Scalable Simulation of Cellular Signaling Networks

Abstract

Given the combinatorial nature of cellular signalling pathways, where biological agents can bind and modify each other in a large number of ways, concurrent or agent-based languages seem particularly suitable for their representation and simulation [1,2,3,4]. Graphical modelling languages such as κ [5, 6, 7, 8], or the closely related BNG language [9,10,11,12,13,14], seem to afford particular ease of expression. It is unclear however how such models can be implemented. Even a simple model of the EGF receptor signalling network can generate more than $\oldstylenums{10^{23}}$ non-isomorphic species [5], and therefore no approach to simulation based on enumerating species (beforehand, or even on-the-fly) can handle such models without sampling down the number of potential generated species.

We present in this paper a radically different method which does not attempt to count species. The proposed algorothm uses a representation of the system together with a super-approximation of its ‘event horizon’ (all events that may happen next), and a specific correction scheme to obtain exact timings. Being completely local and not based on any kind of enumeration, this algorithm has a per event time cost which is independent of (i) the size of the set of generable species (which can even be infinite), and (ii) independent of the size of the system (ie, the number of agent instances). We show how to refine this algorithm, using concepts derived from the classical notion of causality, so that in addition to the above one also has that the even cost is depending (iii) only logarithmically on the size of the model (ie, the number of rules). Such complexity properties reflect in our implementation which, on a current computer, generates about $\oldstylenums{10^6}$ events per minute in the case of the simple EGF receptor model mentioned above, using a system with $\oldstylenums{10^5}$ agents.