Process Algebra Approaches to Collective Dynamics.

The aim of the Advanced Research Fellowship and associated project (CODA) was to develop formal modelling techniques and supporting infrastructure to study systems in which the collective behaviour emerges as the result of a large number of similar individuals, acting and interacting in a predefined, but stochastic, manner. A new process algebra Bio-PEPA was the vehicle for the research and the primary focus was naturally occuring systems and biological scenarios.

In particular the original objectives of the project were:
* To define a formal modelling technique based on a process algebra that incorporates notions of prob- abilistic choice and stochastic delays. This language will be equipped with a formal semantics, equivalence relations and appropriate model manipulation strategies.
* To systematically investigate the capabilities of Markovian-based modelling techniques to analyse Bio-PEPA models, including discretisations of continuous state space models.
* To explore the use of continuous state space models as an approximation of very large discrete state spaces, via the use of ordinary, random and stochastic differential equations.
* To develop a supporting logic and use this as the underpinning of a high-level query language to aid modellers in formulating queries to be evaluated against Bio-PEPA models.
* To pursue coarse-grained qualitative analysis techniques, based on model structure and seeking to exploit patterns and motifs which may be found.

The project aimed to study the use of system description techniques called process algebras for modelling systems comprised of large populations of interacting objects. Existing approaches focused on modelling individual objects and could not scale well to such populations. Work was done on how such models might be expressed and techniques to analyse their dynamic behaviour. Intracellular processes in molecular biology were taken as a motivating example, where large collections of different proteins interact to create the functioning of the cell.

A new stochastic process algebra, Bio-PEPA, was defined and equipped with a number of analysis techniques. Each of these relied on a different mathematical interpretation of the model description but these interpretations were shown to be the same. The analysis techniques allowed the dynamic behaviour of the system to be studied and predictions made of how it might behave under perturbations. The modelling formalism was applied to a number of biological examples.