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

Kirchhoff's Law Can Be Exact

Kirchhoff's current law is thought to describe the translational movement of charged particles through resistors. But Kirchhoff's law is widely used to describe movements of current through resistors in high speed devices. Current at high frequencies/short times involves much more than the translation of particles. Transients abound. Augmentation of the resistors with ad hoc 'stray' capacitances is often used to introduce transients into models like those in real resistors. But augmentation hides the underlying problem, rather than solves it: the location, value and dielectric properties of the stray capacitances are not well determined. Here, we suggest a more general approach, that is well determined. If current is redefined as in Maxwell's equations, independent of the properties of dielectrics, Kirchhoff's law is exact and transients arise automatically without ambiguity. The transients in a particular real circuit-a high density integrated circuit for example-can then be described by measured constitutive equations together with Maxwell's equations without the introduction of arbitrary circuit elements.Comment: Version 3: Expanded treatment of continuity equatio

Maxwell Equations without a Polarization Field using a paradigm from biophysics

Electrodynamics is usually written with a polarization vector field to describe the response of matter to electric fields, or more specifically, to describe changes in distribution of charge as an electric field is changed. This approach does not allow unique specification of a polarization field from measurements of electric and magnetic fields. Many polarization fields produce the same electric and magnetic fields, because only the divergence of the polarization enters Maxwell's first equation, relating charge and electric field. The curl of any function can be added to a polarization field without changing the electric field at all. The divergence of the curl is always zero. Models of structures that produce polarization cannot be uniquely determined from electrical measurements for the same reason. Models must describe charge distribution not just distribution of polarization to be unique. I propose a different paradigm to describe field dependent charge, i.e., to describe the phenomena of polarization. I propose an operational definition of polarization that has worked well in biophysics where a field dependent, time dependent polarization provides the gating current that makes neuronal sodium and potassium channels respond to voltage. The operational definition has been applied successfully to experiments for nearly fifty years. Estimates of polarization have been computed from simulations, models, and theories using this definition and they fit experimental data quite well. I propose that the same operational definition be used to define polarization charge in experiments, models, computations, theories, and simulations of other systems. Charge movement needs to be computed from a combination of electrodynamics and mechanics because 'everything interacts with everything else'. The classical polarization field need not enter into that treatment at all.Comment: Typos correcte