Paper #2 titled 'Accurate hybrid stochastic simulation of a coupled system chemical or biochemical reactions' is slated to be in the January 15th issue of the Journal of Chemical Physics.
In short, it's a novel method improving upon the stochastic simulation algorithm of Gillespie as well as previous hybrid methods. It approximates fast reactions as a continuous Markov process (governed by a system of stochastic differential equations) while still representing the slow reactions as a jump Markov process. Partitioning of the system into fast & slow reactions is dynamic and it introduces a new way to quickly monitor when slow reactions occur while still retaining all of their time-dependence on the fast reactions.
On a related note, I saw Dr. Linda Petzold give a presentation today on a partial stochastic equilibrium and its usage to speed up the stochastic simulation algorithm. She only got through maybe half of it because the moderator kept asking boring questions in the middle of her talk (she obviously thought her questions were very insightful and fruitful, but they weren't). Of course, then the moderator proclaims the five minute warning with only 2/3 of the presentation left. Dr. Petzold was much too nice with her. I would have asked to have the conversation after the 15 minute time limit.
For those of you who aren't modelers, the stochastic simulation algorithm is a computational method that simulates the dynamics of a system of bio/chemical reactions. It's especially useful when the numbers of participating molecules are few because alternative simulation methods (like reaction rate equations / ODEs) fail in the 'small' regime. One can use these types of methods to simulate gene expression or signal transduction or the cell cycle. If you can break it down into a system of reactions, then the SSA can simulate it very nicely. The only problem is that it can be very slow in certain circumstances. The challenge now is to identify the circumstances which cause it to slow down and speed it up somehow. Hybrid methods or the partial stochastic equilibrium assumption are two approximations that seek to make the simulation go faster without losing too much accuracy.Posted by sali0090 at November 20, 2004 11:56 PM