A general theory of non-equilibrium dynamics of lipid-protein fluid membranes

Abstract

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.

Fluctuation spectrum of quasispherical membranes with force-dipole activity

“…The φ-field in this term is introduced for convenience, because then the potential V will not be present in the force balance equation of the membrane, see Equations (7) to (9) later. Having specified the free energy in Equation (1), we can now follow the formalism of [9] and write down the dynamics of the membrane. At low Reynolds number the equation of motion for the shape field R is simply the condition of force balance of the membrane.…”

“…The boundary condition that is usually imposed when dealing with viscous fluids is the so-called no-slip boundary condition, where the bulk fluid at the boundary is constrained to have the velocity of the boundary material. In [9] it was argued that for a multicomponent membrane the general form of this boundary condition was a linear combination of the flows of the different species of molecules in the membrane. If we let j α A be the current for the density n A entering the conservation law [9] …”

“…In [9] it was argued that for a multicomponent membrane the general form of this boundary condition was a linear combination of the flows of the different species of molecules in the membrane. If we let j α A be the current for the density n A entering the conservation law [9] …”

“…They should satisfy the constraint A L A ± n A = 1 such that it is possible to have uniform motion of the whole system. In [9] it was argued that the precise values of the L A ± can influence the distribution of proteins in the membrane if the membrane is subjected to a bulk shear flow with velocities of the order k B T /(ηL A ± ). However, the velocities in the bulk fluids induced by thermal noise are of the order k B T /(ηλ 2 ), where λ is the wavelength of the undulation in question.…”

“…Close to equilibrium we can write down a constitutive relation coupling this current linearly to possible driving forces. The only driving force we have that transform in the same way as j α A under symmetry transformations (including the approximate symmetry of exchanging n p + and n p − ) is the gradient of the corresponding chemical potential [9] …”