An adhesion-dependent switch between mechanisms that determine motile cell shape

Migration speed and directionality switch of normal epithelial cells after TGF-β1-induced EMT (tEMT) on micro-structured polydimethylsiloxane (PDMS) substrates with variations in stiffness and topographic patterning

The epithelial to mesenchymal transition (EMT) involves several physiological and pathological phenomena and endows cells with invasive and migratory properties. However, the effects of substrate stiffness and topography on the migration of cells before or after transforming growth factor-β1 (TGF-β1)-induced EMT (tEMT) are unknown. Herein, we seed control or tEMT NMuMG cells on the 2D patterns consisted of 1 μm or 5 μm line-widths and groove or cone patterns on either 2 MPa (1.96 ± 0.48 MPa) or 4 MPa (3.70 ± 0.74 MPa) polydimethylsiloxane (PDMS) substrates. After tEMT, the increased expression of α-SMA with vinculin in focal adhesion (FA) sites led to an acceleration of tEMT cell motility. On the 2 MPa substrate, the most influenced substrate was the 1 μm, cone-patterned substrate, where the tEMT cells' motility decelerated by 0.13 μm/min (36% slower than the cells on groove pattern). However, on the 5 μm, groove-patterned substrate, where the tEMT cells demonstrated the most rapid motility relative to the control cells, with an increment of 0.18 μm/min (100%). Among the different physical cues from substrate, the cone pattern could impede the migration speed of tEMT cells. Furthermore, we recommend the groove-patterned with a 5 μm line-width substrate as a useful tool to differentiate control and tEMT cells by migration speed.

Contraction-driven cell motility

We propose a mechanism for the initiation of cell motility that is based on myosin-induced contraction and does not require actin polymerization. The translocation of a cell is induced by symmetry breaking of the motor-driven flow, and the ensuing asymmetry gives rise to a steady motion of the center of mass of a cell. The predictions of the model are consistent with observations on keratocytes.

Master equation-based analysis of a motor-clutch model for cell traction force

Microenvironmental mechanics play an important role in determining the morphology, traction, migration, proliferation, and differentiation of cells. A stochastic motor-clutch model has been proposed to describe this stiffness sensitivity. In this work, we present a master equation-based ordinary differential equation (ODE) description of the motor-clutch model, from which we derive an analytical expression to for a cell's optimum stiffness (i.e. the stiffness at which the traction force is maximal). This analytical expression provides insight into the requirements for stiffness sensing by establishing fundamental relationships between the key controlling cell-specific parameters. We find that the fundamental controlling parameters are the numbers of motors and clutches (constrained to be nearly equal), and the time scale of the on-off kinetics of the clutches (constrained to favor clutch binding over clutch unbinding). Both the ODE solution and the analytical expression show good agreement with Monte Carlo motor-clutch output, and reduce computation time by several orders of magnitude, which potentially enables long time scale behaviors (hours-days) to be studied computationally in an efficient manner. The ODE solution and the analytical expression may be incorporated into larger scale models of cellular behavior to bridge the gap from molecular time scales to cellular and tissue time scales.

Mathematical modeling of eukaryotic cell migration: insights beyond experiments

A migrating cell is a molecular machine made of tens of thousands of short-lived and interacting parts. Understanding migration means understanding the self-organization of these parts into a system of functional units. This task is one of tackling complexity: First, the system integrates numerous chemical and mechanical component processes. Second, these processes are connected in feedback interactions and over a large range of spatial and temporal scales. Third, many processes are stochastic, which leads to heterogeneous migration behaviors. Early on in the research of cell migration it became evident that this complexity exceeds human intuition. Thus, the cell migration community has led the charge to build mathematical models that could integrate the diverse experimental observations and measurements in consistent frameworks, first in conceptual and more recently in molecularly explicit models. The main goal of this review is to sift through a series of important conceptual and explicit mathematical models of cell migration and to evaluate their contribution to the field in their ability to integrate critical experimental data.

Signaling networks and cell motility: a computational approach using a phase field description

The processes of protrusion and retraction during cell movement are driven by the turnover and reorganization of the actin cytoskeleton. Within a reaction-diffusion model which combines processes along the cell membrane with processes within the cytoplasm a Turing type instability is used to form the necessary polarity to distinguish between cell front and rear and to initiate the formation of different organizational arrays within the cytoplasm leading to protrusion and retraction. A simplified biochemical network model for the activation of GTPase which accounts for the different dimensionality of the cell membrane and the cytoplasm is used for this purpose and combined with a classical Helfrich type model to account for bending and stiffness effects of the cell membrane. In addition streaming within the cytoplasm and the extracellular matrix is taken into account. Combining these phenomena allows to simulate the dynamics of cells and to reproduce the primary phenomenology of cell motility. The coupled model is formulated within a phase field approach and solved using adaptive finite elements.

