Modeling biological systems with delays in Bio-PEPA

TL;DR

This paper introduces Bio-PEPAd, an extension of Bio-PEPA that incorporates delays into actions, enabling more accurate modeling of biological systems with non-Markovian dynamics and providing tools for stochastic simulation and differential equation translation.

Contribution

The paper presents Bio-PEPAd, a novel extension of Bio-PEPA that adds delay capabilities while preserving the original syntax, and details methods for simulation and deterministic modeling.

Findings

Bio-PEPAd can model delays in biological systems effectively.

The approach supports stochastic simulation and translation to delay differential equations.

Two biological system examples demonstrate the method's applicability.

Abstract

Delays in biological systems may be used to model events for which the underlying dynamics cannot be precisely observed, or to provide abstraction of some behavior of the system resulting more compact models. In this paper we enrich the stochastic process algebra Bio-PEPA, with the possibility of assigning delays to actions, yielding a new non-Markovian process algebra: Bio-PEPAd. This is a conservative extension meaning that the original syntax of Bio-PEPA is retained and the delay specification which can now be associated with actions may be added to existing Bio-PEPA models. The semantics of the firing of the actions with delays is the delay-as-duration approach, earlier presented in papers on the stochastic simulation of biological systems with delays. These semantics of the algebra are given in the Starting-Terminating style, meaning that the state and the completion of an action are observed as two separate events, as required by delays. Furthermore we outline how to perform stochastic simulation of Bio-PEPAd systems and how to automatically translate a Bio-PEPAd system into a set of Delay Differential Equations, the deterministic framework for modeling of biological systems with delays. We end the paper with two example models of biological systems with delays to illustrate the approach.