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IMCM starts at top level with a clear goal for the cell: To find a passable migration path within the complex environment. This environment contains opportunities (HSs) as well as hindrances (EOs), and it requires some minimal intelligence to find a solution to this problem.
In such situations, nature often reverts to the evolutionary trial-and-error method: Create a random variety of proposals, evaluate them, then keep the good and reject the bad ones.
Within the cytoskeleton, to provide a known example, the spatial arrangement of microtubuli (MT) is not static, but subject to ongoing dynamic reorganizations. Even if the overall MT arrangement appears constant over extended periods, the individual microtubuli are building and disintegrating on a shorter time scale. They are growing radially outward from some nucleation center, in random directions. But only those individuals that find a stable anchoring point at the other side are stabilized. The others disassemble more quickly. So the seemingly constant arrangement is just a stationary dynamic state. The same exploratory behavior is found again and again in biology and other self-organizing systems.
It therefore seems reasonable to assume a similar mechanism for the cell migration problem: Protrusions into random directions are "seeking" for hard substrate patches.
During the exploratory phase of a PT, preliminary adhesions are formed with the substrate. Next, the PT is applying increasing contractile forces to the adhesions, in order to evaluate the stiffness of the patches.
In the case of soft substrate, no significant tension will build up in the PT, and the unbalanced contractile force will simply pull back the PT to the cell body. But on hard substrate, there will develop tension, and this tension can be used as a signal to reinforce the traction strength of the PT. Only such "successful" PTs enter into the mature phase and become stress fibers with a possibly much longer life time.
Clearly, this scheme requires a kind of molecular tension-sensor, located in the PT-fiber or in the adhesion. Under tension, the sensor changes conformation and activates the biochemical reactions leading to reinforcement of the fibers.
The exploratory mechanism described so far allows the cell to find (even sparsely distributed) hard patches in the close environment and to build stress fibers, firmly connecting the cell body with those anchoring patches. In the model, we can also allow for multiple fibers connecting to the same hard substrate patch (One often observes parallel bundles of fibers).
However, it is reasonable to assume a maximum number of PT/SF-"slots" for each cell body. So let the rate of formation of new exploratory PTs be proportional to the number of currently available "slots".
If the mature stress fibers would live forever, the cell would end up in a state similar to a tree, firmly rooted to the ground, but not mobile. The existing fibers can still fluctuate in their traction forces, leading to bounded spatial fluctuations of the cell body.
But true cell migration requires that stress fibers have a finite life time and can be replaced by new ones, pulling the cell into other directions. The long time dynamics of mature fibers will be discussed in another post.
Even if the cell can migrate efficiently, thanks to an optimized life time statistics of the mature fibers, the (statistically averaged) migration will still be radially symmetric in a homogeneous and isotropic environment.
In such environments it may be necessary for the cell to have a vague sense of the direction. Let us therefore keep in mind the possibility of some chemotactic mechanism. For the simulation, we could simply assume that the probability of formation of new exploratory PTs is slightly higher in the directions of the chemo-attractant.
Finally, I would like to point out that the above exploratory mechanism needs not to be simulated in detail. For the migration process, the only thing that counts are the surviving, stable stress fibers. Thus, it may be sufficient to ascribe an effective rate for stable stress fiber formation to any of the closeby hard patches (Small problem: They can be shadowed by obstacles), with a global rate proportional to the cell bodie's available number of slots.
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