A poroelastic model for cell crawling including mechanical coupling between cytoskeletal contraction and actin polymerization

Abstract

Much is known about the biophysical mechanisms involved in cell crawling, but how these processes are coordinated to produce directed motion is not well understood. Here, we propose a new hypothesis whereby local cytoskeletal contraction generates fluid flow through the lamellipodium, with the pressure at the front of the cell facilitating actin polymerization which pushes the leading edge forward. The contraction, in turn, is regulated by stress in the cytoskeleton. To test this hypothesis, finite element models for a crawling cell are presented. These models are based on nonlinear poroelasticity theory, modified to include the effects of active contraction and growth, which are regulated by mechanical feedback laws. Results from the models agree reasonably well with published experimental data for cell speed, actin flow, and cytoskeletal deformation in migrating fish epidermal keratocytes. The models also suggest that oscillations can occur for certain ranges of parameter values.

Cell Migration with Multiple Pseudopodia: Temporal and Spatial Sensing Models

“…There exist at least four main hypotheses that have been largely explored in the last decades: (i) calcium concentration regulates the expansion and the contraction of the actin network through a sol/gel transition (Oster 1984), (ii) actin polymerization triggered by random thermal fluctuations in the cell membrane or in the actin filaments is the main promoter of protrusion (Carlier and Pantaloni 1997;Mogilner and Oster 1996;Theriot and Mitchison 1991), (iii) the extension of the cellular membrane is regulated by specific mechanisms at the molecular scale (Alt and Tranquillo 1995;Lee et al 1993;Mogilner and Rubinstein 2005;Small et al 1993;Stéphanou et al 2004;Veksler and Gov 2007), and (iv) hydrostatic pressure generated by cytoplasmic flows inside the cell induces the protrusion of the membrane (Alt and Tranquillo 1995;Bereiter-Hahn and Lüers 1998;Oster and Perelson 1987;Taber et al 2011;Young and Mitran 2010;Zhu and Skalak 1988). Finally, there are also those models with a significant mechanical component (see review in Carlsson and Sept (2008), Flaherty et al (2007)), even though most of them are 1D or 2D and only few use a 3D finite element formulation Sakamoto et al 2011;Stolarska et al 2009;Taber et al 2011).…”

“…Finally, there are also those models with a significant mechanical component (see review in Carlsson and Sept (2008), Flaherty et al (2007)), even though most of them are 1D or 2D and only few use a 3D finite element formulation Sakamoto et al 2011;Stolarska et al 2009;Taber et al 2011).…”

“…-as in previous works (Borisy and Svitkina 2000;Carlier and Pantaloni 1997;Condeelis 1993;Mogilner and Oster 1996;Theriot and Mitchison 1991), the oscillating protrusion-contraction movement of the cell is assumed to be controlled by the cyclic polymerization/depolymerization of the actin network, which may occur at any site along the cell membrane where the actin filaments are concentrated; -a purely mechanical approach is used to describe the cell behavior as it has been proposed in previous models (Carlsson and Sept 2008;Flaherty et al 2007;Rubinstein et al 2005;Sakamoto et al 2011;Taber et al 2011). Nevertheless, a different mathematical method is applied.…”

Damped and persistent oscillations in a simple model of cell crawling

“…These coefficients influence the magnitude of the pressure gradient, as seen later (equation (4.8) and following); their values do not correspond directly to physical parameters but can be varied to explore the behaviour of the model. The dependence of 'pressure gradient' on relative fluid velocity in equation (4.1) is a lumped-parameter representation of Darcy's law [11]. Very roughly, v d represents the fluid velocity and v the solid velocity of the poroelastic medium.…”

On the Mechanical Interplay Between Intra- and Inter-Synchronization During Collective Cell Migration: A Numerical Investigation

“…As in previous models of single cell migration (Carlsson and Sept 2008;Flaherty et al 2007;Rubinstein et al 2005;Sakamoto et al 2011;Taber et al 2011), we have decided here to only focus on the mechanical aspects of the phenomenon. Such a choice is motivated by the following reasons.…”