Multi-scale modelling of biological systems in process algebra

Degasperi, Andrea (2011) Multi-scale modelling of biological systems in process algebra. PhD thesis, University of Glasgow.

Abstract

There is a growing interest in combining different levels of detail of biological phenomena into unique multi-scale models that represent both biochemical details and higher order structures such as cells, tissues or organs.

The state of the art of multi-scale models presents a variety of approaches often tailored around specific problems and composed of a combination of mathematical techniques. As a result, these models are difficult to build, compose, compare and analyse.

In this thesis we identify process algebra as an ideal formalism to multi-scale modelling of biological systems.

Building on an investigation of existing process algebras, we define process algebra with hooks (PAH), designed to be a middle-out approach to multi-scale modelling. The distinctive features of PAH are: the presence of two synchronisation operators, distinguishing interactions within and between scales, and composed actions, representing events that occur at multiple scales. A stochastic semantics is provided, based on functional rates derived from kinetic laws.
A parametric version of the algebra ensures that a model description is compact.

This new formalism allows for: unambiguous definition of scales as processes and interactions within and between scales as actions, compositionality between scales using a novel vertical cooperation operator and compositionality within scales using a traditional cooperation operator, and relating models and their behaviour using equivalence relations that can focus on specified scales.

Finally, we apply PAH to define, compose and relate models of pattern formation and tissue growth, highlighting the benefits of the approach.

• Item Type: Thesis (PhD)
• Qualification Level: Doctoral
• Keywords: multi-scale modelling, biological systems, process algebra, middle-out, composition, relations, congruences, tissue growth
• Subjects: Q Science > QA Mathematics > QA75 Electronic computers. Computer science; Q Science > QA Mathematics
• Colleges/Schools: College of Science and Engineering > School of Computing Science
• Supervisor's Name: Calder, Prof. Muffy
• Date of Award: 2011
• Depositing User: Dr Andrea Degasperi
• Unique ID: glathesis:2011-2946
• Copyright: Copyright of this thesis is held by the author.
• Date Deposited: 19 Oct 2011
• Last Modified: 10 Dec 2012 14:02
• URI: https://theses.gla.ac.uk/id/eprint/2946