Membrane tension in rapidly moving cells is determined by cytoskeletal forces

BACKGROUND

Membrane tension plays an essential role in cell motility. The load imposed by the tensed membrane restrains actin polymerization, promotes rear retraction, and influences membrane transport. Moreover, membrane tension is crucial for large-scale coordination of cell boundary dynamics. Despite its importance, little is known about how membrane tension is set and regulated in cells. The prevailing hypothesis is that membrane tension is largely controlled by membrane-cytoskeleton adhesion and/or changes in membrane area.

RESULTS

In this work, we measure the apparent membrane tension in rapidly moving fish epithelial keratocytes under normal and perturbed conditions with a tether-pulling assay. We find that enlargement of the cell surface area by fusion with giant unilamellar vesicles (GUVs) has only minor effects on membrane tension and on cell movement. However, modulation of the cytoskeletal forces has a substantial influence on tension: reduction of the actin-pushing forces along the cell's leading edge leads to a significant decrease in membrane tension, whereas increase of the strength of adhesion and/or decrease of myosin-induced contraction leads to higher tension.

CONCLUSIONS

We find that the membrane tension in rapidly moving keratocytes is primarily determined by a mechanical force balance between the cell membrane and cytoskeletal forces. Our results highlight the role of membrane tension as a global mechanical regulator of cell behavior.

Electroporation of adherent cells with low sample volumes on a microscope stage

The labeling of specific molecules and their artificial control in living cells are powerful techniques for investigating intracellular molecular dynamics. To use these techniques, molecular compounds (hereinafter described simply as 'samples') need to be loaded into cells. Electroporation techniques are exploited to load membrane-impermeant samples into cells. Here, we developed a new electroporator with four special characteristics. (1) Electric pulses are applied to the adherent cells directly, without removing them from the substratum. (2) Samples can be loaded into the adherent cells while observing them on the stage of an inverted microscope. (3) Only 2 μl of sample solution is sufficient. (4) The device is very easy to use, as the cuvette, which is connected to the tip of a commercially available auto-pipette, is manipulated by hand. Using our device, we loaded a fluorescent probe of actin filaments, Alexa Fluor 546 phalloidin, into migrating keratocytes. The level of this probe in the cells could be easily adjusted by changing its concentration in the electroporation medium. Samples could be loaded into keratocytes, neutrophil-like HL-60 cells and Dictyostelium cells on a coverslip, and keratocytes on an elastic silicone substratum. The new device should be useful for a wide range of adherent cells and allow electroporation for cells on various types of the substrata.

Effects of adhesion dynamics and substrate compliance on the shape and motility of crawling cells

Computational modeling of eukaryotic cells moving on substrates is an extraordinarily complex task: many physical processes, such as actin polymerization, action of motors, formation of adhesive contacts concomitant with both substrate deformation and recruitment of actin etc., as well as regulatory pathways are intertwined. Moreover, highly nontrivial cell responses emerge when the substrate becomes deformable and/or heterogeneous. Here we extended a computational model for motile cell fragments, based on an earlier developed phase field approach, to account for explicit dynamics of adhesion site formation, as well as for substrate compliance via an effective elastic spring. Our model displays steady motion vs. stick-slip transitions with concomitant shape oscillations as a function of the actin protrusion rate, the substrate stiffness, and the rates of adhesion. Implementing a step in the substrate's elastic modulus, as well as periodic patterned surfaces exemplified by alternating stripes of high and low adhesiveness, we were able to reproduce the correct motility modes and shape phenomenology found experimentally. We also predict the following nontrivial behavior: the direction of motion of cells can switch from parallel to perpendicular to the stripes as a function of both the adhesion strength and the width ratio of adhesive to non-adhesive stripes.

Envisioning migration: mathematics in both experimental analysis and modeling of cell behavior

The complex nature of cell migration highlights the power and challenges of applying mathematics to biological studies. Mathematics may be used to create model equations that recapitulate migration, which can predict phenomena not easily uncovered by experiments or intuition alone. Alternatively, mathematics may be applied to interpreting complex data sets with better resolution--potentially empowering scientists to discern subtle patterns amid the noise and heterogeneity typical of migrating cells. Iteration between these two methods is necessary in order to reveal connections within the cell migration signaling network, as well as to understand the behavior that arises from those connections. Here, we review recent quantitative analysis and mathematical modeling approaches to the cell migration problem.

