] contains some pretty poor quality sketches from the early Luger structures (that is, all the way back in 1997), which really underscores the value of Song and colleagues’ work. It does however also contain a type of diagram I’ve never seen for DNA before — a schematic phase diagram of native nucleosome core particles.

Do we expect similar organizations of nucleosome core particles
in the living cell?

In chromosomes, NCPs are connected together by the continuous DNA link. Other components are also present, namely the fifth histone protein H1 and other proteins involved in the functional activity of the genetic material. The living system is therefore of a much higher complexity, with local variations in the concentrations of the multiples components of chromatin. These local heterogeneities offer the possibilities to monitor local changes of short-range interactions between NCPs, via histone tails interactions (the current hypothesis predicts that distinct covalent modifications of the histone tails, such as acetylation, methylation, etc., would determine a code (Jenuwein & Allis 2001). Interestingly, phase transitions can be triggered experimentally using living cells. The whole nucleus already engaged in a process of cell division can be swollen to several times its initial size by changing the ionic conditions, further condensed again by returning to initial ionic conditions to finally complete its cell division process.

image

Such experiments demonstrate the reversibility of chromatin structural changes upon variations of ionic conditions. Similar reversible phase transitions of unique chromosomes were also obtained experimentally by changing ionic conditions and using micromanipulation techniques (Poirier et al. 2002).

Unfortunately, structural data to understand how chromatin reorganizes during these processes are missing. The ordered phases formed by isolated NCPs in solution can be considered as possible models for the organization of chromatin in vivo. They provide a library of structures that may possibly exist in situ, since they were found under biologically relevant salt and NCP concentration ranges. Telomeric chromatin (a chromatin located at the extremity of chromosomes and playing a crucial role in the control of the lifetime of a given cell; Blackburn 2005) was proposed to be organized in a columnar phase for biochemical reasons, such as the lack of nucleosome positioning and a specific spacing along the DNA (Fajkus & Trifonov 2001). Lamellar structures with a periodicity of about 50 nm were also described in the fish Scyliorhinus sperm cell at a given step of the spermiogenesis process (Gusse & Chevaillier 1978). This organization may remind us of the lamello-columnar phase of NCPs. These and other examples lead us to suspect the possible regular organization of nucleosomes in special types of chromatin, but the structures remain to be analysed carefully, using new available developments of ultrastructural methodology.

More generally, in the classical eukaryotic chromatin, we do not expect the organization of NCPs to extend over long distances, but to be most probably restricted to micro-domains. In the context of the living cell, not only physico-chemical processes but also the activity of numerous enzymes and cofactors would help chromatin to organize in a sophisticated way, following an unknown path in the extremely complex phase diagram of chromatin. We guess that this complexity may offer extremely high possibilities of adaptation of chromatin organization to multiple local constraints.

▚  Huang et al. (2014) Snapshot: Histone Modifications. Cell, 159(2), 458-458.e1

▞  Draker Ryan’s PhD thesis — A Characterization of the Role of Post-translational Modification in Transcriptional Regulation by the Histone Variant H2A.Z

▚  Ewan Birney’s Cheat’s guide to histone modifications

▞  Perner et al. (2014) Inference of interactions between chromatin modifiers and histone modifications: from ChIP-Seq data to chromatin-signaling. bioRxiv, doi: 10.1101/010132

▚  Zhang et al. (2014) Uncoupling Transcription from Covalent Histone Modification. PLOS Genetics10(4): e1004202

▞  Song et al. (2014) Cryo-EM Study of the Chromatin Fiber Reveals a Double Helix Twisted by Tetranucleosomal UnitsScience344, 376

▚  Andrew Travers (2014) The 30-nm Fiber Redux. Science344, 370

▞  Livolant et al. (2006) Are liquid crystalline properties of nucleosomes involved in chromosome structure and dynamics? Phil. Trans. R. Soc. A364, 2615-2633

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The 2014 Nobel prize for Chemistry: Super-resolution microscopy

Two separate principles are rewarded. One enables the method stimulated emission depletion (STED) microscopy, developed by Stefan Hell in 2000. Two laser beams are utilized; one stimulates fluorescent molecules to glow, another cancels out all fluorescence except for that in a nanometre-sized volume. Scanning over the sample, nanometre for nanometre, yields an image with a resolution better than Abbe’s stipulated limit.

Eric Betzig and William Moerner, working separately, laid the foundation for the second method, single-molecule microscopy. The method relies upon the possibility to turn the fluorescence of individual molecules on and off. Scientists image the same area multiple times, letting just a few interspersed molecules glow each time. Superimposing these images yields a dense super-image resolved at the nanolevel. In 2006 Eric Betzig utilized this method for the first time.

Today, nanoscopy is used world-wide and new knowledge of greatest benefit to mankind is produced on a daily basis.

The three scientists awarded this year’s Chemistry Nobel work across 3 separate institutes, and despite its categorisation it has found application and inspiration, as well as driven advance in both the biological and physical sciences. As the committee head Sven Lidin told the Nobel press junket earlier, “Super-resolution microscopy doesn’t only tell us where, but also when and how. Biology has turned to chemistry, Chemistry has turned into Biology. Guesswork has turned into hard facts, and obscurity has turned into clarity.”

The technique is fairly new, born just 14 years ago, and at its outset was greeted with widespread derision owing to the suggestion that the Abbe diffraction limit for a microscope, first shown by Ernst Abbe in 1873 (translation of the work in question can be found here), could be wriggled free of. From Nikon MicroscopyU:

The resolution limits imposed by the physical laws that govern optical microscopy can be exceeded, however, by taking advantage of “loopholes” in the law that underscore the fact that the limitations are true only under certain assumptions. There exist three particularly important assumptions that are brought into play during assessment of resolution criteria, including the conventional geometry in which light is gathered by the objective, the uniformity of excitation light throughout the specimen, and the linear characteristics (absorption and emission) of fluorescence involving a single photon. In brief, resolution can be enhanced by gathering light over a larger set of angles around the specimen or using excitation light that varies with position. The diffraction barrier can also be broken using fluorescence processes that involve two or more photons in a non-linear manner.

Having been vindicated and then some by the technique’s (or rather set of techniques’) ascent into wide usage amongst biophysical/cell biological studies, here’s a look into what the trio who first pioneered it have been working on.

Eric Betzig, at Janelia Farm Research Campus, HHMI (USA)

Betzig’s lab dissects its interests across 4 key projects:

  1. Spatial resolution

    Transfected cells expressing fluorescent proteins contain information on the spatial organization of specific target proteins that is accurate at the molecular level. However, conventional optical microscopy is limited by diffraction to imaging on a scale coarser by two orders of magnitude. Together, my colleague Harald Hess and I invented PALM, a microscope which uses the serial photoconversion and localization of hundreds of thousands of individual molecules, including fluorescent proteins or photoswitchable dyes, to build an image at near-molecular resolution. At Janelia, we have each pursued various extensions and applications of this technology, including multicolor and live cell imaging in my lab, and three dimensional interferometric PALM in Harald’s.

  2. Temporal resolution

    Although many methods exist to image fixed, frozen, or sectioned cells at high resolution, fluorescence microscopy is unique in its ability to study the dynamics of specific target proteins and organelles within living cells. However, since cells evolve in three dimensions, a key challenge is how to image fast enough to follow this evolution continuously in time throughout the entire cellular volume. In my lab, we have developed a variant of plane illumination microscopy that uses scanned Bessel beams to image living cells with 3D isotropic resolution at hundreds of image frames per second.

    For high speed 3D imaging in scattering tissues, my colleague Na Ji and I have developed another technology, the passive pulse splitter – a self-contained unit that, when placed in the path of an ultrafast laser, can increase the pulse repetition rate, and hence the imaging speed, by more than a hundred-fold. Potential applications include high throughput anatomical mapping of neural circuits or rapid functional imaging of activity in neural populations.

  3. Noninvasive imaging

    Sadly, even optical microscopy is somewhat invasive: extended imaging of living cells or tissues often leads to light-induced damage. Furthermore, in fluorescence microscopy, every sample contains a finite number of fluorescent molecules, each of which will emit a finite number of photons before irrevocably bleaching. In other words, every fluorescent sample has a finite photon budget. As spatiotemporal resolution improves, it becomes imperative to devise methods that use this budget efficiently. By confining the light excitation to a plane of submicron thickness, our Bessel beam plane illumination microscope substantially reduces photobleaching and phototoxicity compared to popular epi-illumination techniques (e.g., widefield or confocal microscopy), thereby permitting hundreds of 3D image stacks encompassing tens of thousands of image frames to be acquired from a single living cell.

    The high peak excitation intensity required in nonlinear optical imaging methods, such as two photon fluorescence microscopy, can also lead to significant photodamage. Together, Na, I, and our colleague Jeff Magee have shown that our pulse splitter, when used with N-fold splitting and N1/2 higher average laser power, produces the same signal level as a two photon system without splitting, but with up to nine-fold less photobleaching in vivo and a six- to twenty-fold reduction in the rate of photodamage during calcium recording of neural activity in acute brain slices.

  4. Multicellular and deep tissue imaging

    Optical microscopes achieve diffraction-limited performance only when imaging through the immersion medium for which they are designed – usually water in the case of in vivo imaging. However, nearly all biological specimens larger than a single cell are rife with refractive index inhomogeneities. As a result, many biologists do not approach the level of spatial resolution in their images that they might assume. Similar problems, confronted by astronomers when imaging through Earth’s turbulent atmosphere, have long been addressed by using adaptive optics. Motivated by their success, Na Ji and I have developed an approach for adaptive optics suited to the constraints of biological microscopy. Using the approach, we can recover near-diffraction-limited performance in a variety of specimens, including those exhibiting large amplitude and/or spatially complex aberrations.

The lab’s publication on Bessel beam plane illumination gives a nice introduction to the theory underpinning the method:

3D live imaging is important for a better understanding of biological processes, but it is challenging with current techniques such as spinning-disk confocal microscopy. Bessel beam plane illumination microscopy allows high-speed 3D live fluorescence imaging of living cellular and multicellular specimens with nearly isotropic spatial resolution, low photobleaching and low photodamage. Unlike conventional fluorescence imaging techniques that usually have a unique operation mode, Bessel plane illumination has several modes that offer different performance with different imaging metrics. To achieve optimal results from this technique, the appropriate operation mode needs to be selected and the experimental setting must be optimized for the specific application and associated sample properties.

3D live fluorescence imaging with subcellular spatial resolution is challenging because it requires a good balance between spatial resolution, optical sectioning, imaging speed, photobleaching, photodamage and other factors.

Echoing his lab’s key stated projects, the paper describes how 3D spatial resolution must be nearly isotropic (uniform in all orientations) over a few 100nm nanometers to spot subcellular structures; with high quality sectioning of the material (no thick samples, or overly dense fluorescent labelling); imaging itself must be fast enough to capture subcellular dynamics (up to 100s of planes per second is possible) which must increase in line with desired spatial resolution improvements to avoid blurry images; and lastly the photobleaching and photodamage induced must be low enough to allow dense enough (and long enough) imaging protocols to follow the timescale of the biological process “while leaving the specimen undisturbed so that the true physiological process is revealed“.

It is worth mentioning that this problem represents a huge challenge for many 3D live imaging techniques because at least ten times and as many as 100 times or more 2D image planes must be collected per 3D time point over typical cellular dimensions. Finally, these issues do not exist independently; they are often in opposition. For instance, higher spatial resolution almost always results in lower imaging speed, increased photobleaching and higher photodamage, and vice versa.

The Bessel beam gets its name from the Bessel function, since the beam,

one of a class of so-called ‘non-diffracting beams’ propagates indefinitely with no change in its cross-sectional intensity profile I(r) ∝ |J0(αr)|2 where J0(αr) is the zero-order Bessel function of the first kind.

The 1987 reference here compares Bessel and Gaussian beams (named for the fact that their intensities spread out to following a Gaussian, a.k.a. normal, distribution), deals with [disproving] a power phenomenon that would write off Bessel beams as useful tools to highlight the optimisations required for this intricate optical method, but crucially, that beam spreading is nonexistent compared to the factor of √2 ‘blurring’ of Gaussian ones.

The paper concludes that total Bessel power ≈ N × total Gaussian power, where N is the total number of rings in the Bessel function in the plane z = 0. These rings can be seen in Table 1 of the lab’s paper.

the central peak of this ideal beam is surrounded by an infinite series of concentric side lobes of decreasing peak intensity, but with equal integrated intensity in each lobe. The ideal beam would exist at the front focal plane of a lens illuminated at its back focal plane with an infinitesimally thin annulus of light.

In practice, this is not possible. An experimental ‘Bessel beam’ is actually a Bessel-Gauss beam created with annular illumination of finite width. For a given [excitation], the thinner the annulus, the more Bessel-like the beam becomes, the longer its axial extent (i.e., the beam length), and the more energy exists in the side lobes (Fig. 1b). Conversely, the wider the annulus, the more Gaussian the character of the beam, the shorter its axial extent, and the smaller the side lobe energy.

In short, the proportion of this ideal Bessel beam achieved in an experimental laser beam compared to the proportion of blurry Gaussian beam is maximised by using the smallest possible area of illumination. Increasing the size of this annulus will obviously enable ‘scanning’ of a larger area (“the width of the central peak, and hence the thickness of the central core of a virtual light sheet made by sweeping the beam…”) as is desirable for surveying the landscape of the cell but at the cost of reduced imaging quality (“increased energy in excitation tails”).

Hence, a key aspect of Bessel beam plane illumination is to use a beam that is only as long as is necessary to cover the desired field of view and no longer. Beyond this, other tricks, such as nonlinear excitation or structured illumination, are needed to mitigate the effects of the reduced optical sectioning and increased out-of-focus background and photobleaching resulting from the residual side lobe energy.

…the selection of “appropriate operation mode…optimized for the specific application” mentioned earlier.

image

The lab also works on imaging single-molecules of actin in the brain using single particle tracking PALM (sptPALM), error correction around the inhomogeneities of real-world biological specimens, and found evidence that stochastic self-assembly can create and maintain roughly periodic structures in biological membranes without direct cytoskeletal involvement or active transport using PALM.

Recommended reading for those interested in joining his lab is the transcription of a 1986 seminar from Bell labs computer scientist, information theorist and mathematician Richard Hamming, You and Your Research, which broached the question, “Why do so few scientists make significant contributions and so many are forgotten in the long run?”

The title of my talk is, “You and Your Research.” It is not about managing research, it is about how you individually do your research. I could give a talk on the other subject - but it’s not, it’s about you. I’m not talking about ordinary run-of-the-mill research; I’m talking about great research. And for the sake of describing great research I’ll occasionally say Nobel-Prize type of work. It doesn’t have to gain the Nobel Prize, but I mean those kinds of things which we perceive are significant things. Relativity, if you want, Shannon’s information theory, any number of outstanding theories - that’s the kind of thing I’m talking about.

I won’t spoil it for you, but I did like an answer to one of the closing questions regarding extent and method of scientific reading, when Dick prescribed the scientist to take caution:

If you read all the time what other people have done you will think the way they thought. If you want to think new thoughts that are different, then do what a lot of creative people do - get the problem reasonably clear and then refuse to look at any answers until you’ve thought the problem through carefully how you would do it, how you could slightly change the problem to be the correct one. So yes, you need to keep up. You need to keep up more to find out what the problems are than to read to find the solutions. The reading is necessary to know what is going on and what is possible. But reading to get the solutions does not seem to be the way to do great research. So I’ll give you two answers. You read; but it is not the amount, it is the way you read that counts.

Books by Hamming include Numerical Methods for Scientists and Engineers (1962), Methods of Mathematics Applied to Calculus, Probability and Statistics (1985), and The Art of Doing Science and Engineering: Learning to Learn (1997).

Stefan Hell, at Max Planck Institute for Biophysical Chemistry, Gottingen, and German Cancer Research Center, Heidelberg (Germany)

I was reading a paper, and going through the details of a paper [when the news came]… [After I’d received the news] I read the paragraph that I wanted to read to the end… and then I called up my wife

— From an interview from earlier today with Stefan Hell posted to Soundcloud.

“I thought, so much physics happened in the 20th century that it’s impossible that there’s no phenomenon, or specifically chemistry phenomenon that would allow you to overcome the diffraction barrier that was coined in 1873 or so - I got kind of convinced that there must be something and so I tried to find something, and eventually I found a way to overcome that limit.”

His lab pioneers use of STED, RESOLFT, GSDIM and PALMIRA, and has archived all of their papers on the site, including an interesting one on silicon-rhodamine derivatives, a rheological study on multi-protein assemblies underlying the mesoscale organisation of the plasma membrane using a genetically encoded ‘click chemistry’ approach (pictured) and the paper I recently wrote about here on super-resolution microscopy of mitochondriaEdit: it seems Betzig’s lab is by far the most prolific - these are just those published within 2014!

There’s also an intriguing spin-off (if you’ll pardon the pun) in collaboration with Max Planck Institute’s Balasubramanian group just last month into quantum computing — Room temperature high-fidelity holonomic single-qubit gate on a solid-state spin which would appear to have arisen from 2013 work in which STED was used to resolve ‘individual Nitrogen vacancy centres in diamond nanocrystals‘:

Nitrogen-vacancy (NV) color centers in nanodiamonds are highly promising for bioimaging and sensing… Combining this atom-sized solid-state system with subdiffraction resolution optical microscopy should allow sensing the interior of cells at the nanoscale in a unique, multifunctional way… However, resolving individual NV centers within nanodiamond particles and the controlled addressing and readout of their spin state has remained a major challenge.

Spatially stochastic super-resolution techniques cannot provide this capability in principle, whereas coordinate-controlled super-resolution imaging methods, like stimulated emission depletion (STED) microscopy, have been predicted to fail in nanodiamonds. Here we show that, contrary to these predictions, STED can resolve single NV centers in 40–250 nm sized nanodiamonds with a resolution of ≈10 nm. Even multiple adjacent NVs located in single nanodiamonds can be imaged individually down to relative distances of ≈15 nm. Far-field optical super-resolution of NVs inside nanodiamonds is highly relevant for bioimaging applications of these fluorescent nanolabels. The targeted addressing and readout of individual NV spins inside nanodiamonds by STED should also be of high significance for quantum sensing and information applications.

These Nitrogen-vacancy centres, pictured above, are importance as spin sensors for bioscience, upon which various techniques including most importantly NMR spectroscopy rely. The NV centre itself is a unique defect in a diamond lattice with ‘astounding properties‘. From the Balasubramanian lab blurb:

The single spins associated with the defect can be optically polarized, manipulated and read-out. To date these defects hold the record for the longest spin coherence time in solid-state spin system at room temperature. These remarkable properties make NV center a unique atom sized, optically readable, ultra-precision magnetic field sensor. The research focus is directed towards developing nanoscale diamond sensor for biomolecular applications. The experimentally achieved sensitivities using single NV centers have shown to reach few nT/√Hz. The magnitude of magnetic field and the fluctuations caused by a single electron spin or a few nuclear spins exceeds these values at nanoscopic proximities. The NV sensor has the ability to map the spin density and strength giving an idea about the molecular structure and assembly of biomolecular complexes. A molecular structure microscope using NV center holds potentials to emerge as a method for structure elucidation of single biomolecules reaching atomic resolutions.

