Sequence Evolution Under Constraints: Lessons Learned from Sudoku.

Abstract

The complex structures of all proteins in nature are outcomes of a random walk driven by mutation and selection. Reconstructing the fitness landscape staging this process based on first-principle physical rules or experimental measurements is difficult. In this article we turn the popular Sudoku game into an artificial fitness landscape and use it as a model system to study sequence evolution under constraints. The Sudoku rules, which are human-mind friendly, intertwine a rugged landscape for sequences composed of digits, mimicking the functional constraints felt by a tightly folded protein. Simulated evolution reveals interesting properties of the valley-crossing dynamics on this complex landscape. It is found that (i) the mutation accumulation rate during valley-crossing is constant among different evolutionary pathways and depends on the ruggedness of the landscape; (ii) genetic drift and neutral networks play constructive roles during the process of searching for novel functions; and (iii) under strong selection, gene duplication can speed up the evolution by relaxing, but not completely liberating, the redundant copy from selective pressure. Insights gained from this prototype model may help us understand the evolution of real proteins.