Deterministic and stochastic descriptions of gene expression dynamics

A key goal of systems biology is the predictive mathematical description of gene regulatory circuits. Different approaches are used such as deterministic and stochastic models, models that describe cell growth and division explicitly or implicitly etc. Here we consider simple systems of unregulated (constitutive) gene expression and compare different mathematical descriptions systematically to obtain insight into the errors that are introduced by various common approximations such as describing cell growth and division by an effective protein degradation term. In particular, we show that the population average of protein content of a cell exhibits a subtle dependence on the dynamics of growth and division, the specific model for volume growth and the age structure of the population. Nevertheless, the error made by models with implicit cell growth and division is quite small. Furthermore, we compare various models that are partially stochastic to investigate the impact of different sources of (intrinsic) noise. This comparison indicates that different sources of noise (protein synthesis, partitioning in cell division) contribute comparable amounts of noise if protein synthesis is not or only weakly bursty. If protein synthesis is very bursty, the burstiness is the dominant noise source, independent of other details of the model. Finally, we discuss two sources of extrinsic noise: cell-to-cell variations in protein content due to cells being at different stages in the division cycles, which we show to be small (for the protein concentration and, surprisingly, also for the protein copy number per cell) and fluctuations in the growth rate, which can have a significant impact.Comment: 23 pages, 5 figures; Journal of Statistical physics (2012

Modeling Subtilin Production in Bacillus subtilis Using Stochastic Hybrid Systems

Abstract. The genetic network regulating the biosynthesis of subtilin in Bacillus subtilis is modeled as a stochastic hybrid system. The continuous state of the hybrid system is the concentrations of subtilin and various regulating proteins, whose productions are controlled by switches in the genetic network that are in turn modeled as Markov chains. Some preliminary results are given by both analysis and simulations. 1 Background of Subtilin Production In order to survive, bacteria develop a number of strategies to cope with harsh environmental conditions. One of the survival strategies employed by bacteria is the release of antibiotics to eliminate competing microbial species in the same ecosystem [15]. It is observed that the production of antibiotics in the cells is affected by not only the environmental stimuli (e.g. nutrient levels, aeration, etc.) but also the local population density of their own species [12]. Therefore, the physiological states of the cell and the external signals both contribute to the regulation of antibiotic synthesis. Our study focuses on the subtilin, an antibioti

Noise with memory as a model of lemming cycles

87.23.Cc Population dynamics and ecological pattern formation, 02.50.Ey Stochastic processes, 05.40.Ca Noise,

Approximation of event probabilities in noisy cellular processes

Abstract. Molecular noise, which arises from the randomness of the discrete events in the cell, significantly influences fundamental biological processes. Discrete-state continuous-time stochastic models (CTMC) can be used to describe such effects, but the calculation of the probabilities of certain events is computationally expensive. We present a comparison of two analysis approaches for CTMC. On one hand, we estimate the probabilities of interest using repeated Gillespie simulation and determine the statistical accuracy that we obtain. On the other hand, we apply a numerical reachability analysis that approximates the probability distributions of the system at several time instances. We use examples of cellular processes to demonstrate the superiority of the reachability analysis if accurate results are required.