The Hell lab paper out last month contains a schematic of their geometry and level structure. I’d need to brush up on my solid state chemistry to make much of this, but interesting nonetheless. The team describe their advance as “a promising step towards quantum computing at room temperature”.

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William Moerner, at Stanford University (USA)

Moerner wins not just the Nobel but also without a doubt the honour of most fun website, including both an online shop with personalised children’s clothing and wall-clocks bearing ensemble averaging-related insignia, and a page dedicated to “the GUACAmole”.

What is a GUACAmole? A guacamole is one single molecule [that is, 1/(Avocado’s Number) of moles]. Read the basics of single-molecule spectroscopy in the Research Section for details. Here are few citations noting our definition of “guacamole”:

W. E. Moerner, “Optical Spectroscopy of Individual Molecules Trapped in Solids,” AIP Conf. Proc. Vol. 323, AIP, New York, 1995, p. 467.
W. E. Moerner, “High-Resolution Optical Spectroscopy of Single Molecules in Solids,” Accounts of Chemical Research, 1996, 29, 563.
K. M. Reese, “Plus ca change, plus c’cest la meme guacamole,” Chemical and Engineering News, March 10, 1997, p. 200.

The list of accolades and achievements on the site shows the group are far from goofing off though. The coverage in various media outlets on super-resolution microscopy charts the rise of these methods to prominence over the past two decades.

The earliest of these was a Science piece, ‘Cancelling Brownian Motion‘, which in a very brief Applied Physics research highlight noted the Moerner lab’s development of the anti-Brownian electrophoretic, or ABEL, trap that cancels Brownian motion, all stated very matter-of-factly, its significance yet to be grasped outside of the pages of Appl. Phys. Lett.

One problem in trapping small particles or cells in solution for further study is the ever-present jostling caused by Brownian motion. Cohen and Moerner have developed an anti-Brownian electrophoretic, or ABEL, trap that cancels Brownian motion. Particle movement was followed via fluorescence microscopy. Images were acquired and processed in real time, and the resulting analysis was used to apply voltages to a set of four electrodes, which create a gap of 10 to 15 μm around the particle. The applied electric fields create electrophoretic drift that cancels Brownian motion in the plane. Excursions of polystyrene nanospheres of more than 5 μm from the center of the trap were rare.

There’s also an informative interview about super-resolution microscopy with Moerner from 2009, which he concludes with a suggestion as to where the field would be heading in coming years.

The outlook is truly exciting. As more and more molecules and methods for super-resolution imaging are developed, the power of optical microscopy to observe complex nanoscale systems non-invasively will increase. I find it particularly exciting that the ability of single molecules to act as nanoscale light sources inside materials is now being used to achieve super-resolution imaging. In most cases, these methods do not require complex sectioning or freezing (as electron or X-ray methods do), so the actual structures in living systems, and structures that undergo time-dependent changes, can be observed. The gap between X-ray/electron microscopy and optical microscopy is narrowing rapidly.

Previous posts on super-resolution microscopy:

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Structural variations efficiently orchestrate the gain and loss of cancer gene cassettes that engage many oncogenic pathways simultaneously and such oncogenic cassettes are favoured during the evolution of a cancer

Genetic changes through somatic mutations span from single nucleotide alterations to breakpoints interrupting gene contiguity, segmental copy number changes, and imbalances of entire chromosomes

Beginning their review with a description of the basics of cancer, from the genetic events to citing Hardy and Weinberg’s Hallmarks of Cancer paper, the authors of a new paper in Genome Research provide evidence to support a fresh consideration of the disease’s evolution.
Though the traditional view of somatic mutations in oncogenesis is one largely of point mutation, recent reports have notably suggested otherwise: . Similarly, earlier focus on single driver oncogenes within amplicons has matured into greater concern for the multiplicity of such ‘drivers’.

Moreover, each amplicon or region of copy number loss alters the expression of many adjacent genes, some with proven conjoint cancer effects (Zhang et al. 2009; Curtis et al. 2012). Thus, any cancer is likely to be a composite of hundreds to thousands of gene changes that contribute to the cancer state. Although specific point mutations contribute to adaptive evolutionary processes, recent genomic analyses from controlled evolutionary experiments in model systems suggest that copy number changes through segmental duplications and rearrangements may play a more prominent role (Chang et al. 2013; Fares et al. 2013).
… From whole-genome sequencing data, we learned that, although there are some common oncogenic drivers, each cancer shows combinations of genomic aberrations that often are unique for that individual tumor. These structural aberrations and their consequent expression profiles engage a range of biochemical and cellular functions that, as a whole, cannot be ascribed to a single oncogenic pathway. Using deep genomic analyses of breast cancers to reveal the detailed genetic landscape of each tumor, we sought to find coherence in how the many different somatic mutations may be related.
By examining the detailed structural genomic alterations associated with common amplicons, we found evidence for a sequence of structural variations affecting recurrent regions of genomic amplification. In five of the seven analyzed breast cancers with evidence of copy number gain at the ERBB2 locus, large tandem duplications encompassing the ERBB2 gene appeared to initiate the amplification of the region. In most cases, ERBB2 amplification was associated with copy number loss of BRCA1 through different genomic mechanisms. In three samples, unpaired inversions joined the ERBB2 locus with the region on 17q21.3* that would be subsequently amplified; and in all three cases, we found structural evidence for a deletion of the intervening chromosomal segment containing the BRCA1 gene. In the remaining samples, ERBB2 is amplified through more complex rearrangements that included translocation to other chromosomes and multiple unpaired inversions.

* 17q21.3 here is cytogenetic notation addressing a genomic locus, specifically one on the long arm ( “q” ) of chromosome 17, region 2, band 1, sub-band 3.
Previous work from the group into “transcriptional consequences of somatic structural variations” in primary breast cancers and associated cell lines showed that a single tandem duplication in a particular amplified locus led to selection of cancers “with augmented expression of two adjacent oncogenic components“.

Generalizing from this observation, we hypothesize that conjoint expression of adjacent oncogenes or loss of adjacent cancer suppressors may provide a “systems genetic” strategy for activating cassettes of oncogenic signals.

The paper assesses how these structural variations play a role in establishing transcriptional programs optimal for evolution of individual cancers.
In summary, through analysing “deep-sequencing” (also known paradoxically as ‘next generation’ sequencing) data, they find reason to believe that rearrangements, such as unpaired inversions connecting the ERBB2 and 17q21.3 loci or a direct deletion of BRCA1, followed by coamplification of the newly linked ERBB2 and 17q21.3 loci, are “among the key events leading such an optimal genomic rearrangement“.

in the vast majority of cases, BRCA1 is lost before the ERBB2-17q21.3 linked region is amplified… amplification of 17q21.3 and loss of BRCA1 represent a frequent configuration among ERBB2-amplified tumors.
If one views the genetic landscape of a tumor as an indication of evolutionary optimization for any specific cancer, then the identification of frequent conjoint genetic events can be a means to discover additive or synergistic actions of oncogenic elements.

In a really nice turn to their ‘systems genetics’ paradigm they validated this hypothesis (in vitro), showing overexpressed ERBB2 and enforced knockdown of BRCA1 expression augmented growth of human mammary epithelial cells (“HMECs“) together to a greater extent than either genomic modification did individually.
With proof of principle in hand, the team turned to this 17q21.3 locus, finding 19 of the 21 genes there exerted “*positive growth effects that were at least additive, and in seven cases possibly synergistic with those elicited by ERBB2 activity.*”

Finally, the observation that TP53 copy number loss occurs in 79% of the cases in which BRCA1 is also lost (Fig. 3) strongly suggests some functional interaction. Indeed, it has been noted that TP53 and BRCA1 interact together to optimally induce the expression of SFN (14-3-3ς), a major G2/M checkpoint control gene that blocks progression of cells with DNA damage through mitosis (Aprelikova et al. 2001). The loss of SFN regulation would lead to abnormal checkpoint control, a mechanism for genomic instability.

Give yourself a pat on the back if you can decipher how the 0.79 equates to 79% TP53 copy number loss, this chart just boggles my mind: 

Thus, the chromosomal “origami” generated by the conjoint rearrangements on 17q (ERBB2 tandem duplication followed by unpaired inversions or deletions disrupting BRCA1 and linking ERBB2 with the downstream 17q21.3 amplicon) appears to be a topologically parsimonious strategy to generate a genomic state favoring tumor growth (Fig. 6, [ed: main image, top of post]). In addition, through only a few genomic rearrangements, the simultaneous activation by copy number gain and the attenuation by copy number loss of genes affecting cancer cell growth suggest that rearrangements significantly restructure the cancer genome to engage the maximal number of oncogenic elements with each rearrangement, so that even small copy number changes manifest to global changes in levels of gene expression.

By “topologically parsimonious” the authors mean to direct their reader’s attention to the evolutionary landscape in which these rearrangements take place — frugality, being canny with resources [parsimony] is needed to achieve the tumour’s “goal” of sorts, which is growth promotion without genomic catastrophe resulting from an overly rearranged genome being left without sufficiently viable genome [which via a variety of safeguarding mechanisms leads to cell apoptosis; if I’m reading this correctly].

It has been previously recognized that some cancer-associated genes are colocalized in the genome. A classic example of this is the overlapping localization of the p16INK4a and p14ARF tumor suppressors encoded within the CDKN2A locus on 9p21. Deletions at this locus routinely inactivate both cell-cycle regulators (Bates et al. 1998; Stott et al. 1998). Recent evidence also suggests that oncogenes and tumor suppressor genes (TSGs) are clustered, including several TSGs on 8p21-23 in hepatocellular carcinoma, three oncogenes (NKX2-1, NKX2-8, and PAX9) on 14q13 in lung cancer, two oncogenes (CCND1 and FGF19) on 11q13, and two oncogenes (BIRC2 and YAP1) on 11q22 in liver cancer (Zender et al. 2006; Kendall et al. 2007; Sawey et al. 2011; Solimini et al. 2012; Xue et al. 2012). Similar to the results presented here, phenotypes induced by the manipulation of individual genes are relatively weak, whereas the concerted deregulation of entire cancer gene clusters result in more significant effects. We found evidence that poor or good breast cancer prognosis associated genes, which include a significant number of oncogenes and TSGs, as well as markers of cancerous elements (Zhang et al. 2009; Soon et al. 2011; Lee et al. 2012), cluster in regions of aberrant copy number and gene expression in breast cancer (Fig. 2; Supplemental Figs. 6A, 14A), further supporting the hypothesis that clusters of cancer-relevant genes are distributed over the entire genome and are activated or inactivated by copy number imbalances that contribute to the oncogenic state.



In summary, our work suggests that putative oncogenes aggregate and separate from tumor suppressors in the human genome. This clustering of oncogenic elements augments the biological effect of segmental amplification and deletions commonly found in cancers as evidenced by their combined effects on tumor growth in vitro. Therefore structural variations in breast cancer act as systems organizers for gene cassettes that together have a significant role in maintaining the cancer phenotype. When viewed in evolutionary terms, the multitude of structural rearrangements and mutations are not necessarily randomly derived. Instead, it is a process of selection for the gain and loss of adjacent clusters of gene cassettes that, when combined, optimize tumor survivability and growth within a single individual. Given that the combinatorics are immense, a systems analysis focusing on multigene as opposed to single gene effects will be the best approach in deciphering this level of complexity.

There’s an interesting note in the Results section of this paper regarding fusion genes in the breast cancer cells.

By cataloging fusion genes and gene truncations… caused by structural variations in four of the sequenced breast cancers, we confirmed that nearly 60% of somatic structural variations affect gene structures. We tested 61 predicted gene fusions by RT-PCR and found that 37 of them (61%) were expressed. Of these, only eight fusion transcripts are in-frame and possess intact protein functional domains, although none are recurrent fusions, and the fusion partners have little plausible involvement in cancer, so that their functional consequences remain unknown. These findings are consistent with our previously published observations, which noted such fusion events that do not directly create a functional oncogene through the fusion but are indicative of a genomic process that initiates more critical downstream oncogenic mutations.

On chromosome 22, they also observed cases of chromothripsis: single events of multiple genomic rearrangements, right on the cusp of being wholly destructive (the word is derived from chromo[some] and thripsis meaning “shattering into pieces”), marking the upper limit of tolerance to genomic catastrophe.
The all-important clinical conclusions to be drawn here are that if conjointly expressed targets are targeted in combination therapy, the synergistic effects exploited by cancer could be leveraged to a patient’s advantage:

Our results also suggest that the genomic configuration of a breast cancer may identify conjointly expressed targets for combination therapy. One example is the coamplification of ERBB2 and genes on the downstream 17q21.3 amplicon. The best possible targets would be those that exhibit additive or synergistic effects with Lapatinib treatment. Intriguing new candidates include SNF8, a component of the endosomal sorting complex (ESCRT-II), which is required for multivesicular body formation and involved in endosomal sorting. The ESCRT-II complex is involved in the degradation of both endocytosed EGF and EGFR. EME1, another gene showing greater than additive effect with ERBB2, encodes a protein that is part of an endonuclease complex and may be involved in DNA damage repair and maintaining genomic stability (Sengerová et al. 2011). Other druggable candidate targets on 17q21.3 include UBE2Z, an ubiquitin ligase, and KAT7 (previously known as MYST2), a histone acetyltransferase, both of which showed an additive effect.

Inaki et al. (2014) Systems consequences of amplicon formation in human breast cancer. Genome Research, 24: 1559-1571

Structural variations efficiently orchestrate the gain and loss of cancer gene cassettes that engage many oncogenic pathways simultaneously and such oncogenic cassettes are favoured during the evolution of a cancer

Genetic changes through somatic mutations span from single nucleotide alterations to breakpoints interrupting gene contiguity, segmental copy number changes, and imbalances of entire chromosomes

Beginning their review with a description of the basics of cancer, from the genetic events to citing Hardy and Weinberg’s Hallmarks of Cancer paper, the authors of a new paper in Genome Research provide evidence to support a fresh consideration of the disease’s evolution.

Though the traditional view of somatic mutations in oncogenesis is one largely of point mutation, recent reports have notably suggested otherwise: . Similarly, earlier focus on single driver oncogenes within amplicons has matured into greater concern for the multiplicity of such ‘drivers’.

Moreover, each amplicon or region of copy number loss alters the expression of many adjacent genes, some with proven conjoint cancer effects (Zhang et al. 2009; Curtis et al. 2012). Thus, any cancer is likely to be a composite of hundreds to thousands of gene changes that contribute to the cancer state. Although specific point mutations contribute to adaptive evolutionary processes, recent genomic analyses from controlled evolutionary experiments in model systems suggest that copy number changes through segmental duplications and rearrangements may play a more prominent role (Chang et al. 2013; Fares et al. 2013).

… From whole-genome sequencing data, we learned that, although there are some common oncogenic drivers, each cancer shows combinations of genomic aberrations that often are unique for that individual tumor. These structural aberrations and their consequent expression profiles engage a range of biochemical and cellular functions that, as a whole, cannot be ascribed to a single oncogenic pathway. Using deep genomic analyses of breast cancers to reveal the detailed genetic landscape of each tumor, we sought to find coherence in how the many different somatic mutations may be related.

By examining the detailed structural genomic alterations associated with common amplicons, we found evidence for a sequence of structural variations affecting recurrent regions of genomic amplification. In five of the seven analyzed breast cancers with evidence of copy number gain at the ERBB2 locus, large tandem duplications encompassing the ERBB2 gene appeared to initiate the amplification of the region. In most cases, ERBB2 amplification was associated with copy number loss of BRCA1 through different genomic mechanisms. In three samples, unpaired inversions joined the ERBB2 locus with the region on 17q21.3* that would be subsequently amplified; and in all three cases, we found structural evidence for a deletion of the intervening chromosomal segment containing the BRCA1 gene. In the remaining samples, ERBB2 is amplified through more complex rearrangements that included translocation to other chromosomes and multiple unpaired inversions.

* 17q21.3 here is cytogenetic notation addressing a genomic locus, specifically one on the long arm ( “q” ) of chromosome 17, region 2, band 1, sub-band 3.

Previous work from the group into “transcriptional consequences of somatic structural variations” in primary breast cancers and associated cell lines showed that a single tandem duplication in a particular amplified locus led to selection of cancers “with augmented expression of two adjacent oncogenic components“.

Generalizing from this observation, we hypothesize that conjoint expression of adjacent oncogenes or loss of adjacent cancer suppressors may provide a “systems genetic” strategy for activating cassettes of oncogenic signals.

The paper assesses how these structural variations play a role in establishing transcriptional programs optimal for evolution of individual cancers.

In summary, through analysing “deep-sequencing” (also known paradoxically as ‘next generation’ sequencing) data, they find reason to believe that rearrangements, such as unpaired inversions connecting the ERBB2 and 17q21.3 loci or a direct deletion of BRCA1, followed by coamplification of the newly linked ERBB2 and 17q21.3 loci, are “among the key events leading such an optimal genomic rearrangement“.

in the vast majority of cases, BRCA1 is lost before the ERBB2-17q21.3 linked region is amplified… amplification of 17q21.3 and loss of BRCA1 represent a frequent configuration among ERBB2-amplified tumors.

If one views the genetic landscape of a tumor as an indication of evolutionary optimization for any specific cancer, then the identification of frequent conjoint genetic events can be a means to discover additive or synergistic actions of oncogenic elements.

In a really nice turn to their ‘systems genetics’ paradigm they validated this hypothesis (in vitro), showing overexpressed ERBB2 and enforced knockdown of BRCA1 expression augmented growth of human mammary epithelial cells (“HMECs“) together to a greater extent than either genomic modification did individually.

With proof of principle in hand, the team turned to this 17q21.3 locus, finding 19 of the 21 genes there exerted “*positive growth effects that were at least additive, and in seven cases possibly synergistic with those elicited by ERBB2 activity.*”

Finally, the observation that TP53 copy number loss occurs in 79% of the cases in which BRCA1 is also lost (Fig. 3) strongly suggests some functional interaction. Indeed, it has been noted that TP53 and BRCA1 interact together to optimally induce the expression of SFN (14-3-3ς), a major G2/M checkpoint control gene that blocks progression of cells with DNA damage through mitosis (Aprelikova et al. 2001). The loss of SFN regulation would lead to abnormal checkpoint control, a mechanism for genomic instability.

Give yourself a pat on the back if you can decipher how the 0.79 equates to 79% TP53 copy number loss, this chart just boggles my mind:

Thus, the chromosomal “origami” generated by the conjoint rearrangements on 17q (ERBB2 tandem duplication followed by unpaired inversions or deletions disrupting BRCA1 and linking ERBB2 with the downstream 17q21.3 amplicon) appears to be a topologically parsimonious strategy to generate a genomic state favoring tumor growth (Fig. 6, [ed: main image, top of post]). In addition, through only a few genomic rearrangements, the simultaneous activation by copy number gain and the attenuation by copy number loss of genes affecting cancer cell growth suggest that rearrangements significantly restructure the cancer genome to engage the maximal number of oncogenic elements with each rearrangement, so that even small copy number changes manifest to global changes in levels of gene expression.

