Matlab and Femlab for simulating actin transport
and viscoelastic lamellipodial deformations
Note: In order to use the code you need
Matlab (ver. 6 or higher) and Femlab (ver. 2.3 or higher)
1.
Distribution of G-actin in the moving cell of constant shape.
Cytoplasmic fluid flow is determined by the porous F-actin mesh.
First, the fluid velocity field is computed using known F-actin density
and retrograde velocity fields. Then, knowing fluid velocity field,
G-actin density
distribution is found by solving reaction-diffusion-advection equation.
FG2WaterCell3_SIAM.m
main file
vel0.m
Matlab
m-file defining the F-actin retrograde velocity field
ggauss.m
auxiliary
m-file required for F-actin density distribution inside the cell
2.
Distribution of G-actin-profilin and G-actin-thymosin in the moving
cell
of constant shape.
Cytoplasmic fluid flow is determined by the porous F-actin density
distribution,
which in its turn is computed from the known F-actin retrograde
velocity field,
F-actin density on the boundary of the cell and disassembly rate.
FGActinWaterCell_SIAM.m
main file
vel0.m
Matlab
m-file defining the F-actin retrograde velocity field
profile.m
Matlab m-file defining the
F-actin density on the cell boundary
Below you see the results of the computations performed with the code -
the
left picture shows the distribution of F-actin and the streamlines of
the
induced water flow. This flow created steady nonuniform density
distribution
of G-actin-profilin and G-actin-thymosin, their total distribution is
shown
on the right picture.
3.
Dynamics of Viscoelastic Compressible Medium (Example: Actin Polymer
Network
in the Cell).
In the low Reynolds numbers approximation the model describing the
dynamics
of compressible non-Newtonian fluid in one dimension may be described
by
a system of three nonlinear equations - one is for the fluid
continuity,
another one is the Stokes type equation for the mommentum (it describes
the
velocity field dynamics affected by both Newtonian (deformation rate
tensor)
and non-Newtonian (stress tensor) components of the fluid. The third
equation
depends on the chosen model for the non-Newtonian stress tensor
dynamics.
In case when the only source of instability lies in the non-zero
external
stress tensor such that the external force applied to the 1D medium is
directed
inside the medium and is linearly proportional to the distance from the
midpoint.
In this case the qualitative dynamics is the following.
At the initial stage the external force induces the shrinking of the
medium,
shrinkage velocity grows with time at this stage (see the left picture
below).
This process leads to continuous growth of the fluid pressure in the
central
part of the medium. This pressure induces the inner force acting
against
the external force, so that the shrinkage velocity decreases (see
the
right picture below) and it tends to zero at exponentially large time.
Compress1DLoop.m
4. You also may need several utilities from COMSOL (makers of
Femlab)
when running the above codes:
femval_stat1.m
(to transfer data from given
one-dimensional FEM structure to another one for stationary problems)
femval_stat.m
(to transfer data
from given two-dimensional FEM structure to another for stationary
problems)
femval_statBnd.m (to
transfer boundary data from given two-dimensional
FEM structure to another)
femval_time.m
(to transfer data from given
two-dimensional FEM structure to another for time-dependent problems)