AbstractAccurate phenotype prediction based on genotypical information has numerous societal applications, such as design of useful crops of cellular factories. However, the prevalence of epistasis, a phenomenon that prevents many biological systems to perform in accordance with the sum of its parts, necessitates modelling the complex path between genotype and phenotype. Defining intermediate levels in this path reduces the complexity of prediction, and may also elucidate the phenotype coupling to other levels by evolution. Inconveniently, the latter requires definitions that maintain biophysical justification from the bottom-up, which conflicts with tractability. By means of a cell growth model, we exemplify a resolution for this conflict by polarization of Cdc42p in budding yeast, a process requiring clustering of active Cdc42p to one zone on the membrane and known to generate ample epistasis. Concretely, our model parsimoniously encompasses constant membrane area growth, stochastic Cdc42p turnover and a simple, justifiable polarity rule we define as the ‘mesotype’. Through intuitively interpretable simulations, we describe previously documented, yet puzzling epistasis inside the polarity module. Moreover, we generate evolutionary relevant predictions e.g., on environmental perturbations, which are general enough to apply to other systems. We quantify how poor growth medium can equalize fitness differentials and enables, otherwise very distinct, evolutionary paths. For example, the fitness of the crippled Δbem1 relative to WT can easily be raised from 0.2 to above 0.95. Finally, we can extend our predictions on epistasis to other modules. We determine that modelled epistasis predictions only add predictive value when functional information of the involved modules is included. This inspires a road-map towards modelling the bidirectional genotype-phenotype map for other model systems with abundant interactions, where the intermediate levels reveal targets that evolution can optimize and facilitate a biophysical justifiable incorporation of epistasis.Author summaryEfforts to understand how traits follow from genes facilitate a broad range of applications. For example, crops can be engineered faster to better resist drought, salt and heat stress, and medicines can be better tailored to individuals. Unfortunately, the path from genes to traits can generally involve a complex interplay of hundreds of genes and gene products whose individual contributions can be heavily context-dependent. In this work, we provide the proof-of-concept in a relatively simple system for a road-map towards elucidating this path. We have constructed a cell growth model for budding yeast, only involving simple rules on membrane growth, protein production and centrally, polarity, the process where yeast chooses the future division site. Despite the simplicity, the polarity rule is fully justifiable from underlying biophysics. Model simulations show good accordance with formerly puzzling traits, and also predict the ease with which the environment can change evolutionary paths. While lab conditions may prohibit the emergence of certain polarity mutations, this becomes much more feasible ‘in the wild’. The tractable model nature allows us to extrapolate the context dependence of mutational effects beyond polarity, showing that this method for understanding trait generation also helps to elucidate protein evolution.
EIGENFUNCTIONS ARISING FROM A FIRST-ORDER FUNCTIONAL DIFFERENTIAL EQUATION IN A CELL GROWTH MODEL