Abstract
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.
Highlights
The purpose of this paper is to remedy pedagogical error in matters pertaining to the thermodynamics and kinetics of biological transport phenomena
This is done by using a minimal model of facilitated diffusion, based on the mass action law and constrained by the probability isotherm, to provide straightforward thermodynamic and kinetic insights that elude the competing approaches of Michaelis–Menten kinetics (MMK) and linear non-equilibrium thermodynamics (LNET)
This new approach is aptly named intuitive non-equilibrium thermodynamics (INET) for what, it is hoped, will become obvious reasons. It is a persistent and dreary oral tradition in the folklore of chemical energetics pedagogy that ‘thermodynamics has nothing to say about reaction rates except at equilibrium’
Summary
The purpose of this paper is to remedy pedagogical error in matters pertaining to the thermodynamics and kinetics of biological transport phenomena This is done by using a minimal model of facilitated diffusion, based on the mass action law and constrained by the probability isotherm, to provide straightforward thermodynamic and kinetic insights that elude the competing approaches of Michaelis–Menten kinetics (MMK) and linear non-equilibrium thermodynamics (LNET). This new approach is aptly named intuitive non-equilibrium thermodynamics (INET) for what, it is hoped, will become obvious reasons. This line of enquiry was pursued further by Wagg and co-workers in the 1990s for theoretical analysis of membrane transport [3,4,5], an important limitation affecting experimental application of such theory is the inability of radioisotopic fluxes to distinguish between the various entry and exit points of ions involved in branched transport mechanisms [6]
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