A simple route to functionalize polyacrylamide hydrogels for the independent tuning of mechanotransduction cues

Physico-chemical and biochemical factors in the local cellular microenvironment are known to impact on multiple aspects of cell behaviour through specific signal pathways. These mechanotransduction cues can couple each other to regulate cell fate, and it remains unclear whether mechanotransduction in different contexts shares common mechanisms. Undoubtedly, a challenge will involve the further characterization of such cooperative mechanisms, as well as clearly defining the individual role of each mechanical and biochemical parameter. To control these mechanotransduction cues in an independent manner, we developed a simple and efficient strategy to immobilize any desired nature of proteins on polyacrylamide hydrogels and independently control various parameters of the cell microenvironment, such as matrix stiffness, cell-binding ligand density and confined adhesiveness. This novel platform is validated by conducting single-cell experiments and opens a broad avenue for studying complex interplays involved in mechanotransduction with a facile and versatile approach.

Asymmetry between pushing and pulling for crawling cells

Eukaryotic cells possess motility mechanisms allowing them not only to self-propel but also to exert forces on obstacles (to push) and to carry cargoes (to pull). To study the inherent asymmetry between active pushing and pulling we model a crawling acto-myosin cell extract as a one-dimensional layer of active gel subjected to external forces. We show that pushing is controlled by protrusion and that the macroscopic signature of the protrusion dominated motility mechanism is concavity of the force-velocity relation. In contrast, pulling is driven by protrusion only at small values of the pulling force and it is replaced by contraction when the pulling force is sufficiently large. This leads to more complex convex-concave structure of the force-velocity relation; in particular, competition between protrusion and contraction can produce negative mobility in a biologically relevant range. The model illustrates active readjustment of the force generating machinery in response to changes in the dipole structure of external forces. The possibility of switching between complementary active mechanisms implies that if necessary "pushers" can replace "pullers" and vice versa.

Force mapping during the formation and maturation of cell adhesion sites with multiple optical tweezers

Focal contacts act as mechanosensors allowing cells to respond to their biomechanical environment. Force transmission through newly formed contact sites is a highly dynamic process requiring a stable link between the intracellular cytoskeleton and the extracellular environment. To simultaneously investigate cellular traction forces in several individual maturing adhesion sites within the same cell, we established a custom-built multiple trap optical tweezers setup. Beads functionalized with fibronectin or RGD-peptides were placed onto the apical surface of a cell and trapped with a maximum force of 160 pN. Cells form adhesion contacts around the beads as demonstrated by vinculin accumulation and start to apply traction forces after 30 seconds. Force transmission was found to strongly depend on bead size, surface density of integrin ligands and bead location on the cell surface. Highest traction forces were measured for beads positioned on the leading edge. For mouse embryonic fibroblasts, traction forces acting on single beads are in the range of 80 pN after 5 minutes. If two beads were positioned parallel to the leading edge and with a center-to-center distance less than 10 µm, traction forces acting on single beads were reduced by 40%. This indicates a spatial and temporal coordination of force development in closely related adhesion sites. We also used our setup to compare traction forces, retrograde transport velocities, and migration velocities between two cell lines (mouse melanoma and fibroblasts) and primary chick fibroblasts. We find that maximal force development differs considerably between the three cell types with the primary cells being the strongest. In addition, we observe a linear relation between force and retrograde transport velocity: a high retrograde transport velocity is associated with strong cellular traction forces. In contrast, migration velocity is inversely related to traction forces and retrograde transport velocity.

Multidimensional traction force microscopy reveals out-of-plane rotational moments about focal adhesions

Recent methods have revealed that cells on planar substrates exert both shear (in-plane) and normal (out-of-plane) tractions against the extracellular matrix (ECM). However, the location and origin of the normal tractions with respect to the adhesive and cytoskeletal elements of cells have not been elucidated. We developed a high-spatiotemporal-resolution, multidimensional (2.5D) traction force microscopy to measure and model the full 3D nature of cellular forces on planar 2D surfaces. We show that shear tractions are centered under elongated focal adhesions whereas upward and downward normal tractions are detected on distal (toward the cell edge) and proximal (toward the cell body) ends of adhesions, respectively. Together, these forces produce significant rotational moments about focal adhesions in both protruding and retracting peripheral regions. Temporal 2.5D traction force microscopy analysis of migrating and spreading cells shows that these rotational moments are highly dynamic, propagating outward with the leading edge of the cell. Finally, we developed a finite element model to examine how rotational moments could be generated about focal adhesions in a thin lamella. Our model suggests that rotational moments can be generated largely via shear lag transfer to the underlying ECM from actomyosin contractility applied at the intracellular surface of a rigid adhesion of finite thickness. Together, these data demonstrate and probe the origin of a previously unappreciated multidimensional stress profile associated with adhesions and highlight the importance of new approaches to characterize cellular forces.

