dorsal/arxiv
View SchemaGreen's Function Reaction Dynamics: a new approach to simulate biochemical networks at the particle level and in time and space
| Authors | Jeroen S. van Zon, Pieter Rein ten Wolde |
|---|---|
| Categories | |
| ArXiv ID | q-bio/0404002 |
| URL | https://arxiv.org/abs/q-bio/0404002 |
Abstract
Biochemical networks are the analog computers of life. They allow living cells to control a large number of biological processes, such as gene expression and cell signalling. In biochemical networks, the concentrations of the components are often low. This means that the discrete nature of the reactants and the stochastic character of their interactions have to be taken into account. Moreover, the spatial distribution of the components can be of crucial importance. However, the current numerical techniques for simulating biochemical networks either ignore the particulate nature of matter or treat the spatial fluctuations in a mean-field manner. We have developed a new technique, called Green's Function Reaction Dynamics (GFRD), that makes it possible to simulate biochemical networks at the particle level and in both time and space. In this scheme, a maximum time step is chosen such that only single particles or pairs of particles have to be considered. For these particles, the Smoluchowski equation can be solved analytically using Green's functions. The main idea of GFRD is to exploit the exact solution of the Smoluchoswki equation to set up an event-driven algorithm. This allows GFRD to make large jumps in time when the particles are far apart from each other. Here, we apply the technique to a simple model of gene expression. The simulations reveal that the scheme is highly efficient. Under biologically relevant conditions, GFRD is up to six orders of magnitude faster than conventional particle-based techniques for simulating biochemical networks in time and space.
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"abstract": "Biochemical networks are the analog computers of life. They allow living\ncells to control a large number of biological processes, such as gene\nexpression and cell signalling. In biochemical networks, the concentrations of\nthe components are often low. This means that the discrete nature of the\nreactants and the stochastic character of their interactions have to be taken\ninto account. Moreover, the spatial distribution of the components can be of\ncrucial importance. However, the current numerical techniques for simulating\nbiochemical networks either ignore the particulate nature of matter or treat\nthe spatial fluctuations in a mean-field manner. We have developed a new\ntechnique, called Green\u0027s Function Reaction Dynamics (GFRD), that makes it\npossible to simulate biochemical networks at the particle level and in both\ntime and space. In this scheme, a maximum time step is chosen such that only\nsingle particles or pairs of particles have to be considered. For these\nparticles, the Smoluchowski equation can be solved analytically using Green\u0027s\nfunctions. The main idea of GFRD is to exploit the exact solution of the\nSmoluchoswki equation to set up an event-driven algorithm. This allows GFRD to\nmake large jumps in time when the particles are far apart from each other.\nHere, we apply the technique to a simple model of gene expression. The\nsimulations reveal that the scheme is highly efficient. Under biologically\nrelevant conditions, GFRD is up to six orders of magnitude faster than\nconventional particle-based techniques for simulating biochemical networks in\ntime and space.",
"arxiv_id": "q-bio/0404002",
"authors": [
"Jeroen S. van Zon",
"Pieter Rein ten Wolde"
],
"categories": [
"q-bio.MN"
],
"title": "Green\u0027s Function Reaction Dynamics: a new approach to simulate biochemical networks at the particle level and in time and space",
"url": "https://arxiv.org/abs/q-bio/0404002"
},
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