Simulation of Biochemical Reaction Networks
From PBDN
Contents |
Introduction
Understanding the chemistry of cells is important to our understanding of living things, from bacteria to human beings. In recent years, computer simulation has played an increasingly important rôle in furthering our understanding of biochemical reactions, with applications as far-reaching as the development of new drugs and medical treatments.
Few biochemical reactions are so simple as to permit the derivation of an exact mathematical solution. Common mathematical models of chemical reactions hold very well for a test-tube full of reactants, but break down on the scale of a cell, where the number of interacting molecules may number only in the hundreds. In these cases, stochastic simulation plays a very important rôle.
Stochastic Simulation
Stochastic simulations combine the results of many thousands of individual simulations to produce a result. In this context, an individual simulation is called a trajectory. The more trajectories that contribute to the result, the more accurate it becomes. The error can be estimated mathematically, so we know in advance how many trajectories are needed to get a solution at a desired level of accuracy.
When chemical reactions are simulated in this way using the Stochastic Simulation Algorithm, many tens, even hundreds, of thousands of trajectories are needed to get accurate results, which can take a long time. If the number of trajectories needed to get a desired level of accuracy can be reduced significantly, more comprehensive simulations, and simulations of more complex systems, become feasible.
The animation below shows the refinement of the solution to metabolite-enzyme model as more trajectories are incorporated into the result. It becomes smoother (more accurate) as more are added. By the end of the simulation, almost 100,000 trajectories are used.
In this project 4 different variance reduction techniques, which may reduce the number of trajectories needed to get accurate results, were applied to 2 different chemical models, and the results were analyzed.
Cost of Implementation
Reducing the number of trajectories computed is not the end of the story, however. Implementing any variance reduction technique takes more computation and carries a penalty in running time. For example, if a particular technique halves the number of trajectories needed, but the technique takes twice as long to compute each trajectory, then there is no net gain. If this cost of implementing the particular variance reduction technique exceeds the savings from variance reduction, then the technique is of no practical value.
Results
It was found that all of the techniques investigated have the potential to reduce the number of trajectories needed, but the reduction is modest, and the additional running time needed to implement the technique offsets, or exceeds, any gains from the reduction in the number of trajectories.
In the only case where a very large gain was observed, it was seen for one of the chemical systems tested, but not the other. This means that the general applicability of the technique is questionable.
Detailed Results
Detailed results for each technique are presented on that technique's page:
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