The Product neutrality function defining genetic interactions emerges from mechanistic models of cell growth

Reviewer #1 (Public review):

Summary:

Detecting unexpected epistatic interactions among multiple mutations requires a robust null expectation - or neutral function - that predicts the combined effects of multiple mutations on phenotype, based on the effects of individual mutations. This study assessed the validity of the product neutrality function, where the fitness of double mutants is represented as the multiplicative combination of the fitness of single mutants, in the absence of epistatic interactions. The authors utilized a comprehensive dataset on fitness, specifically measuring yeast colony size, to analyze epistatic interactions.

The study confirmed that the product function outperformed other neutral functions in predicting the fitness of double mutants, showing no bias between negative and positive epistatic interactions. Additionally, in the theoretical portion of the study, the authors applied a well-established theoretical model of bacterial cell growth to simulate the growth rates of both single and double mutants under various parameters. The simulations further demonstrated that the product function was superior to other functions in predicting the fitness of hypothetical double mutants. Based on these findings, the authors concluded that the product function is a robust tool for analyzing epistatic interactions in growth fitness and effectively reflects how growth rates depend on the combination of multiple biochemical pathways.

Strengths:

By leveraging a previously published extensive dataset of yeast colony sizes for single- and double-knockout mutants, this study validated the relevance of the product function, commonly used in genetics to analyze epistatic interactions. The finding that the product function provides a more reliable prediction of double-mutant fitness compared to other neutral functions offers significant value for researchers studying epistatic interactions, particularly those using the same dataset.

Notably, this dataset has previously been employed in studies investigating epistatic interactions using the product neutrality function. The current study's findings affirm the validity of the product function, potentially enhancing confidence in the conclusions drawn from those earlier studies. Consequently, both researchers utilizing this dataset and readers of previous research will benefit from the confirmation provided by this study's results.

Weaknesses:

This study exhibits several significant logical flaws, primarily arising from the following issues: a failure to differentiate between distinct phenotypes, instead treating them as identical; an oversight of the substantial differences in the mechanisms regulating cell growth between prokaryotes and eukaryotes; and the adoption of an overly specific and unrealistic set of assumptions in the mutation model. Additionally, the study fails to clearly address its stated objective-investigating the mechanistic origin of the multiplicative model. Although it discusses conditions under which deviations occur, it falls short of achieving its primary goal. Moreover, the paper includes misleading descriptions and unsubstantiated reasoning, presented without proper citations, as if they were widely accepted facts. Readers should consider these issues when evaluating this paper. Further details are discussed below.

(1) Misrepresentation of the dataset and phenotypes

The authors analyze a dataset on the fitness of yeast mutants, describing it as representative of the Malthusian parameter of an exponential growth model. However, they provide no evidence to support this claim. They assert that the growth of colony size in the dataset adheres to exponential growth kinetics; in contrast, it is known to exhibit linear growth over time, as indicated in [Supplementary Note 1 of https://doi.org/10.1038/nmeth.1534]. Consequently, fitness derived from colony size should be recognized as a different metric and phenotype from the Malthusian parameter. Equating these distinct phenotypes and fitness measures constitutes a fundamental error, which significantly compromises the theoretical discussions based on the Malthusian parameter in the study.

(2) Misapplication of prokaryotic growth models

The study attempts to explain the mechanistic origin of the multiplicative model observed in yeast colony fitness using a bacterial cell growth model, particularly the Scott-Hwa model. However, the application of this bacterial model to yeast systems lacks valid justification. The Scott-Hwa model is heavily dependent on specific molecular mechanisms such as ppGpp-mediated regulation, which plays a crucial role in adjusting ribosome expression and activity during translation. This mechanism is pivotal for ensuring the growth-dependency of the ribosome fraction in the proteome, as described in [https://doi.org/10.1073/pnas.2201585119]. Unlike bacteria, yeast cells do not possess this regulatory mechanism, rendering the direct application of bacterial growth models to yeast inappropriate and potentially misleading. This fundamental difference in regulatory mechanisms undermines the relevance and accuracy of using bacterial models to infer yeast colony growth dynamics.

