Cortical factor feedback model for cellular locomotion and cytofission

Learning dynamical models of single and collective cell migration: a review

Single and collective cell migration are fundamental processes critical for physiological phenomena ranging from embryonic development and immune response to wound healing and cancer metastasis. To understand cell migration from a physical perspective, a broad variety of models for the underlying physical mechanisms that govern cell motility have been developed. A key challenge in the development of such models is how to connect them to experimental observations, which often exhibit complex stochastic behaviours. In this review, we discuss recent advances in data-driven theoretical approaches that directly connect with experimental data to infer dynamical models of stochastic cell migration. Leveraging advances in nanofabrication, image analysis, and tracking technology, experimental studies now provide unprecedented large datasets on cellular dynamics. In parallel, theoretical efforts have been directed towards integrating such datasets into physical models from the single cell to the tissue scale with the aim of conceptualising the emergent behaviour of cells. We first review how this inference problem has been addressed in both freely migrating and confined cells. Next, we discuss why these dynamics typically take the form of underdamped stochastic equations of motion, and how such equations can be inferred from data. We then review applications of data-driven inference and machine learning approaches to heterogeneity in cell behaviour, subcellular degrees of freedom, and to the collective dynamics of multicellular systems. Across these applications, we emphasise how data-driven methods can be integrated with physical active matter models of migrating cells, and help reveal how underlying molecular mechanisms control cell behaviour. Together, these data-driven approaches are a promising avenue for building physical models of cell migration directly from experimental data, and for providing conceptual links between different length-scales of description.

Mechanochemical subcellular-element model of crawling cells

Constructing physical models of living cells and tissues is an extremely challenging task because of the high complexities of both intra- and intercellular processes. In addition, the force that a single cell generates vanishes in total due to the law of action and reaction. The typical mechanics of cell crawling involve periodic changes in the cell shape and in the adhesion characteristics of the cell to the substrate. However, the basic physical mechanisms by which a single cell coordinates these processes cooperatively to achieve autonomous migration are not yet well understood. To obtain a clearer grasp of how the intracellular force is converted to directional motion, we develop a basic mechanochemical model of a crawling cell based on subcellular elements with the focus on the dependence of the protrusion and contraction as well as the adhesion and de-adhesion processes on intracellular biochemical signals. By introducing reaction-diffusion equations that reproduce traveling waves of local chemical concentrations, we clarify that the chemical dependence of the cell-substrate adhesion dynamics determines the crawling direction and distance with one chemical wave. Finally, we also perform multipole analysis of the traction force to compare it with the experimental results. Our present work sheds light on how intracellular chemical reactions are converted to a directional cell migration under the force-free condition. Although the detailed mechanisms of actual cells are far more complicated than our simple model, we believe that this mechanochemical model is a good prototype for more realistic models.

Spontaneous transitions between amoeboid and keratocyte-like modes of migration

The motility of adherent eukaryotic cells is driven by the dynamics of the actin cytoskeleton. Despite the common force-generating actin machinery, different cell types often show diverse modes of locomotion that differ in their shape dynamics, speed, and persistence of motion. Recently, experiments in Dictyostelium discoideum have revealed that different motility modes can be induced in this model organism, depending on genetic modifications, developmental conditions, and synthetic changes of intracellular signaling. Here, we report experimental evidence that in a mutated D. discoideum cell line with increased Ras activity, switches between two distinct migratory modes, the amoeboid and fan-shaped type of locomotion, can even spontaneously occur within the same cell. We observed and characterized repeated and reversible switchings between the two modes of locomotion, suggesting that they are distinct behavioral traits that coexist within the same cell. We adapted an established phenomenological motility model that combines a reaction-diffusion system for the intracellular dynamics with a dynamic phase field to account for our experimental findings.

