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Asymptotic Hitting Time for a Simple Evolutionary Model of Protein Folding

Part of: Markov processes Limit theorems Physiological, cellular and medical topics

Published online by Cambridge University Press:  14 July 2016

Véronique Ladret
Véronique Ladret*
Affiliation:
Université Claude Bernard Lyon 1
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Abstract

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We consider two versions of a simple evolutionary algorithm (EA) model for protein folding at zero temperature, namely 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 some c ∈ ℝ+ (0 ≤ c ≤ n). For each algorithm, we prove a law of large numbers, a central limit theorem, and compare the performance of the two models.

Keywords

Evolutionary algorithmMarkov chainprotein folding

MSC classification

Secondary: 60J10: Markov chains (discrete-time Markov processes on discrete state spaces) 60F05: Central limit and other weak theorems 92D20: Protein sequences, DNA sequences 92C05: Biophysics
Type
Research Papers
Information
Journal of Applied Probability , Volume 42 , Issue 1 , March 2005 , pp. 39 - 51
Copyright
© Applied Probability Trust 2005 

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