We present a general and systematic theory of non-equilibrium dynamics of multi-component fluid membranes, in general, and membranes containing transmembrane proteins, in particular. Developed based on a minimal number of principles of statistical physics and designed to be a meso/macroscopic-scale effective description, the theory is formulated in terms of a set of equations of hydrodynamics and linear constitutive relations. As a particular emphasis of the theory, the equations and the constitutive relations address both the thermodynamic and the hydrodynamic consequences of the unconventional material characteristics of lipid-protein membranes and contain proposals as well as predictions which have not yet been made in already existing work on membrane hydrodynamics and which may have experimental relevance. The framework structure of the theory makes possible its applications to a range of non-equilibrium phenomena in a range of membrane systems, as discussions in the paper of a few limit cases demonstrate.
European Physical Journal E. Soft Matter, 2005, Vol 16, Issue 4, p. 439-461