Continuum model of cell adhesion and migration

Abstract

The motility of cells crawling on a substratum has its origin in a thin cell organ called lamella. We present a 2-dimensional continuum model for the lamella dynamics of a slowly migrating cell, such as a human keratinocyte. The central components of the model are the dynamics of a viscous cytoskeleton capable to produce contractile and swelling stresses, and the formation of adhesive bonds in the plasma cell membrane between the lamella cytoskeleton and adhesion sites at the substratum. We will demonstrate that a simple mechanistic model, neglecting the complicated signaling pathways and regulation processes of a living cell, is able to capture the most prominent aspects of the lamella dynamics, such as quasi-periodic protrusions and retractions of the moving tip, retrograde flow of the cytoskeleton and the related accumulation of focal adhesion complexes in the leading edge of a migrating cell. The developed modeling framework consists of a nonlinearly coupled system of hyperbolic, parabolic and ordinary differential equations for the various molecular concentrations, two elliptic equations for cytoskeleton velocity and hydrodynamic pressure in a highly viscous two-phase flow, with appropriate boundary conditions including equalities and inequalities at the moving boundary. In order to analyse this hybrid continuum model by numerical simulations for different biophysical scenarios, we use suitable finite element and finite volume schemes on a fixed triangulation in combination with an adaptive level set method describing the free boundary dynamics.

Computational approaches to substrate-based cell motility

“…[60][61][62][63][64][65][66] For instance, using this method considering different internal cytoskeleton dynamics, the important point has been made that the motility machinery of cells has a certain redundancy: several underlying biological and physical mechanisms (actomyosin contractility; actin polymerisation limited either by G-actin transport or by microtubule-associated vesicle transport; and a model using a simpified regulation mechanism) all can induce cell motility. 32 However, the best agreement with experiments is for a certain combination of all these factors.…”

Quantitative mapping of averaged focal adhesion dynamics in migrating cells by shape normalization

“…To date, it is still unclear how regulated FA assembly and disassembly contribute to this pattern of traction forces. Computational simulations are a promising way of gaining a deeper insight into the interplay between cytoskeleton and FA dynamics and the resulting tractions (Mogilner and Verzi, 2003;Kruse et al, 2006;Kuusela and Alt, 2009). However, theoretical modeling requires structural information and validation based on experimental data.…”

On a poroviscoelastic model for cell crawling

“…It was first considered for modelling cell motility by Dembo et al (1984) and since developed by e.g. Dembo and Harlow (1986); Alt and Dembo (1999); Herant et al (2003); Oliver et al (2005); Rubinstein et al (2005); Zajac et al (2008); Kuusela and Alt (2009);Cogan and Guy (2010) and Kimpton et al (2012). The key advantages of this framework over those discussed above are its ability to: describe polymerization and depolymerization with actin monomers moving out of and into the aqueous cytosol; capture drag between the phases and swelling of the network.…”