Universal length fluctuations of actin structures found in cells
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eLife assessment
This is a theoretical analysis that gives compelling evidence that length control of bundles of actin filaments undergoing assembly and disassembly emerges even in the absence of a length control mechanism at the individual filament level. Furthermore, the length distribution should exhibit a variance that grows quadratically with the average bundle length. The experimental data are compatible with these fundamental theoretical findings, but further investigations are necessary to make the work conclusive concerning the validity of the inferences for filamentous actin structures in cells.
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Abstract
Actin is a key cytoskeletal protein that forms filaments that bundle into linear structures in vivo, which are involved in motility, signaling, and cell division. Despite the rapid turnover of individual actin monomers, these structures are often maintained at a specific length, which is important for their function. Length control is commonly attributed to length-dependent assembly or disassembly of the structure, whereby a stable length is achieved when the two opposing processes are balanced. Here we show that regardless of the nature of the length-dependent feedback, such “balance point” models predict a Gaussian distribution of lengths with a variance that is proportional to the steady state length. Contrary to this prediction, a reexamination of experimental measurements on the lengths of stereocilia, microvilli, actin cables, and filopodia reveals that the variance scales with the square of the steady state length. We propose a model in which the individual filaments in bundles undergo independent assembly dynamics, and the length of the bundle is set by the length of the longest filament. This model predicts a non-Gaussian distribution of bundle lengths with a variance that scales with the square of the steady state length. Our theory underscores the importance of crosslinking filaments into networks for size control of cytoskeleton structures.
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eLife assessment
This is a theoretical analysis that gives compelling evidence that length control of bundles of actin filaments undergoing assembly and disassembly emerges even in the absence of a length control mechanism at the individual filament level. Furthermore, the length distribution should exhibit a variance that grows quadratically with the average bundle length. The experimental data are compatible with these fundamental theoretical findings, but further investigations are necessary to make the work conclusive concerning the validity of the inferences for filamentous actin structures in cells.
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Reviewer #1 (Public Review):
Actin filaments and their kinetics have been the subject of extensive research, with several models for filament length control already existing in the literature. The work by Rosario et al. focuses instead on bundle length dynamics and how their fluctuations can inform us of the underlying kinetics. Surprisingly, the authors show that irrespective of the details, typical "balance point" models for filament kinetics give the wrong scaling of bundle length variance with mean length compared to experiments. Instead, the authors show that if one considers a bundle made of several individual filaments, length control for the bundle naturally emerges even in the absence of such a mechanism at the individual filament level. Furthermore, the authors show that the fluctuations of the bundle length display the same …
Reviewer #1 (Public Review):
Actin filaments and their kinetics have been the subject of extensive research, with several models for filament length control already existing in the literature. The work by Rosario et al. focuses instead on bundle length dynamics and how their fluctuations can inform us of the underlying kinetics. Surprisingly, the authors show that irrespective of the details, typical "balance point" models for filament kinetics give the wrong scaling of bundle length variance with mean length compared to experiments. Instead, the authors show that if one considers a bundle made of several individual filaments, length control for the bundle naturally emerges even in the absence of such a mechanism at the individual filament level. Furthermore, the authors show that the fluctuations of the bundle length display the same scaling with respect to the average as experimental measurements from different systems. This work constitutes a simple yet nuanced and powerful theoretical result that challenges our current understanding of actin filament kinetics and helps relate accessible experimental measurements such as actin bundle length fluctuations to their underlying kinetics. Finally, I found the manuscript to be very well written, with a particularly clear structure and development which made it very accessible.
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Reviewer #2 (Public Review):
Summary:
The authors present a theoretical study of the length dynamics of bundles of actin filaments. They first show a "balance point model" in which the bundle is described as an effective polymer. The corresponding assembly and disassembly rates can depend on bundle length. This model generates a steady-state bundle-length distribution with a variance that is proportional to the average bundle length. Numerical simulations confirm this analytic result. The authors then present an analysis of previously published length distributions of actin bundles in various contexts and argue that these distributions have variances that depend quadratically with the average length. They then consider a bundle of N-independent filaments that each grow in an unregulated way. Defining the bundle length to be that of the …Reviewer #2 (Public Review):
Summary:
The authors present a theoretical study of the length dynamics of bundles of actin filaments. They first show a "balance point model" in which the bundle is described as an effective polymer. The corresponding assembly and disassembly rates can depend on bundle length. This model generates a steady-state bundle-length distribution with a variance that is proportional to the average bundle length. Numerical simulations confirm this analytic result. The authors then present an analysis of previously published length distributions of actin bundles in various contexts and argue that these distributions have variances that depend quadratically with the average length. They then consider a bundle of N-independent filaments that each grow in an unregulated way. Defining the bundle length to be that of the longest filament, the resulting length distribution has a variance that scales quadratically with the average bundle length.Strengths:
The manuscript is very well written, and the computations are nicely presented. The work gives fundamental insights into the length distribution of filamentous actin structures. The universal dependence of the variance on the mean length is of particular interest. It will be interesting to see in the future, how many universality classes there are, and which features of a growth process determine to which class it belongs.Weaknesses:
You present the data in Fig. 3 as arguments against the balance point model. Although I agree that the data is compatible with your description of a bundle of filaments, I think that the range of mean lengths you can explore is too limited to conclusively argue against the balance point model. In most cases, your data extend over half an order of magnitude only. Could you provide a measure to quantify how much your model of independent filaments fits better than the balance point model?
Concerning your bundled-filament model, why do you consider the polymerizing ends to be all aligned? Similarly to the opposite end, fluctuations should be present. Furthermore, it is not clear to me, where the presence of crosslinking proteins enters your description. Finally, linked to my first remark on this model, why is the longest filament determining the length of the bundle in all the biological examples you cite? I am thinking in particular about the actin cables in yeast.
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