Last modified: 2014-06-09
Abstract
In this talk I will present a model for cell deformation and cell movement that
couples the mechanical and biochemical properties of the cortical network of
actin _laments with its concentration. Actin is a polymer that can exist either
in _lamentous form (F-actin) or in monometric form (G-actin) (Chen et al., in
Trends Biochem Sci 25:19-23, 2000) and the _lamentous form is arranged in a
paired helix of two proto_laments (Ananthakrishnan et al., in Recent Res Devel
Biophys 5:39-69, 2006). By assuming that cell deformations are a result of the
cortical actin dynamics in the cell cytoskeleton, we consider a continuum math-
ematical model that couples the mechanics of the network of actin _laments
with its biochemical dynamics. Numerical treatment of the model is carried out
using the moving grid _nite element method (Madzvamuse et al., in J Com-
put Phys 190:478-500, 2003). Furthermore, by assuming slow deformations of
the cell, we use linear stability theory to validate the numerical simulation re-
sults close to bifurcation points. Far from bifurcation points, we show that the
mathematical model is able to describe the complex cell deformations typically
observed in experimental results. Our numerical results illustrate cell expansion,
cell contraction, cell translation and cell relocation as well as cell protrusions
in agreement with experimental observations. In all these results, the contrac-
tile tonicity formed by the association of actin _laments to the myosin II motor
proteins is identi_ed as a key bifurcation parameter. Cell migration plays a crit-
ical and pivotal role in a variety of biological and biomedical disease processes
and is important for emerging areas of biotechnology which focus on cellular
transplantation and the manufacture of arti_cial tissues and surfaces, as well as
for the development of new therapeutic strategies for controlling invasive tumor
cells.