By “topologically parsimonious” the authors mean to direct their reader’s attention to the evolutionary landscape in which these rearrangements take place — frugality, being canny with resources [parsimony] is needed to achieve the tumour’s “goal” of sorts, which is growth promotion without genomic catastrophe resulting from an overly rearranged genome being left without sufficiently viable genome [which via a variety of safeguarding mechanisms leads to cell apoptosis; if I’m reading this correctly].

It has been previously recognized that some cancer-associated genes are colocalized in the genome. A classic example of this is the overlapping localization of the p16INK4a and p14ARF tumor suppressors encoded within the CDKN2A locus on 9p21. Deletions at this locus routinely inactivate both cell-cycle regulators (Bates et al. 1998; Stott et al. 1998). Recent evidence also suggests that oncogenes and tumor suppressor genes (TSGs) are clustered, including several TSGs on 8p21-23 in hepatocellular carcinoma, three oncogenes (NKX2-1, NKX2-8, and PAX9) on 14q13 in lung cancer, two oncogenes (CCND1 and FGF19) on 11q13, and two oncogenes (BIRC2 and YAP1) on 11q22 in liver cancer (Zender et al. 2006; Kendall et al. 2007; Sawey et al. 2011; Solimini et al. 2012; Xue et al. 2012). Similar to the results presented here, phenotypes induced by the manipulation of individual genes are relatively weak, whereas the concerted deregulation of entire cancer gene clusters result in more significant effects. We found evidence that poor or good breast cancer prognosis associated genes, which include a significant number of oncogenes and TSGs, as well as markers of cancerous elements (Zhang et al. 2009; Soon et al. 2011; Lee et al. 2012), cluster in regions of aberrant copy number and gene expression in breast cancer (Fig. 2; Supplemental Figs. 6A, 14A), further supporting the hypothesis that clusters of cancer-relevant genes are distributed over the entire genome and are activated or inactivated by copy number imbalances that contribute to the oncogenic state.

In summary, our work suggests that putative oncogenes aggregate and separate from tumor suppressors in the human genome. This clustering of oncogenic elements augments the biological effect of segmental amplification and deletions commonly found in cancers as evidenced by their combined effects on tumor growth in vitro. Therefore structural variations in breast cancer act as systems organizers for gene cassettes that together have a significant role in maintaining the cancer phenotype. When viewed in evolutionary terms, the multitude of structural rearrangements and mutations are not necessarily randomly derived. Instead, it is a process of selection for the gain and loss of adjacent clusters of gene cassettes that, when combined, optimize tumor survivability and growth within a single individual. Given that the combinatorics are immense, a systems analysis focusing on multigene as opposed to single gene effects will be the best approach in deciphering this level of complexity.

There’s an interesting note in the Results section of this paper regarding fusion genes in the breast cancer cells.

By cataloging fusion genes and gene truncations… caused by structural variations in four of the sequenced breast cancers, we confirmed that nearly 60% of somatic structural variations affect gene structures. We tested 61 predicted gene fusions by RT-PCR and found that 37 of them (61%) were expressed. Of these, only eight fusion transcripts are in-frame and possess intact protein functional domains, although none are recurrent fusions, and the fusion partners have little plausible involvement in cancer, so that their functional consequences remain unknown. These findings are consistent with our previously published observations, which noted such fusion events that do not directly create a functional oncogene through the fusion but are indicative of a genomic process that initiates more critical downstream oncogenic mutations.

On chromosome 22, they also observed cases of chromothripsis: single events of multiple genomic rearrangements, right on the cusp of being wholly destructive (the word is derived from chromo[some] and thripsis meaning “shattering into pieces”), marking the upper limit of tolerance to genomic catastrophe.

The all-important clinical conclusions to be drawn here are that if conjointly expressed targets are targeted in combination therapy, the synergistic effects exploited by cancer could be leveraged to a patient’s advantage:

Our results also suggest that the genomic configuration of a breast cancer may identify conjointly expressed targets for combination therapy. One example is the coamplification of ERBB2 and genes on the downstream 17q21.3 amplicon. The best possible targets would be those that exhibit additive or synergistic effects with Lapatinib treatment. Intriguing new candidates include SNF8, a component of the endosomal sorting complex (ESCRT-II), which is required for multivesicular body formation and involved in endosomal sorting. The ESCRT-II complex is involved in the degradation of both endocytosed EGF and EGFR. EME1, another gene showing greater than additive effect with ERBB2, encodes a protein that is part of an endonuclease complex and may be involved in DNA damage repair and maintaining genomic stability (Sengerová et al. 2011). Other druggable candidate targets on 17q21.3 include UBE2Z, an ubiquitin ligase, and KAT7 (previously known as MYST2), a histone acetyltransferase, both of which showed an additive effect.

Inaki et al. (2014) Systems consequences of amplicon formation in human breast cancer. Genome Research, 24: 1559-1571

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Fortune magazine cover designed by Arthur Lidov, depicting Maxwell’s thermodynamic surface of an “imaginary substance” similar to (though not quite) water based on J. W. Gibbs's work, alongside Gibbs's formula for the phase rule, bottom left

To describe a closed, homogeneous system — that is one of constant composition, such as an ideal gas — we need two parameters of state (e.g. T and p). For a heterogeneous system in equilibrium, consisting of one component (e.g. water) and two phases (e.g. liquid and vapour), we require only one parameter of state (e.g. T).
This can be expressed with Gibbs’s phase rule, which specifically describes the number of possible degrees of freedom (or variance) of a chemical system (where C = number of components, P = number of phases in the system): F = C ‒ P + 2
The number 2 is specified because this formulation assumes both T and p can be varied.

The thermodynamic surface for a typical substance is shown in this diagram, with the x axis (width) indicating volume, y axis (height) indicating pressure and z axis (depth) indicating temperature.
Water is thermodynamically atypical, as is readily observed from icebergs that float on liquid water — this can be seen by comparing this diagram to the illustration above, after Maxwell’s 1874 sculpture (itself based on Gibbs’s papers). Maxwell used coordinates of volume (x), entropy (y) and energy (z) — plotted from surrogate measures of pressure and temperature.
Maxwell stated that this model allowed “the principal features of known substances [to] be represented on a convenient scale”.
The construction of this was far more interesting than that of any automatist dream painting (though here the cover art is clearly trying to conjure up the surrealist landscapes of Magritte and contemporaries)

The numerical data about entropy can only be obtained by integration from data which are for most bodies very insufficient, and besides it would require a very unwieldy model to get all the features, say of CO2, well represented, so I made no attempt at accuracy, but modelled a fictitious substance, in which the volume is greater when solid than when liquid; and in which, as in water, the saturated vapour becomes superheated by compression. When I had at last got a plaster cast I drew on it lines of equal pressure and temperature, so as to get a rough motion of their forms. This I did by placing the model in sunlight, and tracing the curve when the rays just grazed the surface…


A superb summary of the two scientists’ graphical methods was put together by Ron Kriz at Virginia Tech (view full size image here). The melée of multi-coloured lines is a bit perplexing, and bringing a physical sculpture in to demonstrate the concept — stepping away from the 2D triple point plots still used in undergraduate lectures today — was a stroke of genius in a time long before the advent of sophisticated computer visualisations.
This general graphic method was not just to plot existing thermodynamic data, but rather to envision total derivatives — related to the work on vector calculus Gibbs was renowned for (his lectures on the subject were collected at the start of the 20th century to form an influential textbook).
Dr Kriz feels this object should provoke reflection on how we consider visualisation methods in science:

The development of the thermodynamic theory of state is a rare but excellent example that demonstrates how scientists combine analytic and graphical methods together with how they understand science. How scientists combine analytical and graphical models into new knowledge exemplifies a cognitive processes that includes visual thinking or what Dr. Daniel Coy describes as “geometric reasoning”. This new knowledge was reported and documented by Gibbs as a graphical method, so that others could reproduce and build on that understanding. As the graphical method was being developed by Gibbs the intent was not to use graphics for presentation but rather to develop the theory. This is contrary to the popular belief that imaging in science is used for presentation which can at times be insightful. 
After reading and studying Gibbs and Maxwell, perhaps the reader would agree that neither Gibbs nor Maxwell developed their graphical method for presentation, a metaphor, or as an intriguing anecdotal experience that could not be scientifically reproduced. Rather the graphical method was sufficiently developed and described by Gibbs to be inclusive with developing the thermodynamic theory of state, which was reproduced and further developed graphically by Maxwell. Recall in summary Gibbs states,

In the foregoing discussion, the equations which express the fundamental principles of thermodynamics in an analytical form have been assumed, and the aim has only been to show how the same relations may be expressed geometrically. It would, however, be easy, starting from the first and second laws of thermodynamics as usually enunciated, to arrive at the same results without the aid of analytical formulae, to arrive, for example, at the conception of energy, of entropy, of absolute temperature, in the construction of the diagram without the analytical definitions of these quantities, and to obtain the various properties of the diagram without the analytical expression of the thermodynamic properties which they involve.

This is not a subjective process, e.g. what visual tools were used, how were they used, or how were the tools designed. The integrity of Gibbs’ and Maxwell’s graphical method is a well established, scientific, objective, and a reproducible process that has nothing to do with the subjective use of tools. This graphical method is inclusive with the developement of the thermodynamic theory of state where Gibbs demonstrates that understanding this theory can be accomplished “...without the aid of analytic formulae”, e.g. his equation of state. In fact Gibbs thought his graphical method was so important that,

Such a course would have been better fitted to show the independence and sufficiency of a graphical method, but perhaps less suitable for an examination of the comparative advantages or disadvantages of different graphical methods.

Hopefully the independence and sufficiency of a graphical method, as proposed by Gibbs, was developed and demonstrated here by envisioning energy as a surface defined as a scalar function of two independent variables, e.g. entropy and volume, where the gradient of the scalar function are slopes tangent to this surface and equal to temperature and negative pressure, as defined in Figs. 5 and 8. However since neither this surface nor the gradient lines tangent to this surface are not associated with a specific set of physical properties, this general graphical method is indeed coextensive in its application.

Further reading:
◉  Ronald D. Kriz (2007) Thermodynamic Case Study: Gibbs’s Thermodynamic Graphical Method — Envisioning total derivatives of scalar functions with two independent variables as raised surfaces and tangent planes. Virginia Tech.
◉  Preface to Elementary principles in statistical mechanics. JW Gibbs, 1902 and full text transcribed at Wikisource
◉  Open University PHYS 7.3 (1996) Internal energy, heat and energy transfer. University of Reading◉  Desmond Fearnley-Sander (1979) Hermann Grassmann and the creation of linear algebra.

Fortune magazine cover designed by Arthur Lidov, depicting Maxwell’s thermodynamic surface of an “imaginary substance” similar to (though not quite) water based on J. W. Gibbs's work, alongside Gibbs's formula for the phase rule, bottom left

To describe a closed, homogeneous system — that is one of constant composition, such as an ideal gas — we need two parameters of state (e.g. T and p). For a heterogeneous system in equilibrium, consisting of one component (e.g. water) and two phases (e.g. liquid and vapour), we require only one parameter of state (e.g. T).

This can be expressed with Gibbs’s phase rule, which specifically describes the number of possible degrees of freedom (or variance) of a chemical system (where C = number of components, P = number of phases in the system): F = C ‒ P + 2

The number 2 is specified because this formulation assumes both T and p can be varied.

image

The thermodynamic surface for a typical substance is shown in this diagram, with the x axis (width) indicating volume, y axis (height) indicating pressure and z axis (depth) indicating temperature.

Water is thermodynamically atypical, as is readily observed from icebergs that float on liquid water — this can be seen by comparing this diagram to the illustration above, after Maxwell’s 1874 sculpture (itself based on Gibbs’s papers). Maxwell used coordinates of volume (x), entropy (y) and energy (z) — plotted from surrogate measures of pressure and temperature.

Maxwell stated that this model allowed “the principal features of known substances [to] be represented on a convenient scale”.

The construction of this was far more interesting than that of any automatist dream painting (though here the cover art is clearly trying to conjure up the surrealist landscapes of Magritte and contemporaries)

The numerical data about entropy can only be obtained by integration from data which are for most bodies very insufficient, and besides it would require a very unwieldy model to get all the features, say of CO2, well represented, so I made no attempt at accuracy, but modelled a fictitious substance, in which the volume is greater when solid than when liquid; and in which, as in water, the saturated vapour becomes superheated by compression. When I had at last got a plaster cast I drew on it lines of equal pressure and temperature, so as to get a rough motion of their forms. This I did by placing the model in sunlight, and tracing the curve when the rays just grazed the surface…

image

A superb summary of the two scientists’ graphical methods was put together by Ron Kriz at Virginia Tech (view full size image here). The melée of multi-coloured lines is a bit perplexing, and bringing a physical sculpture in to demonstrate the concept — stepping away from the 2D triple point plots still used in undergraduate lectures today — was a stroke of genius in a time long before the advent of sophisticated computer visualisations.

This general graphic method was not just to plot existing thermodynamic data, but rather to envision total derivatives — related to the work on vector calculus Gibbs was renowned for (his lectures on the subject were collected at the start of the 20th century to form an influential textbook).

Dr Kriz feels this object should provoke reflection on how we consider visualisation methods in science:

The development of the thermodynamic theory of state is a rare but excellent example that demonstrates how scientists combine analytic and graphical methods together with how they understand science. How scientists combine analytical and graphical models into new knowledge exemplifies a cognitive processes that includes visual thinking or what Dr. Daniel Coy describes as “geometric reasoning”. This new knowledge was reported and documented by Gibbs as a graphical method, so that others could reproduce and build on that understanding. As the graphical method was being developed by Gibbs the intent was not to use graphics for presentation but rather to develop the theory. This is contrary to the popular belief that imaging in science is used for presentation which can at times be insightful. 

After reading and studying Gibbs and Maxwell, perhaps the reader would agree that neither Gibbs nor Maxwell developed their graphical method for presentation, a metaphor, or as an intriguing anecdotal experience that could not be scientifically reproduced. Rather the graphical method was sufficiently developed and described by Gibbs to be inclusive with developing the thermodynamic theory of state, which was reproduced and further developed graphically by Maxwell. Recall in summary Gibbs states,

In the foregoing discussion, the equations which express the fundamental principles of thermodynamics in an analytical form have been assumed, and the aim has only been to show how the same relations may be expressed geometrically. It would, however, be easy, starting from the first and second laws of thermodynamics as usually enunciated, to arrive at the same results without the aid of analytical formulae, to arrive, for example, at the conception of energy, of entropy, of absolute temperature, in the construction of the diagram without the analytical definitions of these quantities, and to obtain the various properties of the diagram without the analytical expression of the thermodynamic properties which they involve.

This is not a subjective process, e.g. what visual tools were used, how were they used, or how were the tools designed. The integrity of Gibbs’ and Maxwell’s graphical method is a well established, scientific, objective, and a reproducible process that has nothing to do with the subjective use of tools. This graphical method is inclusive with the developement of the thermodynamic theory of state where Gibbs demonstrates that understanding this theory can be accomplished “...without the aid of analytic formulae”, e.g. his equation of state. In fact Gibbs thought his graphical method was so important that,

Such a course would have been better fitted to show the independence and sufficiency of a graphical method, but perhaps less suitable for an examination of the comparative advantages or disadvantages of different graphical methods.

Hopefully the independence and sufficiency of a graphical method, as proposed by Gibbs, was developed and demonstrated here by envisioning energy as a surface defined as a scalar function of two independent variables, e.g. entropy and volume, where the gradient of the scalar function are slopes tangent to this surface and equal to temperature and negative pressure, as defined in Figs. 5 and 8. However since neither this surface nor the gradient lines tangent to this surface are not associated with a specific set of physical properties, this general graphical method is indeed coextensive in its application.

Further reading:

◉  Ronald D. Kriz (2007) Thermodynamic Case Study: Gibbs’s Thermodynamic Graphical Method — Envisioning total derivatives of scalar functions with two independent variables as raised surfaces and tangent planesVirginia Tech.

◉  Preface to Elementary principles in statistical mechanics. JW Gibbs, 1902 and full text transcribed at Wikisource

◉  Open University PHYS 7.3 (1996) Internal energy, heat and energy transfer. University of Reading◉  Desmond Fearnley-Sander (1979) Hermann Grassmann and the creation of linear algebra.

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A bioinformatics walk-through: Accessing protein-protein interaction interfaces for all known protein structures with PDBe PISA

If this summer’s posting became a little infrequent, part of the blame lies with computational research I’ve been working on, regarding the systems biology of chromosomal translocations and the ensuing chimeric proteins at the Medical Research Council Laboratory of Molecular Biology in Cambridge.

A sizeable part of bioinformatics ‘dry lab’ work falls into what has been described in the NYT as ‘data wrangling’ (or the work of a ‘data janitor’). This post is about accessing the data held in the Protein Databank in Europe's repository of Proteins, Interfaces, Structures and Assemblies (PDBe PISA).

Sent out onto the web to find a source of structural protein-protein interaction data with amino acid-level resolution, my first port of call was the Nucleic Acids Research Molecular Biology Online Database Collection (which I’d read of in the opening chapters of Arthur Lesk’s Introduction to Bioinformatics) where I found a sizeable list of PPI databases.

Not wanting to click through each, I chose to browse this programmatically, using Javascript-automated AJAX requests (effectively asking the website to give me web pages but without displaying them) and just ‘scrape’ what I wanted (full workings here), as follows:

From these results, here’s a little background info on PDBe:

  {
    "name": "PDBe",
    "url": "http://www.ebi.ac.uk/pdbe/",
    "entryurl": "http://www.oxfordjournals.org/nar/database/summary/456",
    "desc": "EMBL-EBI's Protein Data Bank in Europe (PDBe) is the European resource for the collection, organization and dissemination of data about biological macromolecular structures. PDBe is one of four partners in the worldwide Protein Data Bank (wwPDB), the consortium entrusted with the collation, maintenance and distribution of the global repository of macromolecular structure data. PDBe uses a relational database that presents the data derived from the Protein Data Bank (PDB) in a consistent way and allows users to retrieve meaningful data using complex and sophisticated searches including simple textual queries or more complex 3D structure-based queries. PDBe has also developed a number of advanced tools for analysis of macromolecules. The \"Structure Integration with Function, Taxonomy and Sequence\" (SIFTS) initiative integrates data from a number of bioinformatics resources that is used by major global sequence, structure and protein-family resources. Furthermore, PDBe works actively with the X-ray crystallography, Nuclear Magnetic Resonance (NMR) spectroscopy and cryo-Electron Microscopy (EM) communities and is a partner in the Electron Microscopy Data Bank (EMDB). The active involvement with the scientific communities has resulted in improved tools for structure deposition and analysis.",
    "ref": null,
    "absurl": "http://nar.oxfordjournals.org/cgi/content/abstract/42/D1/D285",
    "email": "pdbe@ebi.ac.uk"
  },

Web scraping can feel quite kludgy, and there are doubtless better ways to do the above. Having said that, it’s great for prototyping: you can use Javascript within a web browser console, i.e. without littering your computer with temporary files. What’s more, dedicated communities like the ScraperWiki forum are around to support and develop the associated tools, and in its more elaborate incarnations ‘scraping’ features in journals like Briefings in Bioinformatics (“Web scraping technologies in an API World” was published there just this week).

