A rigorous framework for multiscale simulation of stochastic cellular networks.
ABSTRACT Noise and stochasticity are fundamental to biology and derive from the very nature of biochemical reactions where thermal motion of molecules translates into randomness in the sequence and timing of reactions. This randomness leads to cell-cell variability even in clonal populations. Stochastic biochemical networks are modeled as continuous time discrete state Markov processes whose probability density functions evolve according to a chemical master equation (CME). The CME is not solvable but for the simplest cases, and one has to resort to kinetic Monte Carlo techniques to simulate the stochastic trajectories of the biochemical network under study. A commonly used such algorithm is the stochastic simulation algorithm (SSA). Because it tracks every biochemical reaction that occurs in a given system, the SSA presents computational difficulties especially when there is a vast disparity in the timescales of the reactions or in the number of molecules involved in these reactions. This is common in cellular networks, and many approximation algorithms have evolved to alleviate the computational burdens of the SSA. Here, we present a rigorously derived modified CME framework based on the partition of a biochemically reacting system into restricted and unrestricted reactions. Although this modified CME decomposition is as analytically difficult as the original CME, it can be naturally used to generate a hierarchy of approximations at different levels of accuracy. Most importantly, some previously derived algorithms are demonstrated to be limiting cases of our formulation. We apply our methods to biologically relevant test systems to demonstrate their accuracy and efficiency.
Article: Noise in gene expression as the source of non-genetic individuality in the chemotactic response of Escherichia coli.[show abstract] [hide abstract]
ABSTRACT: A deterministic computer model of the signal transduction pathway mediating bacterial chemotaxis was used to examine the variation in both unstimulated swimming behaviour and adaptation time to stimuli in clonal populations of cells. Copy numbers of proteins in the pathway were computed from a simplified model of transcription and translation that predicts greater-than-Poissonian statistics. Simulated and experimental individuality data could be brought into good agreement on varying the noise strength of the protein copy number distributions. In the simulations, all the proteins in the pathway are involved to a significant degree in the appearance of phenotypic diversity, although there is a modest decrease in influence with increasing copy number.FEBS Letters 09/2003; 550(1-3):135-8. · 3.54 Impact Factor
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ABSTRACT: The dynamic process of differentiation depends on the architecture, quantitative parameters, and noise of underlying genetic circuits. However, it remains unclear how these elements combine to control cellular behavior. We analyzed the probabilistic and transient differentiation of Bacillus subtilis cells into the state of competence. A few key parameters independently tuned the frequency of initiation and the duration of competence episodes and allowed the circuit to access different dynamic regimes, including oscillation. Altering circuit architecture showed that the duration of competence events can be made more precise. We used an experimental method to reduce global cellular noise and showed that noise levels are correlated with frequency of differentiation events. Together, the data reveal a noise-dependent circuit that is remarkably resilient and tunable in terms of its dynamic behavior.Science 04/2007; 315(5819):1716-9. · 31.20 Impact Factor
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ABSTRACT: 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.Proceedings of the National Academy of Sciences 03/1997; 94(3):814-9. · 9.68 Impact Factor