Lecture 14: Continuous Petri Nets and Differential Equations

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.

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

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