Lecture 13: More Stochastic Kinetics

5 March 2010

More on Gillespie’s algorithm for stochastic simulation, including the remainder of the slides from Gillespie’s invited CMSB talk. Various tau-leaping methods to more efficiently simulate larger systems; concerns about bounding the errors in these approximate techniques. Further approximation with continuous models, still stochastic, and then by deterministic systems of differential equations for even large scales.

This is discussed in Chapter 8 of Wilkinson’s book on stochastic modelling.

You can also read Gillespie’s own papers on this: his original SSA proposal, and a more recent survey of progress since then.

Return of coursework, and discussion of some particular issues.

  • Reachability graph for the repressilator model.
  • Drawing subnets arising from transition and place invariants.
  • Eight minimal place invariants for the ECA synthesis network; invariants for preservation of uridine, saccharide, phosphate and undecaprenyl groups.
  • Logical formulae in LTL, CTL and HML: decoding and coding them.
  • The until connective denotes that the statement will eventually hold; release may not.
  • HML must modality [a]p means that if a happens, p is then true — but it doesn’t say anything about whether a does happen, or is even possible.

Any more questions or answers about the coursework, please post on the comments below.