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In order to probe the fundamental principles that govern protein evolution, we use a minimalist model of proteins to provide a mapping from genotype to phenotype. The model is based on physically realistic forces of protein folding and includes an explicit definition of protein function. Thus, we can find the fitness of a sequence from its ability to fold to a stable structure and perform a function. We study the fitness landscapes of these functional model proteins, that is, the set of all sequences mapped on to their corresponding fitnesses and connected to their one mutant neighbors. Through population dynamics simulations we directly study the influence of the nature of the fitness landscape on evolution. Populations are observed to move to a steady state, the distribution of which can often be predicted prior to the population dynamics simulations from the nature of the fitness landscape and a quantity analogous to a partition function. In this paper, we develop a scheme for predicting the steady-state population on a fitness landscape, based on the nature of the fitness landscape, thereby obviating the need for explicit population dynamics simulations and providing some insight into the impact on molecular evolution of the nature of fitness landscapes. Poor predictions are indicative of fitness landscapes that consist of a series of weakly connected sublandscapes. [ABSTRACT FROM AUTHOR]

The mapping of phenotype onto genotype for a set of functional model proteins is accomplished by exhaustive enumeration on a three-dimensional diamond lattice. Chains of up to 25 monomers are investigated and their evolution characterized. The model is used to investigate the origins of designability. Highly designable functional model protein structures possess contact maps that have a relatively little commonality with other physically allowed contact maps. Although the diamond lattice has the same coordination number as the square lattice, differences between three-dimensional and two-dimensional functional model proteins are observed. One difference is the lower frequency of structures of low designability on the three-dimensional lattice. In other respects, the conclusions drawn from previous studies using the square lattice remain valid in three dimensions. For example, we observe the tendency for longer chains to form larger networks of sequences with greater stability to mutation. We identify various topographical characteristics of the landscapes: evolutionary bottlenecks bridge otherwise unconnected networks, and hub sequences allow rapid movement between the different neutral networks. The diversity of landscapes that arises from even a minimalist model suggests that real proteins have a rich variety of evolutionary landscapes. [ABSTRACT FROM AUTHOR]