Abstract
A generic 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 generic 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 generic formulation. For instance, the conductance-based formulation for current turns out to be a linear approximation of the generic current. Also, under suitable assumptions, other formulas for current based on electrodiffusion, like the constant field approximation by Goldman, can also be recovered from the generic formulation. The applicability of the generic formulations is illustrated first with fits to existing data, and after, with models of transmembrane potential dynamics for pacemaking cardiocytes and neurons. The generic formulations presented here provide a common ground for the biophysical study of physiological phenomena that depend on transmembrane transport.
Highlights
One of the most important physiological mechanisms underlying communication within and between cells is the transport of molecules across membranes
Molecules are passively transported across a membrane when they move along theirchemical gradient and occurs through channels that may be spontaneously formed within the lipid bilayer (Blicher & Heimburg, 2013), or lined by transmembrane proteins (Hille, 1992; Stein & Litman, 2014) that may be selective for molecules of specific types (Almers & McCleskey, 1984; Doyle et al, 1998; Favre et al, 1996)
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
One of the most important physiological mechanisms underlying communication within and between cells is the transport of molecules across membranes. Consider transmembrane electrodiffusive transport of a single ionic type x, with zx and vx representing the valence and the Nernst potential for x-ions, respectively In this case, the reversal potential satisfies v o n (c xx d )z v x xx ηxvx, and the generic expression (16) can be rewritten as ix qηxrx ηx bx. To show the application of the formulations discussed earlier, let us build a generic model of transmembrane potential dynamics with currents generated by N different electrogenic transport mechanisms. The system includes an equation for the dynamics for c in which c converges to a steady state c∞ in the absence of Ca2+ fluxes, and increases proportionally to the total transport of Ca2+ ions via L-type channels and Na+-Ca2+ exchangers (Figure 4). Ca2+ enters the cell in exchange for Na+ that moves out when v > vNaCa, during most of the increasing phase and the initial depolarization phase of the action potential (blue lines in Figure 4A and C, and Figure 6)
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