Biological membranes in living organisms play the fundamental role of acting as boundaries and facilitate compartmentalization. From a structural perspective they are essentially constituted by an amphiphilic lipid membrane in which sugars, peptides and proteins are incorporated. These quasi-2-dimensional layers are literally vital for the cell, as membranes work as catalysts for some of the main chemical reactions involved in cell survival and homeostasis and govern all communication between a cell and its surroundings. The focus of the work presented in this thesis is to understand how the physical properties of lipid membranes relate to the behavior and functional properties of biological membranes, with special attention to the role of biological membranes in nerve signal propagation.

We start by exploring the properties of polar lipid membranes in order to tackle the problem of the coupling between the membrane and the electrical eld within a universal thermodynamic framework. Within this framework, known electrical phenomena associated with lipid membranes such as o set voltage, electrostriction, piezoelectricity and exoelectricity can be captured and viewed as special cases of a more general treatment. This purely thermodynamical treatment only describes the equilibrium properties of the membrane, however biological processes are of course dynamical in nature. A clear understanding of the dynamical behavior of lipid membranes is therefore essential when we aim at unraveling the functional behavior of membranes in biological systems. In order to do so we apply linear response theory and non-equilibrium thermodynamics to lipid membranes and propose a new approach: we investigate the relaxation behavior of lipid membranes in the vicinity of their lipid melting transition, taking into account the coupling between thermodynamical uctuations and the available heat reservoir. The next step is to combine the knowledge on lipid membranes subjected to an electrical eld with the knowledge on their relaxation behavior and use our understanding to attempt to re-evaluate the results of common electrophysiological methods such as \jump experiments" and impedance spectroscopy performed on lipid membranes. By doing so we observe that a number of non-linear phenomena previously thought to be associated with the presence of proteins embedded in the membrane can just as well be produced by a 'pure' lipid membrane.