On the Accessibility of Adaptive Phenotypes of a Bacterial Metabolic Network

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Abstract
The mechanisms by which adaptive phenotypes spread within an evolving population after their emergence are understood fairly well. Much less is known about the factors that influence the evolutionary accessibility of such phenotypes, a pre-requisite for their emergence in a population. Here, we investigate the influence of environmental quality on the accessibility of adaptive phenotypes of Escherichia coli's central metabolic network. We used an established flux-balance model of metabolism as the basis for a genotype-phenotype map (GPM). We quantified the effects of seven qualitatively different environments (corresponding to both carbohydrate and gluconeogenic metabolic substrates) on the structure of this GPM. We found that the GPM has a more rugged structure in qualitatively poorer environments, suggesting that adaptive phenotypes could be intrinsically less accessible in such environments. Nevertheless, on average ∼74% of the genotype can be altered by neutral drift, in the environment where the GPM is most rugged; this could allow evolving populations to circumvent such ruggedness. Furthermore, we found that the normalized mutual information (NMI) of genotype differences relative to phenotype differences, which measures the GPM's capacity to transmit information about phenotype differences, is positively correlated with (simulation-based) estimates of the accessibility of adaptive phenotypes in different environments. These results are consistent with the predictions of a simple analytic theory that makes explicit the relationship between the NMI and the speed of adaptation. The results suggest an intuitive information-theoretic principle for evolutionary adaptation; adaptation could be faster in environments where the GPM has a greater capacity to transmit information about phenotype differences. More generally, our results provide insight into fundamental environment-specific differences in the accessibility of adaptive phenotypes, and they suggest opportunities for research at the interface between information theory and evolutionary biology. Adaptation involves the discovery by mutation and spread through populations of traits (or “phenotypes”) that have high fitness under prevailing environmental conditions. While the spread of adaptive phenotypes through populations is mediated by natural selection, the likelihood of their discovery by mutation depends primarily on the relationship between genetic information and phenotypes (the genotype-phenotype mapping, or GPM). Elucidating the factors that influence the structure of the GPM is therefore critical to understanding the adaptation process. We investigated the influence of environmental quality on GPM structure for a well-studied model of Escherichia coli's metabolism. Our results suggest that the GPM is more rugged in qualitatively poorer environments and, therefore, the discovery of adaptive phenotypes may be intrinsically less likely in such environments. Nevertheless, we found that the GPM contains large neutral networks in all studied environments, suggesting that populations adapting to these environments could circumvent the frequent “hill descents” that would otherwise be required by a rugged GPM. Moreover, we demonstrated that adaptation proceeds faster in environments for which the GPM transmits information about phenotype differences more efficiently, providing a connection between information theory and evolutionary theory. These results have implications for understanding constraints on adaptation in nature.
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