Abstract
The global force-flow equations of nonequilibrium thermodynamics are obtained by solving the local equations of motion for a system ofn-components (n−1 solutes plus water) passing through a membrane. When viscous forces and position dependent membranepermeating species frictional interactions are considered, it becomes more difficult to obtain the result because even the stationary state problem becomes one of solving a second order linear ordinary differential equation for the barycentric velocity in a space divided inton+1 regions. Using the continuity of the boundary velocities and their gradients as well as the usual boundary conditions for the hydrodynamic problem, a set of 2n+1 linear equations in the intergration constants can be obtained and a closed form solution is possible. The resultant global description of the system does not obey Onsager reciprocity. What is more, the interpretation of global phenomenological coefficients in terms of local interactions in any simple way is next to impossible. This makes the hope of a molecular level interpretation of phenomenological membrane transport coefficients very slim. The relevance of this finding to the validity of reductionist approaches to biological transport is discussed.
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Mikulecky, D.C. Global flow equations for membrane transport from local equations of motion: I. The general case for (n−1) nonelectrolyte solutes plus water. Bltn Mathcal Biology 40, 791–805 (1978). https://doi.org/10.1007/BF02460607
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DOI: https://doi.org/10.1007/BF02460607