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Environmental Statistics and Optimal Regulation

Sivak, David A. and Thomson, Matt (2014) Environmental Statistics and Optimal Regulation. PLOS Computational Biology, 10 (9). Art. No. e1003826. ISSN 1553-7358. PMCID PMC4177669. doi:10.1371/journal.pcbi.1003826.

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Any organism is embedded in an environment that changes over time. The timescale for and statistics of environmental change, the precision with which the organism can detect its environment, and the costs and benefits of particular protein expression levels all will affect the suitability of different strategies–such as constitutive expression or graded response–for regulating protein levels in response to environmental inputs. We propose a general framework–here specifically applied to the enzymatic regulation of metabolism in response to changing concentrations of a basic nutrient–to predict the optimal regulatory strategy given the statistics of fluctuations in the environment and measurement apparatus, respectively, and the costs associated with enzyme production. We use this framework to address three fundamental questions: (i) when a cell should prefer thresholding to a graded response; (ii) when there is a fitness advantage to implementing a Bayesian decision rule; and (iii) when retaining memory of the past provides a selective advantage. We specifically find that: (i) relative convexity of enzyme expression cost and benefit influences the fitness of thresholding or graded responses; (ii) intermediate levels of measurement uncertainty call for a sophisticated Bayesian decision rule; and (iii) in dynamic contexts, intermediate levels of uncertainty call for retaining memory of the past. Statistical properties of the environment, such as variability and correlation times, set optimal biochemical parameters, such as thresholds and decay rates in signaling pathways. Our framework provides a theoretical basis for interpreting molecular signal processing algorithms and a classification scheme that organizes known regulatory strategies and may help conceptualize heretofore unknown ones.

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Additional Information:© 2014 Sivak, Thomson. This is an open-access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited. Received: May 12, 2014; Accepted: July 26, 2014; Published: September 25, 2014. We thank Hana El-Samad, Wendell Lim, Amir Mitchell, Michael Fischbach, and Hao Li for enlightening discussions, and especially Hyun Youk for detailed feedback on the manuscript. DAS and MT were funded by National Institute of General Medical Sciences Systems Biology Center grant P50 GM081879. MT also acknowledges support from NIH 5DP5OD012194. The funders had no role in study design, data collection and analysis, decision to publish, or preparation of the manuscript.
Errata:This article was republished on October 10, 2014, to correct errors in the formatting of the equations and paragraphs. These errors were introduced during the typesetting process. Please download this article again to view the correct version. The originally published, uncorrected article and the republished, corrected article are provided here for reference.
Funding AgencyGrant Number
NIHP50 GM081879
Issue or Number:9
PubMed Central ID:PMC4177669
Record Number:CaltechAUTHORS:20170206-153034371
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Official Citation:Sivak DA, Thomson M (2014) Environmental Statistics and Optimal Regulation. PLoS Comput Biol 10(9): e1003826. doi:10.1371/journal.pcbi.1003826
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:74105
Deposited By: Donna Wrublewski
Deposited On:07 Feb 2017 00:13
Last Modified:11 Nov 2021 05:24

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