Homeostasis in a feed forward loop gene regulatory motif

Journal of Theoretical Biology
Fernando AntoneliIan Stewart

Abstract

The internal state of a cell is affected by inputs from the extra-cellular environment such as external temperature. If some output, such as the concentration of a target protein, remains approximately constant as inputs vary, the system exhibits homeostasis. Special sub-networks called motifs are unusually common in gene regulatory networks (GRNs), suggesting that they may have a significant biological function. Potentially, one such function is homeostasis. In support of this hypothesis, we show that the feed-forward loop GRN produces homeostasis. Here the inputs are subsumed into a single parameter that affects only the first node in the motif, and the output is the concentration of a target protein. The analysis uses the notion of infinitesimal homeostasis, which occurs when the input-output map has a critical point (zero derivative). In model equations such points can be located using implicit differentiation. If the second derivative of the input-output map also vanishes, the critical point is a chair: the output rises roughly linearly, then flattens out (the homeostasis region or plateau), and then starts to rise again. Chair points are a common cause of homeostasis. In more complicated equations or networks, numerical e...Continue Reading

References

Jun 13, 2000·Nature·A Becskei, L Serrano
May 11, 2005·Nature Reviews. Genetics·Mads KaernJames J Collins
Apr 10, 2007·Nature Genetics·Zhanzhi HuVishwanath R Iyer
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Oct 1, 2013·Journal of Applied Genetics·Bartłomiej Kozera, Marcin Rapacz
Sep 23, 2014·Mathematical Biosciences·H Frederik NijhoutMichael C Reed
Jun 4, 2016·Journal of Mathematical Biology·Martin Golubitsky, Ian Stewart
Jul 6, 2016·Journal of Theoretical Biology·Zhe F Tang, David R McMillen
Sep 9, 2017·Bulletin of Mathematical Biology·Michael ReedH Frederik Nijhout

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Citations

Oct 30, 2018·Wiley Interdisciplinary Reviews. Systems Biology and Medicine·H Frederik NijhoutMichael C Reed
Jan 11, 2020·Journal of Mathematical Biology·Martin Golubitsky, Yangyang Wang
Aug 12, 2018·International Journal of Molecular Sciences·Chi-Dung YangChing-Ping Tseng
May 23, 2021·Journal of Mathematical Biology·Yangyang WangMartin Golubitsky

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