If the authors intend to apply a growth model with macroscopic variables to yeast double-mutant experimental data, they should avoid simply repurposing a bacterial growth model. Instead, they should develop and rigorously validate a yeast-specific growth model before incorporating it into their study.

(3) Overly specific assumptions in the theoretical model

The theoretical model in question assumes that two mutations affect only independent parameters of specific biochemical processes, an overly restrictive premise that undermines its ability to broadly explain the occurrence of the multiplicative model in mutations. Additionally, experimental evidence highlights significant limitations to this approach. For example, in most viable yeast deletion mutants with reduced growth rates, the expression of ribosomal proteins remains largely unchanged, in direct contradiction to the predictions of the Scott-Hwa model, as indicated in [https://doi.org/10.7554/eLife.28034]. This discrepancy emphasizes that the Scott-Hwa model and its derivatives do not reliably explain the growth rates of mutants based on current experimental data, suggesting that these models may need to be reevaluated or alternative theories developed to more accurately reflect the complex dynamics of mutant growth.

(4) Lack of clarity on the mechanistic origin of the multiplicative model

The study falls short of providing a definitive explanation for its primary objective: elucidating the "mechanistic origin" of the multiplicative model. Notably, even in the simplest case involving the Scott-Hwa model, the underlying mechanistic basis remains unexplained, leaving the central research question unresolved. Furthermore, the study does not clearly specify what types of data or models would be required to advance the understanding of the mechanistic origin of the multiplicative model. This omission limits the study's contribution to uncovering the biological principles underlying the observed fitness patterns.

Reviewer #2 (Public review):

The paper deals with the important question of gene epistasis, focusing on asking what is the correct null model for which we should declare no epistasis.

In the first part, they use the Synthetic Genetic Array dataset to claim that the effects of a double mutation on growth rate are well predicted by the product of the individual effects (much more than e.g. the additive model). The second (main) part shows this is also the prediction of two simple, coarse-grained models for cell growth.

I find the topic interesting, the paper well-written, and the approach innovative.

One concern I have with the first part is that they claim that:
"In these experiments, the colony area on the plate, a proxy for colony size, followed exponential growth kinetics. The fitness of a mutant strain was determined as the rate of exponential growth normalized to the rate in wild type cells."

There are many works on "range expansions" showing that colonies expand at a constant velocity, the speed of which scales as the square root of the growth rate (these are called "Fisher waves", predicted in the 1940', and there are many experimental works on them, e.g. https://www.pnas.org/doi/epdf/10.1073/pnas.0710150104) If that's the case, the area of the colony should be proportional to growth_rate X time^2 , rather than exp(growth_rate*time), so the fitness they might be using here could be the log(growth_rate) rather than growth_rate itself? That could potentially have a big effect on the results.

Additional comments/questions:

(1) What is the motivation for the model where the effect of two genes is the minimum of the two?

(2) How seriously should we take the Scott-Hwa model? Should we view it as a toy model to explain the phenomenon or more than that? If the latter, then since the number of categories in the GO analysis is much more than two (47?) in many cases the analysis of the experimental data would take pairs of genes that both affect one process in the Scott-Hwa model - and then the product prediction should presumably fail? The same comment applies to the other coarse-grained model.

(3) There are many works in the literature discussing additive fitness contributions, including Kaufmann's famous NK model as well as spin-glass-type models (e.g. Guo and Amir, Science Advances 2019, Reddy and Desai, eLife 2021, Boffi et al., eLife 2023) These should be addressed in this context.

(4) The experimental data is for deletions, but it would be interesting to know the theoretical model's prediction for the expected effects of beneficial mutations and how they interact since that's relevant (as mentioned in the paper) for evolutionary experiments. Perhaps in this case the question of additive vs. multiplicative matters less since the fitness effects are much smaller.