Stochastic Semantics of Signaling as a Composition of Agent-view Automata

In this paper we present a formalism based on stochastic automata to describe the stochastic dynamics of signal transduction networks that are specified by rule-sets. Our formalism gives a modular description of the underlying stochastic process, in the sense that it is a composition of smaller units – agent-views. The view of an agent is an automaton that identifies all local modification changes of that agent, including internal state modifications and (un)binding changes but also – those of interacting agents, that are tested by that agent within a rule. We show how to represent the generator matrix of the underlying Markov process of the whole rule-set as Kronecker sums of the rate matrices belonging to individual view-automata. In the absence of birth the automata are finite, since the number of different contexts of one agent that appear in a rule-set are finite. Moreover, the construction of the automata network is linear in the size of the rule-set. We illustrate the framework by examples that are related to cellular signaling events.