Tuesday, February 24, 2009

IMCM [1]: Cell in a complex environment


I start with a 2D model, but the generalization to 3D is straight forward.

Let the main body of the cell be an elastic ball (viscous properties can be added later) of a certain diameter D_cell. The cell can be squeezed in order to pass through environmental constrictions, but in the relaxed state this is its standard size. Originating from the main cell body, there can grow radial protrusions (PTs). I'll come back to that point soon.

The environment is inhomogeneous. Consider a 2D regular grid of quadratic patches. Each patch can be in any of three different states: Soft substrate (SS), hard substrate (HS), or elastic obstacle (EO).

A cell can freely move parts of its body (which is larger than a single patch) over soft SS patches.

Elastic obstacles, however, produce a local potential barrier (finite range and height, radial symmetric, centered at the respective EO patch). The potential wells of the many individual, randomely distributed EOs add up to a complex potential landscape with tunable parameters. Mathematically, the force between the cell and each individual obstacle is simply a function of the distance between cell center and EO center, and all EO forces add up.

The cell can form stable adhesions only at the hard substrate patches. When a radial cell protrusion finds a HS patch, it forms an initial adhesion there. This stabilizes the protrusion and it has then a chance to develop into a stress fiber (SF).

Some final remarks: It may be advantageous to describe the repulsive EOs by potentials that drop (sharply yet smoothly) at the borders of the obstacle, but continue to decay on a low level until infinity. That way, the total potential landscape of all obstacles is a continuous field and has well-defined minima (in the absence of stress fibers), where the cell will naturally rest.

The formation of stress fibers can be viewed as the self-creation of attractive potentials by the cell, which tend to compensate for the repulsions. So, in order to move, the cell is actively reshaping its surrounding potential landscape in a time-dependent manner.

By the way: The cell can, as another known strategy, actively reduce the height of repulsive potentials by chemically dissolving the obstacles. This effect could also be simulated rather easily.


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