Asymptotic hitting time for a simple evolutionary model of protein folding

Details Asymptotic hitting time for a simple evolutionary model of protein folding Asymptotic hitting time for a simple evolutionary model of protein folding

2003-08-25

arxiv.org/abs/math/0308237v1

Mathematics

Probability

Scientific paper

We consider two versions of a simple evolutionary algorithm model for protein folding at temperature zero: the (1+1)-EA on the LeadingOnes problem. In this schematic model, the structure of the protein, which is encoded as a bit-string of length n, is evolved to its native conformation through a stochastic pathway of sequential contact bindings. We study the asymptotic behavior of the hitting time, in the mean case scenario, under two different mutations: the one flip which flips a unique bit chosen uniformly at random in the bit-string, and the Bernoulli flip which flips each bit in the bit-string independently with probability c/n. For each algorithm we prove a law of large numbers, a central limit theorem and compare the performance of the two models.

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