Splitting nodes and linking channels: A method for assembling biocircuits from stochastic elementary units

Abstract

Akin to electric circuits, we construct biocircuits that are manipulated by cutting and assembling channels through which stochastic information flows. This diagrammatic manipulation allows us to create a method which constructs networks by joining building blocks selected so that (a) they cover only basic processes; (b) it is scalable to large networks; (c) the mean and variance-covariance from the Pauli master equation form a closed system and; (d) given the initial probability distribution, no special boundary conditions are necessary to solve the master equation. The method aims to help with both designing new synthetic signalling pathways and quantifying naturally existing regulatory networks.

Hill functions for stochastic gene regulatory networks from master equations with split nodes and time-scale separation

“…which is a simple monomial where the recurrent molecule appears at power n. From a stochastic point of view, the same cascade is described by a master equation where each complex formation node brings a second derivative as in (3). To ensure a closed system of equations at second-order moments, we split each complex formation node [23]. The resulting master equation contains a set of λ i parameters,…”

“…Closing the system of equations at second order is another challenge, which is addressed through the loop-closing (LC) method from Ref. [23]. This method is easily scalable, allowing it to be used for either small or large genetic networks and, specifically for this study, generates stochastic Hill functions in a closed analytical form.…”

“…Details on application of the LC method to different systems, including bistable systems, are presented in Ref. [23].…”