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Delineating the respective impacts of stochastic curl- and grad-forces in a family of idealized core genetic commitment circuits |
Marc Turcotte1,2,*( ) |
1. Department of Mathematics, The University of Texas at Arlington, Arlington, TX 76109, USA
2. Biological Sciences, The University of Texas at Dallas, Richardson, TX 75080, USA |
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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”.
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Author Summary
Living systems are impacted by randomness rooted in the paucity of molecular regulators. Mathematical stochastic analysis thereof is more subtle than a mere blur of determinism. Stochasticity splits into distinct origins: a gradient source and a curl source. Herein, consequences among a family of prototypical gene regulation circuits are investigated. It is shown that, very near resting points of the dynamics, those effects sourced in the gradient vanish, whereas the effects sourced in the curl do not. Thus, the randomness in the vicinity of biologically stable states differs from that afar. Interestingly, locally, this difference may assist in destabilization. |
Keywords
systems biology
theoretical biology
gene regulation
nonlinear dynamics
stochasticity
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Fund: |
Corresponding Author(s):
Marc Turcotte
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Just Accepted Date: 05 April 2016
Online First Date: 13 May 2016
Issue Date: 26 May 2016
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