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Non-Equilibrium Thermodynamics View on Kinetics of Autocatalytic Reactions-Two Illustrative Examples.

ABSTRACT: Autocatalytic reactions are in certain contrast with the linear algebra of reaction stoichiometry, on which rate equations respecting the permanence of atoms are constructed. These mathematical models of chemical reactions are called conservative. Using a non-equilibrium thermodynamics-based theory of chemical kinetics, it is shown how to introduce autocatalytic step into such (conservative) rate equation properly. Further, rate equations based on chemical potentials or affinities are derived, and conditions for the consistency of rate equations with the entropic inequality (the second law of thermodynamics) are illustrated. The theory illustrated here can be viewed as a tool for verifying and generalizing traditional mass-action kinetics by means of modern non-equilibrium thermodynamics, which is able to deal also with such rather problematic cases.

SUBMITTER: Pekar M

PROVIDER: S-EPMC7866015 | biostudies-literature | 2021 Jan

REPOSITORIES: biostudies-literature

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Non-Equilibrium Thermodynamics View on Kinetics of Autocatalytic Reactions-Two Illustrative Examples.

Pekař Miloslav M

Molecules (Basel, Switzerland) 20210122 3

Autocatalytic reactions are in certain contrast with the linear algebra of reaction stoichiometry, on which rate equations respecting the permanence of atoms are constructed. These mathematical models of chemical reactions are called conservative. Using a non-equilibrium thermodynamics-based theory of chemical kinetics, it is shown how to introduce autocatalytic step into such (conservative) rate equation properly. Further, rate equations based on chemical potentials or affinities are derived, a ...[more]

PMID: 33499305

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Project description:BackgroundWe consider a focal adhesion to be made up of molecular complexes, each consisting of a ligand, an integrin molecule, and associated plaque proteins. Free energy changes drive the binding and unbinding of these complexes and thereby controls the focal adhesion's dynamic modes of growth, treadmilling and resorption.Principal findingsWe have identified a competition among four thermodynamic driving forces for focal adhesion dynamics: (i) the work done during the addition of a single molecular complex of a certain size, (ii) the chemical free energy change associated with the addition of a molecular complex, (iii) the elastic free energy change associated with deformation of focal adhesions and the cell membrane, and (iv) the work done on a molecular conformational change. We have developed a theoretical treatment of focal adhesion dynamics as a nonlinear rate process governed by a classical kinetic model. We also express the rates as being driven by out-of-equilibrium thermodynamic driving forces, and modulated by kinetics. The mechanisms governed by the above four effects allow focal adhesions to exhibit a rich variety of behavior without the need to introduce special constitutive assumptions for their response. For the reaction-limited case growth, treadmilling and resorption are all predicted by a very simple chemo-mechanical model. Treadmilling requires symmetry breaking between the ends of the focal adhesion, and is achieved by driving force (i) above. In contrast, depending on its numerical value (ii) causes symmetric growth, resorption or is neutral, (iii) causes symmetric resorption, and (iv) causes symmetric growth. These findings hold for a range of conditions: temporally-constant force or stress, and for spatially-uniform and non-uniform stress distribution over the FA. The symmetric growth mode dominates for temporally-constant stress, with a reduced treadmilling regime.SignificanceIn addition to explaining focal adhesion dynamics, this treatment can be coupled with models of cytoskeleton dynamics and contribute to the understanding of cell motility.

Dataset Information

Non-Equilibrium Thermodynamics View on Kinetics of Autocatalytic Reactions-Two Illustrative Examples.

Publications

Non-Equilibrium Thermodynamics View on Kinetics of Autocatalytic Reactions-Two Illustrative Examples.

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