Prevalent positive epistasis in Escherichia coli and Saccharomyces cerevisiae metabolic networks

Abstract

Epistasis refers to the interaction between genes. Although high-throughput epistasis data from model organisms are being generated and used to construct genetic networks, the extent to which genetic epistasis reflects biologically meaningful interactions remains unclear. We have addressed this question through in silico mapping of positive and negative epistatic interactions amongst biochemical reactions within the metabolic networks of Escherichia coli and Saccharomyces cerevisiae using flux balance analysis. We found that negative epistasis occurs mainly between nonessential reactions with overlapping functions, whereas positive epistasis usually involves essential reactions, is highly abundant and, unexpectedly, often occurs between reactions without overlapping functions. We offer mechanistic explanations of these findings and experimentally validate them for 61 S. cerevisiae gene pairs.

Fig. 1

Functions of E. coli metabolic reactions under the glucose minimal medium. (a) Functions of 255 important reactions in producing 49 biomass constituents. Columns represent reactions and rows represent biomass constituents. (b) Distribution of the number of biomass constituents affected by a reaction.

Fig. 2

Pairwise epistasis and functional association among 255 important reactions in E. coli. (a) An overview of epistasis and functional association among reactions. Both rows and columns represent reactions. Scaled epistasis between reactions is shown in the lower-left triangle by the heat map. Functional association between reactions is presented in the upper-right triangle, where a grey dot is shown when two reactions have overlapping functions. Epistasis and reaction functions are both determined in the glucose minimal medium. (b) Frequency distribution of scaled epistasis between nonessential reactions. (c) Frequency distribution of scaled epistasis between two reactions that include at least one essential reaction. E, essential; N, nonessential. Note the difference in Y-scale between panel b and c.

Fig. 3

Pairwise epistasis and functional association among 212 important reactions in yeast. (a) Frequency distribution of scaled epistasis between nonessential reactions. (b) Frequency distribution of scaled epistasis between two reactions that include at least one essential reaction. E, essential; N, nonessential. Note the difference in Y-scale between panel a and b.

Fig. 4

Epistasis (ε) and scaled epistasis (ε̃) among 17 yeast genes. Circles show ε, whereas squares show ε̃. Blue and red colors indicate positive and negative epistasis, respectively, whereas the areas of the circles and squares are proportional to the absolute values of ε and ε̃, respectively, with the scales given on the top and left sides of each panel. Solid symbols indicate statistically significant epistasis (P < 0.05), whereas open symbols indicate insignificant epistasis. The shaded area in the lower-right corner shows relationships between nonessential genes. Fitness values of strains with genes replaced/inserted by LEU2, relative to the wild-types, are presented on the X-axis. (a) Epistasis among 8 haploinsufficient genes, measured in diploid cells after deletion of one allele per gene. All genes belong to different functional categories with the exception of RPS5 and RPL14A, both of which encode ribosomal proteins. (b) Epistasis among 9 haplosufficient genes, measured in haploid cells after reduction of protein expression of essential genes and deletion of nonessential genes. All genes belong to different functional categories with the exception of GAA1 and GAS1. MET22 and CHO2 are metabolic genes, with FBA-predicted scaled epistasis equal to 1. “-”, double-perturbation cells could not be obtained, likely due to unsuccessful experiments or synthetic lethality. “?”, epistasis could not be measured due to the lack of fitness effect of single perturbations. In Supplementary Figure 5, we explain why here negative epistasis between nonessential genes appears more abundant than expected.