On the deformability of an empirical fitness landscape by microbial evolution

Abstract

A fitness landscape is a map between the genotype and its reproductive success in a given environment. The topography of fitness landscapes largely governs adaptive dynamics, constraining evolutionary trajectories and the predictability of evolution. Theory suggests that this topography can be deformed by mutations that produce substantial changes to the environment. Despite its importance, the deformability of fitness landscapes has not been systematically studied beyond abstract models, and little is known about its reach and consequences in empirical systems. Here we have systematically characterized the deformability of the genome-wide metabolic fitness landscape of the bacterium Escherichia coli Deformability is quantified by the noncommutativity of epistatic interactions, which we experimentally demonstrate in mutant strains on the path to an evolutionary innovation. Our analysis shows that the deformation of fitness landscapes by metabolic mutations rarely affects evolutionary trajectories in the short range. However, mutations with large environmental effects produce long-range landscape deformations in distant regions of the genotype space that affect the fitness of later descendants. Our results therefore suggest that, even in situations in which mutations have strong environmental effects, fitness landscapes may retain their power to forecast evolution over small mutational distances despite the potential attenuation of that power over longer evolutionary trajectories. Our methods and results provide an avenue for integrating adaptive and eco-evolutionary dynamics with complex genetics and genomics.

Keywords: eco-evolutionary feedbacks; ecologically mediated gene interactions; fitness landscapes; gene × environment × gene interactions; noncommutative epistasis.

Fig. 1.

Measuring deformability in the E. coli metabolic fitness landscape. (A) Schematic depiction of dFBA simulations. Given an input in the form of nutrients, metabolic fluxes through an explicit and empirically curated metabolic model are optimized to maximize the biomass growth yield. The optimal metabolic fluxes produce metabolic byproducts that are released to the external environment, becoming part of future inputs. (B) A subset of genotypes differing from our E. coli metabolic model by a single mutation (an added or deleted reaction), colored according to their effect on fitness in competition with the ancestor (A). (C) Environmental effects of a subset of mutants expressed as the variation in the profile of secreted metabolites compared with the ancestral E. coli genotype (computed as log-modulus transformed difference in the amount of a given secreted molecule; Materials and Methods). Mutant labels are given in Biochemical Genetic and Genomic (BiGG) database notation. (D) Two loci fitness landscapes in the absence of gene–gene interactions in which the fitness effect of each mutation is the same in all genetic backgrounds. The fitness of each genotype was calculated in direct competition with its immediate ancestor. Mutations A and B correspond to the addition of GLYCL_2 (glycine cleavage system) and AIRCr (phosphoribosylaminoimidazole carboxylase), respectively. (E) Two-loci fitness landscapes with gene–gene interactions giving rise to epistasis (ε). Mutations A and B were SO3R (sulfite reductase) and PAPSSH (phosphoadenylylsulfatase), respectively, simulated in a constant environment. (F) Two-loci fitness landscapes in which one of the mutants transforms the environment, leading to cross-feeding toward the double mutant. Mutations A and B correspond to the addition of PAPSSH and HADPCOADH (3-hydroxyadipyl-CoA dehydrogenase). In addition to regular epistasis, this led to a noncommutative epistatic shift (δ = ε_A,B − ε_B,A).

Fig. 2.

Noncommutative epistasis in the evolution of aerobic citrate use in E. coli. (A) Function of the two transporters involved in the innovation of strong aerobic growth on citrate (Cit⁺⁺) in E. coli. CitT is an antiporter that exchanges extracellular citrate for internal C₄-dicarboxylates (e.g., succinate, fumarate, and malate). DctA is a carboxylic acid transporter that imports C₄-dicarboxylates from the extracellular space into the cytoplasm. (B) The two possible mutational trajectories leading to the Cit⁺⁺ trait. If the mutation leading to expression of citT (+citT) occurs first, it will transform the environment leading to cross-feeding toward the double mutant. This should not occur if the dctA overexpression mutation (+dctA) occurs first. (C and D) Simulated (C) and experimentally measured (D) fitness landscapes in the DM25 medium used in the LTEE (Materials and Methods). Experimentally obtained values are reported as mean ± SEM (n = 10).

Fig. 3.

Short-range deformability in E. coli is rare, weak, and directional. (A) Systematic exploration of the second-order mutational neighborhood of E. coli. We exhaustively simulated every possible mutational trajectory starting from the ancestral (A) metabolism and ending in each double mutant. Noncommutative epistasis (δ) was measured for each pair of mutants and was normalized by F_MAX, i.e., the maximal cumulative fitness effect of the double mutant: F_MAX = max[ |F_i^(A) + F_ij⁽ⁱ⁾|, |F_j^(A) + F_ij^(j)| ], where, e.g., F_x^(y) denotes the fitness of mutant x when invading its immediate ancestor y at low frequency (Materials and Methods). (B) Network representation of all noncommutative epistatic pairs. Nodes represent mutations, and two nodes are joined by an edge if δ/F_MAX >0.01 for that pair. Node labels (BiGG database notation) are shown for hubs (mutations with more than four noncommutative interactions). (C) Distribution of deformability for each gene in the network, measured as the number of other genes with which it has a noncommutative epistatic interaction. (D) Strength of all noncommutative epistatic interactions, i.e., the percentage of epistatic pairs with δ/F_MAX > T as a function of T.

Fig. 4.

Long-range deformability of the E. coli metabolic fitness landscape. (A) We performed random walks (length = 1,000 mutations) in genotype space starting from an E. coli ancestor (A; gray) and first passing through a mutant (M; orange) with large environmental effect. (B and C) Fitness of mutants along these random walks was measured in competition with A (gray) in the environment it generates (E_A), as well as in competition with M (orange) in the environment it generates (E_M). In B we show the result for a single example of a random walk. Note that fitness in competition with M is shifted by the difference in fitness between M and A so all observed differences in fitness are due to deformation (for any genotype G, ΔFitness = |F_G^(A) − F_G^(M) − F_M^(A) |). (C) Average ΔFitness at increasing mutational distances from A in over n = 100 random walks (error bars represent SEM; n = 100). (D) Average difference (absolute value) in growth rate between environments E_M and E_A (in grams of dry cell weight × h⁻¹) at varying genotype distances (gray line; shading represents SEM; n = 1,000). In red, we show the predicted difference in growth rates for a null model that assumes independent effects of mutations (Materials and Methods). (E) An example of an adaptive trajectory showing complex genetic interactions in a long-range deformation. The addition of LDH leads to the release of lactate as a by-product. Three additional mutations, ACKr, ATPS, and PFL, are required together for lactate to be used by a descendant genotype.