Computer Simulations of Mechano-Chemical Networks Choreographing Actin Dynamics in Cell Motility - Computational Modeling of Biological Systems - page 251

cell membrane, which in turn exerts the force on the barbed ends of actin filaments
and inhibits the growth of filaments. Besides the physical confinement on filaments
and the mechanical impedance on the polymerization of actin filaments, the cell
membrane also plays an important role in the nucleation of actin filaments since
the activation of Arp2/3 relies on signals from receptors on cell membrane. The
cell membrane is also involved in cell adhesion connecting the cytoskeleton to the
extracellular matrix.
To incorporate the cell membrane in mechanical models of actin-based motility,
it is necessary to have a proper representation of the membrane. While membrane
may be modeled as a rigid obstacle against which the branched actin network
grows [ 67 , 68 ], models with simplified flexible membrane offer more realistic
representation of the membrane behavior [ 9 ]. Finite element method has also
been applied to model cell membrane in lamellipodial studies [ 20 , 60 ]. With
the representation of the membrane set, the energy of the membrane including
bending and tension terms could then be written, and the interaction between the
membrane and actin filaments can also be introduced to mimic the force generation
process [ 9 , 35 ]. Since the protruding plasma membrane grows against the external
obstacle, this additional resistive force in turn impact the polymerizing filaments
below the membrane. The effect of external load can be modeled by introducing
an effective external field which acts on the cell membrane [ 35 ]. Higher load from
membrane would slow down the growth of actin filaments.

4.3.2 Re-organization of the Actin Network: From Lamellipodia

to Filopodia

Actin filaments are commonly present in cells, and they may form different struc-
tures including the branched network—lamellipodia and the bundled network—
filopodia, as reviewed in preceding section of this chapter. These different types of
actin networks are mediated by different regulatory proteins: in branched network,
filaments are cross-linked by Arp2/3; while in bundled network, filaments are
connected by actin-binding proteins such as fascin and Ena/VASP. Elucidating how
the different types of actin networks are controlled by physico-chemical factors
is of fundamental significance in understanding the shape and motile behaviors
of cells. Understanding the mechanism of bundling process may help understand
the formation of filopodia from lamellipodia. The convergent elongation model
provides an insightful explanation on the mechanism of filopodia initiation by re-
organization of the dendritic network [ 15 ].
The phase behavior of charged rods in the presence of inter-rod linkers has
been studied theoretically as a model for the equilibrium behavior underlying
the organization of actin filaments by linker proteins in the cytoskeleton [ 92 ].
The phases include bundle-dominant structure, network-dominant structure and
phase containing both types of structures. The reconstitution of the transition from
lamellipodium (2D aster) to filopodium (star) in membrane-free system has also
been carried out: in the motility system containing no fascin, there is spontaneous
formation of aster-like structure; and in the presence of fascin, these asters transition