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1.  F-actin mechanics control spindle centring in the mouse zygote 
Nature Communications  2016;7:10253.
Mitotic spindle position relies on interactions between astral microtubules nucleated by centrosomes and a rigid cortex. Some cells, such as mouse oocytes, do not possess centrosomes and astral microtubules. These cells rely only on actin and on a soft cortex to position their spindle off-centre and undergo asymmetric divisions. While the first mouse embryonic division also occurs in the absence of centrosomes, it is symmetric and not much is known on how the spindle is positioned at the exact cell centre. Using interdisciplinary approaches, we demonstrate that zygotic spindle positioning follows a three-step process: (1) coarse centring of pronuclei relying on the dynamics of an F-actin/Myosin-Vb meshwork; (2) fine centring of the metaphase plate depending on a high cortical tension; (3) passive maintenance at the cell centre. Altogether, we show that F-actin-dependent mechanics operate the switch between asymmetric to symmetric division required at the oocyte to embryo transition.
How the mitotic spindle is positioned in the centre of the cell during the first mitotic division is not clear. Here Chaigne et al. show that the pronucleus coarsely centres using F-actin/Myosin-Vb dynamics, and the metaphase plate is finely centred by an F-actin cage influenced by high cortical tension.
PMCID: PMC4725770  PMID: 26727405
2.  Ant groups optimally amplify the effect of transiently informed individuals 
Nature Communications  2015;6:7729.
To cooperatively transport a large load, it is important that carriers conform in their efforts and align their forces. A downside of behavioural conformism is that it may decrease the group's responsiveness to external information. Combining experiment and theory, we show how ants optimize collective transport. On the single-ant scale, optimization stems from decision rules that balance individuality and compliance. Macroscopically, these rules poise the system at the transition between random walk and ballistic motion where the collective response to the steering of a single informed ant is maximized. We relate this peak in response to the divergence of susceptibility at a phase transition. Our theoretical models predict that the ant-load system can be transitioned through the critical point of this mesoscopic system by varying its size; we present experiments supporting these predictions. Our findings show that efficient group-level processes can arise from transient amplification of individual-based knowledge.
Group conformity is crucial for collective behaviours, but may decrease overall responsiveness to external cues. Here the authors show that load-carrying ant groups function at a transition between ballistic and random motions, where the influence of informed individuals is maximized.
PMCID: PMC4525283  PMID: 26218613
3.  A Biophysical Model for the Staircase Geometry of Stereocilia 
PLoS ONE  2015;10(7):e0127926.
Cochlear hair cell bundles, made up of 10s to 100s of individual stereocilia, are essential for hearing, and even relatively minor structural changes, due to mutations or injuries, can result in total deafness. Consistent with its specialized role, the staircase geometry (SCG) of hair cell bundles presents one of the most striking, intricate, and precise organizations of actin-based cellular shapes. Composed of rows of actin-filled stereocilia with increasing lengths, the hair cell’s staircase-shaped bundle is formed from a progenitor field of smaller, thinner, and uniformly spaced microvilli with relatively invariant lengths. While recent genetic studies have provided a significant increase in information on the multitude of stereocilia protein components, there is currently no model that integrates the basic physical forces and biochemical processes necessary to explain the emergence of the SCG. We propose such a model derived from the biophysical and biochemical characteristics of actin-based protrusions. We demonstrate that polarization of the cell’s apical surface, due to the lateral polarization of the entire epithelial layer, plays a key role in promoting SCG formation. Furthermore, our model explains many distinct features of the manifestations of SCG in different species and in the presence of various deafness-associated mutations.
PMCID: PMC4514777  PMID: 26207893
4.  Gap geometry dictates epithelial closure efficiency 
Nature Communications  2015;6:7683.
Closure of wounds and gaps in tissues is fundamental for the correct development and physiology of multicellular organisms and, when misregulated, may lead to inflammation and tumorigenesis. To re-establish tissue integrity, epithelial cells exhibit coordinated motion into the void by active crawling on the substrate and by constricting a supracellular actomyosin cable. Coexistence of these two mechanisms strongly depends on the environment. However, the nature of their coupling remains elusive because of the complexity of the overall process. Here we demonstrate that epithelial gap geometry in both in vitro and in vivo regulates these collective mechanisms. In addition, the mechanical coupling between actomyosin cable contraction and cell crawling acts as a large-scale regulator to control the dynamics of gap closure. Finally, our computational modelling clarifies the respective roles of the two mechanisms during this process, providing a robust and universal mechanism to explain how epithelial tissues restore their integrity.