A chemically-defined screening platform reveals behavioral similarities between primary human mesenchymal stem cells and endothelial cells

Chemically defined substrates, which rigorously control protein-surface and cell-surface interactions, can be used to probe the effects of specific biomolecules on cell behavior. Here we combined a chemically-defined, array-based format with automated, time-lapse microscopy to efficiently screen cell-substrate interactions. Self-assembled monolayers (SAMs) of alkanethiolates bearing oligo(ethylene glycol) units and reactive terminal groups were used to present cell adhesion peptides while minimizing non-specific protein interactions. Specifically, we describe rapid fabrication of arrays of 1 mm spots, which present varied densities of the integrin-binding ligand Gly-Arg-Gly-Asp-Ser-Pro (GRGDSP). Results indicate that cell attachment, cell spreading, and proliferation exhibit strong dependencies on GRGDSP density for both human mesenchymal stem cells (hMSCs) and human umbilical vein endothelial cells (HUVECs). Furthermore, relative spreading and proliferation over a broad range of GRGDSP densities were similar for both primary cell types, and detailed comparison between cell behaviors identified a 1 : 1 correlation between spreading and proliferation for both HUVECs and hMSCs. Finally, time-lapse microscopy of SAM arrays revealed distinct adhesion-dependent migratory behaviors for HUVECs and hMSCs. These results demonstrate the benefits of using an array-based screening platform for investigating cell function. While the proof-of-concept focuses on simple cellular properties, the quantitative similarities observed for hMSCs and HUVECs provides a direct example of how phenomena that would not easily be predicted can be shown to correlate between different cell types.

Cell-scale dynamic recycling and cortical flow of the actin-myosin cytoskeleton for rapid cell migration

Actin and myosin II play major roles in cell migration. Whereas pseudopod extension by actin polymerization has been intensively researched, less attention has been paid to how the rest of the actin cytoskeleton such as the actin cortex contributes to cell migration. In this study, cortical actin and myosin II filaments were simultaneously observed in migrating Dictyostelium cells under total internal reflection fluorescence microscopy. The cortical actin and myosin II filaments remained stationary with respect to the substratum as the cells advanced. However, fluorescence recovery after photobleaching experiments and direct observation of filaments showed that they rapidly turned over. When the cells were detached from the substratum, the actin and myosin filaments displayed a vigorous retrograde flow. Thus, when the cells migrate on the substratum, the cortical cytoskeleton firmly holds the substratum to generate the motive force instead. The present studies also demonstrate how myosin II localizes to the rear region of the migrating cells. The observed dynamic turnover of actin and myosin II filaments contributes to the recycling of their subunits across the whole cell and enables rapid reorganization of the cytoskeleton.

Scar/WAVE3 contributes to motility and plasticity of lamellipodial dynamics but not invasion in three dimensions

The Scar (suppressor of cAMP receptor)/WAVE [WASP (Wiskott-Aldrich syndrome protein) verprolin homologous] complex plays a major role in the motility of cells by activating the Arp2/3 complex, which initiates actin branching and drives protrusions. Mammals have three Scar/WAVE isoforms, which show some tissue-specific expression, but their functions have not been differentiated. In the present study we show that depletion of Scar/WAVE3 in the mammalian breast cancer cells MDA-MB-231 results in larger and less dynamic lamellipodia. Scar/WAVE3-depleted cells move more slowly but more persistently on a two-dimensional matrix and they typically only show one lamellipod. However, Scar/WAVE3 appears to have no role in driving invasiveness in a three-dimensional Matrigel™ invasion assay or a three-dimensional collagen invasion assay, suggesting that lamellipodial persistence as seen in two-dimensions is not crucial in three-dimensional environments.

Crawling from soft to stiff matrix polarizes the cytoskeleton and phosphoregulates myosin-II heavy chain

Cytoskeletal polarization occurs in response to mechanosensing of a transition from soft to stiff matrix during migration and promotes dephosphorylation of myosin-IIA, rearward localization of myosin-IIB, and durotaxis.

On rigid surfaces, the cytoskeleton of migrating cells is polarized, but tissue matrix is normally soft. We show that nonmuscle MIIB (myosin-IIB) is unpolarized in cells on soft matrix in 2D and also within soft 3D collagen, with rearward polarization of MIIB emerging only as cells migrate from soft to stiff matrix. Durotaxis is the tendency of cells to crawl from soft to stiff matrix, and durotaxis of primary mesenchymal stem cells (MSCs) proved more sensitive to MIIB than to the more abundant and persistently unpolarized nonmuscle MIIA (myosin-IIA). However, MIIA has a key upstream role: in cells on soft matrix, MIIA appeared diffuse and mobile, whereas on stiff matrix, MIIA was strongly assembled in oriented stress fibers that MIIB then polarized. The difference was caused in part by elevated phospho-S1943–MIIA in MSCs on soft matrix, with site-specific mutants revealing the importance of phosphomoderated assembly of MIIA. Polarization is thus shown to be a highly regulated compass for mechanosensitive migration.

