Versatile patterns in the actin cortex of motile cells: Self-organized pulses can coexist with macropinocytic ring-shaped waves
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Curated by eLife
Evaluation Summary:
Individual cells may act in response to stimuli or in a self-organized fashion. The relative weight of these two modes determines in the end to which degree cells or rather organs/organisms carry function. This study reports an example of very complex self-organization of actin waves as the coexistence of slowly moving broad waves of high F-actin concentration and rapidly propagating planar F-actin pulses. The paper is interesting for everybody interested in conceptual questions like signalling versus self-organization, in cellular morpho-dynamics and theory of dynamic patterns.
(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. The reviewers remained anonymous to the authors.)
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Abstract
Self-organized patterns in the actin cytoskeleton are essential for eukaryotic cellular life. They are the building blocks of many functional structures that often operate simultaneously to facilitate, for example, nutrient uptake and movement of cells. However, to identify how qualitatively distinct actin patterns can coexist remains a challenge. Here, we use bifurcation theory to reveal a generic mechanism of pattern coexistence, showing that different types of wave patterns can simultaneously emerge in the actin system. Our theoretical analysis is complemented by live-cell imaging experiments revealing that narrow, planar, and fast-moving excitable pulses may indeed coexist with ring-shaped macropinocytic actin waves in the cortex of motile amoeboid cells.
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Evaluation Summary:
Individual cells may act in response to stimuli or in a self-organized fashion. The relative weight of these two modes determines in the end to which degree cells or rather organs/organisms carry function. This study reports an example of very complex self-organization of actin waves as the coexistence of slowly moving broad waves of high F-actin concentration and rapidly propagating planar F-actin pulses. The paper is interesting for everybody interested in conceptual questions like signalling versus self-organization, in cellular morpho-dynamics and theory of dynamic patterns.
(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. The reviewers remained anonymous to the authors.)
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Reviewer #1 (Public Review):
The study presents the observation of the coexistence of slowly moving broad waves of high F-actin concentration and rapidly propagating planar F-actin pulses in giant Dictyostelium discoideum cells and focuses on their theoretical analysis on the basis of a 3 component activator-inhibitor reaction-diffusion model with globally conserved actin. The authors conclude that the pattern coexistence is generic in a system with mass conservation close to a primary codimension-2 T-point bifurcation. The observation of the wave patterns in Dictyostelium discoideum is interesting and adds new phenomena to intracellular self-organization and patterns. The theoretical analysis is very careful and provides deep insight into the pattern mechanism in terms of non-linear dynamics. A very interesting and careful study. Well …
Reviewer #1 (Public Review):
The study presents the observation of the coexistence of slowly moving broad waves of high F-actin concentration and rapidly propagating planar F-actin pulses in giant Dictyostelium discoideum cells and focuses on their theoretical analysis on the basis of a 3 component activator-inhibitor reaction-diffusion model with globally conserved actin. The authors conclude that the pattern coexistence is generic in a system with mass conservation close to a primary codimension-2 T-point bifurcation. The observation of the wave patterns in Dictyostelium discoideum is interesting and adds new phenomena to intracellular self-organization and patterns. The theoretical analysis is very careful and provides deep insight into the pattern mechanism in terms of non-linear dynamics. A very interesting and careful study. Well written, excellent figures.
While the observation of the wave patterns in Dictyostelium discoideum is interesting, the focus is on the theoretical analysis - which indeed is excellent. Unfortunately, the authors did not use their experimental abilities to verify predictions of their theoretical analysis, and thus in the end the conclusions lean heavily to the theoretical side. There are little biological conclusions from the theoretical analysis. In particular, a clear discussion on whether the observations are restricted to the artificial giant cells or may also have meaning for normal-sized cells is missing.
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Reviewer #2 (Public Review):
Summary and appraisal:
The authors aim to establish the coexistence of waves in enlarged Dictyostelium cells and in a mathematical model, and to establish that these have a correspondence. Without more analysis, it is not possible to evaluate whether the dichotomy of traveling waves in Dictyostelium is real, nor whether the model provides a useful way of understanding this dichotomy.
Strengths and weaknesses:
The experimental data are not quantitatively analyzed.
The velocities and widths (eg full-width at half-max) are not reported or statistically analyzed. For most statistical analysis that would inform whether there are really two categories, greater than a few dozen waves would be required. There is no evidence that the distributions of any wave property are bimodal. Such an analysis would allow the …
Reviewer #2 (Public Review):
Summary and appraisal:
The authors aim to establish the coexistence of waves in enlarged Dictyostelium cells and in a mathematical model, and to establish that these have a correspondence. Without more analysis, it is not possible to evaluate whether the dichotomy of traveling waves in Dictyostelium is real, nor whether the model provides a useful way of understanding this dichotomy.
Strengths and weaknesses:
The experimental data are not quantitatively analyzed.
The velocities and widths (eg full-width at half-max) are not reported or statistically analyzed. For most statistical analysis that would inform whether there are really two categories, greater than a few dozen waves would be required. There is no evidence that the distributions of any wave property are bimodal. Such an analysis would allow the conclusion that two categories of waves exist, and further that they coexist in the same cell.
The authors discuss the shape of the wave front, but this is not characterized. If there are reported differences in the curvature (planar versus circular), then, e.g., the curvature would need to be measured to support that claim
The mathematical model would need to be analyzed further to establish its relevance to the data.
The authors propose a mathematical model, in Eq 3abc, with parameters in Eq 4. They perform wave coordinate analysis, linear stability analysis, and bifurcation analysis via numerical continuation. However, they do not show a solution (either on 1d or 2d or 3d) with coexisting traveling waves. The model is a reaction-diffusion equation with 3 components, so is readily solvable numerically.
Other than the fact that the model has a parameter regime that allows two categories of traveling wave to coexist, no further evidence is presented that these correspond with the waves observed experimentally. What are the velocities ("s" in their notation) and widths of these? The authors discuss curvature in experimental data, but there is no explanation for whether the curvatures of the two mathematical wave solutions are different. (Note this would require solutions in at least 2d, since there is no curvature in a 1d wave front). The wave velocity, in particular, should be readily accessible, since it is needed to construct the homoclinic and heteroclinic orbits in Fig 3e.
The authors use the average actin concentration, "A", as a control parameter for the bifurcation diagrams, pointing to "A" as a way to correspond to the experiments where cell size is changed. The authors also argue that the novel two-category waves emerge upon cell-cell fusion, and were not observed in regular-sized cells. If two cells with average concentration "A" merge, the average concentration is still "A". It is currently not shown whether, by changing L alone and keeping "A" constant, that one-wave solution regime moves into the two-wave solution regime.
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