Epithelial wound closure proceeds through both crawling into the wound and by constricting an actomyosin cable in a so-called purse-string mechanism. Here the authors show that the two mechanisms are mechanically coupled and the curvature of the wound regulates the overall dynamics of wound closure.
PMCID: PMC4510701  PMID: 26158873
5.  Dynamics of Actin Waves on Patterned Substrates: A Quantitative Analysis of Circular Dorsal Ruffles 
PLoS ONE  2015;10(1):e0115857.
Circular Dorsal Ruffles (CDRs) have been known for decades, but the mechanism that organizes these actin waves remains unclear. In this article we systematically analyze the dynamics of CDRs on fibroblasts with respect to characteristics of current models of actin waves. We studied CDRs on heterogeneously shaped cells and on cells that we forced into disk-like morphology. We show that CDRs exhibit phenomena such as periodic cycles of formation, spiral patterns, and mutual wave annihilations that are in accord with an active medium description of CDRs. On cells of controlled morphologies, CDRs exhibit extremely regular patterns of repeated wave formation and propagation, whereas on random-shaped cells the dynamics seem to be dominated by the limited availability of a reactive species. We show that theoretical models of reaction-diffusion type incorporating conserved species capture partially the behavior we observe in our data.
PMCID: PMC4289068  PMID: 25574668
6.  Propagating Waves of Directionality and Coordination Orchestrate Collective Cell Migration 
PLoS Computational Biology  2014;10(7):e1003747.
The ability of cells to coordinately migrate in groups is crucial to enable them to travel long distances during embryonic development, wound healing and tumorigenesis, but the fundamental mechanisms underlying intercellular coordination during collective cell migration remain elusive despite considerable research efforts. A novel analytical framework is introduced here to explicitly detect and quantify cell clusters that move coordinately in a monolayer. The analysis combines and associates vast amount of spatiotemporal data across multiple experiments into transparent quantitative measures to report the emergence of new modes of organized behavior during collective migration of tumor and epithelial cells in wound healing assays. First, we discovered the emergence of a wave of coordinated migration propagating backward from the wound front, which reflects formation of clusters of coordinately migrating cells that are generated further away from the wound edge and disintegrate close to the advancing front. This wave emerges in both normal and tumor cells, and is amplified by Met activation with hepatocyte growth factor/scatter factor. Second, Met activation was found to induce coinciding waves of cellular acceleration and stretching, which in turn trigger the emergence of a backward propagating wave of directional migration with about an hour phase lag. Assessments of the relations between the waves revealed that amplified coordinated migration is associated with the emergence of directional migration. Taken together, our data and simplified modeling-based assessments suggest that increased velocity leads to enhanced coordination: higher motility arises due to acceleration and stretching that seems to increase directionality by temporarily diminishing the velocity components orthogonal to the direction defined by the monolayer geometry. Spatial and temporal accumulation of directionality thus defines coordination. The findings offer new insight and suggest a basic cellular mechanism for long-term cell guidance and intercellular communication during collective cell migration.
Author Summary
The fundamental mechanisms underlying intercellular coordination during collective cell migration remain elusive despite considerable research efforts. We present a novel analytical framework that considers spatiotemporal dynamics across several traits. Our approach was applied to discover new modes of organized collective dynamics of cancer and normal cells. Following disruption of a cell monolayer, a propagating wave of coordinated migration emerges as clusters of coordinately moving cells are formed away from the wound and disintegrate near the advancing front. Activation of Met signal transduction by hepatocyte growth factor/scatter factor, master regulators of cell motility in malignant and normal processes, generates coinciding waves of cellular acceleration and stretching that propagate backward from the wound front and trigger a delayed wave of directional migration. Amplified coordination is intrinsically associated with enhanced directionality suggesting that even a weak directional cue is sufficient to promote a coordinated response that is transmitted to cells within the cell sheet. Our findings provide important novel insights on the basic cellular organization during collective cell migration and establish a mechanism of long-range cell guidance, intercellular coordination and pattern formation during monolayer wound healing.
PMCID: PMC4109844  PMID: 25058592
7.  Competition and compensation 
Bioarchitecture  2012;2(5):171-174.
Stereocilia are actin protrusions with remarkably well-defined lengths and organization. A flurry of recent papers has reported multiple myosin motor proteins involved in regulating stereocilia structures by transporting actin-regulatory cargo to the tips of stereocilia.1-13 In our recent paper, we show that two paralogous class 3 myosins — Myo3a and Myo3b — both transport the actin-regulatory protein Espin 1 (Esp1) to stereocilia and filopodia tips in a remarkably similar, albeit non-identical fashion.1 Here we present experimental and computational data that suggests that subtle differences between these two proteins’ biophysical and biochemical properties can help us understand how these myosin species target and regulate the lengths of actin protrusions.