Physical model for self-organization of actin cytoskeleton and adhesion complexes at the cell front

Cell motion is driven by interplay between the actin cytoskeleton and the cell adhesions in the front part of the cell. The actin network segregates into lamellipodium and lamellum, whereas the adhesion complexes are characteristically distributed underneath the actin system. Here, we suggest a computational model for this characteristic organization of the actin-adhesion system. The model is based on the ability of the adhesion complexes to sense mechanical forces, the stick-slip character of the interaction between the adhesions and the moving actin network, and a hypothetical propensity of the actin network to disintegrate upon sufficiently strong stretching stresses. We identify numerically three possible types of system organization, all observed in living cells: two states in which the actin network exhibits segregation into lamellipodium and lamellum, whereas the cell edge either remains stationary or moves, and a state where the actin network does not undergo segregation. The model recovers the asynchronous fluctuations and outward bulging of the cell edge, and the dependence of the edge protrusion velocity on the rate of the nascent adhesion generation, the membrane tension, and the substrate rigidity.

Self-organized cell motility from motor-filament interactions

Cell motility is driven primarily by the dynamics of the cell cytoskeleton, a system of filamentous proteins and molecular motors. It has been proposed that cell motility is a self-organized process, that is, local short-range interactions determine much of the dynamics that are required for the whole-cell organization that leads to polarization and directional motion. Here we present a mesoscopic mean-field description of filaments, motors, and cell boundaries. This description gives rise to a dynamical system that exhibits multiple self-organized states. We discuss several qualitative aspects of the asymptotic states and compare them with those of living cells.

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.

Stick-slip motion and elastic coupling in crawling cells

Crawling cells exhibit a variety of cell shape dynamics, ranging from complex ruffling and bubbling to oscillatory protrusion and retraction. Periodic shape changes during cell migration are recorded in fast-moving fish epithelial keratocytes where sticking and slipping at opposite sides of the cell's broad trailing edge generate bipedal locomotion. Barnhart et al. [Biophys. J. 98, 933 (2010)] recently proposed a mechanical spring model specifically designed to capture bipedal locomotion in these cells. We extend their model by benchmarking the dynamics of four mechanical configurations against those of crawling keratocytes. Our analysis shows that elastic coupling to the cell nucleus is necessary to generate its lateral motion. We select one configuration to study the effects of cell elasticity, size, and aspect ratio on crawling dynamics. This configuration predicts that shape dynamics are highly dependent on the lamellipodial elasticity but less sensitive to elasticity at the trailing edge. The model predicts a wide range of dynamics seen in actual crawling keratocytes, including coherent bipedal, coherent nonbipedal, and decoherent motions. This work highlights how the dynamical behavior of crawling cells can be derived from mechanical properties through which biochemical factors may operate to regulate cellular locomotion.

TRPM7 is required for breast tumor cell metastasis

TRPM7 encodes a Ca2+-permeable nonselective cation channel with kinase activity. TRPM7 has been implicated in control of cell adhesion and migration, but whether TRPM7 activity contributes to cancer progression has not been established. Here we report that high levels of TRPM7 expression independently predict poor outcome in breast cancer patients and that it is functionally required for metastasis formation in a mouse xenograft model of human breast cancer. Mechanistic investigation revealed that TRPM7 regulated myosin II-based cellular tension, thereby modifying focal adhesion number, cell-cell adhesion and polarized cell movement. Our findings therefore suggest that TRPM7 is part of a mechanosensory complex adopted by cancer cells to drive metastasis formation.

Spontaneous symmetry breaking in active droplets provides a generic route to motility

We explore a generic mechanism whereby a droplet of active matter acquires motility by the spontaneous breakdown of a discrete symmetry. The model we study offers a simple representation of a "cell extract" comprising, e.g., a droplet of actomyosin solution. (Such extracts are used experimentally to model the cytoskeleton). Actomyosin is an active gel whose polarity describes the mean sense of alignment of actin fibres. In the absence of polymerization and depolymerization processes ('treadmilling'), the gel's dynamics arises solely from the contractile motion of myosin motors; this should be unchanged when polarity is inverted. Our results suggest that motility can arise in the absence of treadmilling, by spontaneous symmetry breaking (SSB) of polarity inversion symmetry. Adapting our model to wall-bound cells in two dimensions, we find that as wall friction is reduced, treadmilling-induced motility falls but SSB-mediated motility rises. The latter might therefore be crucial in three dimensions where frictional forces are likely to be modest. At a supracellular level, the same generic mechanism can impart motility to aggregates of nonmotile but active bacteria; we show that SSB in this (extensile) case leads generically to rotational as well as translational motion.

