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| - Transition Event Statistics in Genetics and Disordered Kinetics. Theoretical Approaches forExtracting Rate Distributions from Experimental Data
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| - We study the analogies between the theory of rate processes in disordered systems and the overdispersedmolecular clocks in evolutionary biology. A biological “molecular clock” expresses the statistics of the numberof amino acid or nucleotide substitutions during evolution. Random variations of the evolution rates lead tostatistical (overdispersed) molecular clocks which are described by random point processes with randomsubstitution rates. We find that the models for overdispersed molecular clocks are equivalent to those of therandom-rate or random channel models used in disordered kinetics. The number of transport (reaction) eventsin disordered kinetics plays the same role as the number of substitution events in molecular biology. Westudy the connections between the (observed) statistics of the transition events and the statistics of randomrate coefficients and random channels; a unified approach is developed which is valid both in molecularbiology and in disordered kinetics. We develop methods for extracting statistical information about the variationsof rate coefficients from experimental or observed data regarding the fluctuations of the numbers of substitution,reaction, or transport events. For systems with static disorder, the observed statistics of the number of reactionevents, expressed in terms of probabilities at a given time or by the cumulants of the number of transitionevents at a given time, contains the information necessary for evaluating the cumulants or the probabilitydensity of the rate coefficients or the density of states for random channel kinetics. For dynamic disorder thisis not possible; further information about multitime probability distributions of the reaction events is needed.
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