Abstract
BackgroundStochastic genetic switching driven by intrinsic noise is an important process in gene expression. When the rates of gene activation/inactivation are relatively slow, fast, or medium compared with the synthesis/degradation rates of mRNAs and proteins, the variability of protein and mRNA levels may exhibit very different dynamical patterns. It is desirable to provide a systematic approach to identify their key dynamical features in different regimes, aiming at distinguishing which regime a considered gene regulatory network is in from their phenotypic variations.ResultsWe studied a gene expression model with positive feedbacks when genetic switching rates vary over a wide range. With the goal of providing a method to distinguish the regime of the switching rates, we first focus on understanding the essential dynamics of gene expression system in different cases. In the regime of slow switching rates, we found that the effective dynamics can be reduced to independent evolutions on two separate layers corresponding to gene activation and inactivation states, and the transitions between two layers are rare events, after which the system goes mainly along deterministic ODE trajectories on a particular layer to reach new steady states. The energy landscape in this regime can be well approximated by using Gaussian mixture model. In the regime of intermediate switching rates, we analyzed the mean switching time to investigate the stability of the system in different parameter ranges. We also discussed the case of fast switching rates from the viewpoint of transition state theory. Based on the obtained results, we made a proposal to distinguish these three regimes in a simulation experiment. We identified the intermediate regime from the fact that the strength of cellular memory is lower than the other two cases, and the fast and slow regimes can be distinguished by their different perturbation-response behavior with respect to the switching rates perturbations.ConclusionsWe proposed a simulation experiment to distinguish the slow, intermediate and fast regimes, which is the main point of our paper. In order to achieve this goal, we systematically studied the essential dynamics of gene expression system when the switching rates are in different regimes. Our theoretical understanding provides new insights on the gene expression experiments.Electronic supplementary materialThe online version of this article (doi:10.1186/s12918-015-0172-0) contains supplementary material, which is available to authorized users.
Highlights
Stochastic genetic switching driven by intrinsic noise is an important process in gene expression
In the regime when the rates of gene activation/inactivation are relatively small compared with the synthesis/degradation rates of mRNAs and proteins, we found that the effective dynamics can be reduced to independent evolutions on two separate layers
In this paper, we proposed a methodology to distinguish the regime of genetic switching rates from phenotypic variations in a simulation experiment
Summary
Stochastic genetic switching driven by intrinsic noise is an important process in gene expression. Several recent studies discovered strong connections between noise and gene regulation mechanisms through measuring variability in protein and mRNA levels [9, 10]. Both experimental and theoretical results suggested that the switching rates of gene between its active and inactive states have significant effects on the noise of gene expression [11, 12] and are highly responsible to different gene expression dynamics. It is important and desirable to provide an approach which can effectively identify the key dynamical features of gene expression system when switching rates are slow, and to distinguish the regime of gene regulatory networks from different phenotypic variations
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