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Abstract: Modelling is becoming a necessity in studying biological signalling pathways, because the combinatorial complexity of such systems rapidly overwhelms intuitive and qualitative forms of reasonning. Yet, this same combinatorial explosion makes the traditional modelling paradigm based on systems of differential equations impractical. In contrast, agent-based on concurrent languages, such as K or the closely related BioNetGen language, describe biological interactions in terms of rules, thereby avoiding the combinatorial explosion besetting differential equations. Rules are expressed in an intuitive graphical form that transparently represents biological knowledge. In this way, rules become a natural unit of model building, modification, and discussion. We illustrate this with a sizeable example obtained from refactoring two models of EGF receptor that are based on differential equations. An exciting aspect of the agent-based approach is that it naturally lends itself to the identification and analysis of the causal structures that deeply shape the dynamical, and perhaps even evolutionary, charactetistics of complex distributed biological systems. In particular, one can adapt the notions of causality and conflict, familiar from the concurrency theory, to K, our representation language of choice. Using the EGF receptor model as an example, we show how causality enables the formalization of the colloquial concept of pathway and, perhaps more surprisingly, how conflict can be used to dissect the signalling dynamics to obtain a qualitative handle on the range of system behaviours. By taming the combinatorial explosion, and exposing the causal structures and key kinetic junctures in a model, agent- and rule-based representations hold promise for making modelling more powerful, more perspicuous, and of appeal to a wider audience.
@inProceedings{DanosEtAl-CONCUR07,
author = {V.\ Danos and J.\ Feret and W.\ Fontana and R.\ Harmer and J.\ Krivine},
title = {Rule-Based Modelling of Cellular Signalling, invited paper},
editor = {L.\ Caires and V{.}T.\ Vasconcelos},
booktitle = {Proceedings of the Eighteenth International Conference on Concurrency Theory, CONCUR$\,$'2007, Lisbon, Portugal},
address = {Lisbon, Portugal},
series = {Lecture Notes in Computer Science},
volume = {4703},
publisher = {Springer, Berlin, Germany},
pages = {17--41},
month = {3--8 September},
year = {2007},
}