Fluctuations of a driven membrane in an electrolyte

¹  Laboratoire Physico-Chimie Théorique, ESPCI - 10 rue Vauquelin, 75005 Paris, France
²  UMR 168/Institut Curie - 26 rue d'Ulm, 75005 Paris, France
³  Università degli Studi di Milano, Dipartimento di Fisica - Via Celoria 16, 20133 Milano, Italy

Received: 8 June 2006
Accepted: 9 November 2006

Abstract

We develop a model for a driven cell or artificial membrane in an electrolyte. The system is kept far from equilibrium by the application of a DC electric field or by concentration gradients, which causes ions to flow through specific ion-conducting units (representing pumps, channels or natural pores). We consider the case of planar geometry and Debye-Hückel regime, and obtain the membrane equation of motion within Stokes hydrodynamics. At steady state, the applied field causes an accumulation of charges close to the membrane, which, similarly to the equilibrium case, can be described with renormalized membrane tension and bending modulus. However, as opposed to the equilibrium situation, we find new terms in the membrane equation of motion, which arise specifically in the out-of-equilibrium case. We show that these terms lead in certain conditions to instabilities.