After having decided on PDBe PISA thanks to my scraped-together report, and finding no guidance on how to tackle the task, I turned to the bioinformatician’s equivalent of [computing/programming Q&A site] Stack Overflow known as Biostars. My question got a grand total of 0 answers(!), so what follows is my approach — which may either be of interest as a peek into the work going under the banner of ‘bioinformatics’ or as a guide to other scientists seeking to access the same information.

First off, a Python script parcelled up a list of every PDB code (the unique identifier to an author-deposited structure from X-ray crystallography, NMR etc.) in PDB into comma-separated chunks of 50, which were stuck onto the end of a web-service query as recommended. The server would process these queries, understood through its “API”: the CGI of cgi-bin in the URL means it’s invoking a script on the server, which in turn expects interfaces.pisa? to be followed by comma-separated PDB codes. Given these expectations, the API will respond in a regular manner each time, enabling reliable scripting.

With over 2000 such queries for interface data (each of them requesting 50 PDB-code-identified structures), this isn’t something you want to be doing manually. It wasn’t clear exactly which PDB entries were needed at the time, so the full complement was downloaded.

This download script just works for one query, putting the received XML in one file - to handle all 2029 queries, a bit of lateral thinking was required. 50 queries (each containing 50 PDB codes) were executed to make up a single interfacesi-j.xml file, where i is an integer 1 to 4, and likewise j from 1 to 10 (plus a bonus 4-11 to get those final 29). Download scripts (named similarly as getxmli-j.py) were written individually by another script — code writing code…

With download scripts written, the task of running each of them consecutively fell to yet another Python script, playing the sound of Super Mario picking up a coin when each file finished downloading, or the Mario pause-game sound upon encountering an error, because I could because clear feedback becomes necessary on something taking days across multiple computers.

Inevitably a minority of the queries failed, and had to be obtained separately.

Once downloaded, various pattern matching text-processing programs were run on the XML from within a shell script — readers unfamiliar with programming may have heard of these this week thanks to the 22 year old security bug(s) being referred to as shellshock. Shell scripts make looping through files in this manner a simple task, and are becoming essential for everyday file manipulation now that I’m a reformed Windows user. For the 41 XML files, a function runprocessor was called, with instructions to:

  1. Split each file successively at every <pisa_interfaces> tag through to the closing </pisa_interfaces> tag, the line numbers of which were stored together in an ordered list (an “array variable”) pisapairs
  2. Write each of these sections to a cache file xmlcache.xml, of suitable size for parsing by a Python XML parser.
  3. Reduce the time spent by the parser by in turn splitting this cache into just the PDB entries in the shortlist of interest with a function extractsubsets
  4. Initiate a Python script to read the entire cachesubset.xml file into memory, and write the pertinent structural data into a report formatted as tab-separated values (TSV). This file is a mere few hundred megabytes compared to the 120 GB grand total for the XML.

Clicking Details for an interface on the list of all interfaces for a given protein structure, e.g. for the only one in spider silk precursor protein spidroin, shows the interfacial residues in yellow:
image

The output threads together all interfacial residues and the associated statistical figures for each on a single line for every interface, but it’s simple enough to separate out each according to commas (then colons) to get a longform residue-per-line output once all XML is processed.

Progress is indicated in terminal output, where the current i and j values are printed followed by the pisapair (i.e. which of the 50 pisa_interfaces tags) is being worked through:

image

As shown in the logfile, there are inevitable errors, such as Entry not found: it’s simple enough to find the difference between the output report file’s list of PDB codes and the input ‘shortlist’, which can be mapped back to the constituent files for any follow-up investigation (the “wrangling” facet of computational science alluded to earlier) since the order of the original 2029 queries is known:

I’m putting these together in a code repository on GitHub, with a disclaimer that it’s not fit for all purposes (for instance if you’re interested in H-bonds, in brown on the PISA website residue table, above).

A lot of this was painfully slow — there’s nothing to be done about the speed of downloading the files, given that its rate is limited by the server. Yes there was a lot of data to get through, but Python’s sluggishness at the final step makes me wonder if I could implement some leaner algorithm, parallelise, etc., but with term recommenced code optimisation on a successfully completed task isn’t top priority. Advice on improvements would be appreciated if you have any.

I’m currently reading Jones & Pevzner’s An Introduction to Bioinformatics Algorithms which gives insight into how you can analyse and improve these types of operations (the book is core reading for a Coursera.org lecture series which kicks off next month), and have been recommended Goldwasser & Tamassia’s Data Structures and Algorithms in Python (a few online resources in a similar vein are available here).

I’ve also been fiddling with Julia, an R-like language with C-like speeds — in a 2012 blog post its creators say they “created Julia, in short, because we are greedy”. Fernando Perez is overseeing its incorporation into IPython Notebooks as ‘Project Jupyter’ and a port of R’s ggplot2 library has recently emerged for Julia under the name of Gadfly (a tutorial IPy NB is up here).

I’m starting a final year undergraduate project as of this week, on mapping small RNA-seq data to miRNAs, under the supervision of the founder of the database central to cataloguing this class of non-coding RNA ‒ super exciting stuff! :¬)

If you’ve got questions on PISA you think I could help with, feel free to ask here, or shoot me an email.

PDBe PISA homepage

✣ Peter Briggs, a scientific programmer at STFC Daresbury Laboratory, has a nice little guide to the service here.

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Pairing and stacking
Everybody knows GC base pairs are stronger than AT base pairs because they form three hydrogen bonds rather than 2, right?

The specificity of Watson-Crick base pairing is crucial to DNA duplex formation and covered early on in any good introductory genetics course. I&#8217;d always thought that these were what primarily led to the stability of the duplex, and was sure this is what was taught in first year too, but earlier this year I noted base stacking effects were in fact the primary determinants of this fundamental molecular phenomenon.
Taking a look around online it&#8217;s easy to find contradicting opinions on the subject, which makes me feel a bit less foolish over my uncertainty.
Hydrophobic, electrostatic base-stacking interactions depend on base aromaticity and dipole moments
Maxim Frank-Kamenetskii (whose father also worked in bio-/chemical physics) and colleagues at Boston University published a paper resolving the ambiguity as late as 2006(!) in which they studied DNA molecules with ‘solitary nicks and gaps [to] measure temperature and salt-dependence of the stacking free energy of the DNA double helix’

For the first time, DNA stacking parameters are obtained directly (without extrapolation) for temperatures from below room temperature to close to melting temperature.
From stacking parameters of individual contacts, we calculate base-stacking contribution to the stability of A•T- and G•C-containing DNA polymers. We find that temperature and salt dependences of the stacking term fully determine the temperature and the salt dependence of DNA stability parameters. For all temperatures and salt concentrations employed in present study, base-stacking is the main stabilizing factor in the DNA double helix. A•T pairing is always destabilizing and G•C pairing contributes almost no stabilization. Base-stacking interaction dominates not only in the duplex overall stability but also significantly contributes into the dependence of the duplex stability on its sequence.

This might seem trivial, but the significance comes from the dependence of a base pair&#8217;s stability on its neighbours when stacking is more important.

Nearest-neighbor stability parameters have been introduced to account for sequence effects in DNA stability. These parameters are obtained from the analysis of the melting data for DNA polymers, DNA oligomers and DNA dumbbells, and present the cumulative (base pairing and stacking) contribution of each dinucleotide stack to the overall stability of the molecule. In fact, DNA melting experiments do not allow separation of the two contributions.

I&#8217;d definitely heard the Frank-Kamenetskii family name somewhere before, but rather than his father it&#8217;s more likely to have been from readings in DNA topology.

Partitioning of base pairing and stacking contributions to DNA stability not only delivers a new aspect in the fundamental understanding of DNA structure and energetics, but also it has significant implications in a number of biological processes. Fluctuations in local helical conformation of DNA, the phenomenon known as DNA breathing, lead to infrequent events of base pair opening thus making normally buried groups available for modification and interaction with proteins. Fluctuational base pair opening implies disruption of hydrogen bonds between the complementary bases and flipping the base out of the helical stack disrupting two contacts. Heterogeneous stacking at these contacts determine sequence dependence of the base pair fluctuational motility.
Moreover, single-stranded break (a nick) in the DNA double helix is stabilized by stacking interactions between base pairs flanking the lesion; these interactions are sequence-dependent. In the cell, DNA nicks are substrates for DNA damage-detecting and DNA-repair proteins.

Frank-Kamenetskii reviewed DNA breathing, or ‘fraying’ last year in Nucleic Acids Research, noting how the issue of ‘strong bending of the double helix has attracted a lot of attention’ over the last decade.

It was suggested by Crick and Klug that sharp kinks of the double helix, which maintain base pairing but disrupt the stacking interaction between two adjacent base pairs, can be energetically favorable way to make strong bends of the double helix. Although such kinks have to be energetically costly, they can essentially reduce the bends and, correspondingly, the bending energy in the neighboring stacks of base pairs.
Similar, but not identical, to Crick &amp; Klug kinks are kinks associated with base pair openings. Probably, energetic cost of such disruptions should be even higher than for Crick &amp; Klug kinks. However, the disruptions that include open base pairs should provide even more local flexibility and could be a preferable way of changing twist of the double helix, if a stressed conformation requires it.

To divert from the topic a little here, the conclusions regarding DNA breathing were fascinating:

The free energy of a base pair opening is close to 7 kcal/mol for opening AT base pairs. If we assume that this free energy corresponds to formation of flexible hinges… we find that the average number of kinks approaches 1 for DNA circles of 70 bp.
[These data] make it very possible that the real nature of the double helix disruption, when short fragments are circularized, consists in the single base pair openings. However, there are no conformational data on DNA segments with opened base pairs detected by the cited methods. Thus, at present time we do not have sufficient information on structural and energetic properties of DNA disruptions to solve this challenging problem solely by the computations.


Essentially, this breathing/fraying phenomenon can lead to circularisation, which helps explain the abundance of these compared to predictions made from the wormlike chain model of DNA. In unstressed DNA, the probability of these openings is around 1 in 10,000 but shoots up in small DNA circles to 1 open bp per circle of 70bp.
Stacking is mentioned fleetingly once more in the final paragraph, with reference to Hoogsteen (certain non-canonical i.e. non-CG/AT) base pairs, which appear in ~1% of linear DNA.

Although it looks like stacking with adjacent pairs is well preserved when a Hoogsteen base pair is formed, it may still produce a point of higher flexibility that can facilitate strong bending of the double helix.

The experiments of the 2006 paper were pretty elegant ‒ nick a strand of DNA at a set position (making it migrate more slowly on a gel) and match up stacking interactions to changes in migration distance

Differential retardation of nicked DNA is due to specific interactions characteristic to each nicked dinucleotide stack. Quantitatively, equilibrium between stacked/closed and unstacked/open conformations at the nick site is governed by stacking free energy, ΔGST, so that:
Nclosed / Nopen = e − ΔGST / RT
where Nclosed and Nopen are occupancies of stacked and unstacked conformations at the DNA nick, respectively, R is the universal gas constant and T is the absolute temperature.

To get really esoteric here, the authors note that while “presence of a single-stranded gap precludes stacking interactions between two helical interfaces… this is not the case for 1 nt gaps”.

…it appears that stacking between the base pairs flanking the gap is restored to some degree leading to anisotropic, directional bending of the molecule reducing the size of the gapped cavity 48,55.
Molecules with longer gaps however, have been shown to possess isotropic bending flexibility which manifests itself in the absence of helical periodicity in electrophoretic mobility and cyclization kinetics measurements 50,53. Molecules with gaps 2, 3 and 4 nt in length migrate very closely during PAGE revealing similarity of their effective conformations. Additional factors [i.e. sequence of single-stranded linker] come into effect once the gap size is longer than persistent length of single chains—in this case, the gap is likely to act as a hinge.

Upon going still further into their own results, the authors concede that while this represents very strong evidence for stacking contribution to stability predominating over base pairing, the model used is still simplistic.
Briefly, H-bond breaking between complementary bases and base stacking along the helical axis are disrupted upon melting, increasing conformational entropy, releasing counterions and changing solvent interactions — since as stated above, base stacking effects are hydrophobic, a model which doesn&#8217;t examine these solvation effects isn&#8217;t wholly conclusive.

Strictly speaking, partitioning of these effects between ΔGST and ΔGBP terms is not known.

This isn&#8217;t challenging the main result, rather commenting on a finer point. The extended discussion however is approaching my limit for one night; if you&#8217;re interested to read more, as usual the links are below.

GC pairing does not contribute to stabilization of DNA duplex, while A•T pairing is always destabilizing. This finding presents a paradigm shift in the understanding of the interplay of the forces stabilizing DNA double helix. For all temperatures heterogeneity of stacking interactions in A•T- and G•C-containing contacts accounts for at least half of heterogeneity in the stability of A•T- and G•C-polymers; the other half is due to the difference in the energetics of A•T and G•C base pairing. The data on separation of stacking and base pairing contributions have made it possible to describe sequence-dependent fluctuational opening of the DNA double helix

• Yakovchuk et al (2006) Base-stacking and base-pairing contributions into thermal stability of the DNA double helix. Nucleic Acids Res, 34(2)•• Krueger and Frank-Kamenetskii (2006) Sequence-dependent base pair opening in DNA double helix. Biophys J, 90(9)

Pairing and stacking

Everybody knows GC base pairs are stronger than AT base pairs because they form three hydrogen bonds rather than 2, right?

image

The specificity of Watson-Crick base pairing is crucial to DNA duplex formation and covered early on in any good introductory genetics course. I’d always thought that these were what primarily led to the stability of the duplex, and was sure this is what was taught in first year too, but earlier this year I noted base stacking effects were in fact the primary determinants of this fundamental molecular phenomenon.

Taking a look around online it’s easy to find contradicting opinions on the subject, which makes me feel a bit less foolish over my uncertainty.

Hydrophobic, electrostatic base-stacking interactions depend on base aromaticity and dipole moments

Maxim Frank-Kamenetskii (whose father also worked in bio-/chemical physics) and colleagues at Boston University published a paper resolving the ambiguity as late as 2006(!) in which they studied DNA molecules with ‘solitary nicks and gaps [to] measure temperature and salt-dependence of the stacking free energy of the DNA double helix

For the first time, DNA stacking parameters are obtained directly (without extrapolation) for temperatures from below room temperature to close to melting temperature.

From stacking parameters of individual contacts, we calculate base-stacking contribution to the stability of A•T- and G•C-containing DNA polymers. We find that temperature and salt dependences of the stacking term fully determine the temperature and the salt dependence of DNA stability parameters. For all temperatures and salt concentrations employed in present study, base-stacking is the main stabilizing factor in the DNA double helix. A•T pairing is always destabilizing and G•C pairing contributes almost no stabilization. Base-stacking interaction dominates not only in the duplex overall stability but also significantly contributes into the dependence of the duplex stability on its sequence.

This might seem trivial, but the significance comes from the dependence of a base pair’s stability on its neighbours when stacking is more important.

Nearest-neighbor stability parameters have been introduced to account for sequence effects in DNA stability. These parameters are obtained from the analysis of the melting data for DNA polymers, DNA oligomers and DNA dumbbells, and present the cumulative (base pairing and stacking) contribution of each dinucleotide stack to the overall stability of the molecule. In fact, DNA melting experiments do not allow separation of the two contributions.

I’d definitely heard the Frank-Kamenetskii family name somewhere before, but rather than his father it’s more likely to have been from readings in DNA topology.

Partitioning of base pairing and stacking contributions to DNA stability not only delivers a new aspect in the fundamental understanding of DNA structure and energetics, but also it has significant implications in a number of biological processes. Fluctuations in local helical conformation of DNA, the phenomenon known as DNA breathing, lead to infrequent events of base pair opening thus making normally buried groups available for modification and interaction with proteins. Fluctuational base pair opening implies disruption of hydrogen bonds between the complementary bases and flipping the base out of the helical stack disrupting two contacts. Heterogeneous stacking at these contacts determine sequence dependence of the base pair fluctuational motility.

Moreover, single-stranded break (a nick) in the DNA double helix is stabilized by stacking interactions between base pairs flanking the lesion; these interactions are sequence-dependent. In the cell, DNA nicks are substrates for DNA damage-detecting and DNA-repair proteins.

Frank-Kamenetskii reviewed DNA breathing, or ‘fraying’ last year in Nucleic Acids Research, noting how the issue of ‘strong bending of the double helix has attracted a lot of attention’ over the last decade.

It was suggested by Crick and Klug that sharp kinks of the double helix, which maintain base pairing but disrupt the stacking interaction between two adjacent base pairs, can be energetically favorable way to make strong bends of the double helix. Although such kinks have to be energetically costly, they can essentially reduce the bends and, correspondingly, the bending energy in the neighboring stacks of base pairs.

Similar, but not identical, to Crick & Klug kinks are kinks associated with base pair openings. Probably, energetic cost of such disruptions should be even higher than for Crick & Klug kinks. However, the disruptions that include open base pairs should provide even more local flexibility and could be a preferable way of changing twist of the double helix, if a stressed conformation requires it.

To divert from the topic a little here, the conclusions regarding DNA breathing were fascinating:

image

The free energy of a base pair opening is close to 7 kcal/mol for opening AT base pairs. If we assume that this free energy corresponds to formation of flexible hinges… we find that the average number of kinks approaches 1 for DNA circles of 70 bp.

[These data] make it very possible that the real nature of the double helix disruption, when short fragments are circularized, consists in the single base pair openings. However, there are no conformational data on DNA segments with opened base pairs detected by the cited methods. Thus, at present time we do not have sufficient information on structural and energetic properties of DNA disruptions to solve this challenging problem solely by the computations.

Essentially, this breathing/fraying phenomenon can lead to circularisation, which helps explain the abundance of these compared to predictions made from the wormlike chain model of DNA. In unstressed DNA, the probability of these openings is around 1 in 10,000 but shoots up in small DNA circles to 1 open bp per circle of 70bp.

Stacking is mentioned fleetingly once more in the final paragraph, with reference to Hoogsteen (certain non-canonical i.e. non-CG/AT) base pairs, which appear in ~1% of linear DNA.

Although it looks like stacking with adjacent pairs is well preserved when a Hoogsteen base pair is formed, it may still produce a point of higher flexibility that can facilitate strong bending of the double helix.

The experiments of the 2006 paper were pretty elegant ‒ nick a strand of DNA at a set position (making it migrate more slowly on a gel) and match up stacking interactions to changes in migration distance

Differential retardation of nicked DNA is due to specific interactions characteristic to each nicked dinucleotide stack. Quantitatively, equilibrium between stacked/closed and unstacked/open conformations at the nick site is governed by stacking free energy, ΔGST, so that:

Nclosed / Nopen = e − ΔGST / RT

where Nclosed and Nopen are occupancies of stacked and unstacked conformations at the DNA nick, respectively, R is the universal gas constant and T is the absolute temperature.

To get really esoteric here, the authors note that while “presence of a single-stranded gap precludes stacking interactions between two helical interfaces… this is not the case for 1 nt gaps”.

…it appears that stacking between the base pairs flanking the gap is restored to some degree leading to anisotropic, directional bending of the molecule reducing the size of the gapped cavity 48,55.