United we stand: integrating the actin cytoskeleton and cell-matrix adhesions in cellular mechanotransduction

Many essential cellular functions in health and disease are closely linked to the ability of cells to respond to mechanical forces. In the context of cell adhesion to the extracellular matrix, the forces that are generated within the actin cytoskeleton and transmitted through integrin-based focal adhesions are essential for the cellular response to environmental clues, such as the spatial distribution of adhesive ligands or matrix stiffness. Whereas substantial progress has been made in identifying mechanosensitive molecules that can transduce mechanical force into biochemical signals, much less is known about the nature of cytoskeletal force generation and transmission that regulates the magnitude, duration and spatial distribution of forces imposed on these mechanosensitive complexes. By focusing on cell-matrix adhesion to flat elastic substrates, on which traction forces can be measured with high temporal and spatial resolution, we discuss our current understanding of the physical mechanisms that integrate a large range of molecular mechanotransduction events on cellular scales. Physical limits of stability emerge as one important element of the cellular response that complements the structural changes affected by regulatory systems in response to mechanical processes.

Cell mechanics control rapid transitions between blebs and lamellipodia during migration

Protrusion formation is an essential step during cell migration. Cells migrating in three-dimensional environments and in vivo can form a wide variety of protrusion types, including actin polymerization-driven lamellipodia, and contractility-driven blebs. The ability to switch between different protrusions has been proposed to facilitate motility in complex environments and to promote cancer dissemination. However, plasticity in protrusion formation has so far mostly been investigated in the context of transitions between amoeboid and mesenchymal migration modes, which involve substantial changes in overall cell morphology. As a result, the minimal requirements of transitions between blebs and lamellipodia, as well as the time scales on which they occur, remain unknown. To address these questions, we investigated protrusion switching during cell migration at the single cell level. Using cells that can be induced to form either blebs or lamellipodia, we systematically assessed the mechanical requirements, as well as the dynamics, of switching between protrusion types. We demonstrate that shifting the balance between actin protrusivity and actomyosin contractility leads to immediate transitions between blebs and lamellipodia in migrating cells. Switching occurred without changes in global cell shape, polarity, or cell adhesion. Furthermore, rapid transitions between blebs and lamellipodia could also be triggered upon changes in substrate adhesion during migration on micropatterned surfaces. Together, our data reveal that the type of protrusion formed by migrating cells can be dynamically controlled independently of overall cell morphology, suggesting that protrusion formation is an autonomous module in the regulatory network that controls the plasticity of cell migration.

Spatiotemporal coordinated hierarchical properties of cellular protrusion revealed by multiscale analysis

We present a methodology for integrative multiscale analysis to highlight hierarchical properties of cellular protrusion and mechanochemical interactions in cellular protrusion based on live cell imaging data with high spatiotemporal resolution. As an appropriate experimental system, we selected non-polarized full-moon-shaped keratocytes that present balanced protrusion around the entire cell periphery at the cellular scale simultaneously with active protrusion and retraction at the subcellular scale. We achieved the observation of a whole cell with sub-micrometer spatial precision and sub-second time resolution for three minutes or more. The multiscale characteristics of cell peripheral activity and those of the cell peripheral shape were extracted from an identical image sequence by estimating the cell protrusion rates and the cell peripheral curvatures at various differential intervals. The spatiotemporal maps of the cell protrusion rates demonstrated a spatiotemporally nested structure of travelling waves of active protruding regions at the cellular and subcellular scales. Moreover, correlation analysis demonstrated the relationship between the cell protrusion rate and peripheral curvature at the subcellular scale. The novel integrative methodology presented here well highlighted the hierarchical properties of organized cellular protrusion, and further provided insight about the underlying mechanochemical interactions between the cell membrane and the actin filaments under the membrane.

Differences in adhesion and protrusion properties correlate with differences in migration speed under EGF stimulation

Background

Cell migration plays an essential role in many biological processes, such as cancer metastasis, wound healing and immune response. Cell migration is mediated through protrusion and focal adhesion (FA) assembly, maturation and disassembly. Epidermal growth factor (EGF) is known to enhance migration rate in many cell types; however it is not known how FA maturation, FA dynamics and protrusion dynamics are regulated during EGF-induced migration. Here we use total internal reflection fluorescence (TIRF) microscopy and image analysis to quantify FA properties and protrusion dynamics under different doses of EGF stimulation.

