Exact time-dependent solutions for a self-regulating gene

The exact time-dependent solution for the stochastic equations governing the behavior of a binary self-regulating gene is presented. Using the generating function technique to rephrase the master equations in terms of partial differential equations, we show that the model is totally integrable and t...

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Bibliographic Details
Published in:Physical review. E, Statistical, nonlinear, and soft matter physics Statistical, nonlinear, and soft matter physics, 2011-06, Vol.83 (6 Pt 1), p.062902-062902
Main Authors: Ramos, A F, Innocentini, G C P, Hornos, J E M
Format: Article
Language:English
Subjects:
Models, Genetic
Probability
Stochastic Processes
Time Factors
Transcription, Genetic - genetics
Online Access:Get full text
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Summary:The exact time-dependent solution for the stochastic equations governing the behavior of a binary self-regulating gene is presented. Using the generating function technique to rephrase the master equations in terms of partial differential equations, we show that the model is totally integrable and the analytical solutions are the celebrated confluent Heun functions. Self-regulation plays a major role in the control of gene expression, and it is remarkable that such a microscopic model is completely integrable in terms of well-known complex functions.
ISSN:1550-2376
DOI:10.1103/PhysRevE.83.062902