Hybrid stochastic simulations of intracellular reaction-diffusion systems.

With the observation that stochasticity is important in biological systems, chemical kinetics have begun to receive wider interest. While the use of Monte Carlo discrete event simulations most accurately capture the variability of molecular species, they become computationally costly for complex reaction-diffusion systems with large populations of molecules. On the other hand, continuous time models are computationally efficient but they fail to capture any variability in the molecular species. In this study a hybrid stochastic approach is introduced for simulating reaction-diffusion systems. We developed an adaptive partitioning strategy in which processes with high frequency are simulated with deterministic rate-based equations, and those with low frequency using the exact stochastic algorithm of Gillespie. Therefore the stochastic behavior of cellular pathways is preserved while being able to apply it to large populations of molecules. We describe our method and demonstrate its accuracy and efficiency compared with the Gillespie algorithm for two different systems. First, a model of intracellular viral kinetics with two steady states and second, a compartmental model of the postsynaptic spine head for studying the dynamics of Ca+2 and NMDA receptors.

DETERMINING THE GENOTYPE-PHENOTYPE CONNECTION IN SYNTHETIC INDUCIBLE GENE EXPRESSION SYSTEMS

Introduction Gene expression is an important process whereby the genotype controls an individual cell’s phenotype. However, even genetically identical cells display a variety of phenotypes, which may be attributed to differences in their environment. Yet, even after controlling for these two factors, individual phenotypes still diverge due to noisy gene expression. Synthetic gene expression systems allow investigators to isolate, control, and measure the effects of noise on cell phenotypes. I used mathematical and computational methods to design, study, and predict the behavior of synthetic gene expression systems in S. cerevisiae, which were affected by noise. Methods I created probabilistic biochemical reaction models from known behaviors of the tetR and rtTA genes, gene products, and their gene architectures. I then simplified these models to account for essential behaviors of gene expression systems. Finally, I used these models to predict behaviors of modified gene expression systems, which were experimentally verified. Results Cell growth, which is often ignored when formulating chemical kinetics models, was essential for understanding gene expression behavior. Models incorporating growth effects were used to explain unexpected reductions in gene expression noise, design a set of gene expression systems with “linear” dose-responses, and quantify the speed with which cells explored their fitness landscapes due to noisy gene expression. Conclusions Models incorporating noisy gene expression and cell division were necessary to design, understand, and predict the behaviors of synthetic gene expression systems. The methods and models developed here will allow investigators to more efficiently design new gene expression systems, and infer gene expression properties of TetR based systems.