Wednesday, February 25, 2009

IMCM [4]: Why long-time correlated fiber growth rates ?


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).
However, I don't want to insist too much on powerlaws as the optimum strategy. Computer experiments could be used to systematically compare the efficiency of the resulting cell migration in given environments when different statistics for R_ass(t) are used.

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