Interactive simulation: Cell motility through actin-adhesion dynamics
Inge Wortel
The following interactive simulation implements the model from:
Steijn et al (2021). Computational modelling of cell motility modes emerging from
cell-matrix adhesion dynamics. bioRxiv, doi: 10.1101/2021.06.09.447692
About the model
See the preprint for model details, but briefly:
When a cell successfully protrudes and gains a new pixel, that pixel gains an
activity for some time that makes it more likely that this pixel will protrude
again (positive feedback, activity indicated by red-yellow color below).
The duration of the "activity memory" is governed by
maxact, the strength of the positive feedback by λact;
In the protrusive region where local activities are >0.75 x maxact,
adhesive sites can spawn with probability ps. Such adhesive sites
(dark pixels in the simulation below) are
harder for the cell to detach if it wants to retract, so copy attempts into an
adhesion get penalty λadh;
Adhesive patches can also expand and decay independently, at rates governed
by the parameters pe and pd, respectively;
Adhesion to the surface determines how well the cell can translate protrusive
force at the front into actual motion, because higher adhesion prevents "slipping"
and staying in place. The fraction of the cell surface occupied by adhesive sites
therefore modifies λact: the effective λact
starts from a baseline fraction b of its value when there are no adhesions
at all, and reaches its full value only when at least a fraction s of the
cell surface is adhered to the substrate.
Try it yourself
You can use the parameter sliders in the dropdown menu below ("simulation parameters")
to explore how changing them affects cell motility. Yellow to red colors indicate
active pixels with protrusive feedback. Dark patches are adhesions, and the blue line
shows the trajectory of the cell's center of mass over time.
Simulation parameters
Act-model:
λact
Scales the strength of the protrusive feedback in the Act-model.
maxact
"Memory" of the protrusive feedback.
ECM interaction:
λadh
Penalty for copy attempts into a stable adhesion.
ps (x10000)
Probability of spawning a new adhesion in regions with local activity > 0.75 x maxact.
pe (x10000)
Probability of adhesion expanding into empty neighbor site during Eden growth.
pd (x10000)
Probability of deleting an existing adhesion, per adhesion-free neighbor site.
Feedback on protrusive strength:
b (x1000)
Baseline multiplier for λact.
s (x1000)
Fractional adhesive area at which (the multiplier for) λact saturates.
Simulation controls
The random seed only takes effect when you reset ( ).
The same parameters + random seed should yield the exact same output every time.
If you tick "record track", then the cell's center of mass will be tracked
in the 'outputs' menu below.
Seed:
Visualize track: draw every
MCS, remember
MCS.
Outputs
(Data from the simulation, only when 'record track' is ticked above)
Cell tracks:
Suggestions to try:
When either λact or maxact is zero, cells should
stop moving because there is no "protrusive feedback" or "activity memory".
When λadh is very high, cells should stop moving because
their adhesions are anchored so firmly that they are impossible to detach.
The number of adhesion patches can be controlled by
ps, pe, and pd. Higher ps/pe
should lead to more adhesive patches because of higher formation rates, and lowering
pd has the same effect by making existing patches more stable.
ps and pe also control the spatial distribution of adhesions:
when only ps > 0, patches are smaller and more evenly distributed because
existing patches cannot expand. By contrast, when ps is lower and pe
is very high, patches tend to be larger and can accumulate at the rear of the cell,
slowing it down and/or making it "pivot" and turn.
when b = 1 and s = 0 (the default), the cell does not slip on the surface
regardless the number of adhesions. Setting b = 0 and s = 1 should make the
cell dependent on adhesions for motion: at these settings, setting ps/pe
to zero and pd to high values will stop motion.