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Let us define the birth of a stress fiber as the moment when a protrusion with preliminary adhesions has "passed the traction test" and starts to grow.

In order to have a clear working model to start with, we can assume that the fiber is subject to disassembly processes at a fixed rate R_dis and to re-assembly processes at a variable rate R_ass(t), the latter depending on various factors (to be discussed later). The "size" or "strength" s(t) of the fiber shall change according to

d/dt s(t) = R_ass(t) - R_dis.

The fiber is alive as long as s(t) exceeds some minimum size s_min. When R_ass(t) is smaller than R_dis for a too long period, s(t) falls below s_min and the fiber dies. After this, its remaining material is recycled by the cell and the fiber "slot" becomes available for a new protrusion. If the assembly rate R_ass(t) has some randomly fluctuating component, the resulting life time of each fiber becomes a random variable, too.

If we now remember our main working hypothesis that the cell has the chief goal (is evolutionary optimized) to migrate efficiently in the complex environment, we come to an interesting question:

How should the assembly rate of each fiber j be controlled, or regulated, in order to optimize migration ?

Is it neccessary for the cell to couple the dynamics of different fibers, analogous to the coupled control of legs in a spider ?

The most simple and biologically un-expensive way of "control" would be that the assembly rates of the individual fibers j are mutually independent, randomely fluctuating functions R_ass_j(t). In this case, the question is: Which statistical properties (distribution function, autocorrelation function, etc.) are optimum for efficient migration in environments of given statistical properties.

For reasons that I shall discuss later, I have the hypothesis that R_ass_j(t) with long-time-correlations (i.e. the autocorrelation function decays with delay time as a power law with fractional exponent e) are the optimum choice for the cell.

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