Transitions in genetic toggle switches driven by dynamic disorder in rate coefficients

Optimal transition paths of phenotypic switching in a non-Markovian self-regulation gene expression

Gene expression is a complex biochemical process involving multiple reaction steps, creating molecular memory because the probability of waiting time between consecutive reaction steps no longer follows exponential distributions. What effect the molecular memory has on metastable states in gene expression remains not fully understood. Here, we study transition paths of switching between bistable states for a non-Markovian model of gene expression equipped with a self-regulation. Employing the large deviation theory for this model, we analyze the optimal transition paths of switching between bistable states in gene expression, interestingly finding that dynamic behaviors in gene expression along the optimal transition paths significantly depend on the molecular memory. Moreover, we discover that the molecular memory can prolong the time of switching between bistable states in gene expression along the optimal transition paths. Our results imply that the molecular memory may be an unneglectable factor to affect switching between metastable states in gene expression.

Quantifying the Stability of Coupled Genetic and Epigenetic Switches With Variational Methods

The Waddington landscape provides an intuitive metaphor to view development as a ball rolling down the hill, with distinct phenotypes as basins and differentiation pathways as valleys. Since, at a molecular level, cell differentiation arises from interactions among the genes, a mathematical definition for the Waddington landscape can, in principle, be obtained by studying the gene regulatory networks. For eukaryotes, gene regulation is inextricably and intimately linked to histone modifications. However, the impact of such modifications on both landscape topography and stability of attractor states is not fully understood. In this work, we introduced a minimal kinetic model for gene regulation that combines the impact of both histone modifications and transcription factors. We further developed an approximation scheme based on variational principles to solve the corresponding master equation in a second quantized framework. By analyzing the steady-state solutions at various parameter regimes, we found that histone modification kinetics can significantly alter the behavior of a genetic network, resulting in qualitative changes in gene expression profiles. The emerging epigenetic landscape captures the delicate interplay between transcription factors and histone modifications in driving cell-fate decisions.

Molecular-memory-driven phenotypic switching in a genetic toggle switch without cooperative binding

A genetic toggle switch would involve multistep reaction processes (e.g., complex promoter activation), creating memories between individual reaction events. Revealing the effect of this molecular memory is important for understanding intracellular processes such as cellular decision making. We propose a generalized genetic toggle switch model and use a generalized chemical master equation theory to account for the memory effect. Interestingly, we find that molecular memory can induce bimodality in this memory system although the corresponding memoryless counterpart is not bimodal. This finding implies a plausible alternative mechanism for phenotypic switching that is driven by molecular memory rather than by ultrasensitivity or cooperative binding as shown in previous studies. We also find that unbalanced memories arising from the processes by which mutually inhibiting transcription factors are produced can give rise to asymmetric bimodality without changing the positions of two peaks in the bimodal protein distribution. Given the prevalence of molecular memory in gene regulation, our findings would provide insights into cell fate decisions in growth and development.

Asymmetric noise-induced large fluctuations in coupled systems

Networks of interacting, communicating subsystems are common in many fields, from ecology, biology, and epidemiology to engineering and robotics. In the presence of noise and uncertainty, interactions between the individual components can lead to unexpected complex system-wide behaviors. In this paper, we consider a generic model of two weakly coupled dynamical systems, and we show how noise in one part of the system is transmitted through the coupling interface. Working synergistically with the coupling, the noise on one system drives a large fluctuation in the other, even when there is no noise in the second system. Moreover, the large fluctuation happens while the first system exhibits only small random oscillations. Uncertainty effects are quantified by showing how characteristic time scales of noise-induced switching scale as a function of the coupling between the two coupled parts of the experiment. In addition, our results show that the probability of switching in the noise-free system scales inversely as the square of reduced noise intensity amplitude, rendering the virtual probability of switching an extremely rare event. Our results showing the interplay between transmitted noise and coupling are also confirmed through simulations, which agree quite well with analytic theory.

Information-based measures for logical stochastic resonance in a synthetic gene network under Lévy flight superdiffusion

We investigate the logical information transmission of a synthetic gene network under Lévy flight superdiffusion by an information-based methodology. We first present the stochastic synthetic gene network model driven by a square wave signal under Lévy noise caused by Lévy flight superdiffusion. Then, to quantify the potential of logical information transmission and logical stochastic resonance, we theoretically obtain an information-based methodology of the symbol error rate, the noise entropy, and the mutual information of the logical information transmission. Consequently, based on the complementary "on" and "off" states shown in the logical information transmission for the repressive proteins, we numerically calculate the symbol error rate for logic gates, which demonstrate that the synthetic gene network under Lévy noise can achieve some logic gates as well as logical stochastic resonance. Furthermore, we calculate the noise entropy and the mutual information between the square wave signal and the logical information transmission, which reveal and quantify the potential of logical information transmission and logical stochastic resonance. In addition, we analyze the synchronization degree of the mutual information for the accomplished logical stochastic resonance of two repressive proteins of the synthetic gene network by synchronization variances, which shows that those mutual information changes almost synchronously.