The immersed boundary method is a widely used mixed Eulerian/Lagrangian framework for simulating the motion of elastic structures immersed in viscous fluids. In this work, we consider a poroelastic immersed boundary method in which a fluid permeates a porous, elastic structure of negligible volume fraction, and extend this method to include stress relaxation of the material. The porous viscoelastic method presented here is validated for a prescribed oscillatory shear and for an expansion driven by the motion at the boundary of a circular material by comparing numerical solutions to an analytical solution of the Maxwell model for viscoelasticity. Finally, an application of the modelling framework to cell biology is provided: passage of a cell through a microfluidic channel. We demonstrate that the rheology of the cell cytoplasm is important for capturing the transit time through a narrow channel in the presence of a pressure drop in the extracellular fluid.

Cells employing amoeboid motility exhibit repetitive cycles of rapid expansion and contraction and apply coordinated traction forces to their environment. Although aspects of this process are well studied, it is unclear how the cell controls the coordination of cell length changes with adhesion to the surface. Here, we develop a simple model to mechanistically explain the emergence of periodic changes in length and spatiotemporal dynamics of traction forces measured in chemotaxing unicellular amoeba, Dictyostelium discoideum. In contrast to the biochemical mechanisms that have been implicated in the coordination of some cellular processes, we show that many features of amoeboid locomotion emerge from a simple mechanochemical model. The mechanism for interaction with the environment in Dictyostelium is unknown and thus, we explore different cell-environment interaction models to reveal that mechanosensitive adhesions are necessary to reproduce the spatiotemporal adhesion patterns. In this modeling framework, we find that the other motility modes, such as smooth gliding, arise naturally with variations in the physical properties of the surface. Thus, our work highlights the prominent role of biomechanics in determining the emergent features of amoeboid locomotion.

Recent research has elucidated mechanochemical pathways of single cell polarization, but much less is known about collective motility initiation in adhesive cell groups. We used galvanotactic assays of zebrafish keratocyte cell groups, pharmacological perturbations, electric field switches, particle imaging velocimetry, and cell tracking to show that large cell groups initiate motility in minutes toward the cathode. Interestingly, while PI3K-inhibited single cells are biased toward the anode, inhibiting PI3K does not affect the cathode-directed cell group migration. We observed that control groups had the fastest cathode-migrating cell at the front, while the front cells in PI3K-inhibited groups were the slowest. Both control and PI3K-inhibited groups rapidly repolarized when the electric field direction was reversed, and the group migration continued after the electric field was switched off. Inhibiting myosin disrupted the cohesiveness of keratocyte groups and abolished the collective directionality and ability to switch direction when the electric field is reversed. Our data are consistent with a model according to which cells in the group sense the electric field individually and mechanical integration of the cells results in coherent group motility.