A mathematical framework for the quantitative analysis of genetic buffering

Genetic buffering plays a pivotal role in orchestrating the relationship between genotype and phenotype in outbred populations. While high-throughput screens have identified many instances of genetic buffering - through the detection of "synthetic lethality" or "synthetic sickness" - a formal and general method for its quantitative analysis across systems is lacking. In this report, an axiomatic mathematical framework that can be used to classify, quantify, and compare buffering relationships between genes is described. Importantly, this methodology employs a ratio scale as its basis, thereby permitting the definition of a novel neutrality model for gene interaction - the "parallel" model - which complements the commonly used "product" model. Evidence supporting the parallel model is provided through the statistical analysis of previously published yeast gene interaction data. This analysis reveals the consistent underestimation of double mutant fitness in strains carrying non-interacting query-array pairings (as predicted by the existence of "parallel" relationships between genes). Moreover, a model incorporating parallel neutrality in the determination of expected double mutant fitness largely corrects the underestimation. Finally, it is shown that simple extensions of this newly developed framework permit the unambiguous definition and classification of gene interactions in a formal, general, and mathematical way. Consequently, the concept of genetic buffering as first conceived by Leland Hartwell becomes a specific case within a comprehensive model of gene interaction.