The crux of Green’s Function Reaction Dynamics is to decompose the many-body reaction-diffusion problem into one- and two-body problems that can be solved analytically using Green’s Function, and use these functions to set up an event-driven algorithm1,2,3,4.
The Green’s functions make it possible to make large jumps in time and space when the particles are far apart from each other. Under biologically relevant conditions, GFRD can be up to 6 orders of magnitude faster than brute-force Brownian Dynamics.
The GFRD algorithm is generic and can be applied to a wide variety of reaction-diffusion problems, including those in population dynamics, evolution, and soft-condensed matter physics. The scheme presented here has been specifically designed to simulate biochemical networks. The original version allows the efficient simulation of signal transduction pathways and gene regulation networks in the cytoplasm. Recently we have also implemented reactions at surfaces including membranes, and reactions at, and passive and active transport along, polymers such as microtubules and DNA.
1 Van Zon JS, Ten Wolde PR (2005) Simulating biochemical networks at the particle level in time and space: Green’s Function Reaction Dynamics. Phys Rev Lett, 94: 128103. (doi)
2 Van Zon JS, Ten Wolde PR (2005) Green’s Function Reaction Dynamics: A particle-based approach for simulating biochemical networks in time and space. J Chem Phys, 123: 234910. (doi, arXiv)
3 Takahashi K, Tanase-Nicola S, Ten Wolde PR (2010) Spatio-temporal correlations can drastically change the response of a MAPK pathway. Proc. Natl Acad Sci USA, 107: 2473 — 2478. (doi, arXiv)
4 Opplestrup T, Bulatov VV, Gilmer GH, Kalos MH, Sadigh B (2006) First-passage Monte Carlo algorithm: diffusion without all the hops. Phys Rev Lett, 97:230602. (doi, arXiv)
Movie (ogv, mp4). A movie of eGFRD in action. The large spheres and cylinders are protective domains with one or two particles inside. The plane at the bottom represents a membrane to which particles can bind. The spherical protective domains model the diffusion and reaction between particles in 3D. The flat cylindrical protective domains are used to calculate the diffusion and reaction of particles in the membrane, whereas the bigger cylindrical protective domains are used to model the association of a 3D particle with the membrane. Note that the color red is used to denote the protective domain that will be updated next.