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Quantitative Biology

, Volume 4, Issue 2, pp 69–83 | Cite as

Delineating the respective impacts of stochastic curl- and grad-forces in a family of idealized core genetic commitment circuits

  • Marc Turcotte
Research Article

Abstract

Stochastic dynamics pervades gene regulation. Despite being random, the dynamics displays a kind of innate structure. In fact, two stochastic forces combine driving efforts: one force originates from the gradient of the underlying stochastic potential, and the other originates from the mathematical curl of the probability flux. The curl force gives rise to rotation. The gradient force gives rise to drift. Together they give rise to helical behavior. Here, it is shown that around and about the vicinity of attractive fixed points, the gradient force naturally wanes but the curl force is found to remain high. This leads to a locally noticeably different type of stochastic track near and about attractive fixed points, compared to tracks in regions where drift dominates. The consistency of this observation with the experimental fact that, in biology, fate commitment appears to not be a-priory locked-in, but rather necessitating active maintenance, is discussed. Hence attractive fixed-points are not only fuzzy, but may effectively be, locally, “more free”.

Keywords

systems biology theoretical biology gene regulation nonlinear dynamics stochasticity 

Supplementary material

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40484_2016_70_MOESM5_ESM.pdf (82 kb)
Supplementary material, approximately 84 KB.

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Copyright information

© Higher Education Press and Springer-Verlag GmbH 2016

Authors and Affiliations

  1. 1.Department of MathematicsThe University of Texas at ArlingtonArlingtonUSA
  2. 2.Biological SciencesThe University of Texas at DallasRichardsonUSA

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