Stochasticity in Transcriptional Regulation: Origins, Consequences and Mathematical Representations
Transcriptional regulation is subject to significant stochasticity due partly to the random waiting times among synthesis and degradation reactions involving a finite collection of transcripts. Additional stochasticity is attributable to the random transitions among the discrete operator states controlling the rate of transcription. We develop a Markov model to which these random reactions are intrinsic as well as a series of simpler models derived explicitly from the first as approximations in different parameter regimes. This innate stochasticity can have quantitative and qualitative impact on the behavior of gene-regulatory networks. We introduce a natural generalization of deterministic bifurcations for classification of stochastic systems and show that simple noisy genetic switches have rich bifurcation structures; among them, bifurcations driven solely by changing the rate of operator fluctuations even as the ``underlying'' deterministic system remains unchanged. We find stochastic bistability where the deterministic equations predict monostability and vice-versa. We derive and solve equations for the mean waiting times for spontaneous transitions between quasistable states in these switches.
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|Date of creation:||Jun 2001|
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Web page: http://www.santafe.edu/sfi/publications/working-papers.html
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