Mechanics of nonplanar membranes with force-dipole activity

Abstract

A study is made of how active membrane proteins can modify the long wavelength mechanics of fluid membranes. The activity of the proteins is modelled as disturbing the protein surroundings through non-local force distributions of which a force-dipole distribution is the simplest example. An analytic expression describing how the activity modifies the force-balance equation for the membrane surface is obtained in the form of a moment expansion of the force distribution. This expression allows for further studies of the consequences of the activity for non-planar membranes. In particular the active contributions to mechanical properties such as tension and bending moments become apparent. It is also explained how the activity can induce a hydrodynamic attraction between the active proteins in the membrane.

Fluctuation spectrum of quasispherical membranes with force-dipole activity

“…In this paper the Gibbs formalism of [7,9] was used to calculate the quasi-spherical shape fluctuation spectrum, given in Equation (57), for the force-dipole model of [6]. This calculation allows for further testing of the forcedipole through video microscopy experiments, something which is needed to test the model more stringently.…”

“…Note that, contrary to [6,7], we have for simplicity ignored any dependence of the protein activity on the local curvature of the membrane, but included internal noise in the model instead.…”

“…Most of the work needed to do this was done in [7], where it was found that the important contribution of the force-dipoles to the dynamics was to modify the force balance condition for the membrane to…”

“…Due to the fast balancing of forces in the tangential directions of the membrane, fluctuations in σ dip will immediately be counterbalanced by changes in σ φ , and therefore only the average value σ 0,dip will have an influence on the dynamics of the membrane shape. A discussion of the magnitude of this contribution can be found in [7]. Q is a measure of how much the bending moments in the membrane is modified by the activity of the force-dipoles.…”

“…In [7] the force-dipole model was reformulated into an equivalent but calculationwise more manageable formulation, which was called the Gibbs formulation for the system. One purpose of the present paper is to show how this reformulation makes it possible to calculate the fluctuation spectrum of a quasi-spherical vesicle.…”