Here my very hand-waving argument:

When R_ass(t) is long-time correlated, the fiber strength s(t), which is essentially an integral over R_ass(t), has also a power-law autocorrelation function. Since the momentary cell position depends linearly on the strengths s_j(t) of the individual fibers, the cell as a whole will perform a persistent, power-law random walk (i.e. the mean square displacement increases with lagtime as a fractional powerlaw).

So what ?

- First of all, a fractional persistent random walk has actually been observed for migrating cells.

- Second, it has been shown in foraging theory that such non-Brownian walks are optimal search strategies when the targets are sparsely distributed.

- Third, there are simple biochemical reaction networks that produce long-time correlated growth rates R_ass(t).

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