Leading edge maintenance in migrating cells is an emergent property of branched actin network growth
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Evaluation Summary:
This paper describes analysis and modeling of leading edge fluctuations in migrating cells driven by a branched Arp2/3 lamellipodial network. A stochastic model shows how branching contributes to shape stability, and reproduces the measured spectrum and dynamics of leading edge fluctuations. Analysis of the model as a function of branching angle suggests that the Arp2/3 branching angle might be selected to smooth lamellipodial shape. The authors provide new ideas to a big field of research, including Fourier analysis of leading edge fluctuations, which is a novel approach. The modeling methods and model design seem valid and the paper is well written.
(This preprint has been reviewed by eLife. We include the public reviews from the reviewers here; the authors also receive private feedback with suggested changes to the manuscript. Reviewer #1 agreed to share their name with the authors.)
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Abstract
Animal cell migration is predominantly driven by the coordinated, yet stochastic, polymerization of thousands of nanometer-scale actin filaments across micron-scale cell leading edges. It remains unclear how such inherently noisy processes generate robust cellular behavior. We employed high-speed imaging of migrating neutrophil-like HL-60 cells to explore the fine-scale shape fluctuations that emerge and relax throughout the process of leading edge maintenance. We then developed a minimal stochastic model of the leading edge that reproduces this stable relaxation behavior. Remarkably, we find lamellipodial stability naturally emerges from the interplay between branched actin network growth and leading edge shape – with no additional feedback required – based on a synergy between membrane-proximal branching and lateral spreading of filaments. These results thus demonstrate a novel biological noise-suppression mechanism based entirely on system geometry. Furthermore, our model suggests that the Arp2/3-mediated ~70–80° branching angle optimally smooths lamellipodial shape, addressing its long-mysterious conservation from protists to mammals.
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Author Response:
Reviewer #1 (Public Review):
Here, Garner and Theriot investigate the question of leading edge maintenance in migrating cells. They analyze small and dynamic fluctuations of the membrane at the cell front in order to understand how membrane stability emerges from these seemingly random and uncoordinated events. Experimental data enable description of fluctuations at different length scales and their relaxation in a visco-elastic manner.
To gain knowledge about this system, a stochastic model of branched actin network growth against a membrane is developed, taking into account a number of molecular reactions at play. This model recapitulates correctly the cellular observations, with correct orientation of the filaments and similar membrane fluctuations. Also, addition of Latrunculin B which leads in vivo to …
Author Response:
Reviewer #1 (Public Review):
Here, Garner and Theriot investigate the question of leading edge maintenance in migrating cells. They analyze small and dynamic fluctuations of the membrane at the cell front in order to understand how membrane stability emerges from these seemingly random and uncoordinated events. Experimental data enable description of fluctuations at different length scales and their relaxation in a visco-elastic manner.
To gain knowledge about this system, a stochastic model of branched actin network growth against a membrane is developed, taking into account a number of molecular reactions at play. This model recapitulates correctly the cellular observations, with correct orientation of the filaments and similar membrane fluctuations. Also, addition of Latrunculin B which leads in vivo to increased amplitude of the fluctuations with decreased fluctuation rates is described in the model when nucleation and elongation rates are decreased.
Changing the different parameters of the model reveals that two features are critically important (2): a branching reaction occurring solely at proximity of the membrane, and the possibility for filaments to spread laterally. Other important parameter includes the Arp2/3 complex branching angle, where a 70-80{degree sign} geometry is found to be optimal for minimizing actin density fluctuations and leading edge fluctuation amplitudes.
This work is of excellent quality and its conclusions seem justified. However, it would be important to have more details on the limit of detection of membrane shape fluctuations and network growth by phase contrast microscopy.
The reviewer raises an important point on the differences in spatial resolution between the experimental and theoretical aspects of our work. We appreciate this opportunity to further clarify which of our conclusions are directly demonstrated by experimental data, and which are theoretical predictions that are grounded in experimental data but not explicitly measured. Our updated manuscript includes an expanded discourse on this topic in the Results and Discussion. I outline the major points below:
In lines 92-99 of the Results, we estimate our experimental spatial resolution for measuring leading edge fluctuations, emphasizing that imaging by phase-contrast is not sufficient to resolve individual filaments or polymerization events. We also clarify our hypothesis that the measured fluctuations are a micron-scale property arising from stochastic monomer addition at the molecular scale, now more directly stating that simultaneous stochastic polymerization of filaments throughout the leading edge might act collectively to generate large scale curvature.
In lines 142-143, we make more clear that we developed the molecular-scale actin network growth model to explore how molecular interactions might lead to the observed larger scale fluctuation behavior.