Deletion of gmfA induces keratocyte-like migration in Dictyostelium

Glia maturation factor (GMF) has been established as an inactivating factor of the actin‐related protein 2/3 (Arp2/3) complex, which regulates actin assembly. Regulation of actin assembly and reorganization is crucial for various cellular events, such as cell migration, cell division, and development. Here, to examine the roles of ADF‐H domain‐containing protein (also known as glia maturation factor; GmfA), the product of a single GMF homologous gene in Dictyostelium, gmfA‐null cells were generated. They had moderate defects in cell growth and cytokinesis. Interestingly, they showed a keratocyte‐like fan shape with a broader pseudopod, where Arp3 accumulated at higher levels than in wild‐type cells. They migrated with higher persistence, but their velocities were comparable to those of wild‐type cells. The polar pseudopods during cell division were also broader than those in wild‐type cells. However, GmfA did not localize at the pseudopods in migrating cells or the polar pseudopods in dividing cells. Adhesions of mutant cells to the substratum were much stronger than that of wild‐type cells. Although the mutant cells showed chemotaxis comparable to that of wild‐type cells, they formed disconnected streams during the aggregation stage; however, they finally formed normal fruiting bodies. These results suggest that GmfA plays a crucial role in cell migration.

Tools for computational analysis of moving boundary problems in cellular mechanobiology

A cell's ability to change shape is one of the most fundamental biological processes and is essential for maintaining healthy organisms. When the ability to control shape goes awry, it often results in a diseased system. As such, it is important to understand the mechanisms that allow a cell to sense and respond to its environment so as to maintain cellular shape homeostasis. Because of the inherent complexity of the system, computational models that are based on sound theoretical understanding of the biochemistry and biomechanics and that use experimentally measured parameters are an essential tool. These models involve an inherent feedback, whereby shape is determined by the action of regulatory signals whose spatial distribution depends on the shape. To carry out computational simulations of these moving boundary problems requires special computational techniques. A variety of alternative approaches, depending on the type and scale of question being asked, have been used to simulate various biological processes, including cell motility, division, mechanosensation, and cell engulfment. In general, these models consider the forces that act on the system (both internally generated, or externally imposed) and the mechanical properties of the cell that resist these forces. Moving forward, making these techniques more accessible to the non-expert will help improve interdisciplinary research thereby providing new insight into important biological processes that affect human health. This article is categorized under: Cancer > Cancer>Computational Models Cancer > Cancer>Molecular and Cellular Physiology.

A minimal computational model for three-dimensional cell migration

During migration, eukaryotic cells can continuously change their three-dimensional morphology, resulting in a highly dynamic and complex process. Further complicating this process is the observation that the same cell type can rapidly switch between different modes of migration. Modelling this complexity necessitates models that are able to track deforming membranes and that can capture the intracellular dynamics responsible for changes in migration modes. Here we develop an efficient three-dimensional computational model for cell migration, which couples cell mechanics to a simple intracellular activator-inhibitor signalling system. We compare the computational results to quantitative experiments using the social amoeba Dictyostelium discoideum. The model can reproduce the observed migration modes generated by varying either mechanical or biochemical model parameters and suggests a coupling between the substrate and the biomechanics of the cell.

Plasticity of cell migration resulting from mechanochemical coupling

Eukaryotic cells can migrate using different modes, ranging from amoeboid-like, during which actin filled protrusions come and go, to keratocyte-like, characterized by a stable morphology and persistent motion. How cells can switch between these modes is not well understood but waves of signaling events are thought to play an important role in these transitions. Here we present a simple two-component biochemical reaction-diffusion model based on relaxation oscillators and couple this to a model for the mechanics of cell deformations. Different migration modes, including amoeboid-like and keratocyte-like, naturally emerge through transitions determined by interactions between biochemical traveling waves, cell mechanics and morphology. The model predictions are explicitly verified by systematically reducing the protrusive force of the actin network in experiments using Dictyostelium discoideum cells. Our results indicate the importance of coupling signaling events to cell mechanics and morphology and may be applicable in a wide variety of cell motility systems.

A DISCRETE MATHEMATICAL MODEL FOR SINGLE AND COLLECTIVE MOVEMENT IN AMOEBOID CELLS

In this paper, we develop a new discrete mathematical model for individual and collective cell motility. We introduce a mechanical model for the movement of a cell on a two-dimensional rigid surface to describe and investigate the cell–cell and cell–substrate interactions. The cell cytoskeleton is modeled as a series of springs and dashpots connected in parallel. The cell–substrate attachments and the cell protrusions are also included. In particular, this model is used to describe the directed movement of endothelial cells on a Matrigel plate. We compare the results from our model with experimental data. We show that cell density and substrate rigidity play an important role in network formation.

