A Comparison Between Stochastic and Deterministic Models of a Biological Oscillator

Abstract

We look at the behavior of biological oscillators, specifically analyzing a genetic circuit that has oscillatory behavior. Implementing the system in deterministic and stochastic models, we compare the two models using various tests and analyze the effect of stochastic noise on these oscillations. We first investigate the effect of volume and find that at small system volumes, stochastic events cause the system to exhibit more sporadic oscillations and a longer period of oscillation. Next, we develop classification systems for discerning the boundary in the parameter space where the model begins to show oscillations. This is more challenging in the stochastic model, due to persistent fluctuations. We compare different methods of analysis of our deterministic and stochastic models and visualize the conditions which lead to oscillation in each model. We find that the parameter range of oscillation is larger in the stochastic model than in the deterministic model. Finally, we find an increased rate of mRNA production can create greater noise in a system and amplify the difference between a stochastic and deterministic system.