PMCID: PMC3696061  PMID: 22954581
myosin; actin; filopodia; cytoskeleton; motor proteins; stereocilia; deafness
8.  Sarcomeric Pattern Formation by Actin Cluster Coalescence 
PLoS Computational Biology  2012;8(6):e1002544.
Contractile function of striated muscle cells depends crucially on the almost crystalline order of actin and myosin filaments in myofibrils, but the physical mechanisms that lead to myofibril assembly remains ill-defined. Passive diffusive sorting of actin filaments into sarcomeric order is kinetically impossible, suggesting a pivotal role of active processes in sarcomeric pattern formation. Using a one-dimensional computational model of an initially unstriated actin bundle, we show that actin filament treadmilling in the presence of processive plus-end crosslinking provides a simple and robust mechanism for the polarity sorting of actin filaments as well as for the correct localization of myosin filaments. We propose that the coalescence of crosslinked actin clusters could be key for sarcomeric pattern formation. In our simulations, sarcomere spacing is set by filament length prompting tight length control already at early stages of pattern formation. The proposed mechanism could be generic and apply both to premyofibrils and nascent myofibrils in developing muscle cells as well as possibly to striated stress-fibers in non-muscle cells.
Author Summary
Muscle contraction driving voluntary movements and the beating of the heart relies on the contraction of highly regular bundles of actin and myosin filaments, which share a periodic, sarcomeric pattern. We know little about the mechanisms by which these ‘biological crystals’ are assembled and it is a general question how order on a scale of 100 micrometers can emerge from the interactions of micrometer-sized building blocks, such as actin and myosin filaments. In our paper, we consider a computational model for a bundle of actin filaments and discuss physical mechanisms by which periodic order emerges spontaneously. Mutual crosslinking of actin filaments results in the formation and coalescence of growing actin clusters. Active elongation and shrinkage dynamics of actin filaments generates polymerization forces and causes local actin flow that can act like a conveyor belt to sort myosin filaments in place.
PMCID: PMC3369942  PMID: 22685394
9.  Releasing the brakes while hanging on 
Bioarchitecture  2012;2(1):11-14.
Actin polymerization plays a major role in many cellular processes, including cell motility, vesicle trafficking, and pathogen propulsion. The transformation of the (protrusive) polymerization forces into directed motion requires that the growing filaments are positioned next to the surface. This is achieved by localization of surface actin nucleators (WASP), which then activate Arp2/3 complex to form new actin branches. Yet, the same surface-bound WASP molecule which initiates the nucleation of new actin branches, also inherently prevents the translation of the polymerization forces into motion, essentially because the WASP molecule has to be in contact with the network during the formation of the new branch. In our recent paper we show that cortactin relaxes this internal inhibition by enhancing the release of WASP-VCA molecule from the new branching site after nucleation is initiated. We show that this enhanced release has two major effects; it increases the turnover rate of branching per WASP molecule, and it decreases the friction-like force caused by the binding of the moving surface with respect to the growing actin network.
PMCID: PMC3383711  PMID: 22754622
Arp2/3 complex; WASP-VCA; actin-based motility; cortactin; friction-like force; propulsion velocity
10.  The Eps8/IRSp53/VASP Network Differentially Controls Actin Capping and Bundling in Filopodia Formation 
PLoS Computational Biology  2011;7(7):e1002088.
There is a body of literature that describes the geometry and the physics of filopodia using either stochastic models or partial differential equations and elasticity and coarse-grained theory. Comparatively, there is a paucity of models focusing on the regulation of the network of proteins that control the formation of different actin structures. Using a combination of in-vivo and in-vitro experiments together with a system of ordinary differential equations, we focused on a small number of well-characterized, interacting molecules involved in actin-dependent filopodia formation: the actin remodeler Eps8, whose capping and bundling activities are a function of its ligands, Abi-1 and IRSp53, respectively; VASP and Capping Protein (CP), which exert antagonistic functions in controlling filament elongation. The model emphasizes the essential role of complexes that contain the membrane deforming protein IRSp53, in the process of filopodia initiation. This model accurately accounted for all observations, including a seemingly paradoxical result whereby genetic removal of Eps8 reduced filopodia in HeLa, but increased them in hippocampal neurons, and generated quantitative predictions, which were experimentally verified. The model further permitted us to explain how filopodia are generated in different cellular contexts, depending on the dynamic interaction established by Eps8, IRSp53 and VASP with actin filaments, thus revealing an unexpected plasticity of the signaling network that governs the multifunctional activities of its components in the formation of filopodia.
