Session E39: Cell Motility: From Single Cell to Collective Dynamics I

Superdiffusive cell motility on 2D substrates modeled as a persistent Lévy walk

Cell motility is an essential part of many biological processes such as morphogenesis, wound healing and tumorigenesis. We quantified cell motility by tracking mouse fibroblast and human breast carcinoma nuclei to construct cell trajectories. The mean-squared displacement of these trajectories reveals that cell motion is super diffusive, where displacements scale faster than $t^{1/2}$ in all directions. Existing self-propelled particle (SPP) models that do not explicitly incorporate ensemble heterogeneity are unable to predict this super-diffusive behavior. Therefore we developed a run-and-tumble SPP model with Levy distributed run times that captures observed super-diffusive behavior in the mean-squared displacement as well as scaling collapse exponents of displacement probability distributions which match those of mouse fibroblast and human breast carcinoma cell trajectories. We additionally introduced small fluctuations in particle orientation during runs, which generates a crossover from super-diffusive to diffusive dynamics at a very long times. This timescale can be extracted in experiments from the velocity auto-correlation function, allowing us to explicitly test this model prediction.   

Modelling Rho GTPase biochemistry to predict collective cell migration

The collective migration of cells, due to individual cell polarization and intercellular contact inhibition of locomotion, features prominently in embryogenesis and metastatic cancers. Existing methods for modelling collectively migrating cells tend to rely either on highly abstracted agent-based models, or on continuum approximations of the group. Both of these frameworks represent intercellular interactions such as contact inhibition of locomotion as hard-coded rules defining model cells. In contrast, we present a vertex-dynamics framework which predicts polarization and contact inhibition of locomotion naturally from an underlying model of Rho GTPase biochemistry and cortical mechanics. We simulate the interaction between many such model cells, and study how modulating Rho GTPases affects migratory characteristics of the group, in the context of long-distance collective migration of neural crest cells during embryogenesis.   

Two distinct actin networks mediate traction oscillations to confer mechanosensitivity of focal adhesions

Cells sense the mechanical stiffness of their extracellular matrix (ECM) by exerting traction force through focal adhesions (FAs), which are integrin-based protein assemblies. Strikingly, FA-mediated traction forces oscillate in time and space and govern durotaxis -- the tendency of most cell types to migrate toward stiffer ECM. The underlying mechanism of this intriguing oscillation of FA traction force is unknown. Combing theory and experiment, we develop a model of FA growth, which integrates coordinated contributions of a branched actin network and stress fibers in the process. We show that retrograde flux of branched actin network contributes to a traction peak near the FA distal tip and that stress fiber-mediated actomyosin contractility generates a second traction peak near the FA center. Formin-mediated stress fiber elongation negatively feeds back with actomyosin contractility, resulting in the central traction peak oscillation. This underpins observed spatio-temporal patterns of the FA traction, and broadens the ECM stiffness range, over which FAs could accurately adapt with traction force generation. Our findings shed light on the fundamental mechanism of FA mechanosensing and hence durotaxis.   

Cell Shapes and Traction Forces Determine Stress in Motile Confluent Tissue

Collective cell migration is a highly regulated process involved in wound healing, cancer metastasis and morphogenesis. The understanding of the regulatory mechanism requires the study of mechanical interactions among cells that coordinate their active motion. To this end, we develop a method that determines cellular forces and tissue stresses from experimentally accessible cell shapes and traction forces. This approach allows us for the first time to calculate membrane tensions and hydrostatic pressures at a cellular level in collective migrating cell layers out of equilibrium. It helps us understand the mechanical origin of tissue stresses as previous inferred using Traction Force Microscopy (TFM). We test this approach on a new model of motile confluent tissue, which we term Self-propelled Voronoi Model (SPV) that incorporates cell elasticity, contractility and motility. With the model, we explore the mechanical properties of confluent motile tissue as a function of cell activities and cell shapes in various geometries.   

Elastic mismatch enhances cell motility

In recent years, the study of physics phenomena in cancer has drawn considerable attention. In cancer metastasis, a soft cancer cell leaves the tumor, and must pass through the endothelium before reaching the bloodstream. Using a phase-field model we have shown [1] that the elasticity mismatch between cells alone is sufficient to enhance the motility of thesofter cancer cell by means of bursty migration, in agreement with experiment [2]. We will present further characterization of these behaviour, as well as new possible applications for this model. [1] Palmieri, B. et al. Sci. Rep. 5, 11745; [2] Lee, M. et al. Biophys. J 102, 2731 (2012).   

Two interacting active dimers on a rigid track

Cell migration in morphogenesis and cancer metastasis typically involves an interplay between different cell types. The rules governing such interplay remain largely unknown; however, a recent experiment studying the interaction between neural crest (NC) cells and placodal cells reveals an example of such rules. The study found that NC cells chase the placodal cells by chemotaxis, while placodal cells run away from NC cells when contacted by them. Motivated by this observation, we construct and study a minimal one-dimensional cell-cell model comprised of two cells with each cell represented by two-beads-connected-by-an-active spring. The active spring for each moving cell models the stress fibers with their myosin-driven contractility (and alpha-actinin extendability), while the friction coefficients of the beads describe the catch/slip bond behavior of the integrins in focal adhesions. We also include a dynamic contact interaction between the two cells to decipher the chase-and-run dynamics observed in the experiment. We then use our model to construct a "phase diagram" consisting of chase-and-run behavior, clumping (of the two cells) with repolarization behavior and clumping with no repolarization behavior that can be qualitatively compared to experiments.   

