Landscape ruggedness

In this section, we describe several statistical quantities that capture the gross structural features of the landscape. In Section II.C.l, we discuss the experimental observations of the tolerance of proteins to mutation and describe a correlation between the tolerance and the interresidue coupling. In Section II.C.2, landscape ruggedness is described in terms... 

Fig. 6. The optimal DNA mutation rate as determined from a model that incorporates one-body and two-body fitness contributions (similar to a spin glass). The genetic code is included in the model. The data are for a N = 50 protein. The fitness improvement is the maximum change in fitness averaged over 10,000 landscapes. To compare the relative location of the optima, the curves have been scaled such that the optima are at 1.0. (a) The optimum mutation rate for the uncoupled landscape as the number of mutants screened increases M= 1000 (O), 10,000 ( ), and 50,000 (A), (b) The optimal mutation rate as the landscape ruggedness increases. The number of coupling interactions is 75 (O), 25 ( ), and 0 (A). As the landscape ruggedness increases, the optimal mutation rate decreases. Reprinted from Voigt et ol. (2000a), with permission.

The parameters to be optimized for experimental recombination include the crossover frequency, the number of parents, and the sequence similarity between parents. Additionally, it is important to understand the conditions under which recombination is useful. For all these questions, the optimal parameters represent a balance between the exploration and exploitation capabilities of the search algorithm. Any process that creates more diversity, such as using many parents, very disparate parents, or small fragment sizes, will improve exploration at the cost of exploitation. The balance between these effects will shift according to the landscape ruggedness and the sampling ability of the mutant library. 

Mean-field theory can be used to predict the effects of mutation rate, landscape ruggedness, and parental fitness on the moments of the mutant fitness distribution1791. In this analysis, only the portion of the mutant distribution that is not dead (zero fitness) or parent (unmutated) is considered. The mutant effects are averaged over the transition probabilities. In order to obtain the fitness distribution, two sets of probabilities are required (1) the probabilities P (o) that a particular amino acid identity o exists at a residue i, and (2) the transition probabilities that one amino acid... 

Schlosshauer, M., Baker, D. Realistic protein-protein association rates from a simple diffusional model neglecting long-range interactions, free energy barriers, and landscape ruggedness. Protein Sci. 2004,13,1660-9. 

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