Computer Simulations of Mechano-Chemical Networks Choreographing Actin Dynamics in Cell Motility - Computational Modeling of Biological Systems - page 232

cellular protrusions comprising a bundle of actin filaments [ 1 ]. These filamentous
networks are highly dynamic, where actin polymerization processes and mechanical
interactions continuously remodel the network structure. Actin polymerization
in vivo is regulated spatially and temporally by an intricate web of signaling proteins
and mechano-chemical feedback. Mechanical interactions include, among others,
actin filament buckling, interactions with the cell membrane and adhesion to the
outside environment.
Given the enormous complexity of chemical interactions networks, mechanical
and transport processes governing in vivo actin dynamics, modeling based on
physical principles can be very useful in making sense of sometimes contradictory
experimental results, and perhaps more importantly set theoretical foundations for
making physically reasonable interpretations. Below, we review recent progress on
modeling filopodia and lamellipodia, focusing mainly on simulations and theory at
a single molecule resolution. The latter was historically preceded by macroscopic
description of actin protrusion dynamics, which has played an important role in
formulating the larger framework for understanding cell motility processes. In
general, when macroscopic models work, they often provide elegant conceptual
understanding of the problem, however, they also fail from time to time, where a
recourse to microscopic physics becomes the only solution. A few such examples
are discussed below.
In the following, we first describe general aspects of modeling reaction-diffusion
processes at the cellular scale. It turns out that inherent microscopic randomness
of chemical reactions, which usually averages out on the macroscopic level,
may sometime dominate the behavior of cellular signal transduction networks.
We also briefly describe mechanical processes necessary for modeling cell motility
dynamics. These general mesoscopic modeling sections are followed by discussions
focusing on dynamics of filopodia and lamellipodia, respectively. The emerging
understanding from modeling various actin-based protrusions suggests that the
overall behavior of actin network growth and remodeling dynamics is determined
by a subtle interplay among chemical interactions, transport bottlenecks, and
mechanical feedbacks. The specific nature of this interplay is discussed in sections
on filopodial and lamellipodial dynamics. Finally, various topics in biology and
biophysics of actin networks were thoroughly reviewed in a recent topic edited by
M.-F. Carlier [ 7 ]. The present chapter provides discussion largely complementary
to the contents of this noteworthy volume, which we recommend as further
reading.

2 Mechano-Chemical Networks Regulating Actin Dynamics

Extension and retraction of filopodia and lamellipodia are based on actin poly-
merization and depolymerization processes, which are, in turn, affected by various
regulatory proteins [ 8 ]. Actin filaments ( F-actin ) are asymmetric, and, hence, the
polymerization-depolymerization rates are different on the two ends called the