Stochastic modelling of biochemical systems of multi-step reactions using a simplified two-variable model

Stochastic modeling of biochemical systems with multistep reactions using state-dependent time delay

To deal with the growing scale of molecular systems, sophisticated modelling techniques have been designed in recent years to reduce the complexity of mathematical models. Among them, a widely used approach is delayed reaction for simplifying multistep reactions. However, recent research results suggest that a delayed reaction with constant time delay is unable to describe multistep reactions accurately. To address this issue, we propose a novel approach using state-dependent time delay to approximate multistep reactions. We first use stochastic simulations to calculate time delay arising from multistep reactions exactly. Then we design algorithms to calculate time delay based on system dynamics precisely. To demonstrate the power of proposed method, two processes of mRNA degradation are used to investigate the function of time delay in determining system dynamics. In addition, a multistep pathway of metabolic synthesis is used to explore the potential of the proposed method to simplify multistep reactions with nonlinear reaction rates. Simulation results suggest that the state-dependent time delay is a promising and accurate approach to reduce model complexity and decrease the number of unknown parameters in the models.

Single-molecule modeling of mRNA degradation by miRNA: Lessons from data

Recent experimental results on the effect of miRNA on the decay of its target mRNA have been analyzed against a previously hypothesized single molecule degradation pathway. According to that hypothesis, the silencing complex (miRISC) first interacts with its target mRNA and then recruits the protein complexes associated with NOT1 and PAN3 to trigger deadenylation (and subsequent degradation) of the target mRNA. Our analysis of the experimental decay patterns allowed us to refine the structure of the degradation pathways at the single molecule level. Surprisingly, we found that if the previously hypothesized network was correct, only about 7% of the target mRNA would be regulated by the miRNA mechanism, which is inconsistent with the available knowledge. Based on systematic data analysis, we propose the alternative hypothesis that NOT1 interacts with miRISC before binding to the target mRNA. Moreover, we show that when miRISC binds alone to the target mRNA, the mRNA is degraded more slowly, probably through a deadenylation-independent pathway. The new biochemical pathway proposed here both fits the data and paves the way for new experimental work to identify new interactions.