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Rapid modeling of experimental molecular kinetics with simple electronic circuits instead of with complex differential equations

Kinetic modeling has relied on using a tedious number of mathematical equations to describe molecular kinetics in interacting reactions. The long list of differential equations with associated abstract variables and parameters inevitably hinders readers’ easy understanding of the models. However, th...

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Autores principales: Deng, Yijie, Beahm, Douglas Raymond, Ran, Xinping, Riley, Tanner G., Sarpeshkar, Rahul
Formato: Online Artículo Texto
Lenguaje:English
Publicado: Frontiers Media S.A. 2022
Materias:
Acceso en línea:https://www.ncbi.nlm.nih.gov/pmc/articles/PMC9554301/
https://www.ncbi.nlm.nih.gov/pubmed/36246369
http://dx.doi.org/10.3389/fbioe.2022.947508
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author Deng, Yijie
Beahm, Douglas Raymond
Ran, Xinping
Riley, Tanner G.
Sarpeshkar, Rahul
author_facet Deng, Yijie
Beahm, Douglas Raymond
Ran, Xinping
Riley, Tanner G.
Sarpeshkar, Rahul
author_sort Deng, Yijie
collection PubMed
description Kinetic modeling has relied on using a tedious number of mathematical equations to describe molecular kinetics in interacting reactions. The long list of differential equations with associated abstract variables and parameters inevitably hinders readers’ easy understanding of the models. However, the mathematical equations describing the kinetics of biochemical reactions can be exactly mapped to the dynamics of voltages and currents in simple electronic circuits wherein voltages represent molecular concentrations and currents represent molecular fluxes. For example, we theoretically derive and experimentally verify accurate circuit models for Michaelis-Menten kinetics. Then, we show that such circuit models can be scaled via simple wiring among circuit motifs to represent more and arbitrarily complex reactions. Hence, we can directly map reaction networks to equivalent circuit schematics in a rapid, quantitatively accurate, and intuitive fashion without needing mathematical equations. We verify experimentally that these circuit models are quantitatively accurate. Examples include 1) different mechanisms of competitive, noncompetitive, uncompetitive, and mixed enzyme inhibition, important for understanding pharmacokinetics; 2) product-feedback inhibition, common in biochemistry; 3) reversible reactions; 4) multi-substrate enzymatic reactions, both important in many metabolic pathways; and 5) translation and transcription dynamics in a cell-free system, which brings insight into the functioning of all gene-protein networks. We envision that circuit modeling and simulation could become a powerful scientific communication language and tool for quantitative studies of kinetics in biology and related fields.
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spelling pubmed-95543012022-10-13 Rapid modeling of experimental molecular kinetics with simple electronic circuits instead of with complex differential equations Deng, Yijie Beahm, Douglas Raymond Ran, Xinping Riley, Tanner G. Sarpeshkar, Rahul Front Bioeng Biotechnol Bioengineering and Biotechnology Kinetic modeling has relied on using a tedious number of mathematical equations to describe molecular kinetics in interacting reactions. The long list of differential equations with associated abstract variables and parameters inevitably hinders readers’ easy understanding of the models. However, the mathematical equations describing the kinetics of biochemical reactions can be exactly mapped to the dynamics of voltages and currents in simple electronic circuits wherein voltages represent molecular concentrations and currents represent molecular fluxes. For example, we theoretically derive and experimentally verify accurate circuit models for Michaelis-Menten kinetics. Then, we show that such circuit models can be scaled via simple wiring among circuit motifs to represent more and arbitrarily complex reactions. Hence, we can directly map reaction networks to equivalent circuit schematics in a rapid, quantitatively accurate, and intuitive fashion without needing mathematical equations. We verify experimentally that these circuit models are quantitatively accurate. Examples include 1) different mechanisms of competitive, noncompetitive, uncompetitive, and mixed enzyme inhibition, important for understanding pharmacokinetics; 2) product-feedback inhibition, common in biochemistry; 3) reversible reactions; 4) multi-substrate enzymatic reactions, both important in many metabolic pathways; and 5) translation and transcription dynamics in a cell-free system, which brings insight into the functioning of all gene-protein networks. We envision that circuit modeling and simulation could become a powerful scientific communication language and tool for quantitative studies of kinetics in biology and related fields. Frontiers Media S.A. 2022-09-28 /pmc/articles/PMC9554301/ /pubmed/36246369 http://dx.doi.org/10.3389/fbioe.2022.947508 Text en Copyright © 2022 Deng, Beahm, Ran, Riley and Sarpeshkar. https://creativecommons.org/licenses/by/4.0/This is an open-access article distributed under the terms of the Creative Commons Attribution License (CC BY). The use, distribution or reproduction in other forums is permitted, provided the original author(s) and the copyright owner(s) are credited and that the original publication in this journal is cited, in accordance with accepted academic practice. No use, distribution or reproduction is permitted which does not comply with these terms.
spellingShingle Bioengineering and Biotechnology
Deng, Yijie
Beahm, Douglas Raymond
Ran, Xinping
Riley, Tanner G.
Sarpeshkar, Rahul
Rapid modeling of experimental molecular kinetics with simple electronic circuits instead of with complex differential equations
title Rapid modeling of experimental molecular kinetics with simple electronic circuits instead of with complex differential equations
title_full Rapid modeling of experimental molecular kinetics with simple electronic circuits instead of with complex differential equations
title_fullStr Rapid modeling of experimental molecular kinetics with simple electronic circuits instead of with complex differential equations
title_full_unstemmed Rapid modeling of experimental molecular kinetics with simple electronic circuits instead of with complex differential equations
title_short Rapid modeling of experimental molecular kinetics with simple electronic circuits instead of with complex differential equations
title_sort rapid modeling of experimental molecular kinetics with simple electronic circuits instead of with complex differential equations
topic Bioengineering and Biotechnology
url https://www.ncbi.nlm.nih.gov/pmc/articles/PMC9554301/
https://www.ncbi.nlm.nih.gov/pubmed/36246369
http://dx.doi.org/10.3389/fbioe.2022.947508
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