In Vitro Microfluidic Models for Neurodegenerative Disorders

Microfluidic devices enable novel means of emulating neurodegenerative disease pathophysiology in vitro. These organ-on-a-chip systems can potentially reduce animal testing and substitute (or augment) simple 2D culture systems. Reconstituting critical features of neurodegenerative diseases in a biomimetic system using microfluidics can thereby accelerate drug discovery and improve our understanding of the mechanisms of several currently incurable diseases. This review describes latest advances in modeling neurodegenerative diseases in the central nervous system and the peripheral nervous system. First, this study summarizes fundamental advantages of microfluidic devices in the creation of compartmentalized cell culture microenvironments for the co-culture of neurons, glial cells, endothelial cells, and skeletal muscle cells and in their recapitulation of spatiotemporal chemical gradients and mechanical microenvironments. Then, this reviews neurodegenerative-disease-on-a-chip models focusing on Alzheimer's disease, Parkinson's disease, and amyotrophic lateral sclerosis. Finally, this study discusses about current drawbacks of these models and strategies that may overcome them. These organ-on-chip technologies can be useful to be the first line of testing line in drug development and toxicology studies, which can contribute significantly to minimize the phase of animal testing steps.

Crawling and Gliding: A Computational Model for Shape-Driven Cell Migration

Cell migration is a complex process involving many intracellular and extracellular factors, with different cell types adopting sometimes strikingly different morphologies. Modeling realistically behaving cells in tissues is computationally challenging because it implies dealing with multiple levels of complexity. We extend the Cellular Potts Model with an actin-inspired feedback mechanism that allows small stochastic cell rufflings to expand to cell protrusions. This simple phenomenological model produces realistically crawling and deforming amoeboid cells, and gliding half-moon shaped keratocyte-like cells. Both cell types can migrate randomly or follow directional cues. They can squeeze in between other cells in densely populated environments or migrate collectively. The model is computationally light, which allows the study of large, dense and heterogeneous tissues containing cells with realistic shapes and migratory properties.

Cell migration is involved in vital processes like morphogenesis, regeneration and immune system responses, but can also play a central role in pathological processes like metastasization. Computational models have been successfully employed to explain how single cells migrate, and to study how diverse cell-cell interactions contribute to tissue level behavior. However, there are few models that implement realistic cell shapes in multicellular simulations. The method we present here is able to reproduce two different types of motile cells—amoeboid and keratocyte-like cells. Amoeboid cells are highly motile and deform frequently; many cells can act amoeboid in certain circumstances e.g., immune system cells, epithelial cells, individually migrating cancer cells. Keratocytes are (fish) epithelial cells which are famous for their ability to preserve their shape and direction when migrating individually; during wound healing, keratocytes migrate collectively, in sheets, to the site needing reepithelialization. Our method is computationally simple, improves the realism of multicellular simulations and can help assess the tissue level impact of specific cell shapes. For example, it can be employed to study the tissue scanning strategies of leukocytes, the circumstances in which cancer cells adopt amoeboid migration strategies, or the collective migration of keratocytes.

The mechanisms of spatial and temporal patterning of cell-edge dynamics

Adherent cells migrate and change their shape by means of protrusion and retraction at their edges. When and where these activities occur defines the shape of the cell and the way it moves. Despite a great deal of knowledge about the structural organization, components, and biochemical reactions involved in protrusion and retraction, the origins of their spatial and temporal patterns are still poorly understood. Chemical signaling circuitry is believed to be an important source of patterning, but recent studies highlighted mechanisms based on physical forces, motion, and mechanical feedback.

Modeling large-scale dynamic processes in the cell: polarization, waves, and division

The past decade has witnessed significant developments in molecular biology techniques, fluorescent labeling, and super-resolution microscopy, and together these advances have vastly increased our quantitative understanding of the cell. This detailed knowledge has concomitantly opened the door for biophysical modeling on a cellular scale. There have been comprehensive models produced describing many processes such as motility, transport, gene regulation, and chemotaxis. However, in this review we focus on a specific set of phenomena, namely cell polarization, F-actin waves, and cytokinesis. In each case, we compare and contrast various published models, highlight the relevant aspects of the biology, and provide a sense of the direction in which the field is moving.

