Predicting Molecular Evolutionary Trajectories in Principle and in Practice

Abstract

The discrete, digital nature of DNA (deoxyribonucleic acid) defines a large but countable number of mutational trajectories between any two alleles. Even though some set of mutations jointly confer an improvement in an organism's reproductive success, it need not follow that all mutational trajectories to that allele are equivalent in the eyes of evolution by natural selection. To a good approximation, the key question is whether all mutations improve reproductive success in all combinations; if they do not, then some subset (even, possibly all) trajectories will be selectively inaccessible. Mutations that are only conditionally beneficial are said to exhibit sign epistasis, which several recent empirical studies demonstrate is pervasive. Biochemical and biophysical considerations of protein biology are beginning to shed light on the underlying mechanisms of sign epistasis and current theoretical attention is focused on its influence on selectively accessible trajectories in sexual population.

Key concepts:

  • Phenotypic change over evolutionary time must reflect underlying changes in genetic constitution of the population.

  • Under reasonable assumptions, it is possible to enumerate all mutational trajectories a population might follow in the course of evolving from one genetic variant to another.

  • Recent experimental work demonstrates that for several proteins, only a very small fraction of mutational trajectories are accessible to populations evolving under the action of natural selection.

  • The identity of selectively accessible mutational trajectories reflects the underlying biochemistry and biophysics of the protein in question.

Keywords: epistasis; fitness landscapes; molecular evolution; natural selection; population genetics; protein evolution

Figure 1.

Sequence space. Shown here for k=3 variable nucleotides, designated left‐to‐right ‘A’, ‘B’ and ‘C’. Left: We associate a distinct spatial dimension with each mutation (see key), so mutationally adjacent alleles are spatially adjacent. Centre: Representative trajectories from allele abc to allele ABC, named by the order in which mutations appear (reversions designated by lower‐case, simultaneous fixations designated by multiple mutations in a single column). Top‐to‐bottom: a classical trajectory in which mutations fix individually and without reversion, two nonclassical trajectories in which mutations transiently revert, two nonclassical trajectories in which more than one mutation fixes simultaneously, one nonclassical trajectory in which a mutation reverts and two mutations fix simultaneously. Right: The fitness function maps from each allele (indicated by a string of +'s and −'s signalling presence or absence of each mutation) to the reproductive success conferred to the organism (represented by the symbol w). Note that this mapping is sometimes referred as a fitness or adaptive surface or landscape (beginning with Wright, ). However, this usage is mathematically less precise than fitness function and connotations and intuitions based on everyday experience of three‐dimensional surfaces and landscapes can be misleading (e.g. Gavrilets, ).

Figure 2.

Phenotypic decomposition of two β‐lactamase mutations conferring increased drug resistance in terms of catalytic activity and thermodynamic folding stability. M182T exhibits sign epistasis for cefotaxime resistance, because it reduces drug resistance (grey bars) on the wild‐type background but increases it sharply in the presence of G238S. (data from Wang et al., ; Weinreich et al., ). Note that neither catalytic activity nor thermodynamic folding stability exhibit sign epistasis, which instead is the consequence of pleiotropic effects of both mutations on these traits.

Figure 3.

Fisher's geometric model of adaptation for n=2 traits. All combinations of trait values are represented in n‐dimensional space (here, the plane); the optimal value is represented by the point labelled O and an individual labelled X, is displaced from this optimum (as perhaps following an environmental perturbation) by distance d. Fitness is some declining function of d. Mutations may simultaneously influence multiple traits. Left: To be beneficial, a mutation in wild‐type X must yield a phenotype X′ lying within the circle passing through X and centred at O. Thus, the probability that a mutation will be beneficial rises to half as its phenotypic perturbation r drops to zero. Inset: Y represents another organism with fitness equal to that of X. Note, however, that the phenotypically identical mutation exhibits sign epistasis: it is beneficial on X but deleterious on Y. Right: Mutational interactions in TEM‐1 β‐lactamase between catalytic activity and thermodynamic stability in determining cefotaxime resistance (see Figure ), represented qualitatively in Fisher's geometric model.

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Weinreich, Daniel M(Mar 2010) Predicting Molecular Evolutionary Trajectories in Principle and in Practice. In: eLS. John Wiley & Sons Ltd, Chichester. http://www.els.net [doi: 10.1002/9780470015902.a0022174]