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Abstract

We have developed a new numerical 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, which combines in one step the propagation of the particles in space with the reactions between them. The event-driven nature allows GFRD to make large jumps in time and space 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 spatial fluctuations can be a major source of noise in biochemical networks. The calculations also show that GFRD is highly efficient. Under biologically relevant conditions, GFRD is up to five orders of magnitude faster than conventional particle-based techniques for simulating biochemical networks in time and space. GFRD is not limited to biochemical networks. It can also be applied to a large number of other reaction-diffusion problems.

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Stochastic mechanisms in gene expression.

H H McAdams, A Arkin (1997)

In cellular regulatory networks, genetic activity is controlled by molecular signals that determine when and how often a given gene is transcribed. In genetically controlled pathways, the protein product encoded by one gene often regulates expression of other genes. The time delay, after activation of the first promoter, to reach an effective level to control the next promoter depends on the rate of protein accumulation. We have analyzed the chemical reactions controlling transcript initiation and translation termination in a single such "genetically coupled" link as a precursor to modeling networks constructed from many such links. Simulation of the processes of gene expression shows that proteins are produced from an activated promoter in short bursts of variable numbers of proteins that occur at random time intervals. As a result, there can be large differences in the time between successive events in regulatory cascades across a cell population. In addition, the random pattern of expression of competitive effectors can produce probabilistic outcomes in switching mechanisms that select between alternative regulatory paths. The result can be a partitioning of the cell population into different phenotypes as the cells follow different paths. There are numerous unexplained examples of phenotypic variations in isogenic populations of both prokaryotic and eukaryotic cells that may be the result of these stochastic gene expression mechanisms.

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Serial triggering of many T-cell receptors by a few peptide-MHC complexes.

S Valitutti, S. Müller, M. Cella … (1995)

T lymphocytes can recognize and be activated by a very small number of complexes of peptide with major histocompatibility complex (MHC) molecules displayed on the surface of antigen-presenting cells (APCs). The interaction between the T-cell receptor (TCR) and its ligand has low affinity and high off-rate. Both findings suggest that an extremely small number of TCRs must be engaged in interaction with APCs and raise the question of how so few receptors can transduce an activation signal. Here we show that a small number of peptide-MHC complexes can achieve a high TCR occupancy, because a single complex can serially engage and trigger up to approximately 200 TCRs. Furthermore, TCR occupancy is proportional to the T cell's biological response. Our findings suggest that the low affinity of the TCR can be instrumental in enabling a small number of antigenic complexes to be detected.