GFRD decomposes the many-body reaction-diffusion problem into one- and two-body problems that can be solved analytically using Green’s Functions [1,2,3,4]. These Green’s Functions are then employed to set up an event-driven algorithm, which makes it possible to take large jumps in time and space when the particles are far apart from each other. GFRD can be up to 6 orders of magnitude faster than conventional algorithms based on Brownian Dynamics [1].

Movie 1. eGFRD in action.

## Applications

The eGFRD 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.

## eGFRD in all dimensions

The original code to simulate reactions and diffusion in 3D (cytoplasm) has been rewritten in Modern C++, resulting in a very fast simulator. A prototype has been developed that can also simulate systems in 2D (membranes) and 1D (filaments) [5].

## Developers

The eGFRD algorithm was originally developed by the group of Takahashi at the Riken institute in Japan and the group of Ten Wolde at AMOLF in The Netherlands.

## References

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)
5. Sokolowski TR, Paijmans J, Bossen L, Miedema T, Wehrens M, Becker NB, Kaizu K, Takahashi K, Dogterom M, Ten Wolde PR(2019) eGFRD in all dimensions. J Chem Phys, 150: 054108. (doi)