Non equilibrium oscillatory relaxation processes across biological membranes

Abstract

Linear phenomenological equations relating fluxes and driving forces have been largely employed in the study of several phenomena in synthetic membrane systems. 1 These equations contain drag coefficients fulfilling Onsager reciprocity relations. 2,3 Biological membranes are endowed with the ability to allow the transport of ions and molecules against their own concentration gradients. These processes are made thermodynamically possible by a coupled passive transport of another component driven by its own concentration gradient. This kind of coupling cannot be treated as an Onsager coupling. 1 A theory developed by A.M. Liquori to deal with these phenomena is further developed in order to study relaxations around the steady state of the non Onsager coupled diffusion of two components across a membrane microphase containing an allosteric protein in local thermodynamic equilibrium binding at the interphases between the membrane and the two bathing solutions. 1 Starting from two first order linear differential equations describing the two non Onsager coupled fluxes, two second order linear differential equations have been derived which are valid near the steady state. Their solutions correspond to damped oscillations around the steady state. 4 These solutions may be used to deal with the fluxes of Na + and K + across a nerve membrane following stimulation producing the typical temporal changes of electrical potential associated to a nerve spike. 5,6,7,8. It is shown that the “resting state” of a nerve membrane behaves as a “strange attractor” 4,9,10.