Hybrid ODE/SSA Model of the Budding Yeast Cell Cycle Control Mechanism with Mutant Case Study

Abstract

The budding yeast cell cycle is regulated by complex and multi-scale control mechanisms, and is subject to inherent noise in a cell, resulted from low copy numbers of species such as critical mRNAs. Conventional deterministic models cannot capture this inherent noise. Although stochastic models can generate simulation results to better represent inherent noise in system dynamics, the stochastic approach is often computationally too expensive for complex systems, which exhibit multiscale features in two aspects: species with different scales of abundances and reactions with different scales of firing frequencies. To address this challenge, one promising solution is to adopt a hybrid approach. It replaces the single mathematical representation of either discrete-stochastic formulation or continuous deterministic formulation with an integration of both methods, so that the corresponding advantageous features in both methods are well kept to achieve a trade-off between accuracy and efficiency. In this work, we propose a hybrid stochastic model that represents the regulatory network of the budding yeast cell cycle control mechanism, respectively, by Gillespie's stochastic simulation algorithm (SSA) and ordinary differential equations (ODEs). Simulation results of our model were compared with published experimental measurement on the budding yeast cell cycle. The comparison demonstrates that our hybrid model well represents many critical characteristics of the budding yeast cell cycle, and reproduces more than 100 phenotypes of mutant cases. Moreover, the model accounts for partial viability of certain mutant strains. The last but not the least, the proposed scheme is shown to be considerably faster in both modeling and simulation than the equivalent stochastic simulation.