Molecules with longer gaps however, have been shown to possess isotropic bending flexibility which manifests itself in the absence of helical periodicity in electrophoretic mobility and cyclization kinetics measurements 50,53. Molecules with gaps 2, 3 and 4 nt in length migrate very closely during PAGE revealing similarity of their effective conformations. Additional factors [i.e. sequence of single-stranded linker] come into effect once the gap size is longer than persistent length of single chains—in this case, the gap is likely to act as a hinge.

Upon going still further into their own results, the authors concede that while this represents very strong evidence for stacking contribution to stability predominating over base pairing, the model used is still simplistic.

Briefly, H-bond breaking between complementary bases and base stacking along the helical axis are disrupted upon melting, increasing conformational entropy, releasing counterions and changing solvent interactions — since as stated above, base stacking effects are hydrophobic, a model which doesn’t examine these solvation effects isn’t wholly conclusive.

Strictly speaking, partitioning of these effects between ΔGST and ΔGBP terms is not known.

This isn’t challenging the main result, rather commenting on a finer point. The extended discussion however is approaching my limit for one night; if you’re interested to read more, as usual the links are below.

GC pairing does not contribute to stabilization of DNA duplex, while A•T pairing is always destabilizing. This finding presents a paradigm shift in the understanding of the interplay of the forces stabilizing DNA double helix. For all temperatures heterogeneity of stacking interactions in A•T- and G•C-containing contacts accounts for at least half of heterogeneity in the stability of A•T- and G•C-polymers; the other half is due to the difference in the energetics of A•T and G•C base pairing. The data on separation of stacking and base pairing contributions have made it possible to describe sequence-dependent fluctuational opening of the DNA double helix

• Yakovchuk et al (2006) Base-stacking and base-pairing contributions into thermal stability of the DNA double helix. Nucleic Acids Res, 34(2)
•• Krueger and Frank-Kamenetskii (2006) Sequence-dependent base pair opening in DNA double helix. Biophys J90(9)

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Molecular motions inside the cell
A paper in Science this week describes the use of carbon nanotubes to pinpoint the movements of the living cell in fine detail, making for a really nice study in quantitative/mathematical biology.

Noninvasive tracking was accomplished by imaging highly stable near-infrared luminescence of single-walled carbon nanotubes targeted to kinesin-1 motor proteins in COS-7 cells. We observed a regime of active random “stirring” that constitutes an intermediate mode of transport, different from both thermal diffusion and directed motor activity. High-frequency motion was found to be thermally driven. At times greater than 100 milliseconds, nonequilibrium dynamics dominated. In addition to directed transport along microtubules, we observed strong random dynamics driven by myosins that result in enhanced nonspecific transport. We present a quantitative model connecting molecular mechanisms to mesoscopic fluctuations.

The &#8220;mesoscopic" scale is more often seen in the context of pure and applied physics (microelectronics, nanofabrication and nanotechnology), though journals such as Soft Matter present research articles giving the same &#8216;condensed matter&#8217; treatment to biological systems (“Where physics meets chemistry meets biology”).
From ancient Greek μέσος it refers simply to a &#8216;middle&#8217;/intermediate between the molecular and macroscopic scale, where neither atomistic/quantum nor classical physics/bulk models best describe observed behaviour, and novel effects may be described — from interference effects, to quantum confinement (giving rise to band gaps) and charging effects (such as the Coulomb blockade/staircase).
Although often presented as a water-based solvent, the cytosol is more accurately described as a “highly dynamic composite material ” with mechanical properties dominated by microtubules (MTs), F-actin and intermediate filaments; all driven by metabolism-energised polymerisation of actin and tubulin and from motor proteins (specifically nucleotide triphosphate hydrolysis).
The traditional technique to observe cells in motion is fluorescence microscopy, though long-term tracking of single molecules has been hindered by fluorophores&#8217; instabilities and the fluorescence background in cells.
Though biological networks have been termed ‘scale-free’ or ‘-invariant’, and metabolic rate for example is well known to follow a power law, the internal structure of the cell itself is far from self-similar across scales. 

At short times (microseconds to milliseconds), thermal motions should dominate. Between milliseconds and seconds, thermal diffusion might still be relevant, but there is mounting evidence, both in vitro and in vivo, that the motion of larger objects couples to myosin-driven stress fluctuations in the cytoskeleton.

»  Mizuno (2007) Nonequilibrium mechanics of active cytoskeletal networks.
»  Brangwynne (2008) Cytoplasmic diffusion: Molecular motors mix it up.

Here, temporal fluctuations, reminiscent of thermal diffusion in liquids, can arise from nonequilibrium dynamics in the viscoelastic cytoskeleton. On longer time scales, from minutes to hours, directed transport and larger-scale collective motions typically dominate. The motion of probe particles tracked inside cells has been classified as subdiffusive, diffusive, or superdiffusive. Such classifications, however, obscure the distinction between thermally driven and nonequilibrium fluctuations and are inadequate to identify intracellular material properties.

Motor proteins direct a whole host of molecular motions, kinesins and myosins being among the most heavily studied in vitro. Using fluorescence microscopy to track individual motor proteins is not only limited by instability of fluorophores, but the quality of the images taken (&#8220;signal to noise&#8221;) and efficiency of targetting probes to specific molecules.
Modern optical equipment and carefully designed fluorescent dyes have enabled experiments tracking single molecules at a time, though in living cells the authors note these experiments&#8217; timeframes have been limited to around a second.

Their solution was to use single-walled carbon nanotubes (SWNTs), “stiff quasi–one-dimensional tubular all-carbon nanostructures with diameters of ~1 nm and persistence lengths above 10 μm” — which have the convenient property of luminescence in the near-infrared, a region ‘virtually free of autofluorescence in biological tissues’. Not only this, but the excitation time is ~100ps, such that high excitation can give ~1&#160;ms resolution (1&#160;ms = 109 ps).
The nanotubes were dispersed throughout the cell wrapped in short DNA oligonucleotides, with HaloTag protein fusion tags covalently attaching them specifically onto kinesin motor proteins (see Fig. 1, above).

Besides observing directed kinesin-driven transport on MTs, it is possible to directly observe fluctuations of the MT network because a moving kinesin must be bound to a MT. The MT tracks are embedded in the viscoelastic actin cytoskeleton, which in turn fluctuates as a result of stresses generated by cytoplasmic myosins.


With just 100 per cell, the group could track kinesin for up to an hour and a half, observing ~30% of them moving with some sense of direction; the rest locally constrained and moving in a random (stochastic) manner.
Some of the kinesins moved the whole length of the cell, suggesting they had cargo vesicles [along with other motor proteins] attached. Calculating mean squared displacement, MSD, of the molecules&#8217; trajectories showed it grew over time following a power law which could be used to characterise the motion, 〈Δr2(τ)〉∝ τα(where r is distance travelled in the focal plane and τ the lag time). The exponent α shifted from ¼ to 1 between 5&#160;ms and 2.5&#160;s, indicating clear scale variance to the motion.
After this, the group acquired the nanotubes&#8217; fluorescent signal at a rate of four frames per second ‒ using this 250&#160;ms window to observe an intermediate between the thermal diffusion seen on the short timescales and directed motor activity.
With a well-designed control or two, they showed that the transverse motion of the nanotube-marked microtubules was not due to kinesin motors, but reflecting intrinsic dynamics of the cytoskeleton.

The way the relatively rigid MTs report these dynamics depends on two restoring forces: the elastic force of bent MTs and the force exerted by the strained cytoskeletal matrix in which the MTs are embedded. Because it is hard to bend an elastic rod on short length scales, the surrounding matrix yields to the MT when it is deformed on short length scales. By contrast, the MT yields to matrix forces for deflections of wavelength larger than ~1 μm. The shorter-wavelength MT deflections relax faster than our 5-ms frame rate. Therefore, we assume that the transverse MT motion we observe reflects the (active or passive) strain fluctuations of the surrounding matrix.
The MSD power-law exponent α generally reflects the randomness of motion. More precisely, in any medium, the MSD of an embedded probe particle is governed both by the material properties of the medium and the temporal characteristics of the forces driving the particle. For thermally driven Brownian motion in simple liquids, the MSD exponent α = 1. For thermal motion in viscoelastic media, which exhibit time- and frequency-dependent viscosity and elasticity, α &lt; 1 strictly holds. For viscoelastic materials, the stiffness G(ω) typically increases with a power of frequency ω: G(ω) ∝ ωβ. This is observed in polymer solutions, where the viscoelastic exponent β ≈ 0.5 to 0.8, as well as in cells, where β ≈ 0.1 to 0.2 on time scales on the order of seconds. This value of the exponent is close to what is expected for purely elastic materials, where β = 0. 
The nearly elastic behavior of cells can be understood as a consequence of strong cross-linking in the cytoskeleton.
 Knowing the driving forces, it is possible to construct a relation between MSD exponent α and viscoelastic exponent β. For thermal driving forces, the MSD exponent α = β. Thermal fluctuations can therefore never appear as “superdiffusive” motion with α &gt; 1. Nonthermal driving, by contrast, can result in superdiffusive motion. Theory provides a specific prediction for motion in nearly elastic solids driven by random stress fluctuations with long correlation times and sudden transitions: α = 1 + 2β. This prediction is expected to apply for cytoskeletal stress fluctuations caused by randomly distributed cytoplasmic myosin minifilaments. Myosin locally contracts the actin network with an attachment time of several seconds, followed by sudden release. Some hints of this predicted scaling have been reported for cells and reconstituted acto-myosin model systems. When β = 0 (i.e., in the elastic limit), the resulting MSDs can look deceptively like Brownian motion in a simple liquid, although the physical reason is entirely different. For observation times τ longer than the correlation time of the driving forces, the MSD is predicted to level off, as we observed. In our experiments, the stress correlation time should correspond to typical cytoplasmic myosin motor engagement times, which are indeed reported to be ~10&#160;s in cells.

Still attached to microtubules, the kinesin molecules exhibit vigorous random (Brownian-like) motion as they are buffeted by myosins as described ‒ likely thrusting MTs into the path of other cellular particles. Tubulin forms strong tubular filaments embedded in a more flexible actin network. Nonmuscle myosin II exerts mechanical stress on it, which is released ‘suddenly’ as random stirring of the whole filament network, including the microtubules.

We observed a transition between thermal dynamics in the dominantly elastic cytoskeleton at short times to strongly nonequilibrium power-law dynamics, likely driven by myosin activity, at intermediate times. When the time exceeded the correlation time of the random stress generators, the intermediate regime was followed by a saturation to a maximum MSD, nearly constant over time. Note that in this regime, the MSD amplitude corresponds to a root mean square displacement of ~500 nm, which is larger than the estimated mesh size of the actin network, and thus larger than the expected spacing of obstacles in the crowded cytoplasm.

The authors lastly used myosin inhibitor blebbistatin to block myosin from the actin network, confirming their hypothesis with a dose-dependent reduction in what they call the amplitude of active stirring, and exponent α, “establishing nonmuscle myosin II as the dominant driving factor for random cytoskeletal stirring”.

We can explain the regimes we observe by a quantitative model of cytoskeletal fluctuations and directed motor motion that describes the transition from thermal motion to nonequilibrium stirring dynamics driven by myosin, as well as the transition from stirring dynamics to directed transport driven by kinesin. Our observations were made possible by the use of SWNT labels for broadband molecular tracking in cells. Many questions concerning motor transport in cells will now be addressable using this approach. We have focused here on the stirring dynamics, which constitute an important mode of active intracellular transport between the limits of random thermal diffusion and directed transport, accelerating nonspecific transport through the nanoporous cytoskeleton.

Lead author Nikta Fakhri will soon leave the Göttingen Institute for Biophysics to join the faculty at MIT as assistant professor of physics. Fakhri gave a talk in Massachussets last year on the topic, to the Chemical Engineering department in which some of the details of this paper made their debut:

The discovery of fullerenes provided exciting insights into how highly symmetrical structures of pure carbon can have remarkable physical properties. Single-walled carbon nanotubes (SWNTs) are the vanguard of such architectures. The organization of the hexagonal honeycomb carbon lattice into high-aspect-ratio cylinders with a variety of helical symmetries creates very unusual macromolecular structures representing an emerging research area in condensed matter physics and materials science: traditionally hard materials appearing in new soft matter applications and environments.
… the dynamics of SWNTs in liquids are essentially polymer-like. By exploiting the intrinsic near-infrared fluorescence of semiconducting SWNTs, we have imaged the Brownian motion of individual nanotubes in water and have measured directly the bending stiffness of SWNTs. The semiflexible chain model represents accurately the configurational dynamics of SWNTs suspended in water. Interestingly, the persistence length of SWNTs is comparable to that of biopolymers. This finding paves the way for using SWNTs as a model system for semiflexible polymers to answer long-standing fundamental questions in polymer physics.
… the confined dynamics of stiff macromolecules in crowded environments [are] a common feature of polymer composites and the cell cytoskeleton. In fixed porous networks, we find that even a small bending flexibility strongly enhances SWNTs&#8217; motion. This ends a 30-year-old debate in polymer physics: the rotational diffusion constant is proportional to the filament bending compliance and counter-intuitively, independent of the network porosity. The dynamics of SWNTs in equilibrium and non-equilibrium biopolymer networks is more complex.
At long times, SWNTs reptate in the networks. At short times SWNTs can sample the spectrum of local stresses in equilibrium networks. In the non-equilibrium networks we observe strong local shape fluctuations driven by force generating molecular motors. I will discuss a newly developed microrheology technique in which we use nanotubes as “stealth probes” to measure viscoelastic properties of the host media. Finally, I will introduce a new single-molecule technique based on ultra-stable near-infrared fluorescence of short SWNTs, to study intracellular transport dynamics in living cells and in whole organisms. The combination of long-time stability and high signal-to-noise ratio enables the accurate long-term tracking of single motor proteins tagged with SWNTs traversing the entire cell. Remarkably, we can distinguish the motor protein’s motion along its microtubule track from the track’s underlying random non-thermal fluctuations.

She envisions the technology as applicable beyond probing biophysical questions, in the design of 'active' technical materials.
“Imagine a microscopic biomedical device that mixes tiny samples of blood with reagents to detect disease or smart filters that separate squishy from rigid materials.”
Fakhri will join the Physics of Living Systems group, seemingly on such a bio-materials science project. MIT lab colleague Jeremy England, known for work showing that E. coli reproduction is close to thermodynamic limits of efficiency, spoke of common interest in the cytosol and diffusive processes.

“We&#8217;re interested in the non-equilibrium thermodynamics of biological organization, so that could be construed to be about evolution and the origins of life or just about how you make or design self-replicators with desired properties.”
“Increasingly there are now instruments where you can make quantitative measurements on fluorescently labeled proteins in live cells,” England explains. “The cell biologists have their language and their frame of analysis that they&#8217;re most comfortable with for describing the phenomenon, but if there are interesting phenomena that are only going to be identifiable if you do the right quantitative analysis on all these numbers that you can now measure in the cell, then it&#8217;s useful to have people who are a bit more theoretically minded or physics minded who are there, when rubber meets road, when the data is being generated and helping to influence what kind of experiments get done.”
“We&#8217;re looking, for example, at diffusion of proteins in cells. Diffusion as a qualitative phenomenon is just things spreading out over space, but as a quantitative phenomenon, you can look at things like how rapidly a protein that&#8217;s labeled over here in the cell will wander over to another region of the cell that&#8217;s a certain distance away, and if you can make measurements of that, then you can start to say things that are more specific about characteristics of the diffusion that you are observing than simply seeing it spread out. And in those quantitative measurements, you can sometimes then see differences perhaps between different cells, or different conditions for the same type of cell, that may have biological relevance but that you wouldn&#8217;t have necessarily identified without the quantitative analysis,” England says.

⌇  Fakhri et al. (2014) High-resolution mapping of intracellular fluctuations using carbon nanotubes. Science, 344(1687), 1031-5
See also:⌇  Levine and MacKintosh (2009) The mechanics and fluctuation spectrum of active gels. J Phys Chem B, 113, 3820–3830⌇  MacKintosh and Levine (2008) Nonequilibrium mechanics and dynamics of motor-activated gels. Phys Rev Lett, 100, 018104⌇  Lau et al. (2003) Microrheology, stress fluctuations, and active behavior of living cells. Phys Rev Lett, 91, 198101⇢  Related post : water&#8217;s SED failure in molecular orientational diffusion
Molecular motions inside the cell
A paper in Science this week describes the use of carbon nanotubes to pinpoint the movements of the living cell in fine detail, making for a really nice study in quantitative/mathematical biology.

Noninvasive tracking was accomplished by imaging highly stable near-infrared luminescence of single-walled carbon nanotubes targeted to kinesin-1 motor proteins in COS-7 cells. We observed a regime of active random “stirring” that constitutes an intermediate mode of transport, different from both thermal diffusion and directed motor activity. High-frequency motion was found to be thermally driven. At times greater than 100 milliseconds, nonequilibrium dynamics dominated. In addition to directed transport along microtubules, we observed strong random dynamics driven by myosins that result in enhanced nonspecific transport. We present a quantitative model connecting molecular mechanisms to mesoscopic fluctuations.

The &#8220;mesoscopic" scale is more often seen in the context of pure and applied physics (microelectronics, nanofabrication and nanotechnology), though journals such as Soft Matter present research articles giving the same &#8216;condensed matter&#8217; treatment to biological systems (“Where physics meets chemistry meets biology”).
From ancient Greek μέσος it refers simply to a &#8216;middle&#8217;/intermediate between the molecular and macroscopic scale, where neither atomistic/quantum nor classical physics/bulk models best describe observed behaviour, and novel effects may be described — from interference effects, to quantum confinement (giving rise to band gaps) and charging effects (such as the Coulomb blockade/staircase).
Although often presented as a water-based solvent, the cytosol is more accurately described as a “highly dynamic composite material ” with mechanical properties dominated by microtubules (MTs), F-actin and intermediate filaments; all driven by metabolism-energised polymerisation of actin and tubulin and from motor proteins (specifically nucleotide triphosphate hydrolysis).
The traditional technique to observe cells in motion is fluorescence microscopy, though long-term tracking of single molecules has been hindered by fluorophores&#8217; instabilities and the fluorescence background in cells.
Though biological networks have been termed ‘scale-free’ or ‘-invariant’, and metabolic rate for example is well known to follow a power law, the internal structure of the cell itself is far from self-similar across scales. 

At short times (microseconds to milliseconds), thermal motions should dominate. Between milliseconds and seconds, thermal diffusion might still be relevant, but there is mounting evidence, both in vitro and in vivo, that the motion of larger objects couples to myosin-driven stress fluctuations in the cytoskeleton.

»  Mizuno (2007) Nonequilibrium mechanics of active cytoskeletal networks.
»  Brangwynne (2008) Cytoplasmic diffusion: Molecular motors mix it up.

Here, temporal fluctuations, reminiscent of thermal diffusion in liquids, can arise from nonequilibrium dynamics in the viscoelastic cytoskeleton. On longer time scales, from minutes to hours, directed transport and larger-scale collective motions typically dominate. The motion of probe particles tracked inside cells has been classified as subdiffusive, diffusive, or superdiffusive. Such classifications, however, obscure the distinction between thermally driven and nonequilibrium fluctuations and are inadequate to identify intracellular material properties.

