High-throughput gene deletion experiments in budding yeast support a Product neutrality function for double mutant fitness.

A. Budding yeast mutant fitness is defined by the exponential growth rate of the number of cells in a colony relative to the growth rate of wild type cells. Schematic illustration of epistasis in growth rate, and of different laws proposed in the literature. λ denotes the growth rate, and W the fitness. B-D. For each double mutant, we plot the residual of the fitness predicted from the indicated model against the fitness of the fittest of the two separate single mutants (maximum single mutant fitness). Dots indicate the median for 10 equally spaced bins between 0.5 and 1. E. Box plots for the distributions of the residuals for the three neutrality functions as a function of the maximum single mutant fitness. Thick line denotes the median, and boxes denote the 25th and 75th percentiles of the distributions. The data plotted here represents a subset of the entire SGA dataset, corresponding to the Deletion Mutant Array (DMA) at 30°C. Figs. S1& S2 report results for the other sub-datasets.

The Product neutrality function describes interactions between genes associated with two distinct biological processes.

A. Schematic illustration of the analysis process. We first select two different GO biological processes and extract the double mutants in the SGA dataset associated with them. Then, we compute the median residual for each pair of biological processes and each neutrality function. B-D. Median residual for the Minimum, Product, and Additive neutrality functions as a function of the maximum single mutant fitness. Each line denotes mutations to a different pair of distinct GO biological processes. The majority of biological process pairs closely follow the Product model.

A bacterial growth model partially supports the Product neutrality function.

A. Schematic of the bacterial growth model by Scott and Hwa. Growth rate is defined by the translation flux, which is itself equal to the metabolic flux. The cell partitions its proteome so as to maximize growth rate. B. Mutations are modeled such that they affect either of the parameters, separately. Values of κt and κn in the mutant are indicated with primes and are sampled from a uniform distribution from 0 to their value in wild type cells. λ indicates the corresponding growth rate. The analytical expression of the double-mutant fitness consists of the product model with a perturbation. C-E. For each sampled double-mutant, we plot the residual of the fitness predicted from the indicated model against the fitness of the fittest of the two separate single mutants (maximum single mutant fitness). Dots indicate the median for 10 equally spaced bins between 0.5 and 1. F. Box plots for the distributions of the residuals for the three models and the model in C as a function of the maximum single mutant fitness. Thick line denotes the median, and boxes denote the upper and lower quartiles of the data. The analytical model in B, named Scott-Hwa and shown in red, is exact.

The Product neutrality function accurately predicts fitness for many pairs of parameters in a more complex cell growth model.

A. Schematic of the growth model from Weiße et al. 2015. This model includes nutrient intake, metabolism, transcription, and translation. B. Schematic of the mutational analysis. For each pair of parameters α and β, mutations are modeled such that they affect either of the parameters, separately. Then, the median residual is computed for each neutrality function and they are subsequently reported for every pair of parameters considered. C-D. For each parameter pair, we report the mean deviation of the simulated double mutants from (C) the Product neutrality function and (D) the analytical expression of the double mutant fitness under the Scott-Hwa model. Only parameter pairs corresponding to two different biological processes are considered. Those corresponding to the same process are greyed out. Parameter pairs involving translation (gmax, Kp) are the ones described best by the Scott-Hwa model while the others are better described by the Product neutrality function.

Nonlinear kinetics drive deviations from the Product neutrality function in the Weiße model.

A. A subset of parameter pairs we analyzed follow the Product model very closely. We derived an analytical approximation of the growth rate and the double mutant fitness for these pairs, and found that the deviation from the product law is governed by nonlinear kinetics. B. In the case of the parameter pair (vt, ns) we show that the deviation from the Product model is driven by the Michaelis-Menten constant θx associated with transcription (see Supporting Information). C. Tuning the value of γ impacts how good of an approximation the Product neutrality function is for this and other parameter pairs (see text). This analysis validates the analytical approximation, and highlights how nonlinear kinetics, in this case Michaelis-Menten kinetics, can drive deviations from the Product neutrality function.