Computational modelling of cell motility on substrates is a formidable challenge; regulatory pathways are intertwined and forces that influence cell motion are not fully quantified. Additional challenges arise from the need to describe a moving deformable cell boundary.Here, we present a simple mathematical model coupling cell shape dynamics, treated by the phase-field approach, to a vector field describing the mean orientation ( polarization) of the actin filament network. The model successfully reproduces the primary phenomenology of cell motility: discontinuous onset of motion, diversity of cell shapes and shape oscillations. The results are in qualitative agreement with recent experiments on motility of keratocyte cells and cell fragments. The asymmetry of the shapes is captured to a large extent in this simple model, which may prove useful for the interpretation of experiments.

Collective migration of eukaryotic cells plays a fundamental role in tissue growth, wound healing and immune response. The motion, arising spontaneously or in response to chemical and mechanical stimuli, is also important for understanding life-threatening pathologies, such as cancer and metastasis formation. We present a phase-field model to describe the movement of many self-organized, interacting cells. The model takes into account the main mechanisms of cell motility – acto-myosin dynamics, as well as substrate-mediated and cell-cell adhesion. It predicts that collective cell migration emerges spontaneously as a result of inelastic collisions between neighboring cells: collisions lead to a mutual alignment of the cell velocities and to the formation of coherently-moving multi-cellular clusters. Small cell-to-cell adhesion, in turn, reduces the propensity for large-scale collective migration, while higher adhesion leads to the formation of moving bands. Our study provides valuable insight into biological processes associated with collective cell motility.

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.

Self-propelled motion, emerging spontaneously or in response to external cues, is a hallmark of living organisms. Systems of self-propelled synthetic particles are also relevant for multiple applications, from targeted drug delivery to the design of self-healing materials. Self-propulsion relies on the force transfer to the surrounding. While self-propelled swimming in the bulk of liquids is fairly well characterized, many open questions remain in our understanding of self-propelled motion along substrates, such as in the case of crawling cells or related biomimetic objects. How is the force transfer organized and how does it interplay with the deformability of the moving object and the substrate? How do the spatially dependent traction distribution and adhesion dynamics give rise to complex cell behavior? How can we engineer a specific cell response on synthetic compliant substrates? Here we generalize our recently developed model for a crawling cell by incorporating locally resolved traction forces and substrate deformations.The model captures the generic structure of the traction force distribution and faithfully reproduces experimental observations, like the response of a cell on a gradient in substrate elasticity (durotaxis). It also exhibits complex modes of cell movement such as "bipedal" motion. Our work may guide experiments on cell traction force microscopy and substrate-based cell sorting and can be helpful for the design of biomimetic "crawlers" and active and reconfigurable self-healing materials.

All eukaryotic cells rely on the active self-organization of protein filaments to form a responsive intracellular cytoskeleton. The necessity of motility and reaction to stimuli additionally requires pathways that quickly and reversibly change cytoskeletal organization. While thermally driven order-disorder transitions are, from the viewpoint of physics, the most obvious method for controlling states of organization, the timescales necessary for effective cellular dynamics would require temperatures exceeding the physiologically viable temperature range. We report a mechanism whereby the molecular motor myosin II can cause near-instantaneous order-disorder transitions in reconstituted cytoskeletal actin solutions. When motor-induced filament sliding diminishes, the actin network structure rapidly and reversibly self-organizes into various assemblies. Addition of stable cross linkers was found to alter the architectures of ordered assemblies. These isothermal transitions between dynamic disorder and self-assembled ordered states illustrate that the interplay between passive crosslinking and molecular motor activity plays a substantial role in dynamic cellular organization.

The viscosity of a suspension of swimming bacteria is investigated analytically and numerically. We propose a simple model that allows for efficient computation for a large number of bacteria. Our calculations show that long-range hydrodynamic interactions, intrinsic to self-locomoting objects in a viscous fluid, result in a dramatic reduction of the effective viscosity. In agreement with experiments on suspensions of Bacillus subtilis, we show that the viscosity reduction is related to the onset of large-scale collective motion due to interactions between the swimmers. The simulations reveal that the viscosity reduction occurs only for relatively low concentrations of swimmers: Further increases of the concentration yield an increase of the viscosity. We derive an explicit asymptotic formula for the effective viscosity in terms of known physical parameters and show that hydrodynamic interactions are manifested as self-induced noise in the absence of any explicit stochasticity in the system.

We have investigated the consequences of physical aging in thin spin-coated glassy polystyrene films through detailed dewetting studies. A simultaneous and equally fast exponential decay of dewetting velocity, width, and height of the rim with aging time was observed, which is related to a reduction of residual stresses within such films. The temperature dependence of these decay times followed an Arrhenius behavior, yielding an activation energy of 70±6 kJ/mol, on the same order of magnitude as values for the β-relaxation of polystyrene and for relaxations of surface topographical features. Our results suggest that rearrangements at the level of chain segments are sufficient to partially relax frozen-in out-of-equilibrium local chain conformations, i.e., the cause of residual stresses, and they might also be responsible for macroscopic relaxations at polymer surfaces.

Cell movement in vivo is typically characterized by strong confinement and heterogeneous, three-dimensional environments. Such external constraints on cell motility are known to play important roles in many vital processes e.g. during development, differentiation, and the immune response, as well as in pathologies like cancer metastasis. Here we develop a physics-driven three-dimensional computational modeling framework that describes lamellipodium-based motion of cells in arbitrarily shaped and topographically structured surroundings. We use it to investigate the primary in vitro model scenarios currently studied experimentally: motion in vertical confinement, confinement in microchannels, as well as motion on fibers and on imposed modulations of surface topography. We find that confinement, substrate curvature and topography modulate the cell's speed, shape and actin organization and can induce changes in the direction of motion along axes defined by the constraints. Our model serves as a benchmark to systematically explore lamellipodium-based motility and its interaction with the environment.