Experimental Rugged Fitness Landscape in Protein Sequence Space

Yuuki Hayashi,Yuzuru Husimi,Takuyo Aita,Itaru Urabe,Tetsuya Yomo,Hitoshi Toyota,Suzannah Rutherford

doi:10.1371/journal.pone.0000096

Abstract

The fitness landscape in sequence space determines the process of biomolecular evolution. To plot the fitness landscape of protein function, we carried out in vitro molecular evolution beginning with a defective fd phage carrying a random polypeptide of 139 amino acids in place of the g3p minor coat protein D2 domain, which is essential for phage infection. After 20 cycles of random substitution at sites 12–130 of the initial random polypeptide and selection for infectivity, the selected phage showed a 1.7×104-fold increase in infectivity, defined as the number of infected cells per ml of phage suspension. Fitness was defined as the logarithm of infectivity, and we analyzed (1) the dependence of stationary fitness on library size, which increased gradually, and (2) the time course of changes in fitness in transitional phases, based on an original theory regarding the evolutionary dynamics in Kauffman's n-k fitness landscape model. In the landscape model, single mutations at single sites among n sites affect the contribution of k other sites to fitness. Based on the results of these analyses, k was estimated to be 18–24. According to the estimated parameters, the landscape was plotted as a smooth surface up to a relative fitness of 0.4 of the global peak, whereas the landscape had a highly rugged surface with many local peaks above this relative fitness value. Based on the landscapes of these two different surfaces, it appears possible for adaptive walks with only random substitutions to climb with relative ease up to the middle region of the fitness landscape from any primordial or random sequence, whereas an enormous range of sequence diversity is required to climb further up the rugged surface above the middle region.

Highlights

In vitro molecular evolution can be considered an adaptive walk on a fitness landscape in sequence space, where ‘‘fitness’’ is a quantitative measure of a certain physicochemical property of a biopolymer, such as thermostability or enzymatic activity [1,2]
We present the essence of the theory regarding evolutionary dynamics on the n-k fitness landscape, with its precise derivation and justification reported elsewhere (Aita et al., in preparation)
The probability density of DW with Wt fixed is described by: yðDW jWt pffiffiffiffiffiffiffiffiffiffiffi1ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 2pV 1⁄2DW jWt

Summary

Introduction

In vitro molecular evolution can be considered an adaptive walk on a fitness landscape in sequence space, where ‘‘fitness’’ is a quantitative measure of a certain physicochemical property of a biopolymer, such as thermostability or enzymatic activity [1,2]. The statistical properties of fitness landscapes are regarded as the ‘‘evolutionary attributes’’ of biopolymers, such as proteins Properties such as the number of local peaks and the relative area of the mountainous region to the flat region at the bottom provide insight into the degree of diversity among all possible sequences that must be searched to begin functional evolution, the rate at which a given property evolves, and to what extent an evolutionary process proceeds. The n-k landscape model, in which substitutions occurring on one of n sites affect the contribution of residues at k other sites to fitness, was proposed as a model of the fitness landscape [2,3](Figure 1) In this simple model, the only parameters necessary to determine the properties of the fitness landscape, such as ruggedness and frequency of local peaks, are the value of k and the difference in altitude between the global peak and the foot, defined as the region in the sequence space where random sequences are located. There have been a number of theoretical studies of evolutionary dynamics on both

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Conclusion