Motor proteins direct a whole host of molecular motions, kinesins and myosins being among the most heavily studied in vitro. Using fluorescence microscopy to track individual motor proteins is not only limited by instability of fluorophores, but the quality of the images taken (&#8220;signal to noise&#8221;) and efficiency of targetting probes to specific molecules.
Modern optical equipment and carefully designed fluorescent dyes have enabled experiments tracking single molecules at a time, though in living cells the authors note these experiments&#8217; timeframes have been limited to around a second.

Their solution was to use single-walled carbon nanotubes (SWNTs), “stiff quasi–one-dimensional tubular all-carbon nanostructures with diameters of ~1 nm and persistence lengths above 10 μm” — which have the convenient property of luminescence in the near-infrared, a region ‘virtually free of autofluorescence in biological tissues’. Not only this, but the excitation time is ~100ps, such that high excitation can give ~1&#160;ms resolution (1&#160;ms = 109 ps).
The nanotubes were dispersed throughout the cell wrapped in short DNA oligonucleotides, with HaloTag protein fusion tags covalently attaching them specifically onto kinesin motor proteins (see Fig. 1, above).

Besides observing directed kinesin-driven transport on MTs, it is possible to directly observe fluctuations of the MT network because a moving kinesin must be bound to a MT. The MT tracks are embedded in the viscoelastic actin cytoskeleton, which in turn fluctuates as a result of stresses generated by cytoplasmic myosins.


With just 100 per cell, the group could track kinesin for up to an hour and a half, observing ~30% of them moving with some sense of direction; the rest locally constrained and moving in a random (stochastic) manner.
Some of the kinesins moved the whole length of the cell, suggesting they had cargo vesicles [along with other motor proteins] attached. Calculating mean squared displacement, MSD, of the molecules&#8217; trajectories showed it grew over time following a power law which could be used to characterise the motion, 〈Δr2(τ)〉∝ τα(where r is distance travelled in the focal plane and τ the lag time). The exponent α shifted from ¼ to 1 between 5&#160;ms and 2.5&#160;s, indicating clear scale variance to the motion.
After this, the group acquired the nanotubes&#8217; fluorescent signal at a rate of four frames per second ‒ using this 250&#160;ms window to observe an intermediate between the thermal diffusion seen on the short timescales and directed motor activity.
With a well-designed control or two, they showed that the transverse motion of the nanotube-marked microtubules was not due to kinesin motors, but reflecting intrinsic dynamics of the cytoskeleton.

The way the relatively rigid MTs report these dynamics depends on two restoring forces: the elastic force of bent MTs and the force exerted by the strained cytoskeletal matrix in which the MTs are embedded. Because it is hard to bend an elastic rod on short length scales, the surrounding matrix yields to the MT when it is deformed on short length scales. By contrast, the MT yields to matrix forces for deflections of wavelength larger than ~1 μm. The shorter-wavelength MT deflections relax faster than our 5-ms frame rate. Therefore, we assume that the transverse MT motion we observe reflects the (active or passive) strain fluctuations of the surrounding matrix.
The MSD power-law exponent α generally reflects the randomness of motion. More precisely, in any medium, the MSD of an embedded probe particle is governed both by the material properties of the medium and the temporal characteristics of the forces driving the particle. For thermally driven Brownian motion in simple liquids, the MSD exponent α = 1. For thermal motion in viscoelastic media, which exhibit time- and frequency-dependent viscosity and elasticity, α &lt; 1 strictly holds. For viscoelastic materials, the stiffness G(ω) typically increases with a power of frequency ω: G(ω) ∝ ωβ. This is observed in polymer solutions, where the viscoelastic exponent β ≈ 0.5 to 0.8, as well as in cells, where β ≈ 0.1 to 0.2 on time scales on the order of seconds. This value of the exponent is close to what is expected for purely elastic materials, where β = 0. 
The nearly elastic behavior of cells can be understood as a consequence of strong cross-linking in the cytoskeleton.
 Knowing the driving forces, it is possible to construct a relation between MSD exponent α and viscoelastic exponent β. For thermal driving forces, the MSD exponent α = β. Thermal fluctuations can therefore never appear as “superdiffusive” motion with α &gt; 1. Nonthermal driving, by contrast, can result in superdiffusive motion. Theory provides a specific prediction for motion in nearly elastic solids driven by random stress fluctuations with long correlation times and sudden transitions: α = 1 + 2β. This prediction is expected to apply for cytoskeletal stress fluctuations caused by randomly distributed cytoplasmic myosin minifilaments. Myosin locally contracts the actin network with an attachment time of several seconds, followed by sudden release. Some hints of this predicted scaling have been reported for cells and reconstituted acto-myosin model systems. When β = 0 (i.e., in the elastic limit), the resulting MSDs can look deceptively like Brownian motion in a simple liquid, although the physical reason is entirely different. For observation times τ longer than the correlation time of the driving forces, the MSD is predicted to level off, as we observed. In our experiments, the stress correlation time should correspond to typical cytoplasmic myosin motor engagement times, which are indeed reported to be ~10&#160;s in cells.

Still attached to microtubules, the kinesin molecules exhibit vigorous random (Brownian-like) motion as they are buffeted by myosins as described ‒ likely thrusting MTs into the path of other cellular particles. Tubulin forms strong tubular filaments embedded in a more flexible actin network. Nonmuscle myosin II exerts mechanical stress on it, which is released ‘suddenly’ as random stirring of the whole filament network, including the microtubules.

We observed a transition between thermal dynamics in the dominantly elastic cytoskeleton at short times to strongly nonequilibrium power-law dynamics, likely driven by myosin activity, at intermediate times. When the time exceeded the correlation time of the random stress generators, the intermediate regime was followed by a saturation to a maximum MSD, nearly constant over time. Note that in this regime, the MSD amplitude corresponds to a root mean square displacement of ~500 nm, which is larger than the estimated mesh size of the actin network, and thus larger than the expected spacing of obstacles in the crowded cytoplasm.

The authors lastly used myosin inhibitor blebbistatin to block myosin from the actin network, confirming their hypothesis with a dose-dependent reduction in what they call the amplitude of active stirring, and exponent α, “establishing nonmuscle myosin II as the dominant driving factor for random cytoskeletal stirring”.

We can explain the regimes we observe by a quantitative model of cytoskeletal fluctuations and directed motor motion that describes the transition from thermal motion to nonequilibrium stirring dynamics driven by myosin, as well as the transition from stirring dynamics to directed transport driven by kinesin. Our observations were made possible by the use of SWNT labels for broadband molecular tracking in cells. Many questions concerning motor transport in cells will now be addressable using this approach. We have focused here on the stirring dynamics, which constitute an important mode of active intracellular transport between the limits of random thermal diffusion and directed transport, accelerating nonspecific transport through the nanoporous cytoskeleton.

Lead author Nikta Fakhri will soon leave the Göttingen Institute for Biophysics to join the faculty at MIT as assistant professor of physics. Fakhri gave a talk in Massachussets last year on the topic, to the Chemical Engineering department in which some of the details of this paper made their debut:

The discovery of fullerenes provided exciting insights into how highly symmetrical structures of pure carbon can have remarkable physical properties. Single-walled carbon nanotubes (SWNTs) are the vanguard of such architectures. The organization of the hexagonal honeycomb carbon lattice into high-aspect-ratio cylinders with a variety of helical symmetries creates very unusual macromolecular structures representing an emerging research area in condensed matter physics and materials science: traditionally hard materials appearing in new soft matter applications and environments.
… the dynamics of SWNTs in liquids are essentially polymer-like. By exploiting the intrinsic near-infrared fluorescence of semiconducting SWNTs, we have imaged the Brownian motion of individual nanotubes in water and have measured directly the bending stiffness of SWNTs. The semiflexible chain model represents accurately the configurational dynamics of SWNTs suspended in water. Interestingly, the persistence length of SWNTs is comparable to that of biopolymers. This finding paves the way for using SWNTs as a model system for semiflexible polymers to answer long-standing fundamental questions in polymer physics.
… the confined dynamics of stiff macromolecules in crowded environments [are] a common feature of polymer composites and the cell cytoskeleton. In fixed porous networks, we find that even a small bending flexibility strongly enhances SWNTs&#8217; motion. This ends a 30-year-old debate in polymer physics: the rotational diffusion constant is proportional to the filament bending compliance and counter-intuitively, independent of the network porosity. The dynamics of SWNTs in equilibrium and non-equilibrium biopolymer networks is more complex.
At long times, SWNTs reptate in the networks. At short times SWNTs can sample the spectrum of local stresses in equilibrium networks. In the non-equilibrium networks we observe strong local shape fluctuations driven by force generating molecular motors. I will discuss a newly developed microrheology technique in which we use nanotubes as “stealth probes” to measure viscoelastic properties of the host media. Finally, I will introduce a new single-molecule technique based on ultra-stable near-infrared fluorescence of short SWNTs, to study intracellular transport dynamics in living cells and in whole organisms. The combination of long-time stability and high signal-to-noise ratio enables the accurate long-term tracking of single motor proteins tagged with SWNTs traversing the entire cell. Remarkably, we can distinguish the motor protein’s motion along its microtubule track from the track’s underlying random non-thermal fluctuations.

She envisions the technology as applicable beyond probing biophysical questions, in the design of 'active' technical materials.
“Imagine a microscopic biomedical device that mixes tiny samples of blood with reagents to detect disease or smart filters that separate squishy from rigid materials.”
Fakhri will join the Physics of Living Systems group, seemingly on such a bio-materials science project. MIT lab colleague Jeremy England, known for work showing that E. coli reproduction is close to thermodynamic limits of efficiency, spoke of common interest in the cytosol and diffusive processes.

“We&#8217;re interested in the non-equilibrium thermodynamics of biological organization, so that could be construed to be about evolution and the origins of life or just about how you make or design self-replicators with desired properties.”
“Increasingly there are now instruments where you can make quantitative measurements on fluorescently labeled proteins in live cells,” England explains. “The cell biologists have their language and their frame of analysis that they&#8217;re most comfortable with for describing the phenomenon, but if there are interesting phenomena that are only going to be identifiable if you do the right quantitative analysis on all these numbers that you can now measure in the cell, then it&#8217;s useful to have people who are a bit more theoretically minded or physics minded who are there, when rubber meets road, when the data is being generated and helping to influence what kind of experiments get done.”
“We&#8217;re looking, for example, at diffusion of proteins in cells. Diffusion as a qualitative phenomenon is just things spreading out over space, but as a quantitative phenomenon, you can look at things like how rapidly a protein that&#8217;s labeled over here in the cell will wander over to another region of the cell that&#8217;s a certain distance away, and if you can make measurements of that, then you can start to say things that are more specific about characteristics of the diffusion that you are observing than simply seeing it spread out. And in those quantitative measurements, you can sometimes then see differences perhaps between different cells, or different conditions for the same type of cell, that may have biological relevance but that you wouldn&#8217;t have necessarily identified without the quantitative analysis,” England says.

⌇  Fakhri et al. (2014) High-resolution mapping of intracellular fluctuations using carbon nanotubes. Science, 344(1687), 1031-5
See also:⌇  Levine and MacKintosh (2009) The mechanics and fluctuation spectrum of active gels. J Phys Chem B, 113, 3820–3830⌇  MacKintosh and Levine (2008) Nonequilibrium mechanics and dynamics of motor-activated gels. Phys Rev Lett, 100, 018104⌇  Lau et al. (2003) Microrheology, stress fluctuations, and active behavior of living cells. Phys Rev Lett, 91, 198101⇢  Related post : water&#8217;s SED failure in molecular orientational diffusion
Molecular motions inside the cell
A paper in Science this week describes the use of carbon nanotubes to pinpoint the movements of the living cell in fine detail, making for a really nice study in quantitative/mathematical biology.

Noninvasive tracking was accomplished by imaging highly stable near-infrared luminescence of single-walled carbon nanotubes targeted to kinesin-1 motor proteins in COS-7 cells. We observed a regime of active random “stirring” that constitutes an intermediate mode of transport, different from both thermal diffusion and directed motor activity. High-frequency motion was found to be thermally driven. At times greater than 100 milliseconds, nonequilibrium dynamics dominated. In addition to directed transport along microtubules, we observed strong random dynamics driven by myosins that result in enhanced nonspecific transport. We present a quantitative model connecting molecular mechanisms to mesoscopic fluctuations.

The &#8220;mesoscopic" scale is more often seen in the context of pure and applied physics (microelectronics, nanofabrication and nanotechnology), though journals such as Soft Matter present research articles giving the same &#8216;condensed matter&#8217; treatment to biological systems (“Where physics meets chemistry meets biology”).
From ancient Greek μέσος it refers simply to a &#8216;middle&#8217;/intermediate between the molecular and macroscopic scale, where neither atomistic/quantum nor classical physics/bulk models best describe observed behaviour, and novel effects may be described — from interference effects, to quantum confinement (giving rise to band gaps) and charging effects (such as the Coulomb blockade/staircase).
Although often presented as a water-based solvent, the cytosol is more accurately described as a “highly dynamic composite material ” with mechanical properties dominated by microtubules (MTs), F-actin and intermediate filaments; all driven by metabolism-energised polymerisation of actin and tubulin and from motor proteins (specifically nucleotide triphosphate hydrolysis).
The traditional technique to observe cells in motion is fluorescence microscopy, though long-term tracking of single molecules has been hindered by fluorophores&#8217; instabilities and the fluorescence background in cells.
Though biological networks have been termed ‘scale-free’ or ‘-invariant’, and metabolic rate for example is well known to follow a power law, the internal structure of the cell itself is far from self-similar across scales. 

At short times (microseconds to milliseconds), thermal motions should dominate. Between milliseconds and seconds, thermal diffusion might still be relevant, but there is mounting evidence, both in vitro and in vivo, that the motion of larger objects couples to myosin-driven stress fluctuations in the cytoskeleton.

»  Mizuno (2007) Nonequilibrium mechanics of active cytoskeletal networks.
»  Brangwynne (2008) Cytoplasmic diffusion: Molecular motors mix it up.

Here, temporal fluctuations, reminiscent of thermal diffusion in liquids, can arise from nonequilibrium dynamics in the viscoelastic cytoskeleton. On longer time scales, from minutes to hours, directed transport and larger-scale collective motions typically dominate. The motion of probe particles tracked inside cells has been classified as subdiffusive, diffusive, or superdiffusive. Such classifications, however, obscure the distinction between thermally driven and nonequilibrium fluctuations and are inadequate to identify intracellular material properties.

Motor proteins direct a whole host of molecular motions, kinesins and myosins being among the most heavily studied in vitro. Using fluorescence microscopy to track individual motor proteins is not only limited by instability of fluorophores, but the quality of the images taken (&#8220;signal to noise&#8221;) and efficiency of targetting probes to specific molecules.
Modern optical equipment and carefully designed fluorescent dyes have enabled experiments tracking single molecules at a time, though in living cells the authors note these experiments&#8217; timeframes have been limited to around a second.

Their solution was to use single-walled carbon nanotubes (SWNTs), “stiff quasi–one-dimensional tubular all-carbon nanostructures with diameters of ~1 nm and persistence lengths above 10 μm” — which have the convenient property of luminescence in the near-infrared, a region ‘virtually free of autofluorescence in biological tissues’. Not only this, but the excitation time is ~100ps, such that high excitation can give ~1&#160;ms resolution (1&#160;ms = 109 ps).
The nanotubes were dispersed throughout the cell wrapped in short DNA oligonucleotides, with HaloTag protein fusion tags covalently attaching them specifically onto kinesin motor proteins (see Fig. 1, above).

Besides observing directed kinesin-driven transport on MTs, it is possible to directly observe fluctuations of the MT network because a moving kinesin must be bound to a MT. The MT tracks are embedded in the viscoelastic actin cytoskeleton, which in turn fluctuates as a result of stresses generated by cytoplasmic myosins.


With just 100 per cell, the group could track kinesin for up to an hour and a half, observing ~30% of them moving with some sense of direction; the rest locally constrained and moving in a random (stochastic) manner.
Some of the kinesins moved the whole length of the cell, suggesting they had cargo vesicles [along with other motor proteins] attached. Calculating mean squared displacement, MSD, of the molecules&#8217; trajectories showed it grew over time following a power law which could be used to characterise the motion, 〈Δr2(τ)〉∝ τα(where r is distance travelled in the focal plane and τ the lag time). The exponent α shifted from ¼ to 1 between 5&#160;ms and 2.5&#160;s, indicating clear scale variance to the motion.
After this, the group acquired the nanotubes&#8217; fluorescent signal at a rate of four frames per second ‒ using this 250&#160;ms window to observe an intermediate between the thermal diffusion seen on the short timescales and directed motor activity.
With a well-designed control or two, they showed that the transverse motion of the nanotube-marked microtubules was not due to kinesin motors, but reflecting intrinsic dynamics of the cytoskeleton.

The way the relatively rigid MTs report these dynamics depends on two restoring forces: the elastic force of bent MTs and the force exerted by the strained cytoskeletal matrix in which the MTs are embedded. Because it is hard to bend an elastic rod on short length scales, the surrounding matrix yields to the MT when it is deformed on short length scales. By contrast, the MT yields to matrix forces for deflections of wavelength larger than ~1 μm. The shorter-wavelength MT deflections relax faster than our 5-ms frame rate. Therefore, we assume that the transverse MT motion we observe reflects the (active or passive) strain fluctuations of the surrounding matrix.
The MSD power-law exponent α generally reflects the randomness of motion. More precisely, in any medium, the MSD of an embedded probe particle is governed both by the material properties of the medium and the temporal characteristics of the forces driving the particle. For thermally driven Brownian motion in simple liquids, the MSD exponent α = 1. For thermal motion in viscoelastic media, which exhibit time- and frequency-dependent viscosity and elasticity, α &lt; 1 strictly holds. For viscoelastic materials, the stiffness G(ω) typically increases with a power of frequency ω: G(ω) ∝ ωβ. This is observed in polymer solutions, where the viscoelastic exponent β ≈ 0.5 to 0.8, as well as in cells, where β ≈ 0.1 to 0.2 on time scales on the order of seconds. This value of the exponent is close to what is expected for purely elastic materials, where β = 0. 
The nearly elastic behavior of cells can be understood as a consequence of strong cross-linking in the cytoskeleton.
 Knowing the driving forces, it is possible to construct a relation between MSD exponent α and viscoelastic exponent β. For thermal driving forces, the MSD exponent α = β. Thermal fluctuations can therefore never appear as “superdiffusive” motion with α &gt; 1. Nonthermal driving, by contrast, can result in superdiffusive motion. Theory provides a specific prediction for motion in nearly elastic solids driven by random stress fluctuations with long correlation times and sudden transitions: α = 1 + 2β. This prediction is expected to apply for cytoskeletal stress fluctuations caused by randomly distributed cytoplasmic myosin minifilaments. Myosin locally contracts the actin network with an attachment time of several seconds, followed by sudden release. Some hints of this predicted scaling have been reported for cells and reconstituted acto-myosin model systems. When β = 0 (i.e., in the elastic limit), the resulting MSDs can look deceptively like Brownian motion in a simple liquid, although the physical reason is entirely different. For observation times τ longer than the correlation time of the driving forces, the MSD is predicted to level off, as we observed. In our experiments, the stress correlation time should correspond to typical cytoplasmic myosin motor engagement times, which are indeed reported to be ~10&#160;s in cells.