In lines 151-152, and 284-287 of the Results, we discuss the range of wavelengths over which the experiments and modeling output can be directly compared.
Finally, in the Discussion (lines 317-324) we emphasize that we experimentally measured micron-scale lamellipodial shape dynamics, but inferred nanometer-scale details using a molecular-scale model that correctly predicts this emergent behavior (as well as many other experimentally-measured features of lamellipodial actin networks). We then discuss how our results might inspire new super-resolution experimental approaches to directly test molecular-level predictions of the model.
Reviewer #2 (Public Review):
The topic of actin driven cell motility will be of general interest. The authors provide new ideas for the field of research, the modeling methods and model design seem valid and appropriate, and the paper is well written. My main concern is whether the fluctuation spectrum derived from the model corresponds to that of the experimental images.
Visually (and perhaps mistakenly on my part), the experimental analysis of Fig. 1b seems to show a nearly periodic red-blue curvature pattern with a scale of order 4 microns that persists over 10-15 sec, a time over which the cell advances by a distance of order the size of the lamellipodium. While such a nearly periodic pattern would be expected to lead to peaks at the corresponding periods and wavelength in Fig. 1e and 1g, no clear peaks are observed in those figures.
However, the autocorrelation functions in Fig. 1e are not plotted over times comparable to 10-15 sec. Further, the analysis of the leading edge contour is done with a background subtraction method that removes fluctuations over 7 microns, a length scale that may be dampening a real peak at ~4 microns in Fig. 1g.
The feature I am pointing out could be occurring at a length scale in between the shortest length scales (a pixel) and the longest ones (cell size) in the system. Instabilities, a main theme of the paper, frequently get amplified at a characteristic length scale. Here there may be a length scale that is selected by the system that may not be picked up by the analysis or the proposed model.
We thank the reviewer for drawing our attention to an apparent discrepancy between the curvature kymograph shown in Fig. 1b and the results of the autocorrelation analysis, which we now believe we have reconciled. In our updated manuscript, we demonstrate that (1) the feature the reviewer points out in the kymograph is not indicative of a dominant mode or instability; (2) regardless, the feature in question is not removed by our pre-processing step; and (3) an extension of our analysis to longer length and time scales does not affect our results. These points are summarized in an extended description of the curvature kymograph and autocorrelation analyses in the Results (lines 120-125), Methods (lines 416-423, 443-444, 471-473, 487-503), and in three new supplemental figures (Fig. S3 5). Our argument is as follows:
The apparent instability in the curvature kymograph (which the reviewer suggested our autocorrelation analysis might not be detecting) can be reproduced in a model in which there are, by definition, no instabilities, dominant wavemodes, or oscillations – that of a membrane freely fluctuating under Brownian motion (Fig. S3). This proves that one cannot interpret the appearance of such an underlying pattern in the kymograph as evidence of an instability. We note that the apparent “dominant wavemode” of ~4 µm in the curvature kymograph might simply reflect the span used to perform the curvature fitting, as it is approximately twice the size of the curve-fitting window. Overall, this control provides a case-in-point for the potential pitfalls in interpreting kymographs and the necessity of Fourier mode autocorrelation analysis as a more comprehensive approach.
The reviewer raised the possibility that baseline-subtracting features above 7 µm might remove the apparent ~ 4 µm instability from our data, but these visual features remain apparent in curvature kymographs generated after the baseline-subtraction is applied (Fig. S3). Therefore our 7 µm cut-off does not remove the features in question.
As suggested by the reviewer, we extended our analysis to longer length and time scales, and found that it did not affect our results. Consistent with what could be observed from the originally-plotted timescales in Fig. 1e, longer timescales show the signal decays to noise (or at least something which cannot be distinguished from noise in any straightforward way) at all length-scales (Fig. S4). Additionally, repeating the analysis using a 10 µm span for background-subtraction of the leading edge shapes (an increase of ~50% compared to the 7 µm span used in the original manuscript, and more than twice the width of the feature of concern to the reviewer), reveals no new features in the data (Fig. S5).
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Evaluation Summary:
This paper describes analysis and modeling of leading edge fluctuations in migrating cells driven by a branched Arp2/3 lamellipodial network. A stochastic model shows how branching contributes to shape stability, and reproduces the measured spectrum and dynamics of leading edge fluctuations. Analysis of the model as a function of branching angle suggests that the Arp2/3 branching angle might be selected to smooth lamellipodial shape. The authors provide new ideas to a big field of research, including Fourier analysis of leading edge fluctuations, which is a novel approach. The modeling methods and model design seem valid and the paper is well written.
