Modelling Biological and Ecological Systems with the Calculus of Wrapped Compartments

TL;DR

The paper introduces the Calculus of Wrapped Compartments, a formal stochastic framework for modeling biological and ecological systems with compartments, membranes, and spatial properties, offering an alternative to differential equations.

Contribution

It extends the calculus with modeling guidelines, spatial handling, and a hybrid simulation algorithm, demonstrated through biological and ecological case studies.

Findings

Effective modeling of compartments and membranes.

Inclusion of spatial properties in the calculus.

Successful case studies in biology and ecology.

Abstract

The modelling and analysis of biological systems has deep roots in Mathematics, specifically in the field of Ordinary Differential Equations. Alternative approaches based on formal calculi, often derived from process algebras or term rewriting systems, provide a quite complementary way to analyse the behaviour of biological systems. These calculi allow to cope in a natural way with notions like compartments and membranes, which are not easy (sometimes impossible) to handle with purely numerical approaches, and are often based on stochastic simulation methods. The Calculus of Wrapped Compartments is a framework based on stochastic multiset rewriting in a compartmentalised setting used for the description of biological and ecological systems. We provide an extended presentation of the Calculus of Wrapped Compartments, sketch a few modelling guidelines to encode biological and ecological interactions, show how spatial properties can be handled within the framework and define a hybrid simulation algorithm. Several applications in Biology and Ecology are proposed as modelling case studies.