Still attached to microtubules, the kinesin molecules exhibit vigorous random (Brownian-like) motion as they are buffeted by myosins as described ‒ likely thrusting MTs into the path of other cellular particles. Tubulin forms strong tubular filaments embedded in a more flexible actin network. Nonmuscle myosin II exerts mechanical stress on it, which is released ‘suddenly’ as random stirring of the whole filament network, including the microtubules.

We observed a transition between thermal dynamics in the dominantly elastic cytoskeleton at short times to strongly nonequilibrium power-law dynamics, likely driven by myosin activity, at intermediate times. When the time exceeded the correlation time of the random stress generators, the intermediate regime was followed by a saturation to a maximum MSD, nearly constant over time. Note that in this regime, the MSD amplitude corresponds to a root mean square displacement of ~500 nm, which is larger than the estimated mesh size of the actin network, and thus larger than the expected spacing of obstacles in the crowded cytoplasm.

The authors lastly used myosin inhibitor blebbistatin to block myosin from the actin network, confirming their hypothesis with a dose-dependent reduction in what they call the amplitude of active stirring, and exponent α, “establishing nonmuscle myosin II as the dominant driving factor for random cytoskeletal stirring”.

We can explain the regimes we observe by a quantitative model of cytoskeletal fluctuations and directed motor motion that describes the transition from thermal motion to nonequilibrium stirring dynamics driven by myosin, as well as the transition from stirring dynamics to directed transport driven by kinesin. Our observations were made possible by the use of SWNT labels for broadband molecular tracking in cells. Many questions concerning motor transport in cells will now be addressable using this approach. We have focused here on the stirring dynamics, which constitute an important mode of active intracellular transport between the limits of random thermal diffusion and directed transport, accelerating nonspecific transport through the nanoporous cytoskeleton.

Lead author Nikta Fakhri will soon leave the Göttingen Institute for Biophysics to join the faculty at MIT as assistant professor of physics. Fakhri gave a talk in Massachussets last year on the topic, to the Chemical Engineering department in which some of the details of this paper made their debut:

The discovery of fullerenes provided exciting insights into how highly symmetrical structures of pure carbon can have remarkable physical properties. Single-walled carbon nanotubes (SWNTs) are the vanguard of such architectures. The organization of the hexagonal honeycomb carbon lattice into high-aspect-ratio cylinders with a variety of helical symmetries creates very unusual macromolecular structures representing an emerging research area in condensed matter physics and materials science: traditionally hard materials appearing in new soft matter applications and environments.
… the dynamics of SWNTs in liquids are essentially polymer-like. By exploiting the intrinsic near-infrared fluorescence of semiconducting SWNTs, we have imaged the Brownian motion of individual nanotubes in water and have measured directly the bending stiffness of SWNTs. The semiflexible chain model represents accurately the configurational dynamics of SWNTs suspended in water. Interestingly, the persistence length of SWNTs is comparable to that of biopolymers. This finding paves the way for using SWNTs as a model system for semiflexible polymers to answer long-standing fundamental questions in polymer physics.
… the confined dynamics of stiff macromolecules in crowded environments [are] a common feature of polymer composites and the cell cytoskeleton. In fixed porous networks, we find that even a small bending flexibility strongly enhances SWNTs&#8217; motion. This ends a 30-year-old debate in polymer physics: the rotational diffusion constant is proportional to the filament bending compliance and counter-intuitively, independent of the network porosity. The dynamics of SWNTs in equilibrium and non-equilibrium biopolymer networks is more complex.
At long times, SWNTs reptate in the networks. At short times SWNTs can sample the spectrum of local stresses in equilibrium networks. In the non-equilibrium networks we observe strong local shape fluctuations driven by force generating molecular motors. I will discuss a newly developed microrheology technique in which we use nanotubes as “stealth probes” to measure viscoelastic properties of the host media. Finally, I will introduce a new single-molecule technique based on ultra-stable near-infrared fluorescence of short SWNTs, to study intracellular transport dynamics in living cells and in whole organisms. The combination of long-time stability and high signal-to-noise ratio enables the accurate long-term tracking of single motor proteins tagged with SWNTs traversing the entire cell. Remarkably, we can distinguish the motor protein’s motion along its microtubule track from the track’s underlying random non-thermal fluctuations.

She envisions the technology as applicable beyond probing biophysical questions, in the design of 'active' technical materials.
“Imagine a microscopic biomedical device that mixes tiny samples of blood with reagents to detect disease or smart filters that separate squishy from rigid materials.”
Fakhri will join the Physics of Living Systems group, seemingly on such a bio-materials science project. MIT lab colleague Jeremy England, known for work showing that E. coli reproduction is close to thermodynamic limits of efficiency, spoke of common interest in the cytosol and diffusive processes.

“We&#8217;re interested in the non-equilibrium thermodynamics of biological organization, so that could be construed to be about evolution and the origins of life or just about how you make or design self-replicators with desired properties.”
“Increasingly there are now instruments where you can make quantitative measurements on fluorescently labeled proteins in live cells,” England explains. “The cell biologists have their language and their frame of analysis that they&#8217;re most comfortable with for describing the phenomenon, but if there are interesting phenomena that are only going to be identifiable if you do the right quantitative analysis on all these numbers that you can now measure in the cell, then it&#8217;s useful to have people who are a bit more theoretically minded or physics minded who are there, when rubber meets road, when the data is being generated and helping to influence what kind of experiments get done.”
“We&#8217;re looking, for example, at diffusion of proteins in cells. Diffusion as a qualitative phenomenon is just things spreading out over space, but as a quantitative phenomenon, you can look at things like how rapidly a protein that&#8217;s labeled over here in the cell will wander over to another region of the cell that&#8217;s a certain distance away, and if you can make measurements of that, then you can start to say things that are more specific about characteristics of the diffusion that you are observing than simply seeing it spread out. And in those quantitative measurements, you can sometimes then see differences perhaps between different cells, or different conditions for the same type of cell, that may have biological relevance but that you wouldn&#8217;t have necessarily identified without the quantitative analysis,” England says.

⌇  Fakhri et al. (2014) High-resolution mapping of intracellular fluctuations using carbon nanotubes. Science, 344(1687), 1031-5
See also:⌇  Levine and MacKintosh (2009) The mechanics and fluctuation spectrum of active gels. J Phys Chem B, 113, 3820–3830⌇  MacKintosh and Levine (2008) Nonequilibrium mechanics and dynamics of motor-activated gels. Phys Rev Lett, 100, 018104⌇  Lau et al. (2003) Microrheology, stress fluctuations, and active behavior of living cells. Phys Rev Lett, 91, 198101⇢  Related post : water&#8217;s SED failure in molecular orientational diffusion
Molecular motions inside the cell
A paper in Science this week describes the use of carbon nanotubes to pinpoint the movements of the living cell in fine detail, making for a really nice study in quantitative/mathematical biology.

Noninvasive tracking was accomplished by imaging highly stable near-infrared luminescence of single-walled carbon nanotubes targeted to kinesin-1 motor proteins in COS-7 cells. We observed a regime of active random “stirring” that constitutes an intermediate mode of transport, different from both thermal diffusion and directed motor activity. High-frequency motion was found to be thermally driven. At times greater than 100 milliseconds, nonequilibrium dynamics dominated. In addition to directed transport along microtubules, we observed strong random dynamics driven by myosins that result in enhanced nonspecific transport. We present a quantitative model connecting molecular mechanisms to mesoscopic fluctuations.

The &#8220;mesoscopic" scale is more often seen in the context of pure and applied physics (microelectronics, nanofabrication and nanotechnology), though journals such as Soft Matter present research articles giving the same &#8216;condensed matter&#8217; treatment to biological systems (“Where physics meets chemistry meets biology”).
From ancient Greek μέσος it refers simply to a &#8216;middle&#8217;/intermediate between the molecular and macroscopic scale, where neither atomistic/quantum nor classical physics/bulk models best describe observed behaviour, and novel effects may be described — from interference effects, to quantum confinement (giving rise to band gaps) and charging effects (such as the Coulomb blockade/staircase).
Although often presented as a water-based solvent, the cytosol is more accurately described as a “highly dynamic composite material ” with mechanical properties dominated by microtubules (MTs), F-actin and intermediate filaments; all driven by metabolism-energised polymerisation of actin and tubulin and from motor proteins (specifically nucleotide triphosphate hydrolysis).
The traditional technique to observe cells in motion is fluorescence microscopy, though long-term tracking of single molecules has been hindered by fluorophores&#8217; instabilities and the fluorescence background in cells.
Though biological networks have been termed ‘scale-free’ or ‘-invariant’, and metabolic rate for example is well known to follow a power law, the internal structure of the cell itself is far from self-similar across scales. 

At short times (microseconds to milliseconds), thermal motions should dominate. Between milliseconds and seconds, thermal diffusion might still be relevant, but there is mounting evidence, both in vitro and in vivo, that the motion of larger objects couples to myosin-driven stress fluctuations in the cytoskeleton.

»  Mizuno (2007) Nonequilibrium mechanics of active cytoskeletal networks.
»  Brangwynne (2008) Cytoplasmic diffusion: Molecular motors mix it up.

Here, temporal fluctuations, reminiscent of thermal diffusion in liquids, can arise from nonequilibrium dynamics in the viscoelastic cytoskeleton. On longer time scales, from minutes to hours, directed transport and larger-scale collective motions typically dominate. The motion of probe particles tracked inside cells has been classified as subdiffusive, diffusive, or superdiffusive. Such classifications, however, obscure the distinction between thermally driven and nonequilibrium fluctuations and are inadequate to identify intracellular material properties.

Motor proteins direct a whole host of molecular motions, kinesins and myosins being among the most heavily studied in vitro. Using fluorescence microscopy to track individual motor proteins is not only limited by instability of fluorophores, but the quality of the images taken (&#8220;signal to noise&#8221;) and efficiency of targetting probes to specific molecules.
Modern optical equipment and carefully designed fluorescent dyes have enabled experiments tracking single molecules at a time, though in living cells the authors note these experiments&#8217; timeframes have been limited to around a second.

Their solution was to use single-walled carbon nanotubes (SWNTs), “stiff quasi–one-dimensional tubular all-carbon nanostructures with diameters of ~1 nm and persistence lengths above 10 μm” — which have the convenient property of luminescence in the near-infrared, a region ‘virtually free of autofluorescence in biological tissues’. Not only this, but the excitation time is ~100ps, such that high excitation can give ~1&#160;ms resolution (1&#160;ms = 109 ps).
The nanotubes were dispersed throughout the cell wrapped in short DNA oligonucleotides, with HaloTag protein fusion tags covalently attaching them specifically onto kinesin motor proteins (see Fig. 1, above).

Besides observing directed kinesin-driven transport on MTs, it is possible to directly observe fluctuations of the MT network because a moving kinesin must be bound to a MT. The MT tracks are embedded in the viscoelastic actin cytoskeleton, which in turn fluctuates as a result of stresses generated by cytoplasmic myosins.


With just 100 per cell, the group could track kinesin for up to an hour and a half, observing ~30% of them moving with some sense of direction; the rest locally constrained and moving in a random (stochastic) manner.
Some of the kinesins moved the whole length of the cell, suggesting they had cargo vesicles [along with other motor proteins] attached. Calculating mean squared displacement, MSD, of the molecules&#8217; trajectories showed it grew over time following a power law which could be used to characterise the motion, 〈Δr2(τ)〉∝ τα(where r is distance travelled in the focal plane and τ the lag time). The exponent α shifted from ¼ to 1 between 5&#160;ms and 2.5&#160;s, indicating clear scale variance to the motion.
After this, the group acquired the nanotubes&#8217; fluorescent signal at a rate of four frames per second ‒ using this 250&#160;ms window to observe an intermediate between the thermal diffusion seen on the short timescales and directed motor activity.
With a well-designed control or two, they showed that the transverse motion of the nanotube-marked microtubules was not due to kinesin motors, but reflecting intrinsic dynamics of the cytoskeleton.

The way the relatively rigid MTs report these dynamics depends on two restoring forces: the elastic force of bent MTs and the force exerted by the strained cytoskeletal matrix in which the MTs are embedded. Because it is hard to bend an elastic rod on short length scales, the surrounding matrix yields to the MT when it is deformed on short length scales. By contrast, the MT yields to matrix forces for deflections of wavelength larger than ~1 μm. The shorter-wavelength MT deflections relax faster than our 5-ms frame rate. Therefore, we assume that the transverse MT motion we observe reflects the (active or passive) strain fluctuations of the surrounding matrix.
The MSD power-law exponent α generally reflects the randomness of motion. More precisely, in any medium, the MSD of an embedded probe particle is governed both by the material properties of the medium and the temporal characteristics of the forces driving the particle. For thermally driven Brownian motion in simple liquids, the MSD exponent α = 1. For thermal motion in viscoelastic media, which exhibit time- and frequency-dependent viscosity and elasticity, α &lt; 1 strictly holds. For viscoelastic materials, the stiffness G(ω) typically increases with a power of frequency ω: G(ω) ∝ ωβ. This is observed in polymer solutions, where the viscoelastic exponent β ≈ 0.5 to 0.8, as well as in cells, where β ≈ 0.1 to 0.2 on time scales on the order of seconds. This value of the exponent is close to what is expected for purely elastic materials, where β = 0. 
The nearly elastic behavior of cells can be understood as a consequence of strong cross-linking in the cytoskeleton.
 Knowing the driving forces, it is possible to construct a relation between MSD exponent α and viscoelastic exponent β. For thermal driving forces, the MSD exponent α = β. Thermal fluctuations can therefore never appear as “superdiffusive” motion with α &gt; 1. Nonthermal driving, by contrast, can result in superdiffusive motion. Theory provides a specific prediction for motion in nearly elastic solids driven by random stress fluctuations with long correlation times and sudden transitions: α = 1 + 2β. This prediction is expected to apply for cytoskeletal stress fluctuations caused by randomly distributed cytoplasmic myosin minifilaments. Myosin locally contracts the actin network with an attachment time of several seconds, followed by sudden release. Some hints of this predicted scaling have been reported for cells and reconstituted acto-myosin model systems. When β = 0 (i.e., in the elastic limit), the resulting MSDs can look deceptively like Brownian motion in a simple liquid, although the physical reason is entirely different. For observation times τ longer than the correlation time of the driving forces, the MSD is predicted to level off, as we observed. In our experiments, the stress correlation time should correspond to typical cytoplasmic myosin motor engagement times, which are indeed reported to be ~10&#160;s in cells.

Still attached to microtubules, the kinesin molecules exhibit vigorous random (Brownian-like) motion as they are buffeted by myosins as described ‒ likely thrusting MTs into the path of other cellular particles. Tubulin forms strong tubular filaments embedded in a more flexible actin network. Nonmuscle myosin II exerts mechanical stress on it, which is released ‘suddenly’ as random stirring of the whole filament network, including the microtubules.

We observed a transition between thermal dynamics in the dominantly elastic cytoskeleton at short times to strongly nonequilibrium power-law dynamics, likely driven by myosin activity, at intermediate times. When the time exceeded the correlation time of the random stress generators, the intermediate regime was followed by a saturation to a maximum MSD, nearly constant over time. Note that in this regime, the MSD amplitude corresponds to a root mean square displacement of ~500 nm, which is larger than the estimated mesh size of the actin network, and thus larger than the expected spacing of obstacles in the crowded cytoplasm.

The authors lastly used myosin inhibitor blebbistatin to block myosin from the actin network, confirming their hypothesis with a dose-dependent reduction in what they call the amplitude of active stirring, and exponent α, “establishing nonmuscle myosin II as the dominant driving factor for random cytoskeletal stirring”.

We can explain the regimes we observe by a quantitative model of cytoskeletal fluctuations and directed motor motion that describes the transition from thermal motion to nonequilibrium stirring dynamics driven by myosin, as well as the transition from stirring dynamics to directed transport driven by kinesin. Our observations were made possible by the use of SWNT labels for broadband molecular tracking in cells. Many questions concerning motor transport in cells will now be addressable using this approach. We have focused here on the stirring dynamics, which constitute an important mode of active intracellular transport between the limits of random thermal diffusion and directed transport, accelerating nonspecific transport through the nanoporous cytoskeleton.

Lead author Nikta Fakhri will soon leave the Göttingen Institute for Biophysics to join the faculty at MIT as assistant professor of physics. Fakhri gave a talk in Massachussets last year on the topic, to the Chemical Engineering department in which some of the details of this paper made their debut:

The discovery of fullerenes provided exciting insights into how highly symmetrical structures of pure carbon can have remarkable physical properties. Single-walled carbon nanotubes (SWNTs) are the vanguard of such architectures. The organization of the hexagonal honeycomb carbon lattice into high-aspect-ratio cylinders with a variety of helical symmetries creates very unusual macromolecular structures representing an emerging research area in condensed matter physics and materials science: traditionally hard materials appearing in new soft matter applications and environments.
… the dynamics of SWNTs in liquids are essentially polymer-like. By exploiting the intrinsic near-infrared fluorescence of semiconducting SWNTs, we have imaged the Brownian motion of individual nanotubes in water and have measured directly the bending stiffness of SWNTs. The semiflexible chain model represents accurately the configurational dynamics of SWNTs suspended in water. Interestingly, the persistence length of SWNTs is comparable to that of biopolymers. This finding paves the way for using SWNTs as a model system for semiflexible polymers to answer long-standing fundamental questions in polymer physics.
… the confined dynamics of stiff macromolecules in crowded environments [are] a common feature of polymer composites and the cell cytoskeleton. In fixed porous networks, we find that even a small bending flexibility strongly enhances SWNTs&#8217; motion. This ends a 30-year-old debate in polymer physics: the rotational diffusion constant is proportional to the filament bending compliance and counter-intuitively, independent of the network porosity. The dynamics of SWNTs in equilibrium and non-equilibrium biopolymer networks is more complex.
At long times, SWNTs reptate in the networks. At short times SWNTs can sample the spectrum of local stresses in equilibrium networks. In the non-equilibrium networks we observe strong local shape fluctuations driven by force generating molecular motors. I will discuss a newly developed microrheology technique in which we use nanotubes as “stealth probes” to measure viscoelastic properties of the host media. Finally, I will introduce a new single-molecule technique based on ultra-stable near-infrared fluorescence of short SWNTs, to study intracellular transport dynamics in living cells and in whole organisms. The combination of long-time stability and high signal-to-noise ratio enables the accurate long-term tracking of single motor proteins tagged with SWNTs traversing the entire cell. Remarkably, we can distinguish the motor protein’s motion along its microtubule track from the track’s underlying random non-thermal fluctuations.