(This preprint has been reviewed by eLife. We include the public reviews from the reviewers here; the authors also receive private feedback with suggested changes to …
Evaluation Summary:
This paper describes analysis and modeling of leading edge fluctuations in migrating cells driven by a branched Arp2/3 lamellipodial network. A stochastic model shows how branching contributes to shape stability, and reproduces the measured spectrum and dynamics of leading edge fluctuations. Analysis of the model as a function of branching angle suggests that the Arp2/3 branching angle might be selected to smooth lamellipodial shape. The authors provide new ideas to a big field of research, including Fourier analysis of leading edge fluctuations, which is a novel approach. The modeling methods and model design seem valid and the paper is well written.
(This preprint has been reviewed by eLife. We include the public reviews from the reviewers here; the authors also receive private feedback with suggested changes to the manuscript. Reviewer #1 agreed to share their name with the authors.)
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Reviewer #1 (Public Review):
Here, Garner and Theriot investigate the question of leading edge maintenance in migrating cells. They analyze small and dynamic fluctuations of the membrane at the cell front in order to understand how membrane stability emerges from these seemingly random and uncoordinated events. Experimental data enable description of fluctuations at different length scales and their relaxation in a visco-elastic manner.
To gain knowledge about this system, a stochastic model of branched actin network growth against a membrane is developed, taking into account a number of molecular reactions at play. This model recapitulates correctly the cellular observations, with correct orientation of the filaments and similar membrane fluctuations. Also, addition of Latrunculin B which leads in vivo to increased amplitude of the …
Reviewer #1 (Public Review):
Here, Garner and Theriot investigate the question of leading edge maintenance in migrating cells. They analyze small and dynamic fluctuations of the membrane at the cell front in order to understand how membrane stability emerges from these seemingly random and uncoordinated events. Experimental data enable description of fluctuations at different length scales and their relaxation in a visco-elastic manner.
To gain knowledge about this system, a stochastic model of branched actin network growth against a membrane is developed, taking into account a number of molecular reactions at play. This model recapitulates correctly the cellular observations, with correct orientation of the filaments and similar membrane fluctuations. Also, addition of Latrunculin B which leads in vivo to increased amplitude of the fluctuations with decreased fluctuation rates is described in the model when nucleation and elongation rates are decreased.
Changing the different parameters of the model reveals that two features are critically important (2): a branching reaction occurring solely at proximity of the membrane, and the possibility for filaments to spread laterally. Other important parameter includes the Arp2/3 complex branching angle, where a 70-80{degree sign} geometry is found to be optimal for minimizing actin density fluctuations and leading edge fluctuation amplitudes.
This work is of excellent quality and its conclusions seem justified. However, it would be important to have more details on the limit of detection of membrane shape fluctuations and network growth by phase contrast microscopy.
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Reviewer #2 (Public Review):
The topic of actin driven cell motility will be of general interest. The authors provide new ideas for the field of research, the modeling methods and model design seem valid and appropriate, and the paper is well written. My main concern is whether the fluctuation spectrum derived from the model corresponds to that of the experimental images.
Visually (and perhaps mistakenly on my part), the experimental analysis of Fig. 1b seems to show a nearly periodic red-blue curvature pattern with a scale of order 4 microns that persists over 10-15 sec, a time over which the cell advances by a distance of order the size of the lamellipodium. While such a nearly periodic pattern would be expected to lead to peaks at the corresponding periods and wavelength in Fig. 1e and 1g, no clear peaks are observed in those figures.
Reviewer #2 (Public Review):
The topic of actin driven cell motility will be of general interest. The authors provide new ideas for the field of research, the modeling methods and model design seem valid and appropriate, and the paper is well written. My main concern is whether the fluctuation spectrum derived from the model corresponds to that of the experimental images.
Visually (and perhaps mistakenly on my part), the experimental analysis of Fig. 1b seems to show a nearly periodic red-blue curvature pattern with a scale of order 4 microns that persists over 10-15 sec, a time over which the cell advances by a distance of order the size of the lamellipodium. While such a nearly periodic pattern would be expected to lead to peaks at the corresponding periods and wavelength in Fig. 1e and 1g, no clear peaks are observed in those figures.
However, the autocorrelation functions in Fig. 1e are not plotted over times comparable to 10-15 sec. Further, the analysis of the leading edge contour is done with a background subtraction method that removes fluctuations over 7 microns, a length scale that may be dampening a real peak at ~4 microns in Fig. 1g.
The feature I am pointing out could be occurring at a length scale in between the shortest length scales (a pixel) and the longest ones (cell size) in the system. Instabilities, a main theme of the paper, frequently get amplified at a characteristic length scale. Here there may be a length scale that is selected by the system that may not be picked up by the analysis or the proposed model.
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