Splitting Nodes and Linking Channels: A Method for Assembling Biocircuits from Stochastic Elementary Units

TL;DR

This paper introduces a novel method for constructing biocircuits by assembling stochastic elementary units, enabling scalable network design and analysis of signaling pathways with closed-form mean and variance calculations.

Contribution

It presents a diagrammatic approach for building biocircuits from basic stochastic units, facilitating scalable design and analytical tractability of complex biological networks.

Findings

Constructs biocircuits using channels analogous to electric circuits.

Ensures the mean and variance-covariance follow a closed system.

Applicable to designing synthetic pathways and analyzing natural networks.

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.