Results

EGF was found to broaden the distribution of cell migration rates, generating more fast and slow cells. Furthermore, groups based on EGF stimulation condition or cell migration speed were marked by characteristic signatures. When data was binned based on EGF stimulation conditions, FA intensity and FA number per cell showed the largest difference among stimulation groups. FA intensity decreased with increasing EGF concentration and FA number per cell was highest under intermediate stimulation conditions. No difference in protrusion behavior was observed. However, when data was binned based on cell migration speed, FA intensity and not FA number per cell showed the largest difference among groups. FA intensity was lower for fast migrating cells. Additionally, waves of protrusion tended to correlate with fast migrating cells.

Conclusions

Only a portion of the FA properties and protrusion dynamics that correlate with migration speed, correlate with EGF stimulation condition. Those that do not correlate with EGF stimulation condition constitute the most sensitive output for identifying why cells respond differently to EGF. The idea that EGF can both increase and decrease the migration speed of individual cells in a population has particular relevance to cancer metastasis where the microenvironment can select subpopulations based on some adhesion and protrusion characteristics, leading to a more invasive phenotype as would be seen if all cells responded like an “average” cell.

Coupling actin flow, adhesion, and morphology in a computational cell motility model

Cell migration is a pervasive process in many biology systems and involves protrusive forces generated by actin polymerization, myosin dependent contractile forces, and force transmission between the cell and the substrate through adhesion sites. Here we develop a computational model for cell motion that uses the phase-field method to solve for the moving boundary with physical membrane properties. It includes a reaction-diffusion model for the actin-myosin machinery and discrete adhesion sites which can be in a "gripping" or "slipping" mode and integrates the adhesion dynamics with the dynamics of the actin filaments, modeled as a viscous network. To test this model, we apply it to fish keratocytes, fast moving cells that maintain their morphology, and show that we are able to reproduce recent experimental results on actin flow and stress patterns. Furthermore, we explore the phase diagram of cell motility by varying myosin II activity and adhesion strength. Our model suggests that the pattern of the actin flow inside the cell, the cell velocity, and the cell morphology are determined by the integration of actin polymerization, myosin contraction, adhesion forces, and membrane forces.

Excitable actin dynamics in lamellipodial protrusion and retraction

Many animal cells initiate crawling by protruding lamellipodia, consisting of a dense network of actin filaments, at their leading edge. We imaged XTC cells that exhibit flat lamellipodia on poly-L-lysine-coated coverslips. Using active contours, we tracked the leading edge and measured the total amount of F-actin by summing the pixel intensities within a 5-μm band. We observed protrusion and retraction with period 130-200 s and local wavelike features. Positive (negative) velocities correlated with minimum (maximum) integrated actin concentration. Approximately constant retrograde flow indicated that protrusions and retractions were driven by fluctuations of the actin polymerization rate. We present a model of these actin dynamics as an excitable system in which a diffusive, autocatalytic activator causes actin polymerization; F-actin accumulation in turn inhibits further activator accumulation. Simulations of the model reproduced the pattern of actin polymerization seen in experiments. To explore the model's assumption of an autocatalytic activation mechanism, we imaged cells expressing markers for both F-actin and the p21 subunit of the Arp2/3 complex. We found that integrated Arp2/3-complex concentrations spike several seconds before spikes of F-actin concentration. This suggests that the Arp2/3 complex participates in an activation mechanism that includes additional diffuse components. Response of cells to stimulation by fetal calf serum could be reproduced by the model, further supporting the proposed dynamical picture.

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.

Macrophage Migration and Its Regulation by CSF-1

Macrophages are terminally differentiated cells of the mononuclear phagocytic lineage and develop under the stimulus of their primary growth and differentiation factor, CSF-1. Although they differentiate into heterogeneous populations, depending upon their tissue of residence, motility is an important aspect of their function. To facilitate their migration through tissues, macrophages express a unique range of adhesion and cytoskeletal proteins. Notably, macrophages do not form large, stable adhesions or actin stress fibers but rely on small, short lived point contacts, focal complexes and podosomes for traction. Thus, macrophages are built to respond rapidly to migratory stimuli. As well as triggering growth and differentiation, CSF-1 is also a chemokine that regulates macrophage migration via activation the CSF-1 receptor tyrosine kinase. CSF-1R autophosphorylation of several intracellular tyrosine residues leads to association and activation of many downstream signaling molecules. However, phosphorylation of just one residue, Y721, mediates association of PI3K with the receptor to activate the major motility signaling pathways in macrophages. Dissection of these pathways will identify drug targets for the inhibition of diseases in which macrophages contribute to adverse outcomes.

