A Hybrid Stochastic Model Of The Budding Yeast Cell Cycle Control Mechanism

The budding yeast cell cycle is regulated by a complex chemical reaction network. Several deterministic models have been proposed to model this control mechanism. However, experimental data exhibit considerable variability from cell to cell during cell growth and division. It is also observed that certain mutant cells are more vulnerable to noise than wild type cells. The observed variability comes from two sources: intrinsic noise coming from fluctuations of molecules and extrinsic noise introduced by variations in the division process. As a result, molecular fluctuations cannot be neglected, and they may significantly affect the behavior of a cell. To accurately model the cell cycle control mechanism, stochastic models are needed.A rigorous solution to this problem is to convert a deterministic model to its stochastic equivalent and apply Gillespie's stochastic simulation algorithm (SSA). But the conversion process is not straightforward and often results in a much larger system. Moreover, the high computational cost of Gillespie's algorithm make it difficult to simulate a practical budding yeast cell cycle model. In this manuscript, we present a hybrid (ODE/SSA) stochastic model for the budding yeast cell cycle. Based on error analysis for multiscale systems and the observation that fluctuations of mRNAs are the primary sources of noise, in this hybrid model the dynamics of mRNAs are simulated by Gillespie's algorithm, while the cell cycle mechanism at the protein level is modeled by ordinary differential equations (ODEs). Numerical experiments, implemented by Haseltine and Rawlings' hybrid simulation algorithm, demonstrate that the hybrid model matches very well with biological experimental data for both wild-type cells and mutant cells in different nutrient media.