Oct 6, 2014

Scaling properties of evolutionary paths in a biophysical model of protein adaptation

Michael Manhart, Alexandre V. Morozov


The enormous size and complexity of genotypic sequence space frequently requires consideration of coarse-grained sequences in empirical models. We develop scaling relations to quantify the effect of this coarse-graining on properties of fitness landscapes and evolutionary paths. We first consider evolution on a simple Mount Fuji fitness landscape, focusing on how the length and predictability of evolutionary paths scale with the coarse-grained sequence length and number of alleles. We obtain simple scaling relations for both the weak- and strong-selection limits, with a non-trivial crossover regime at intermediate selection strengths. We apply these results to evolution on a biophysical fitness landscape designed to describe how proteins evolve new binding interactions while maintaining their folding stability. We combine numerical calculations for coarse-grained protein sequences with the scaling relations to obtain quantitative properties of the model for realistic binding interfaces and a full amino acid alphabet.

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Mentioned in this Paper

Pathological Fracture
Protein-Protein Interaction
Binding (Molecular Function)
Amino Acid [EPC]

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