Noise-Induced Spatial Pattern Formation in Stochastic Reaction-Diffusion Systems

This paper is concerned with stochastic reaction-diffusion kinetics governed by the reaction-diffusion master equation. Specifically, the primary goal of this paper is to provide a mechanistic basis of Turing pattern formation that is induced by intrinsic noise. To this end, we first derive an approximate reaction-diffusion system by using linear noise approximation. We show that the approximated system has a certain structure that is associated with a coupled dynamic multi-agent system. This observation then helps us derive an efficient computation tool to examine the spatial power spectrum of the intrinsic noise. We numerically demonstrate that the result is quite effective to analyze noise-induced Turing pattern. Finally, we illustrate the theoretical mechanism behind the noise-induced pattern formation with a H2 norm interpretation of the multi-agent system

Turing Instability in Reaction-Diffusion Systems with a Single Diffuser: Characterization Based on Root Locus

Cooperative behaviors arising from bacterial cell-to-cell communication can be modeled by reaction-diffusion equations having only a single diffusible component. This paper presents the following three contributions for the systematic analysis of Turing instability in such reaction-diffusion systems. (i) We first introduce a unified framework to formulate the reaction-diffusion system as an interconnected multi-agent dynamical system. (ii) Then, we mathematically classify biologically plausible and implausible Turing instabilities and characterize them by the root locus of each agent's dynamics, or the local reaction dynamics. (iii) Using this characterization, we derive analytic conditions for biologically plausible Turing instability, which provide useful guidance for the design and the analysis of biological networks. These results are demonstrated on an extended Gray-Scott model with a single diffuser

Existence of Oscillations in Cyclic Gene Regulatory Networks with Time Delay

This paper is concerned with conditions for the existence of oscillations in gene regulatory networks with negative cyclic feedback, where time delays in transcription, translation and translocation process are explicitly considered. The primary goal of this paper is to propose systematic analysis tools that are useful for a broad class of cyclic gene regulatory networks, and to provide novel biological insights. To this end, we adopt a simplified model that is suitable for capturing the essence of a large class of gene regulatory networks. It is first shown that local instability of the unique equilibrium state results in oscillations based on a Poincare-Bendixson type theorem. Then, a graphical existence condition, which is equivalent to the local instability of a unique equilibrium, is derived. Based on the graphical condition, the existence condition is analytically presented in terms of biochemical parameters. This allows us to find the dimensionless parameters that primarily affect the existence of oscillations, and to provide biological insights. The analytic conditions and biological insights are illustrated with two existing biochemical networks, Repressilator and the Hes7 gene regulatory networks

Systematic Design and Implementation of a Novel Synthetic Fold-Change Detector Biocircuit In Vivo

Biological signaling systems not only detect the absolute levels of the signals, but are also able to sense the fold-changes of the signals. The ability to detect fold-changes provides a powerful tool for biological organisms to adapt to the changes in environment. Here we present the first novel synthetic fold-change detector (FCD) circuit built from ground up in vivo. We systematically designed the FCD circuit in silico, prototyped it in cell-free transcription-translation platform (TX-TL), and eventually implemented it in E. coli cells. We were able to show that the FCD circuit can not only generate pulse-like behavior in response to input, but also produce the same pulse response with inputs of the same fold-change, despite of different absolute signal levels