Advantages and challenges of microfluidic cell culture in polydimethylsiloxane devices

Culture of cells using various microfluidic devices is becoming more common within experimental cell biology. At the same time, a technological radiation of microfluidic cell culture device designs is currently in progress. Ultimately, the utility of microfluidic cell culture will be determined by its capacity to permit new insights into cellular function. Especially insights that would otherwise be difficult or impossible to obtain with macroscopic cell culture in traditional polystyrene dishes, flasks or well-plates. Many decades of heuristic optimization have gone into perfecting conventional cell culture devices and protocols. In comparison, even for the most commonly used microfluidic cell culture devices, such as those fabricated from polydimethylsiloxane (PDMS), collective understanding of the differences in cellular behavior between microfluidic and macroscopic culture is still developing. Moving in vitro culture from macroscopic culture to PDMS based devices can come with unforeseen challenges. Changes in device material, surface coating, cell number per unit surface area or per unit media volume may all affect the outcome of otherwise standard protocols. In this review, we outline some of the advantages and challenges that may accompany a transition from macroscopic to microfluidic cell culture. We focus on decisive factors that distinguish macroscopic from microfluidic cell culture to encourage a reconsideration of how macroscopic cell culture principles might apply to microfluidic cell culture.

Oscillatory motions of an active deformable particle

We investigate dynamics of an active particle in which shape deformations occur spontaneously. In two dimensions, the deformations are expanded in terms of the Fourier series and the couplings of different modes are taken into consideration truncated up to lower orders. We focus our attention on the special symmetrical structure between the coupled equations of n- and 2n-mode deformations for n=1, and those for n=2. We show that an oscillatory bifurcation occurs for n=2, which corresponds mathematically to the bifurcation for n=1 where a straight motion becomes unstable and a circular motion appears. At the oscillatory state, the particle undergoes either a spinning motion or a standing oscillation of shape deformations.

Spinning motion of a deformable self-propelled particle in two dimensions

We investigate the dynamics of a single deformable self-propelled particle which undergoes a spinning motion in a two-dimensional space. Equations of motion are derived from symmetry arguments for three kinds of variable. One is a vector which represents the velocity of the center of mass. The second is a traceless symmetric tensor representing deformation. The third is an antisymmetric tensor for spinning degree of freedom. By numerical simulations, we have obtained a variety of dynamical states due to interplay between the spinning motion and the deformation. The bifurcations of these dynamical states are analyzed by the simplified equations of motion.

Traveling waves in actin dynamics and cell motility

Much of current understanding of cell motility arose from studying steady treadmilling of actin arrays. Recently, there have been a growing number of observations of a more complex, non-steady, actin behavior, including self-organized waves. It is becoming clear that these waves result from activation and inhibition feedbacks in actin dynamics acting on different scales, but the exact molecular nature of these feedbacks and the respective roles of biomechanics and biochemistry are still unclear. Here, we review recent advances achieved in experimental and theoretical studies of actin waves and discuss mechanisms and physiological significance of wavy protrusions.

Non-Brownian dynamics and strategy of amoeboid cell locomotion

Amoeboid cells such as Dictyostelium discoideum and Madin-Darby canine kidney cells show the non-Brownian dynamics of migration characterized by the superdiffusive increase of mean-squared displacement. In order to elucidate the physical mechanism of this non-Brownian dynamics, a computational model is developed which highlights a group of inhibitory molecules for actin polymerization. Based on this model, we propose a hypothesis that inhibitory molecules are sent backward in the moving cell to accumulate at the rear of cell. The accumulated inhibitory molecules at the rear further promote cell locomotion to form a slow positive feedback loop of the whole-cell scale. The persistent straightforward migration is stabilized with this feedback mechanism, but the fluctuation in the distribution of inhibitory molecules and the cell shape deformation concurrently interrupt the persistent motion to turn the cell into a new direction. A sequence of switching behaviors between persistent motions and random turns gives rise to the superdiffusive migration in the absence of the external guidance signal. In the complex environment with obstacles, this combined process of persistent motions and random turns drives the simulated amoebae to solve the maze problem in a highly efficient way, which suggests the biological advantage for cells to bear the non-Brownian dynamics.