Author Summary
Cells move and interact with the environment by forming migratory structures composed of self organized polymers of actin. These protrusions can be flat and short surfaces, the lamellipodia, or adopt an elongated, finger-like shape called filopodia. In this article, we analyze the ‘computation’ performed by cells when they opt to form filopodia. We focus our attention on some initiators of filopodia that play an essential role due to their interaction with the cell membrane. We analyze the formation of these filopodia initiators in different genotypes, thus providing a way to rationalize the behaviors of different cells in terms of tendency to form filopodia. Our results, based on the combination of experimental and computational approaches, suggest that cells have developed molecular networks that are extremely flexible in their capability to follow the path leading to filopodia formation. In this sense the role of an element of the network, Eps8, is paradigmatic, as this protein can both induce or inhibit the formation of filopodia depending on the cellular context.
PMCID: PMC3140970  PMID: 21814501
11.  Theoretical Model for Cellular Shapes Driven by Protrusive and Adhesive Forces 
PLoS Computational Biology  2011;7(5):e1001127.
The forces that arise from the actin cytoskeleton play a crucial role in determining the cell shape. These include protrusive forces due to actin polymerization and adhesion to the external matrix. We present here a theoretical model for the cellular shapes resulting from the feedback between the membrane shape and the forces acting on the membrane, mediated by curvature-sensitive membrane complexes of a convex shape. In previous theoretical studies we have investigated the regimes of linear instability where spontaneous formation of cellular protrusions is initiated. Here we calculate the evolution of a two dimensional cell contour beyond the linear regime and determine the final steady-state shapes arising within the model. We find that shapes driven by adhesion or by actin polymerization (lamellipodia) have very different morphologies, as observed in cells. Furthermore, we find that as the strength of the protrusive forces diminish, the system approaches a stabilization of a periodic pattern of protrusions. This result can provide an explanation for a number of puzzling experimental observations regarding cellular shape dependence on the properties of the extra-cellular matrix.
Author Summary
Cells have highly varied and dynamic shapes, which are determined by internal forces generated by the cytoskeleton. These forces include protrusive forces due to the formation of new internal fibers and forces produced due to attachment of the cell to an external substrate. A long standing challenge is to explain how the myriad components of the cytoskeleton self-organize to form the observed shapes of cells. We present here a theoretical study of the shapes of cells that are driven only by protrusive forces of two types; one is the force due to polymerization of actin filaments which acts as an internal pressure on the membrane, and the second is the force due to adhesion between the membrane and external substrate. The key property is that both forces are localized on the cell membrane by protein complexes that have convex spontaneous curvature. This leads to a positive feedback that destabilizes the uniform cell shape and induces the spontaneous formation of patterns. We compare the resulting patterns to observed cellular shapes and find good agreement, which allows us to explain some of the puzzling dependencies of cell shapes on the properties of the surrounding matrix.
PMCID: PMC3088653  PMID: 21573201
12.  Propagating Cell-Membrane Waves Driven by Curved Activators of Actin Polymerization 
PLoS ONE  2011;6(4):e18635.
Cells exhibit propagating membrane waves which involve the actin cytoskeleton. One type of such membranal waves are Circular Dorsal Ruffles (CDR) which are related to endocytosis and receptor internalization. Experimentally, CDRs have been associated with membrane bound activators of actin polymerization of concave shape. We present experimental evidence for the localization of convex membrane proteins in these structures, and their insensitivity to inhibition of myosin II contractility in immortalized mouse embryo fibroblasts cell cultures. These observations lead us to propose a theoretical model which explains the formation of these waves due to the interplay between complexes that contain activators of actin polymerization and membrane-bound curved proteins of both types of curvature (concave and convex). Our model predicts that the activity of both types of curved proteins is essential for sustaining propagating waves, which are abolished when one type of curved activator is removed. Within this model waves are initiated when the level of actin polymerization induced by the curved activators is higher than some threshold value, which allows the cell to control CDR formation. We demonstrate that the model can explain many features of CDRs, and give several testable predictions. This work demonstrates the importance of curved membrane proteins in organizing the actin cytoskeleton and cell shape.
PMCID: PMC3080874  PMID: 21533032

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