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

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Frontiers of Electrical and Electronic Engineering in China 2016年第2期4卷 69-83页

作者： Marc Turcotte Department of Mathematics The University of Texas at Arlington Arlington TX 76109 USA Biological Sciences The University of Texas at Dallas Richardson TX-75080 USA

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＂.

关键词： systems biology theoretical biology gene regulation nonlinear dynamics stochasticity

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Parameter asymmetry and time-scale separation in core genetic commitment circuits

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Frontiers of Electrical and Electronic Engineering in China 2015年第1期10卷 19-45页

作者： Hongguang Xi Marc Turcotte Department of Mathematics University of Texas at Arlington Arlington TX 76109 USA Biological Sciences University of Texas at Dallas Richardson TX 75080 USA

Theory allows studying why Evolution might select core genetic commitment circuit topologies over alternatives. The nonlinear dynamics of the underlying gene regulation together with the unescapable subtle interplay of intrinsic biochemical noise impact the range of possible evolutionary choices. The question of why certain genetic regulation circuits might present robustness to phenotype-delivery breaking over others, is therefore of high interest. Here, the behavior of systematically more complex commitment circuits is studied, in the presence of intrinsic noise, with a focus on two aspects relevant to biology： parameter asymmetry and time-scale separation. We show that phenotype delivery is broken in simple two- and three-gene circuits. In the two-gene circuit, we show how stochastic potential wells of different depths break commitment. In the three-gene circuit, we show that the onset of oscillations breaks the commitment phenotype in a systematic way. Finally, we also show that higher dimensional circuits （four-gene and five-gene circuits） may be intrinsically more robust.

关键词： systems biology theoretical biology gene regulation nonlinear dynamics stochasticity

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