Inferring genetic interactions from comparative fitness data

Abstract

Darwinian fitness is a central concept in evolutionary biology. In practice, however, it is hardly possible to measure fitness for all genotypes in a natural population. Here, we present quantitative tools to make inferences about epistatic gene interactions when the fitness landscape is only incompletely determined due to imprecise measurements or missing observations. We demonstrate that genetic interactions can often be inferred from fitness rank orders, where all genotypes are ordered according to fitness, and even from partial fitness orders. We provide a complete characterization of rank orders that imply higher order epistasis. Our theory applies to all common types of gene interactions and facilitates comprehensive investigations of diverse genetic interactions. We analyzed various genetic systems comprising HIV-1, the malaria-causing parasite Plasmodium vivax, the fungus Aspergillus niger, and the TEM-family of β-lactamase associated with antibiotic resistance. For all systems, our approach revealed higher order interactions among mutations.

Keywords: computational biology; epistasis; fitness graph; fitness landscape; gene interactions; none; partial order; rank order; systems biology.

Figure 1.. All 24 rank orders of the biallelic two-locus system, where the 16 colored rank orders imply epistasis.

Red (top row) indicates positive epistasis and blue (middle row) negative epistasis.

Figure 2.. (a) A partial fitness order of genotypes.

The rank orders that extend this partial order are orders (9 , 10 , 12 , 13 , 14), and (16) in Figure 1. All of them imply negative epistasis (${\epsilon }_2<0$). (b) A partial order of genotypes with all its total extensions shown on the right. The first extension shown in red implies positive epistasis (${\epsilon }_2>0$), while the second one in black does not.

Figure 3.. For a biallelic two-locus system where the genotype 00 has the lowest fitness, there are four fitness graphs.

The graph (a) is compatible with additive fitness, whereas the remaining graphs imply negative epistasis.

Figure 4.. The fitness graph (a) implies three way epistasis, the graph (b) implies epistasis, but not higher order epistasis, and (c) does not imply epistasis, since all arrows point up.

Figure 5.. Interactions detected from fitness summary statistics and from rank orders.

The horizontal axis is labeled by the four interaction coordinates $u_{110}$, $\mathrm{\dots }$, $u_{111}$ and twenty circuits $a$, $\mathrm{\dots }$, $t$. The boxplots show the distributions of the various interactions induced by the empirical fitness distribution. The red star indicates whether the interaction has been detected by our rank order method. Specifically, a star with vertical coordinate $-1$, 0, and one means negative, no, and positive interaction, respectively.

Figure 6.. The TEM-family of β-lactamase contributes to antibiotic resistance problems in hospitals.

The fitness graph shows a four-locus system consisting of the wild type, TEM-1, the quadruple mutant, TEM-50, and all intermediate mutants, including six clinically found mutants in the TEM family. The mutation M69L corresponds to $1000$, E104K to $0100$, G238S to $0010$, and N276D to $0001$. Growth rates were measured for the 16 genotypes under exposure to the antibiotic FEP Cefepime, and the fitness graph was determined accordingly (Mira et al., 2015). The graph reveals higher order epistasis.

Figure 7.. The fitness graph shows a four-locus system for the filamentous fungus Aspergillus Niger.

The system consists of all combinations of the four individually deleteriouis mutations fwnA1, leuA1, oliC2 and crnB12. The landscape has in total four peaks, labeled $0000,1100,0011$ and $1001$.

Figure 8.. The fitness graph is compatible with the two rank orders (5) and (6).

Figure 9.. An example of an isomorphism.

Here, the allele labels ‘0’ and ‘1’ in the first locus have been interchanged, as well as the second and third loci.

Figure 10.. All 54 fitness graph types.

Those depicted in red imply three-way epistasis.