A Model of Electrodiffusion and Osmotic Water Flow and its Energetic Structure

We introduce a model for ionic electrodiffusion and osmotic water flow through cells and tissues. The model consists of a system of partial differential equations for ionic concentration and fluid flow with interface conditions at deforming membrane boundaries. The model satisfies a natural energy equality, in which the sum of the entropic, elastic and electrostatic free energies are dissipated through viscous, electrodiffusive and osmotic flows. We discuss limiting models when certain dimensionless parameters are small. Finally, we develop a numerical scheme for the one-dimensional case and present some simple applications of our model to cell volume control

Maxwell's Current in Mitochondria and Nerve

Maxwell defined true current in a way not widely used today. He said that "... true electric current ... is not the same thing as the current of conduction but that the time-variation of the electric displacement must be taken into account in estimating the total movement of electricity". We show that true current is a universal property independent of properties of matter, shown using mathematics without approximate dielectric constants. The resulting Maxwell Current Law is a generalization of the Kirchhoff Law of Current of circuits, that also includes displacement current. Engineers introduce displacement current through supplementary 'stray capacitances'. The Maxwell Current Law does not require currents to be confined to circuits. It can be applied to three dimensional systems like mitochondria and nerve cells. The Maxwell Current Law clarifies the flow of electrons, protons, and ions in mitochondria that generate ATP, the molecule used to store chemical energy throughout life. The currents are globally coupled because mitochondria are short. The Maxwell Current Law approach reinterprets the classical chemiosmotic hypothesis of ATP production. The conduction current of protons in mitochondria is driven by the protonmotive force including its component electrical potential, just as in the classical chemiosmotic hypothesis. Conduction current is, however, just a part of the true current analyzed by Maxwell. Maxwell's current does not accumulate, in contrast to the conduction current of protons which does accumulate. Details of accumulation do not appear in the true current. The treatment here allows the chemiosmotic hypothesis to take advantage of knowledge of current flow in physical and engineering sciences, particularly Kirchhoff and Maxwell Current Laws. Knowing the current means knowing an important part of the mechanism of ATP synthesis.Comment: Version 3 with typos corrected and revised discussion of stray capacitances and chemiosmotic hypothesi