Branch prioritization motifs in biochemical networks with sharp activation

Roderick Edwards; Michelle Wood; Roderick Edwards; Michelle Wood

doi:10.3934/math.2022066

AIMS Mathematics

2022, Volume 7, Issue 1: 1115-1146. doi: 10.3934/math.2022066

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Branch prioritization motifs in biochemical networks with sharp activation

Roderick Edwards ^,,
Michelle Wood

Department of Mathematics and Statistics, University of Victoria, P.O. Box 1700 STN CSC, Victoria, BC, V8W 2Y2, Canada

Received: 08 March 2021 Accepted: 01 July 2021 Published: 20 October 2021
MSC : Primary: 92C40, 92C42; Secondary: 92C80, 34A36

The Precursor Shutoff Valve (PSV) has been proposed as a motif in biochemical networks, active for example in prioritization of primary over secondary metabolism in plants in low-input conditions. Another branch prioritization mechanism in a biochemical network is a difference in thresholds for activation of the two pathways from the branch point. It has been shown by Adams and colleagues that both mechanisms can play a part in a model of plant metabolism involving Michaelis-Menten kinetics ^[1]. Here we investigate the potential role of these two mechanisms in systems with steeper activation functions, such as those involving highly cooperative reactions, by considering the limit of infinitely steep activation functions, as is done in Glass networks as models of gene regulation. We find that the Threshold Separation mechanism is completely effective in pathway prioritization in such a model framework, while the PSV adds no additional benefit, and is ineffective on its own. This makes clear that the PSV uses the gradual nature of activation functions to help shut off one branch at low input levels, and has no effect if activation is sharp. The analysis also serves as a case study in assessing behaviour of sharply-switching open systems without degradation of species.
- precursor shutoff valve,
- biochemical networks,
- non-smooth systems,
- discontinuous differential equations
Citation: Roderick Edwards, Michelle Wood. Branch prioritization motifs in biochemical networks with sharp activation[J]. AIMS Mathematics, 2022, 7(1): 1115-1146. doi: 10.3934/math.2022066

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Abstract

The Precursor Shutoff Valve (PSV) has been proposed as a motif in biochemical networks, active for example in prioritization of primary over secondary metabolism in plants in low-input conditions. Another branch prioritization mechanism in a biochemical network is a difference in thresholds for activation of the two pathways from the branch point. It has been shown by Adams and colleagues that both mechanisms can play a part in a model of plant metabolism involving Michaelis-Menten kinetics ^[1]. Here we investigate the potential role of these two mechanisms in systems with steeper activation functions, such as those involving highly cooperative reactions, by considering the limit of infinitely steep activation functions, as is done in Glass networks as models of gene regulation. We find that the Threshold Separation mechanism is completely effective in pathway prioritization in such a model framework, while the PSV adds no additional benefit, and is ineffective on its own. This makes clear that the PSV uses the gradual nature of activation functions to help shut off one branch at low input levels, and has no effect if activation is sharp. The analysis also serves as a case study in assessing behaviour of sharply-switching open systems without degradation of species.

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