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].

eGFRD in action
Movie 1. eGFRD in action.


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].


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.


  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)