Stochastic Modular Analysis for Gene Circuits: Interplay Among Retroactivity, Nonlinearity, and Stochasticity

Abstract

This chapter introduces a computational analysis method for analyzing gene circuit dynamics in terms of modules while taking into account stochasticity, system nonlinearity, and retroactivity.

• (1) Analog electrical circuit representation for gene circuits: A connection between two gene circuit components is often mediated by a transcription factor (TF) and the connection signal is described by the TF concentration. The TF is sequestered to its specific binding site (promoter region) and regulates downstream transcription. This sequestration has been known to affect the dynamics of the TF by increasing its response time. The downstream effect—retroactivity—has been shown to be explicitly described in an electrical circuit representation, as an input capacitance increase. We provide a brief review on this topic.

• (2) Modular description of noise propagation: Gene circuit signals are noisy due to the random nature of biological reactions. The noisy fluctuations in TF concentrations affect downstream regulation. Thus, noise can propagate throughout the connected system components. This can cause different circuit components to behave in a statistically dependent manner, hampering a modular analysis. Here, we show that the modular analysis is still possible at the linear noise approximation level.

• (3) Noise effect on module input–output response: We investigate how to deal with a module input–output response and its noise dependency. Noise-induced phenotypes are described as an interplay between system nonlinearity and signal noise.

Lastly, we provide the comprehensive approach incorporating the above three analysis methods, which we call “stochastic modular analysis.” This method can provide an analysis framework for gene circuit dynamics when the nontrivial effects of retroactivity, stochasticity, and nonlinearity need to be taken into account.