Flexible single molecule simulation of reaction-diffusion processes
This article describes a computational methodology for the numerical simulation of the probability density of chemically-reactive Brownian particles at a mesoscopic scale. At the macroscopic scale, chemically-reactive systems are indeed well known to solve a system of reaction rate equations established by the chemical kinetics theory. But this does not take into account the specific spatial mobility of the various species. Various microscopic models exist that keep trace of the trajectory of each molecule. The molecules are typically Brownian ``hard spheres'' that move in space by diffusion in a solvent and then react together following the standard chemical kinetics laws as soon as in close contact. But these models are often computationally expensive. In contrast, the mesoscopic models take into account the specific spatial mobility of the various species and require only the probability density functional (PDF) of the whole system, which, of course, contains less information than the whole family of molecules trajectories. The PDF given by the microscopic model is a solution to the so-called chemical master equation (CME), a difficult high-dimensional problem to solve. Here, one simplifies the problem by considering only two-body reactions. This allows one to perform numerical simulations with an event-driven algorithm like the so-called Green's function reaction dynamics (GFRD). The time-evolution is computed at discrete times on-the-fly. At each discrete time, one forecasts the next time where reactions will occur; this gives the new time step. In between, one considers only the diffusion in space of the molecules using a splitting of the system into subsystems with two or one molecules. (The diffusion problem can be solved almost exactly with analytical solutions in those cases.) The algorithm tells you how to choose the new time step and the subsystems. The authors show a good performance of their method in a number of numerical benchmarks. They also give hints on the relative importance of the errors induced by the various numerical approximations and of the modelling assumptions (comparison with macroscopic and microscopic models in cases where they agree or not).
scientific article; zbMATH DE number 5908112
scientific article