She envisions the technology as applicable beyond probing biophysical questions, in the design of 'active' technical materials.
“Imagine a microscopic biomedical device that mixes tiny samples of blood with reagents to detect disease or smart filters that separate squishy from rigid materials.”
Fakhri will join the Physics of Living Systems group, seemingly on such a bio-materials science project. MIT lab colleague Jeremy England, known for work showing that E. coli reproduction is close to thermodynamic limits of efficiency, spoke of common interest in the cytosol and diffusive processes.

“We&#8217;re interested in the non-equilibrium thermodynamics of biological organization, so that could be construed to be about evolution and the origins of life or just about how you make or design self-replicators with desired properties.”
“Increasingly there are now instruments where you can make quantitative measurements on fluorescently labeled proteins in live cells,” England explains. “The cell biologists have their language and their frame of analysis that they&#8217;re most comfortable with for describing the phenomenon, but if there are interesting phenomena that are only going to be identifiable if you do the right quantitative analysis on all these numbers that you can now measure in the cell, then it&#8217;s useful to have people who are a bit more theoretically minded or physics minded who are there, when rubber meets road, when the data is being generated and helping to influence what kind of experiments get done.”
“We&#8217;re looking, for example, at diffusion of proteins in cells. Diffusion as a qualitative phenomenon is just things spreading out over space, but as a quantitative phenomenon, you can look at things like how rapidly a protein that&#8217;s labeled over here in the cell will wander over to another region of the cell that&#8217;s a certain distance away, and if you can make measurements of that, then you can start to say things that are more specific about characteristics of the diffusion that you are observing than simply seeing it spread out. And in those quantitative measurements, you can sometimes then see differences perhaps between different cells, or different conditions for the same type of cell, that may have biological relevance but that you wouldn&#8217;t have necessarily identified without the quantitative analysis,” England says.

⌇  Fakhri et al. (2014) High-resolution mapping of intracellular fluctuations using carbon nanotubes. Science, 344(1687), 1031-5
See also:⌇  Levine and MacKintosh (2009) The mechanics and fluctuation spectrum of active gels. J Phys Chem B, 113, 3820–3830⌇  MacKintosh and Levine (2008) Nonequilibrium mechanics and dynamics of motor-activated gels. Phys Rev Lett, 100, 018104⌇  Lau et al. (2003) Microrheology, stress fluctuations, and active behavior of living cells. Phys Rev Lett, 91, 198101⇢  Related post : water&#8217;s SED failure in molecular orientational diffusion

Molecular motions inside the cell

A paper in Science this week describes the use of carbon nanotubes to pinpoint the movements of the living cell in fine detail, making for a really nice study in quantitative/mathematical biology.

Noninvasive tracking was accomplished by imaging highly stable near-infrared luminescence of single-walled carbon nanotubes targeted to kinesin-1 motor proteins in COS-7 cells. We observed a regime of active random “stirring” that constitutes an intermediate mode of transport, different from both thermal diffusion and directed motor activity. High-frequency motion was found to be thermally driven. At times greater than 100 milliseconds, nonequilibrium dynamics dominated. In addition to directed transport along microtubules, we observed strong random dynamics driven by myosins that result in enhanced nonspecific transport. We present a quantitative model connecting molecular mechanisms to mesoscopic fluctuations.

The “mesoscopic" scale is more often seen in the context of pure and applied physics (microelectronics, nanofabrication and nanotechnology), though journals such as Soft Matter present research articles giving the same ‘condensed matter’ treatment to biological systems (“Where physics meets chemistry meets biology”).

From ancient Greek μέσος it refers simply to a ‘middle’/intermediate between the molecular and macroscopic scale, where neither atomistic/quantum nor classical physics/bulk models best describe observed behaviour, and novel effects may be described — from interference effects, to quantum confinement (giving rise to band gaps) and charging effects (such as the Coulomb blockade/staircase).

Although often presented as a water-based solvent, the cytosol is more accurately described as a “highly dynamic composite material ” with mechanical properties dominated by microtubules (MTs), F-actin and intermediate filaments; all driven by metabolism-energised polymerisation of actin and tubulin and from motor proteins (specifically nucleotide triphosphate hydrolysis).

The traditional technique to observe cells in motion is fluorescence microscopy, though long-term tracking of single molecules has been hindered by fluorophores’ instabilities and the fluorescence background in cells.

Though biological networks have been termed ‘scale-free’ or ‘-invariant’, and metabolic rate for example is well known to follow a power law, the internal structure of the cell itself is far from self-similar across scales. 

At short times (microseconds to milliseconds), thermal motions should dominate. Between milliseconds and seconds, thermal diffusion might still be relevant, but there is mounting evidence, both in vitro and in vivo, that the motion of larger objects couples to myosin-driven stress fluctuations in the cytoskeleton.

»  Mizuno (2007) Nonequilibrium mechanics of active cytoskeletal networks.

»  Brangwynne (2008) Cytoplasmic diffusion: Molecular motors mix it up.

Here, temporal fluctuations, reminiscent of thermal diffusion in liquids, can arise from nonequilibrium dynamics in the viscoelastic cytoskeleton. On longer time scales, from minutes to hours, directed transport and larger-scale collective motions typically dominate. The motion of probe particles tracked inside cells has been classified as subdiffusive, diffusive, or superdiffusive. Such classifications, however, obscure the distinction between thermally driven and nonequilibrium fluctuations and are inadequate to identify intracellular material properties.

Motor proteins direct a whole host of molecular motions, kinesins and myosins being among the most heavily studied in vitro. Using fluorescence microscopy to track individual motor proteins is not only limited by instability of fluorophores, but the quality of the images taken (“signal to noise”) and efficiency of targetting probes to specific molecules.

Modern optical equipment and carefully designed fluorescent dyes have enabled experiments tracking single molecules at a time, though in living cells the authors note these experiments’ timeframes have been limited to around a second.

Their solution was to use single-walled carbon nanotubes (SWNTs), “stiff quasi–one-dimensional tubular all-carbon nanostructures with diameters of ~1 nm and persistence lengths above 10 μm” — which have the convenient property of luminescence in the near-infrared, a region ‘virtually free of autofluorescence in biological tissues’. Not only this, but the excitation time is ~100ps, such that high excitation can give ~1 ms resolution (1 ms = 109 ps).

The nanotubes were dispersed throughout the cell wrapped in short DNA oligonucleotides, with HaloTag protein fusion tags covalently attaching them specifically onto kinesin motor proteins (see Fig. 1, above).

Besides observing directed kinesin-driven transport on MTs, it is possible to directly observe fluctuations of the MT network because a moving kinesin must be bound to a MT. The MT tracks are embedded in the viscoelastic actin cytoskeleton, which in turn fluctuates as a result of stresses generated by cytoplasmic myosins.

image

With just 100 per cell, the group could track kinesin for up to an hour and a half, observing ~30% of them moving with some sense of direction; the rest locally constrained and moving in a random (stochastic) manner.

Some of the kinesins moved the whole length of the cell, suggesting they had cargo vesicles [along with other motor proteins] attached. Calculating mean squared displacement, MSD, of the molecules’ trajectories showed it grew over time following a power law which could be used to characterise the motion, 〈Δr2(τ)〉∝ τα(where r is distance travelled in the focal plane and τ the lag time). The exponent α shifted from ¼ to 1 between 5 ms and 2.5 s, indicating clear scale variance to the motion.

After this, the group acquired the nanotubes’ fluorescent signal at a rate of four frames per second ‒ using this 250 ms window to observe an intermediate between the thermal diffusion seen on the short timescales and directed motor activity.

With a well-designed control or two, they showed that the transverse motion of the nanotube-marked microtubules was not due to kinesin motors, but reflecting intrinsic dynamics of the cytoskeleton.

The way the relatively rigid MTs report these dynamics depends on two restoring forces: the elastic force of bent MTs and the force exerted by the strained cytoskeletal matrix in which the MTs are embedded. Because it is hard to bend an elastic rod on short length scales, the surrounding matrix yields to the MT when it is deformed on short length scales. By contrast, the MT yields to matrix forces for deflections of wavelength larger than ~1 μm. The shorter-wavelength MT deflections relax faster than our 5-ms frame rate. Therefore, we assume that the transverse MT motion we observe reflects the (active or passive) strain fluctuations of the surrounding matrix.

The MSD power-law exponent α generally reflects the randomness of motion. More precisely, in any medium, the MSD of an embedded probe particle is governed both by the material properties of the medium and the temporal characteristics of the forces driving the particle. For thermally driven Brownian motion in simple liquids, the MSD exponent α = 1. For thermal motion in viscoelastic media, which exhibit time- and frequency-dependent viscosity and elasticity, α < 1 strictly holds. For viscoelastic materials, the stiffness G(ω) typically increases with a power of frequency ω: G(ω) ∝ ωβ. This is observed in polymer solutions, where the viscoelastic exponent β ≈ 0.5 to 0.8, as well as in cells, where β ≈ 0.1 to 0.2 on time scales on the order of seconds. This value of the exponent is close to what is expected for purely elastic materials, where β = 0.

The nearly elastic behavior of cells can be understood as a consequence of strong cross-linking in the cytoskeleton.

Knowing the driving forces, it is possible to construct a relation between MSD exponent α and viscoelastic exponent β. For thermal driving forces, the MSD exponent α = β. Thermal fluctuations can therefore never appear as “superdiffusive” motion with α > 1. Nonthermal driving, by contrast, can result in superdiffusive motion. Theory provides a specific prediction for motion in nearly elastic solids driven by random stress fluctuations with long correlation times and sudden transitions: α = 1 + 2β. This prediction is expected to apply for cytoskeletal stress fluctuations caused by randomly distributed cytoplasmic myosin minifilaments. Myosin locally contracts the actin network with an attachment time of several seconds, followed by sudden release. Some hints of this predicted scaling have been reported for cells and reconstituted acto-myosin model systems. When β = 0 (i.e., in the elastic limit), the resulting MSDs can look deceptively like Brownian motion in a simple liquid, although the physical reason is entirely different. For observation times τ longer than the correlation time of the driving forces, the MSD is predicted to level off, as we observed. In our experiments, the stress correlation time should correspond to typical cytoplasmic myosin motor engagement times, which are indeed reported to be ~10 s in cells.

Still attached to microtubules, the kinesin molecules exhibit vigorous random (Brownian-like) motion as they are buffeted by myosins as described ‒ likely thrusting MTs into the path of other cellular particles. Tubulin forms strong tubular filaments embedded in a more flexible actin network. Nonmuscle myosin II exerts mechanical stress on it, which is released ‘suddenly’ as random stirring of the whole filament network, including the microtubules.

We observed a transition between thermal dynamics in the dominantly elastic cytoskeleton at short times to strongly nonequilibrium power-law dynamics, likely driven by myosin activity, at intermediate times. When the time exceeded the correlation time of the random stress generators, the intermediate regime was followed by a saturation to a maximum MSD, nearly constant over time. Note that in this regime, the MSD amplitude corresponds to a root mean square displacement of ~500 nm, which is larger than the estimated mesh size of the actin network, and thus larger than the expected spacing of obstacles in the crowded cytoplasm.

The authors lastly used myosin inhibitor blebbistatin to block myosin from the actin network, confirming their hypothesis with a dose-dependent reduction in what they call the amplitude of active stirring, and exponent α, “establishing nonmuscle myosin II as the dominant driving factor for random cytoskeletal stirring”.

We can explain the regimes we observe by a quantitative model of cytoskeletal fluctuations and directed motor motion that describes the transition from thermal motion to nonequilibrium stirring dynamics driven by myosin, as well as the transition from stirring dynamics to directed transport driven by kinesin. Our observations were made possible by the use of SWNT labels for broadband molecular tracking in cells. Many questions concerning motor transport in cells will now be addressable using this approach. We have focused here on the stirring dynamics, which constitute an important mode of active intracellular transport between the limits of random thermal diffusion and directed transport, accelerating nonspecific transport through the nanoporous cytoskeleton.

Lead author Nikta Fakhri will soon leave the Göttingen Institute for Biophysics to join the faculty at MIT as assistant professor of physics. Fakhri gave a talk in Massachussets last year on the topic, to the Chemical Engineering department in which some of the details of this paper made their debut:

The discovery of fullerenes provided exciting insights into how highly symmetrical structures of pure carbon can have remarkable physical properties. Single-walled carbon nanotubes (SWNTs) are the vanguard of such architectures. The organization of the hexagonal honeycomb carbon lattice into high-aspect-ratio cylinders with a variety of helical symmetries creates very unusual macromolecular structures representing an emerging research area in condensed matter physics and materials science: traditionally hard materials appearing in new soft matter applications and environments.

… the dynamics of SWNTs in liquids are essentially polymer-like. By exploiting the intrinsic near-infrared fluorescence of semiconducting SWNTs, we have imaged the Brownian motion of individual nanotubes in water and have measured directly the bending stiffness of SWNTs. The semiflexible chain model represents accurately the configurational dynamics of SWNTs suspended in water. Interestingly, the persistence length of SWNTs is comparable to that of biopolymers. This finding paves the way for using SWNTs as a model system for semiflexible polymers to answer long-standing fundamental questions in polymer physics.

… the confined dynamics of stiff macromolecules in crowded environments [are] a common feature of polymer composites and the cell cytoskeleton. In fixed porous networks, we find that even a small bending flexibility strongly enhances SWNTs’ motion. This ends a 30-year-old debate in polymer physics: the rotational diffusion constant is proportional to the filament bending compliance and counter-intuitively, independent of the network porosity. The dynamics of SWNTs in equilibrium and non-equilibrium biopolymer networks is more complex.

At long times, SWNTs reptate in the networks. At short times SWNTs can sample the spectrum of local stresses in equilibrium networks. In the non-equilibrium networks we observe strong local shape fluctuations driven by force generating molecular motors. I will discuss a newly developed microrheology technique in which we use nanotubes as “stealth probes” to measure viscoelastic properties of the host media. Finally, I will introduce a new single-molecule technique based on ultra-stable near-infrared fluorescence of short SWNTs, to study intracellular transport dynamics in living cells and in whole organisms. The combination of long-time stability and high signal-to-noise ratio enables the accurate long-term tracking of single motor proteins tagged with SWNTs traversing the entire cell. Remarkably, we can distinguish the motor protein’s motion along its microtubule track from the track’s underlying random non-thermal fluctuations.

She envisions the technology as applicable beyond probing biophysical questions, in the design of 'active' technical materials.

“Imagine a microscopic biomedical device that mixes tiny samples of blood with reagents to detect disease or smart filters that separate squishy from rigid materials.”

Fakhri will join the Physics of Living Systems group, seemingly on such a bio-materials science project. MIT lab colleague Jeremy England, known for work showing that E. coli reproduction is close to thermodynamic limits of efficiency, spoke of common interest in the cytosol and diffusive processes.

“We’re interested in the non-equilibrium thermodynamics of biological organization, so that could be construed to be about evolution and the origins of life or just about how you make or design self-replicators with desired properties.”

“Increasingly there are now instruments where you can make quantitative measurements on fluorescently labeled proteins in live cells,” England explains. “The cell biologists have their language and their frame of analysis that they’re most comfortable with for describing the phenomenon, but if there are interesting phenomena that are only going to be identifiable if you do the right quantitative analysis on all these numbers that you can now measure in the cell, then it’s useful to have people who are a bit more theoretically minded or physics minded who are there, when rubber meets road, when the data is being generated and helping to influence what kind of experiments get done.”

“We’re looking, for example, at diffusion of proteins in cells. Diffusion as a qualitative phenomenon is just things spreading out over space, but as a quantitative phenomenon, you can look at things like how rapidly a protein that’s labeled over here in the cell will wander over to another region of the cell that’s a certain distance away, and if you can make measurements of that, then you can start to say things that are more specific about characteristics of the diffusion that you are observing than simply seeing it spread out. And in those quantitative measurements, you can sometimes then see differences perhaps between different cells, or different conditions for the same type of cell, that may have biological relevance but that you wouldn’t have necessarily identified without the quantitative analysis,” England says.

⌇  Fakhri et al. (2014) High-resolution mapping of intracellular fluctuations using carbon nanotubesScience344(1687), 1031-5

See also:
⌇  Levine and MacKintosh (2009) The mechanics and fluctuation spectrum of active gels. J Phys Chem B, 113, 3820–3830
⌇  MacKintosh and Levine (2008) Nonequilibrium mechanics and dynamics of motor-activated gels. Phys Rev Lett, 100, 018104
⌇  Lau et al. (2003) Microrheology, stress fluctuations, and active behavior of living cells. Phys Rev Lett91, 198101

⇢  Related post : water’s SED failure in molecular orientational diffusion

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I know that it is a hopeless undertaking to debate about fundamental value judgments. For instance if someone approves, as a goal, the extirpation of the human race from the earth, one cannot refute such a viewpoint on rational grounds. But if there is agreement on certain goals and values, one can argue rationally about the means by which these objectives may be attained. Let us, then, indicate two goals which may well be agreed upon by nearly all who read these lines.

  1. Those instrumental goods which should serve to maintain the life and health of all human beings should be produced by the least possible labor of all.

  2. The satisfaction of physical needs is indeed the indispensable precondition of a satisfactory existence, but in itself it is not enough. In order to be content men must also have the possibility of developing their intellectual and artistic powers to whatever extent accord with their personal characteristics and abilities.

The first of these two goals requires the promotion of all knowledge relating to the laws of nature and the laws of social processes, that is, the promotion of all scientific endeavor. For scientific endeavor is a natural whole the parts of which mutually support one another in a way which, to be sure, no one can anticipate. However, the progress of science presupposes the possibility of unrestricted communication of all results and judgments—freedom of expression and instruction in all realms of intellectual endeavor. By freedom I understand social conditions of such a kind that the expression of opinions and assertions about general and particular matters of knowledge will not involve dangers or serious disadvantages for him who expresses them. This freedom of communication is indispensable for the development and extension of scientific knowledge, a consideration of much practical import. In the first instance it must be guaranteed by law. But laws alone cannot secure freedom of expression; in order that every man may present his views without penalty there must be a spirit of tolerance in the entire population. Such an ideal of external liberty can never be fully attained but must be sought unremittingly if scientific thought, and philosophical and creative thinking in general, are to be advanced as far as possible.

If the second goal, that is, the possibility of the spiritual development of all individuals, is to be secured, a second kind of outward freedom is necessary. Man should not have to work for the achievement of the necessities of life to such an extent that he has neither time nor strength for personal activities. Without this second kind of outward liberty, freedom of expression is useless for him. Advances in technology would provide the possibility of this kind of freedom if the problem of a reasonable division of labor were solved.

The development of science and of the creative activities of the spirit in general requires still another kind of freedom, which may be characterized as inward freedom. It is this freedom of the spirit which consists in the independence of thought from the restrictions of authoritarian and social prejudices as well as from unphilosophical routinizing and habit in general. This inward freedom is an infrequent gift of nature and a worthy objective for the individual. Yet the community can do much to further this achievement, too, at least by not interfering with its development. Thus schools may interfere with the development of inward freedom through authoritarian influences and through imposing on young people excessive spiritual burdens; on the other hand schools may favor such freedom by encouraging independent thought. Only if outward and inner freedom are constantly and consciously pursued is there a possibility of spiritual development and perfection and thus of improving man’s outward and inner life.

“On Freedom” by Albert Einstein, in the anthology of his essays Out of My Later Years.

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