Article
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Summation Laws in Biological Systems
Version 1
: Received: 25 March 2023 / Approved: 27 March 2023 / Online: 27 March 2023 (05:04:24 CEST)
A peer-reviewed article of this Preprint also exists.
Westerhoff, H.V. Summation Laws in Control of Biochemical Systems. Mathematics 2023, 11, 2473. Westerhoff, H.V. Summation Laws in Control of Biochemical Systems. Mathematics 2023, 11, 2473.
Abstract
Dynamic variables in the non-equilibrium systems of life are determined by catalytic activities. These relate to the expression of the genome. The extent to which such a variable depends on the catalytic activity defined by a gene has become more and more important in view of the possibilities to modulate gene expression or intervene with enzyme function through the use of medicinal drugs. With all the complexity of cellular systems biology, there are still some very simple principles that guide the control of variables such as fluxes, concentrations, and half-times. Using time-unit invariance we here derive a multitude of laws governing the sums of the control coefficients that quantify the control of multiple variables by all the catalytic activities. We show that the sum of the control coefficients of any dynamic variable over all catalytic activities is determined by the control of the same property by time. When the variable is at a maximum, minimum or steady, this limits the sums to simple integers like 0, -1, 1, and -2, depending on the variable under consideration. Some of the implications for biological control are discussed as is the dependence of these results on the precise definition of control.
Keywords
Control coefficients; Metabolic Control Analysis; Systems Biology; Genomics; Pharmacokinetic principles; systems biology and PBPK; time-dependent control analysis
Subject
Biology and Life Sciences, Biology and Biotechnology
Copyright: This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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