The nature of epistasis between two mutations depends on genetic background.

(A) Example illustrating how the nature of epistasis between two mutations (red circle and green square) was quantified across all 47 possible genetic backgrounds. For each pair, we calculated the fraction of genomes in which the interaction was classified as positive epistasis (PE), negative epistasis (NE), reciprocal sign epistasis (RSE), single sign epistasis (SSE), other sign epistasis (OSE), or no epistasis. (B–C) Distributions of these fractions across all possible mutation pairs in (B) functional and (C) non-functional backgrounds. Interactions are far more diverse and dynamic in functional backgrounds, whereas in non-functional backgrounds most pairs exhibit no epistasis.

Functionally important sites drive switches in epistasis more often than others.

(A) Schematic of the approach used to measure the impact of a mutation at locus X on the interaction between two other mutations (red circle and green square). For each pair, the six remaining sites (N) were fixed, and the type of epistasis was recorded before and after introducing a mutation at X. Across all 46 genetic backgrounds, we calculated the fraction f of cases in which this mutation altered the nature of epistasis. (B–C) Distributions of f for each locus in (B) functional and (C) non-functional backgrounds. Mutations at positions 4 and 5, which are known to be critical for folA function, cause switches in epistasis far more frequently than other sites.

Synonymous mutations can alter the nature of epistasis between two mutations.

(A) Schematic of the approach: for each pair of mutations (red circle and green square), the codons not directly affected (underlined) were identified, and all possible synonymous substitutions were introduced at these sites. We then assessed whether the type of epistasis between the focal pair changed. (B–C) Distributions of epistasis types and switching frequencies in functional backgrounds. (D–E) Corresponding distributions in non- functional backgrounds. In functional backgrounds, synonymous substitutions frequently altered the nature of epistasis, although less often than non-synonymous substitutions. In non-functional backgrounds, such changes were rare.

The folA fitness landscape exhibits weak patterns of global epistasis, which are absent for synonymous mutations.

(A) Cartoon illustrating global epistasis: the beneficial effect of a mutation decreases as background fitness increases (diminishing returns epistasis). Beyond a pivot point, the same mutation becomes deleterious, and its negative effects increase with higher background fitness (increasing costs epistasis). (B) Empirical test for global epistasis: mutational effects (y-axis) plotted against background fitness (x-axis). A weak but significant negative trend is observed in both low-fitness (R² = 0.1236; left of dotted line) and high-fitness (R² = 0.1284; right of dotted line) backgrounds. Red lines show best linear fits. (C) Synonymous mutations show no such correlation between effect size and background fitness. (D–E) Instead, most synonymous mutations fall into two recurrent patterns. Examples are shown for the synonymous substitution AAA → AAG at position 1 (D) and at position 2 (E). Full plots for all synonymous substitutions are provided in the Supplement.

Only a small fraction of mutations exhibit strong global epistasis.

Among the 108 possible mutations in the folA landscape, only 16 exhibit statistically significant patterns of global epistasis (R² > 0.4). Strikingly, 14 of these are located at nucleotide positions 4 and 5 (highlighted in red boxes), which are functionally critical for folA. Complete statistics for all mutations are provided in Supplementary Table S4.

Most mutations pivot from beneficial to deleterious effects at a common fitness threshold.

Background fitness (y-axis) at which each of the 108 mutations (x-axis) switches from being beneficial to deleterious is shown. The solid black line marks the average pivot fitness (-0.657), while individual bars represent the deviation of each mutation from this mean. More than 80% of mutations (86 out of 108) pivot within the range -0.657 ± 0.0657. The red dotted line indicates the growth rate used in Papkou et al. 40 to distinguish functional and non-functional variants.

Phenotypic DFE captures robust, fitness-dependent patterns.

(A) To define a “phenotypic DFE,” genotypes of near-identical fitness were split into two groups (90% and 10%). The mean DFE of the 90% group was compared with the DFEs of individual genotypes in the 10% group using the Mann–Whitney U test, generating a distribution of p-values. This procedure was repeated across fitness bins. Δ in this work was chosen to be 0.05. (B) Phenotypic DFEs of high-fitness backgrounds were bimodal: one peak centered near neutrality (∼0) and a second comprising deleterious mutations whose magnitude increased with background fitness. (C) Phenotypic DFEs of low-fitness backgrounds were unimodal, with the mean shifting towards more deleterious values as fitness decreased. (D) Fraction of genotypes in each fitness bin whose DFEs differed significantly (p < 0.05) from the phenotypic DFE. As fitness increases, the phenotypic DFE becomes a progressively better predictor of the true DFE.