Cell Growth Model with Stochastic Gene Expression Helps Understand the Growth Advantage of Metabolic Exchange and Auxotrophy

Cooperative behaviors are highly prevalent in the wild, but their evolution is not understood. Metabolic flux models can demonstrate the viability of metabolic exchange as cooperative interactions, but steady-state growth models cannot explain why cooperators grow faster.

Predicting an epistasis-rich genotype-phenotype map with a coarse-grained bottom-up model of budding yeast polarity

Accurate 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.

Predicting an epistasis-rich genotype-phenotype map with a coarse-grained bottom-up model of budding yeast polarity

Accurate 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.

INFLUENCE OF MICRO-ENVIRONMENT ON YEAST POPULATION DYNAMICS

Abundance or scarcity of external nutrients is a metabolic trigger, especially for highly proliferative cells such as bacteria, yeasts, parasites or tumors. In presence of oxygen cells usually adopt efficient metabolism in order to maximize energy production yield in poor diet. If nutrient resource increases, a metabolic shift from efficient metabolism (respiration) to inefficient metabolism (fermentation) is reflecting a minimal cost principle of living systems to optimize fitness. This is known as the Crabtree/Warburg effect. Identifying a model that describes the population dynamics of cells and the input growth condition are the goals of this study. Proof of principle has been constructed using a battery of growth experiments on Crabtree-positive yeasts–Saccharomyces under various conditions of glucose in aerobic and micro-aerobic conditions. General cell growth model estimating metabolic shift has been constructed based on an Auto Regressive approach. Keywords: Yeast, Population dynamics, Modeling, Identification

A modeling approach for cell growth based on enzyme kinetics

The enzyme kinetics reaction scheme of single enzyme-sub-strate dynamics, originally proposed by V. Henri, is considered. The system of ODEs induced by the reaction scheme is compared to two approximate models, namely the Michaelis-Menten model and the model of exponential decay. Validity conditions for the Michaelis-Menten model are briefly reviewed. A case specific for ``superefficient enzymes'' is used as a setting for a comparison between the three models via computational experiments. The case study proves the importance of validating the applicability of the approximate model.A novel cell growth model is proposed and analyzed. The approach of model development is to make use of the original Henri enzyme kinetics law in the context of metabolic processes in living cells, namely cell growth. Two approximations corresponding to different cell growth phases are introduced in order to study the model analytically.

A CELL GROWTH MODEL ADAPTED FOR THE MINIMUM CELL SIZE DIVISION

We study a cell growth model with a division function that models cells which divide only after they have reached a certain minimum size. In contrast to the cases studied in the literature, the determination of the steady size distribution entails an eigenvalue that is not known explicitly, but is defined through a continuity condition. We show that there is a steady size distribution solution to this problem.