Redundancy principle for optimal random search in biology

Abstract

Chemical activation rate is traditionally determined by the diffusion flux into an absorbing ball, as computed by Smoluchowski in 1916. Thus the rate is set by the mean first passage time (MFPT) of a Brownian particle to a small target. This paradigm is shifted in this manuscript to set the time scale of activation in cellular biology to the mean time of the first among many arrivals of particles at the activation site. This rate is very different from the MFPT and depends on different geometrical parameters. The shift calls for the reconsideration of physical modeling such as deterministic and stochastic chemical reactions based on the traditional forward rate, especially for fast activation processes occurring in living cells. Consequently, the biological activation time is not necessarily exponential. The new paradigm clarifies the role of population redundancy in accelerating search processes and in defining cellular-activation time scales. This is the case, for example, in cellular transduction or in the nonlinear dependence of fertilization rate on the number of spermatozoa. We conclude that statistics of the extreme set the new laws of biology, which can be very different from the physical laws derived for individuals.