Moving from discrete events to continuous flow: semantics of continuous Petri nets; correspondence with chemical reaction equations; deriving ordinary differential equations (ODEs); conservation laws, equilibria, numerical solutions and trajectories through phase space. Relating transition rates for discrete events to reaction rates for continuous flow; dependence on reaction stoichiometry.

Some examples, including derivation of Michaelis-Menten semantics.

Thursday’s lecture will be an introduction to *BioPEPA*, followed by Stephen Gilmore on Monday.

*Link:* Slides.

### Homework

Read §§6–9 of Heiner et al., and §§1–4 of Ciocchetta and Hillston, on BioPEPA.

- Monika Heiner, David Gilbert, and Robin Donaldson. Petri Nets for Systems and Synthetic Biology. In
*Formal Methods for Computational Systems Biology*, Lecture Notes in Computer Science 5016, pp. 215–264. Springer-Verlag, 2008. - Federica Ciocchetta and Jane Hillston. Bio-PEPA: A framework for the modelling and analysis of biochemical systems.
*Theoretical Computer Science*, 410(33–34):3065–3084, August 2009.

This earlier paper by Gilbert and Heiner also explains modelling biological processes with continuous Petri nets.

- David Gilbert and Monika Heiner. From Petri nets to differential equations — an integrative approach for biochemical network analysis. In
*Petri Nets and Other Models of Concurrency: Proceedings of ICATPN 2006*, Lecture Notes in Computer Science 4024, pp. 181–200. Springer-Verlag, 2006.