Biological signalling and causality

Modelling is becoming a necessity in studying biological signalling pathways, because the combinatorial complexity of such systems rapidly overwhelms intuitive and qualitative forms of reasoning. Yet, this same combinatorial explosion makes the traditional modelling paradigm based on systems of differential equations quickly impractical, if not conceptually inappropriate. As an alternative, we propose an agent-based / concurrent language, named κ, which places causal reasoning front center. We illustrate how κ transparently represents biological knowledge, thereby making models easier to build, discuss, modify, and merge. By taming the combinatorial explosion, circumventing the frustrations of handling opaque systems of equations, and lowering the mathematical threshold for molecular biologists, κ holds promise for making modelling more widely available. The causal structure of processes, is largely absent from systems of differential equations, yet it deeply shapes the dynamical, and perhaps even evolutionary, characteristics of complex distributed biological systems. We illustrate the use of κ and its associated causal analysis by means of a model of EGFR signalling that would overwhelm any traditional approach. The model is obtained by refactoring two extant models based on differential equations. We formalize the colloquial concept of pathway in terms of a special kind of event structure and illustrate how the juxtaposition of it with relationships of conflict between rules can be used to dissect EGFR signalling dynamics