Redundant mechanisms for stable cell locomotion revealed by minimal models

Crawling of eukaryotic cells on flat surfaces is underlain by the protrusion of the actin network, the contractile activity of myosin II motors, and graded adhesion to the substrate regulated by complex biochemical networks. Some crawling cells, such as fish keratocytes, maintain a roughly constant shape and velocity. Here we use moving-boundary simulations to explore four different minimal mechanisms for cell locomotion: 1), a biophysical model for myosin contraction-driven motility; 2), a G-actin transport-limited motility model; 3), a simple model for Rac/Rho-regulated motility; and 4), a model that assumes that microtubule-based transport of vesicles to the leading edge limits the rate of protrusion. We show that all of these models, alone or in combination, are sufficient to produce half-moon steady shapes and movements that are characteristic of keratocytes, suggesting that these mechanisms may serve redundant and complementary roles in driving cell motility. Moving-boundary simulations demonstrate local and global stability of the motile cell shapes and make testable predictions regarding the dependence of shape and speed on mechanical and biochemical parameters. The models shed light on the roles of membrane-mediated area conservation and the coupling of mechanical and biochemical mechanisms in stabilizing motile cells.

"Self-assisted" amoeboid navigation in complex environments

Background

Living cells of many types need to move in response to external stimuli in order to accomplish their functional tasks; these tasks range from wound healing to immune response to fertilization. While the directional motion is typically dictated by an external signal, the actual motility is also restricted by physical constraints, such as the presence of other cells and the extracellular matrix. The ability to successfully navigate in the presence of obstacles is not only essential for organisms, but might prove relevant in the study of autonomous robotic motion.

Methodology/Principal Findings

We study a computational model of amoeboid chemotactic navigation under differing conditions, from motion in an obstacle-free environment to navigation between obstacles and finally to moving in a maze. We use the maze as a simple stand-in for a motion task with severe constraints, as might be expected in dense extracellular matrix. Whereas agents using simple chemotaxis can successfully navigate around small obstacles, the presence of large barriers can often lead to agent trapping. We further show that employing a simple memory mechanism, namely secretion of a repulsive chemical by the agent, helps the agent escape from such trapping.

Conclusions/Significance

Our main conclusion is that cells employing simple chemotactic strategies will often be unable to navigate through maze-like geometries, but a simple chemical marker mechanism (which we refer to as “self-assistance”) significantly improves success rates. This realization provides important insights into mechanisms that might be employed by real cells migrating in complex environments as well as clues for the design of robotic navigation strategies. The results can be extended to more complicated multi-cellular systems and can be used in the study of mammalian cell migration and cancer metastasis.

Mechanisms of Cell Propulsion by Active Stresses

The mechanisms by which cytoskeletal flows and cell-substrate interactions interact to generate cell motion are explored using a simplified model of the cytoskeleton as a viscous gel containing active stresses. This model yields explicit general results relating cell speed and traction forces to the distributions of active stress and cell-substrate friction. It is found that 1) the cell velocity is given by a function that quantifies the asymmetry of the active-stress distribution, 2) gradients in cell-substrate friction can induce motion even when the active stresses are symmetrically distributed, 3) the traction-force dipole is enhanced by protrusive stresses near the cell edges or contractile stresses near the center of the cell, and 4) the cell velocity depends biphasically on the cell-substrate adhesion strength if active stress is enhanced by adhesion. Specific experimental tests of the calculated dependences are proposed.

