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Mathematical model of galactose regulation and metabolic consumption in yeast

The galactose network is a complex system responsible for galactose metabolism. It has been extensively studied experimentally and mathematically at the unicellular level to broaden our understanding of its regulatory mechanisms at higher order species. Although the key molecular players involved in the metabolic and regulatory processes underlying this system have been known for decades, their interactions and chemical kinetics remain incompletely understood. Mathematical models can provide an alternative method to study the dynamics of this network from a quantitative and a qualitative perspective. Here, we employ such approaches to unravel the main properties of the galactose network, including equilibrium binary and temporal responses, as a way to decipher its adaptation to actively-changing inputs. We combine the two main components of the network; namely, the genetic branch which allows for bistable responses, and a metabolic branch, encompassing the relevant metabolic processes and glucose repressive reactions. We use both computational tools to estimate model parameters based on published experimental data, as well as bifurcation analysis to decipher the properties of the system in various parameter regimes. Our model analysis reveals that the interplay between the inducer (galactose) and the repressor (glucose) creates the bistability regime which dictates the temporal responses of the system. Based on the same bifurcation techniques, we can also explain why the system is robust to genetic mutations and molecular instabilities. These findings may provide experimentalists with a theoretical framework upon which they can determine how the galactose network functions under various conditions.