Abstract
A general formulation for both passive and active transmembrane transport is derived from basic thermodynamical principles. The derivation takes into account the energy required for the motion of molecules across membranes and includes the possibility of modeling asymmetric flow. Transmembrane currents can then be described by the general model in the case of electrogenic flow. As it is desirable in new models, it is possible to derive other well-known expressions for transmembrane currents as particular cases of the general formulation. For instance, the conductance-based formulation for current turns out to be a linear approximation of the general formula for current. Also, under suitable assumptions, other formulas for current based on electrodiffusion, like the constant field approximation by Goldman, can be recovered from the general formulation. The applicability of the general formulations is illustrated first with fits to existing data, and after, with models of transmembrane potential dynamics for pacemaking cardiocytes and neurons. The general formulations presented here provide a common ground for the biophysical study of physiological phenomena that depend on transmembrane transport.
Highlights
A general formulation for both passive and active transmembrane transport is derived from basic thermodynamical principles
The two sections added to the manuscript contain the derivation of the Goldman constant field approximation from the general formula derived in the article, and a model of neuronal membrane potential dynamics that uses the general formulation for transport
The derivation is based on a general thermodynamic scheme that takes into account the rate, stoichiometry, and the direction in which the molecules are transported across the membrane
Summary
Since w models the activation of a population of channels, it makes sense assume that its dynamics follow a logistic scheme, without adding extra powers to w This follows the experimentally observed dynamics which have been reported repeatedly, including those of delayed-rectifier K+ currents recorded in voltage clamp (see for instance Figure 3 in Hodgkin & Huxley, 1952). To include these properties into the model, the membrane capacitance was specified first, the maximum ∂tv was adjusted by fitting the parameter aNaT, and the contributions for the K+ channels and the Na-K ATPase are set to obtain spiking and fit the rheobase. The current mediated by Na/K-ATPase acts as an extra attracting force toward vNaK that increases nonlinearly as the distance between v and vNaK increases
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