Jasmin Fisher, Thomas A. Henzinger, Maria Mateescu, and Nir Piterman
We introduce bounded asynchrony, a notion of concurrency tailored to the modeling of biological cell-cell interactions. Bounded asynchrony is the result of a scheduler that bounds the number of steps that one process can get ahead of other processes; this allows the components of a system to move independently while keeping them coupled. Bounded asynchrony accurately reproduces some experimental observations made about certain cell-cell interactions: its constrained nondeterminism captures the variability observed in cells that, although equally potent, assume distinct fates. Real-life cells are not "scheduled," but we show that distributed real-time behavior can lead to component interactions that are observationally equivalent to bounded asynchrony; this provides a possible mechanistic explanation for the phenomena observed during cell fate specification.
We use model checking to determine cell fates. The nondeterminism of bounded asynchrony causes state explosion during model checking, but partial-order methods are not directly applicable. We present a new algorithm that reduces the number of states that need to be explored: our optimization takes advantage of the bounded-asynchronous progress and the spatially local interactions of components that model cells. We compare our own communication-based reduction with partial-order reduction (on a restricted form of bounded asynchrony), and experiments illustrate that our algorithm leads to significant savings.
Proceedings of the First International Workshop on Formal Methods in Systems Biology (FMSB), Lecture Notes in Computer Science 5054, Springer, 2008, pp. 17-32.