Luigi Sbailò and Frank Noé, Freie Universität Berlin
"What is... greens function reaction dynamics":
"Particle-based reaction-diffusion simulations have been widely used to reproduce several biological systems. In contrast to other molecular kinetics simulations, the trajectory of all mesoscopic particles is resolved, which provides the finest spatio-temporal resolution at this scale. Mesoscopic particles diffuse according to the Langevin equation, and whenever they get close to each other reactions can happen. The most straightforward approach consists in a brute-force integration of the Langevin equation, where all particles are simultaneously propagated over a fixed integration step.
Unfortunately, a brute-force approach is notoriously inefficient in dilute systems, since, in that case, most of the computational time is spent simulating the free particles diffusion. Simulations of multi-scale systems are also challenging. The choice of the integration step size depends, indeed, on the particles mobility and the fastest particles generally determine the integration step size. Hence, the propagation of slow particles can be forced to integration steps shorter than what they would need.
Green's functions reaction-diffusion (GFRD) algorithms are event-based schemes that directly sample events as the encountering time between two particles. These schemes avoid the simulation of all steps in free-particle diffusion, which results in a tremendous improvement on the CPU performances."