Activated membrane patches guide chemotactic cell motility

Many eukaryotic cells are able to crawl on surfaces and guide their motility based on environmental cues. These cues are interpreted by signaling systems which couple to cell mechanics; indeed membrane protrusions in crawling cells are often accompanied by activated membrane patches, which are localized areas of increased concentration of one or more signaling components. To determine how these patches are related to cell motion, we examine the spatial localization of RasGTP in chemotaxing Dictyostelium discoideum cells under conditions where the vertical extent of the cell was restricted. Quantitative analyses of the data reveal a high degree of spatial correlation between patches of activated Ras and membrane protrusions. Based on these findings, we formulate a model for amoeboid cell motion that consists of two coupled modules. The first module utilizes a recently developed two-component reaction diffusion model that generates transient and localized areas of elevated concentration of one of the components along the membrane. The activated patches determine the location of membrane protrusions (and overall cell motion) that are computed in the second module, which also takes into account the cortical tension and the availability of protrusion resources. We show that our model is able to produce realistic amoeboid-like motion and that our numerical results are consistent with experimentally observed pseudopod dynamics. Specifically, we show that the commonly observed splitting of pseudopods can result directly from the dynamics of the signaling patches.

Different types of cells are able to directionally migrate, responding to spatially-varying environmental cues. To do so, the cell needs to sense its environment, decide on the correct direction, and finally implement the needed mechanical changes in order to actually move. In this work we study the relation between the sensing-signaling system and the mechanical motion. We first show that membrane protrusions which drive the overall translocation occur exactly at the same locations at which membrane-bound signal-transduction effectors accumulate. These high concentration areas, also termed “patches”, exhibit interesting dynamics of disappearing and reappearing. Based on these findings, we develop a mathematical-computational model, in which membrane protrusions are driven by these membrane “patches”. These protrusions are then coupled to other cellular forces and the overall model predicts motion and its relationship to shape changes. Using our approach, we show that several observed features of cellular motility, for example the splitting of the cell tip, can be explained by the upstream signaling dynamics.

Continuum modeling and numerical simulation of cell motility

This work proposes a continuum-mechanical model of cell motility which accounts for the dynamics of motility-relevant protein species. For the special case of fish epidermal keratocytes, the stress and cell-substrate traction responses are postulated to depend on selected protein densities in accordance with the structural features of the cells. A one-dimensional version of the model is implemented using Arbitrary Lagrangian-Eulerian finite elements in conjunction with Lagrange multipliers for the treatment of kinematic constraints related to surface growth. Representative numerical tests demonstrate the capacity of the proposed model to simulate stationary and steady crawling states.

Zigzag turning preference of freely crawling cells

The coordinated motion of a cell is fundamental to many important biological processes such as development, wound healing, and phagocytosis. For eukaryotic cells, such as amoebae or animal cells, the cell motility is based on crawling and involves a complex set of internal biochemical events. A recent study reported very interesting crawling behavior of single cell amoeba: in the absence of an external cue, free amoebae move randomly with a noisy, yet, discernible sequence of ‘run-and-turns’ analogous to the ‘run-and-tumbles’ of swimming bacteria. Interestingly, amoeboid trajectories favor zigzag turns. In other words, the cells bias their crawling by making a turn in the opposite direction to a previous turn. This property enhances the long range directional persistence of the moving trajectories. This study proposes that such a zigzag crawling behavior can be a general property of any crawling cells by demonstrating that 1) microglia, which are the immune cells of the brain, and 2) a simple rule-based model cell, which incorporates the actual biochemistry and mechanics behind cell crawling, both exhibit similar type of crawling behavior. Almost all legged animals walk by alternating their feet. Similarly, all crawling cells appear to move forward by alternating the direction of their movement, even though the regularity and degree of zigzag preference vary from one type to the other.

From molecular signal activation to locomotion: an integrated, multiscale analysis of cell motility on defined matrices