Traction force and tension fluctuations in growing axons

Actively generated mechanical forces play a central role in axon growth and guidance during nervous system development. We describe the dynamics of traction stresses from growth cones of actively advancing axons from postnatal rat DRG neurons. By tracking the movement of the growth cone and analyzing the traction stresses in a co-moving reference frame, we show that there is a clear and consistent average stress field underlying the complex spatial stresses present at any one time. The average stress field has strong maxima on the sides of the growth cone, directed inward toward the growth cone neck. This pattern represents a contractile stress contained within the growth cone, and a net force that is balanced by the axon tension. In addition, using high time-resolution measurements, we show that the stress field is composed of fluctuating local stress peaks, with a population of peaks whose lifetime distribution follows an exponential decay, and a small number of very long-lived peaks. We also find that the tension appears to vary randomly over short time scales, roughly consistent with the lifetime of the stress peaks, suggesting that the tension fluctuations originate from stochastic adhesion dynamics.   

Multiscale Modeling of Cell Interaction in Angiogenesis: From the Micro- to Macro-scale

Solid tumors require a supply of nutrients to grow in size. To this end, tumors induce the growth of new blood vessels from existing vasculature through the process of angiogenesis. In this work, we use a discrete agent-based approach to model the behavior of individual endothelial cells during angiogenesis. We incorporate crowding effects through volume exclusion, motility of cells through biased random walks, and include birth and death processes. We use the transition probabilities associated with the discrete models to determine collective cell behavior, in terms of partial differential equations, using a Markov chain and master equation framework. We find that the cell-level dynamics gives rise to a migrating cell front in the form of a traveling wave on the macro-scale. The behavior of this front depends on the cell interactions that are included and the extent to which volume exclusion is taken into account in the discrete micro-scale model. We also find that well-established continuum models of angiogenesis cannot distinguish between certain types of cell behavior on the micro-scale. This may impact drug development strategies based on these models.   

Cellular Polarization and Contractility in Collective Cell Migration

Collective cell migration drives many biological processes such as metastasis, morphogenesis and wound healing. These coordinated motions are driven by active forces. The physical nature of these forces and the mechanisms by which they generate collective cell migration are still not fully understood. We have developed a minimum physical model of a cell monolayer as an elastic continuum whose deformation field is coupled to two internal degrees of freedom: the concentration of a chemical signal, controlling cell contractility, and the polarization field controlling the direction of local cell motion. By combining theory with experiments, we show that these two internal variables account for the sloshing waves and the systematic deviations of the direction of cell polarization from that of local cell velocity observed in confined cell monolayers.   

Analysis of Shape Dynamics and Actin Polymerization of Collectively Migrating Streams of Cells

We use Princiapl Component Analysis (PCA) to investigate cell-cell coupling during collective cell migration of Dictyostelium discoideun, and explore the underlying mechanisms that regulate the coupling. From PCA of the cell boundary motion obtained from time-lapse images of multicellular streams, we find that cells in streams exhibit more localized anterior protrusions than individually migrating cells. We also find that traveling protrusion waves along cell boundaries connect from cell to cell with high correlation. Further analysis of actin polymerization indicates that actin polymerization is significantly enhanced at the leading edge of cells at cell-cell contacts. The coupling of waves disappears when reducing F-actin polymerization with Latrunculin A.   

Connecting single cell to collective cell behavior in a unified theoretical framework

Collective cell behavior is an essential part of tissue and organ morphogenesis during embryonic development, as well as of various disease processes, such as cancer. In contrast to many \textit{in vitro} studies of collective cell migration, most cases of \textit{in vivo} collective cell migration involve rather small groups of cells, with large sheets of migrating cells being less common. The vast majority of theoretical descriptions of collective cell behavior focus on large numbers of cells, but fail to accurately capture the dynamics of small groups of cells. Here we introduce a low-dimensional theoretical description that successfully captures single cell migration, cell collisions, collective dynamics in small groups of cells, and force propagation during sheet expansion, all within a common theoretical framework. Our description is derived from first principles and also includes key phenomenological aspects of cell migration that control the dynamics of traction forces. Among other results, we explain the counter-intuitive observations that pairs of cells repel each other upon collision while they behave in a coordinated manner within larger clusters.   

Emergence of oligarchy in collective cell migration.

Identifying the principles of collective cell migration has the potential to help prevent birth defects, improve regenerative therapies and develop model systems for cancer metastasis. In collaboration with experimental biologists, we use computational simulations of a hybrid model, comprising individual-based stochastic cell movement coupled to a reaction-diffusion equation for a chemoattractant, to explore the role of cell specialisation in the guidance of collective cell migration. In the neural crest, an important migratory cell population in vertebrate embryo development, we present evidence that just a few cells are guiding group migration in a cell-induced chemoattractant gradient that determines the switch between ``leader'' and ``follower'' behaviour in individual cells. This leads us to more generally consider under what conditions cell specialisation might become advantageous for collective migration. Alternatively, individual cell responses to locally different microenvironmental conditions could create the (artefactual) appearance of heterogeneity in a population of otherwise identical cellular agents. We explore these questions using a self-propelled particle model as a minimal description for collective cell migration in two and three dimensions.