Sandro Stucki

Rate Equations for Graphs

Vincent Danos, Tobias Heindel, Ricardo Honorato-Zimmer, and Sandro Stucki. In Proceedings of the 18th International Conference on Computational Methods in Systems Biology (CMSB 2020), in LNCS/LNBI, volume 12314, pp. 3–26, Springer, 2020.


In this paper, we combine ideas from two different scientific traditions:

  1. graph transformation systems (GTSs) stemming from the theory of formal languages and concurrency, and

  2. mean field approximations (MFAs), a collection of approximation techniques ubiquitous in the study of complex dynamics.

Using existing tools from algebraic graph rewriting, as well as new ones, we build a framework which generates rate equations for stochastic GTSs and from which one can derive MFAs of any order (no longer limited to the humanly computable). The procedure for deriving rate equations and their approximations can be automated. An implementation and example models are available online at We apply our techniques and tools to derive an expression for the mean velocity of a two-legged walker protein on DNA.