Flux Analysis in Process Models via Causality

TL;DR

This paper introduces a causality-based flux analysis method for stochastic process algebra models of biological systems, enabling resource flow insights similar to ODE flux analysis.

Contribution

It develops a novel approach linking event structures and Petri nets for flux analysis in stochastic process models, with a supporting software tool.

Findings

Extracts causal resource dependencies in simulations

Transforms partial orders for detailed analysis

Demonstrates applicability on biological models

Abstract

We present an approach for flux analysis in process algebra models of biological systems. We perceive flux as the flow of resources in stochastic simulations. We resort to an established correspondence between event structures, a broadly recognised model of concurrency, and state transitions of process models, seen as Petri nets. We show that we can this way extract the causal resource dependencies in simulations between individual state transitions as partial orders of events. We propose transformations on the partial orders that provide means for further analysis, and introduce a software tool, which implements these ideas. By means of an example of a published model of the Rho GTP-binding proteins, we argue that this approach can provide the substitute for flux analysis techniques on ordinary differential equation models within the stochastic setting of process algebras.