Neutral network

Abstract: Understanding the relationship between robustness and evolvability is key to understand how living things can withstand mutations, while producing ample variation that leads to evolutionary innovations. Mutational robustness and evolvability, a system's ability to produce heritable variation, harbour a paradoxical tension. On one hand, high robustness implies low production of heritable phenotypic variation. On the other hand, both experimental and computational analyses of neutral networks indicate that robustness enhances evolvability. I here resolve this tension using RNA genotypes and their secondary structure phenotypes as a study system. To resolve the tension, one must distinguish between robustness of a genotype and a phenotype. I confirm that genotype (sequence) robustness and evolvability share an antagonistic relationship. In stark contrast, phenotype (structure) robustness promotes structure evolvability. A consequence is that finite populations of sequences with a robust phenotype can access large amounts of phenotypic variation while spreading through a neutral network. Population-level processes and phenotypes rather than individual sequences are key to understand the relationship between robustness and evolvability. My observations may apply to other genetic systems where many connected genotypes produce the same phenotypes.

Abstract: The distribution of fitness effects of protein mutations is still unknown. Of particular interest is whether accumulating deleterious mutations interact, and how the resulting epistatic effects shape the protein's fitness landscape. Here we apply a model system in which bacterial fitness correlates with the enzymatic activity of TEM-1 beta-lactamase (antibiotic degradation). Subjecting TEM-1 to random mutational drift and purifying selection (to purge deleterious mutations) produced changes in its fitness landscape indicative of negative epistasis; that is, the combined deleterious effects of mutations were, on average, larger than expected from the multiplication of their individual effects. As observed in computational systems, negative epistasis was tightly associated with higher tolerance to mutations (robustness). Thus, under a low selection pressure, a large fraction of mutations was initially tolerated (high robustness), but as mutations accumulated, their fitness toll increased, resulting in the observed negative epistasis. These findings, supported by FoldX stability computations of the mutational effects, prompt a new model in which the mutational robustness (or neutrality) observed in proteins, and other biological systems, is due primarily to a stability margin, or threshold, that buffers the deleterious physico-chemical effects of mutations on fitness. Threshold robustness is inherently epistatic-once the stability threshold is exhausted, the deleterious effects of mutations become fully pronounced, thereby making proteins far less robust than generally assumed.

Abstract: We introduce and analyze a general model of a population evolving over a network of selectively neutral genotypes. We show that the population's limit distribution on the neutral network is solely determined by the network topology and given by the principal eigenvector of the network's adjacency matrix. Moreover, the average number of neutral mutant neighbors per individual is given by the matrix spectral radius. This quantifies the extent to which populations evolve mutational robustness: the insensistivity of the phenotype of mutations. Since the average neutrality is independent of evolutionary parameters---such as, mutation rate, population size, and selective advantage---one can infer global statistics of neutral network topology using simple population data available from in vitro or in vivo evolution. Populations evolving on neutral networks of RNA secondary structures show excellent agreement with out theoretical predictions. Submitted to Proceedings of the National Academy of Science.

Abstract: The fitness landscape captures the relationship between genotype and evolutionary fitness and is a pervasive metaphor used to describe the possible evolutionary trajectories of adaptation. However, little is known about the actual shape of fitness landscapes, including whether valleys of low fitness create local fitness optima, acting as barriers to adaptive change. Here we provide evidence of a rugged molecular fitness landscape arising during an evolution experiment in an asexual population of Saccharomyces cerevisiae. We identify the mutations that arose during the evolution using whole-genome sequencing and use competitive fitness assays to describe the mutations individually responsible for adaptation. In addition, we find that a fitness valley between two adaptive mutations in the genes MTH1 and HXT6/HXT7 is caused by reciprocal sign epistasis, where the fitness cost of the double mutant prohibits the two mutations from being selected in the same genetic background. The constraint enforced by reciprocal sign epistasis causes the mutations to remain mutually exclusive during the experiment, even though adaptive mutations in these two genes occur several times in independent lineages during the experiment. Our results show that epistasis plays a key role during adaptation and that inter-genic interactions can act as barriers between adaptive solutions. These results also provide a new interpretation on the classic Dobzhansky-Muller model of reproductive isolation and display some surprising parallels with mutations in genes often associated with tumors.