The adhesion, mechanics, and motility of eukaryotic cells are highly sensitive to the ligand density and stiffness of the extracellular matrix (ECM). This relationship bears profound implications for stem cell engineering, tumor invasion and metastasis. Yet, our quantitative understanding of how ECM biophysical properties, mechanotransductive signals, and assembly of contractile and adhesive structures collude to control these cell behaviors remains extremely limited. Here we present a novel multiscale model of cell migration on ECMs of defined biophysical properties that integrates local activation of biochemical signals with adhesion and force generation at the cell-ECM interface. We capture the mechanosensitivity of individual cellular components by dynamically coupling ECM properties to the activation of Rho and Rac GTPases in specific portions of the cell with actomyosin contractility, cell-ECM adhesion bond formation and rupture, and process extension and retraction. We show that our framework is capable of recreating key experimentally-observed features of the relationship between cell migration and ECM biophysical properties. In particular, our model predicts for the first time recently reported transitions from filopodial to “stick-slip” to gliding motility on ECMs of increasing stiffness, previously observed dependences of migration speed on ECM stiffness and ligand density, and high-resolution measurements of mechanosensitive protrusion dynamics during cell motility we newly obtained for this study. It also relates the biphasic dependence of cell migration speed on ECM stiffness to the tendency of the cell to polarize. By enabling the investigation of experimentally-inaccessible microscale relationships between mechanotransductive signaling, adhesion, and motility, our model offers new insight into how these factors interact with one another to produce complex migration patterns across a variety of ECM conditions.

Leading-edge-gel coupling in lamellipodium motion

We present a model for actin-based motility that combines the dynamics of the semiflexible region at the leading edge of the lamellipodium with actomyosin gel properties in the bulk described by the theory of active polar gels. We calculate the velocity of the lamellipodium determined by the interaction of the gel and adhesion with forces in the semiflexible region. The stationary concave force-velocity relation of the model reproduces experimental results. We suggest that it is determined by retrograde flow at small forces and gel formation and retrograde flow at large ones. The variety of dynamic regimes of the semiflexible region reproducing experimentally observed morphodynamics is conserved when we couple the leading edge to the gel.

Cytopede: a three-dimensional tool for modeling cell motility on a flat surface

When cultured on flat surfaces, fibroblasts and many other cells spread to form thin lamellar sheets. Motion then occurs by extension of the sheet at the leading edge and retraction at the trailing edge. Comprehensive quantitative models of these phenomena have so far been lacking and to address this need, we have designed a three-dimensional code called Cytopede specialized for the simulation of the mechanical and signaling behavior of plated cells. Under assumptions by which the cytosol and the cytoskeleton are treated from a continuum mechanical perspective, Cytopede uses the finite element method to solve mass and momentum equations for each phase, and thus determine the time evolution of cellular models. We present the physical concepts that underlie Cytopede together with the algorithms used for their implementation. We then validate the approach by a computation of the spread of a viscous sessile droplet. Finally, to exemplify how Cytopede enables the testing of ideas about cell mechanics, we simulate a simple fibroblast model. We show how Cytopede allows computation, not only of basic characteristics of shape and velocity, but also of maps of cell thickness, cytoskeletal density, cytoskeletal flow, and substratum tractions that are readily compared with experimental data.

Form and function in cell motility: from fibroblasts to keratocytes

It is plain enough that a horse is made for running, but similar statements about motile cells are not so obvious. Here the basis for structure-function relations in cell motility is explored by application of a new computational technique that allows realistic three-dimensional simulations of cells migrating on flat substrata. With this approach, some cyber cells spontaneously display the classic irregular protrusion cycles and handmirror morphology of a crawling fibroblast, and others the steady gliding motility and crescent morphology of a fish keratocyte. The keratocyte motif is caused by optimal recycling of the cytoskeleton from the back to the front so that more of the periphery can be devoted to protrusion. These calculations are a step toward bridging the gap between the integrated mechanics and biophysics of whole cells and the microscopic molecular biology of cytoskeletal components.

Modeling of protrusion phenotypes driven by the actin-membrane interaction

We propose a mathematical model for simulating the leading-edge dynamics of a migrating cell from the interplay among elastic properties, architecture of the actin cytoskeleton, and the mechanics of the membrane. Our approach is based on the description of the length and attachment dynamics of actin filaments in the lamellipodium network. It is used to determine the total force exerted on the membrane at each position along the leading edge and at each time step. The model reproduces the marked state switches in protrusion morphodynamics found experimentally between epithelial cells in control conditions and cells expressing constitutively active Rac, a signaling molecule involved in the regulation of lamellipodium network assembly. The model also suggests a mechanistic explanation of experimental distortions in protrusion morphodynamics induced by deregulation of Arp2/3 and cofilin activity.