A facilitated diffusion model constrained by the probability isotherm : A pedagogical exercise in intuitive non-equilibrium thermodynamics

**Authors:**Chapman, Brian**Date:**2017**Type:**Text , Journal article**Relation:**Royal Society Open Science Vol. 4, no. 6 (2017), p. 1-22**Full Text:****Reviewed:****Description:**This paper seeks to develop a more thermodynamically sound pedagogy for students of biological transport than is currently available from either of the competing schools of linear non-equilibrium thermodynamics (LNET) or Michaelis–Menten kinetics (MMK). To this end, a minimal model of facilitated diffusion was constructed comprising four reversible steps: cis-substrate binding, cis→trans bound enzyme shuttling, trans-substrate dissociation and trans→cis free enzyme shuttling. All model parameters were subject to the second law constraint of the probability isotherm, which determined the unidirectional and net rates for each step and for the overall reaction through the law of mass action. Rapid equilibration scenarios require sensitive ‘tuning’ of the thermodynamic binding parameters to the equilibrium substrate concentration. All non-equilibrium scenarios show sigmoidal force–flux relations, with only a minority of cases having their quasi-linear portions close to equilibrium. Few cases fulfil the expectations of MMK relating reaction rates to enzyme saturation. This new approach illuminates and extends the concept of rate-limiting steps by focusing on the free energy dissipation associated with each reaction step and thereby deducing its respective relative chemical impedance. The crucial importance of an enzyme’s being thermodynamically ‘tuned’ to its particular task, dependent on the cis- and trans-substrate concentrations with which it deals, is consistent with the occurrence of numerous isoforms for enzymes that transport a given substrate in physiologically different circumstances. This approach to kinetic modelling, being aligned with neither MMK nor LNET, is best described as intuitive non-equilibrium thermodynamics, and is recommended as a useful adjunct to the design and interpretation of experiments in biotransport. © 2017 The Authors.

**Authors:**Chapman, Brian**Date:**2017**Type:**Text , Journal article**Relation:**Royal Society Open Science Vol. 4, no. 6 (2017), p. 1-22**Full Text:****Reviewed:****Description:**This paper seeks to develop a more thermodynamically sound pedagogy for students of biological transport than is currently available from either of the competing schools of linear non-equilibrium thermodynamics (LNET) or Michaelis–Menten kinetics (MMK). To this end, a minimal model of facilitated diffusion was constructed comprising four reversible steps: cis-substrate binding, cis→trans bound enzyme shuttling, trans-substrate dissociation and trans→cis free enzyme shuttling. All model parameters were subject to the second law constraint of the probability isotherm, which determined the unidirectional and net rates for each step and for the overall reaction through the law of mass action. Rapid equilibration scenarios require sensitive ‘tuning’ of the thermodynamic binding parameters to the equilibrium substrate concentration. All non-equilibrium scenarios show sigmoidal force–flux relations, with only a minority of cases having their quasi-linear portions close to equilibrium. Few cases fulfil the expectations of MMK relating reaction rates to enzyme saturation. This new approach illuminates and extends the concept of rate-limiting steps by focusing on the free energy dissipation associated with each reaction step and thereby deducing its respective relative chemical impedance. The crucial importance of an enzyme’s being thermodynamically ‘tuned’ to its particular task, dependent on the cis- and trans-substrate concentrations with which it deals, is consistent with the occurrence of numerous isoforms for enzymes that transport a given substrate in physiologically different circumstances. This approach to kinetic modelling, being aligned with neither MMK nor LNET, is best described as intuitive non-equilibrium thermodynamics, and is recommended as a useful adjunct to the design and interpretation of experiments in biotransport. © 2017 The Authors.

- Chapman, Brian, Mosse, Jennifer, Larkins, Jo-Ann

**Authors:**Chapman, Brian , Mosse, Jennifer , Larkins, Jo-Ann**Date:**2011**Type:**Text , Conference paper**Relation:**Australian Conference on Science and Mathematics Education p. 169-174**Full Text:**false**Reviewed:****Description:**Widespread error exists in the ‘thermodynamics’ and/or ‘bioenergetics’ sections of most biochemical textbooks. Three typical examples are drawn from a premier pedagogical source and shown to encapsulate (1) confusion about entropy and reversibility, (2) confounding of coupled reactions with sequential reactions in misguided attempts to show how exergonic reactions might drive endergonic reactions, and (3) confusion about the proximity to equilibrium of living processes. A fresh approach is developed, based on the Second Law imperative that free energy be dissipated (identical to the requirement that entropy be created). This approach identifies a Probability Isotherm, being a probabilistic expression of the Second Law, relating molar free energy dissipation to the overall ratio of probability of forward reaction to backward reaction. By equating the Probability Isotherm to the Van’t Hoff Isotherm, the overall probability ratio may be decomposed into an intrinsic probability ratio (the equilibrium constant) and an extrinsic probability ratio (dependent on composition). The Probability Isotherm is manifest kinetically as the Rate Isotherm, also thermodynamically determined even for kinetically complex reactions. The concept of ‘bound energy’ is introduced to complement ‘free energy’ in reconciling the Second Law imperative for free energy dissipation with the First Law requirement for total energy conservation

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