Steady state dynamics of a moving model cell

Crawling cell motility results due to treadmilling of a polymerized actin network at the leading edge. Steady state dynamics of a moving cell are governed by actin concentration profiles across the cell. Branching of new filaments implicating Arp2/3 and capping of existing filaments with capZ or Gelsolin are central to the robust functioning of the actin network. Using computer simulations, steady state concentration profiles of globular actin (G actin) and filamentous actin (F actin) are computed. The profiles are in agreement with experimentally observed ones. Simulations unveil that there is an optimal capping and branching rate for which the velocity of the model cell is maximum. Our simulations also indicate that the capping of actin filaments results in an increase in nucleation of new filaments by Arp2/3-induced branching and is in agreement with a recently observed monomer gating model. We observe that Arp2/3 and capping protein exhibit a functional antagonism with respect to the actin network treadmilling.

Membrane tension maintains cell polarity by confining signals to the leading edge during neutrophil migration

Little is known about how neutrophils and other cells establish a single zone of actin assembly during migration. A widespread assumption is that the leading edge prevents formation of additional fronts by generating long-range diffusible inhibitors or by sequestering essential polarity components. We use morphological perturbations, cell-severing experiments, and computational simulations to show that diffusion-based mechanisms are not sufficient for long-range inhibition by the pseudopod. Instead, plasma membrane tension could serve as a long-range inhibitor in neutrophils. We find that membrane tension doubles during leading-edge protrusion, and increasing tension is sufficient for long-range inhibition of actin assembly and Rac activation. Furthermore, reducing membrane tension causes uniform actin assembly. We suggest that tension, rather than diffusible molecules generated or sequestered at the leading edge, is the dominant source of long-range inhibition that constrains the spread of the existing front and prevents the formation of secondary fronts.

Stochastic models of cell protrusion arising from spatiotemporal signaling and adhesion dynamics

During cell migration, local protrusion events are regulated by biochemical and physical processes that are in turn coordinated with the dynamic properties of cell-substratum adhesion structures. In this chapter, we present a modeling approach for integrating the apparent stochasticity and spatial dependence of signal transduction pathways that promote protrusion in tandem with adhesion dynamics. We describe our modeling framework, as well as its abstraction, parameterization, and validation against experimental data. Analytical techniques for identifying and evaluating the effects of model bistability on simulation simulation results are shown, and implications of this analysis for understanding cell protrusion behavior are offered.

Cell migration: PKA and RhoA set the pace

A new study shows that protein kinase A (PKA) activity establishes a signaling loop that governs protrusion-retraction cycles in migrating cells. PKA activity near the leading edge of protrusions phosphorylates RhoA and inhibits its activity via increased association with RhoGDI.

Actin disassembly clock determines shape and speed of lamellipodial fragments

A central challenge in motility research is to quantitatively understand how numerous molecular building blocks self-organize to achieve coherent shape and movement on cellular scales. A classic example of such self-organization is lamellipodial motility in which forward translocation is driven by a treadmilling actin network. Actin polymerization has been shown to be mechanically restrained by membrane tension in the lamellipodium. However, it remains unclear how membrane tension is determined, what is responsible for retraction and shaping of the rear boundary, and overall how actin-driven protrusion at the front is coordinated with retraction at the rear. To answer these questions, we utilize lamellipodial fragments from fish epithelial keratocytes which lack a cell body but retain the ability to crawl. The absence of the voluminous cell body in fragments simplifies the relation between lamellipodial geometry and cytoskeletal dynamics. We find that shape and speed are highly correlated over time within individual fragments, whereby faster crawling is accompanied by larger front-to-rear lamellipodial length. Furthermore, we find that the actin network density decays exponentially from front-to-rear indicating a constant net disassembly rate. These findings lead us to a simple hypothesis of a disassembly clock mechanism in which rear position is determined by where the actin network has disassembled enough for membrane tension to crush it and haul it forward. This model allows us to directly relate membrane tension with actin assembly and disassembly dynamics and elucidate the role of the cell membrane as a global mechanical regulator which coordinates protrusion and retraction.

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.

Modeling cellular processes in 3D

Recent advances in photonic imaging and fluorescent protein technology offer unprecedented views of molecular space-time dynamics in living cells. At the same time, advances in computing hardware and software enable modeling of ever more complex systems, from global climate to cell division. As modeling and experiment become more closely integrated we must address the issue of modeling cellular processes in 3D. Here, we highlight recent advances related to 3D modeling in cell biology. While some processes require full 3D analysis, we suggest that others are more naturally described in 2D or 1D. Keeping the dimensionality as low as possible reduces computational time and makes models more intuitively comprehensible; however, the ability to test full 3D models will build greater confidence in models generally and remains an important emerging area of cell biological modeling.