Mechanics of nonplanar membranes with force-dipole activity

Active morphogenesis of patterned epithelial shells

Shape transformations of epithelial tissues in three dimensions, which are crucial for embryonic development or in vitro organoid growth, can result from active forces generated within the cytoskeleton of the epithelial cells. How the interplay of local differential tensions with tissue geometry and with external forces results in tissue-scale morphogenesis remains an open question. Here, we describe epithelial sheets as active viscoelastic surfaces and study their deformation under patterned internal tensions and bending moments. In addition to isotropic effects, we take into account nematic alignment in the plane of the tissue, which gives rise to shape-dependent, anisotropic active tensions and bending moments. We present phase diagrams of the mechanical equilibrium shapes of pre-patterned closed shells and explore their dynamical deformations. Our results show that a combination of nematic alignment and gradients in internal tensions and bending moments is sufficient to reproduce basic building blocks of epithelial morphogenesis, including fold formation, budding, neck formation, flattening, and tubulation.

Effective tension and fluctuations in active membranes

We calculate the fluctuation spectrum of the shape of a lipid vesicle or cell exposed to a nonthermal source of noise. In particular, we take constraints on the membrane area and the volume of fluid that it encapsulates into account when obtaining expressions for the dependency of the membrane tension on the noise. We then investigate three possible origins of the nonthermal noise taken from the literature: A direct force, which models an external medium pushing on the membrane, a curvature force, which models a fluctuating spontaneous curvature, and a permeation force coming from an active transport of fluid through the membrane. For the direct force and curvature force cases, we compare our results to existing experiments on active membranes.

Elastic moderation of intrinsically applied tension in lipid membranes

Tension in lipid membranes is often controlled externally, by pulling on the boundary of the membrane or changing osmotic pressure across a curved membrane. But modifications of the tension can also be induced in an internal fashion, for instance as a byproduct of changing a membrane's electric potential or, as observed experimentally, by activity of membrane proteins. Here we develop a theory that demonstrates how such internal contributions to the tension are moderated through elastic stretching of the membrane when the membrane is initially in a low-tension floppy state.

Effective zero-thickness model for a conductive membrane driven by an electric field

The behavior of a conductive membrane in a static (dc) electric field is investigated theoretically. An effective zero-thickness model is constructed based on a Robin-type boundary condition for the electric potential at the membrane, originally developed for electrochemical systems. Within such a framework, corrections to the elastic moduli of the membrane are obtained, which arise from charge accumulation in the Debye layers due to capacitive effects and electric currents through the membrane and can lead to an undulation instability of the membrane. The fluid flow surrounding the membrane is also calculated, which clarifies issues regarding these flows sharing many similarities with flows produced by induced charge electro-osmosis (ICEO). Nonequilibrium steady states of the membrane and of the fluid can be effectively described by this method. It is both simpler, due to the zero thickness approximation which is widely used in the literature on fluid membranes, and more general than previous approaches. The predictions of this model are compared to recent experiments on supported membranes in an electric field.

Dynamics of biomembranes with active multiple-state inclusions

Nonequilibrium dynamics of biomembranes with active multiple-state inclusions is considered. The inclusions represent protein molecules which perform cyclic internal conformational motions driven by the energy brought with adenosine triphosphate (ATP) ligands. As protein conformations cyclically change, this induces hydrodynamical flows and also directly affects the local curvature of a membrane. On the other hand, variations in the local curvature of the membrane modify the transition rates between conformational states in a protein, leading to a feedback in the considered system. Moreover, active inclusions can move diffusively through the membrane so that their surface concentration varies. The kinetic description of this system is constructed and the stability of the uniform stationary state is analytically investigated. We show that, as the rate of supply of chemical energy is increased above a certain threshold, this uniform state becomes unstable and stationary or traveling waves spontaneously develop in the system. Such waves are accompanied by periodic spatial variations of the membrane curvature and the inclusion density. For typical parameter values, their characteristic wavelengths are of the order of hundreds of nanometers. For traveling waves, the characteristic frequency is of the order of a thousand Hz or less. The predicted instabilities are possible only if at least three internal inclusion states are present.

Electrostatic and electrokinetic contributions to the elastic moduli of a driven membrane

We discuss the electrostatic contribution to the elastic moduli of a cell or artificial membrane placed in an electrolyte and driven by a DC electric field. The field drives ion currents across the membrane, through specific channels, pumps or natural pores. In steady state, charges accumulate in the Debye layers close to the membrane, modifying the membrane elastic moduli. We first study a model of a membrane of zero thickness, later generalizing this treatment to allow for a finite thickness and finite dielectric constant. Our results clarify and extend the results presented by D. Lacoste, M. Cosentino Lagomarsino, and J.F. Joanny (EPL 77, 18006 (2007)), by providing a physical explanation for a destabilizing term proportional to [see formula in text] in the fluctuation spectrum, which we relate to a nonlinear (E(2)) electrokinetic effect called induced-charge electro-osmosis (ICEO). Recent studies of ICEO have focused on electrodes and polarizable particles, where an applied bulk field is perturbed by capacitive charging of the double layer and drives the flow along the field axis toward surface protrusions; in contrast, we predict "reverse" ICEO flows around driven membranes, due to curvature-induced tangential fields within a nonequilibrium double layer, which hydrodynamically enhance protrusions. We also consider the effect of incorporating the dynamics of a spatially dependent concentration field for the ion channels.

Lipid flip-flop driven mechanical and morphological changes in model membranes

We study, using dissipative particle dynamics simulations, the effect of active lipid flip-flop on model fluid bilayer membranes. We consider both cases of symmetric as well as asymmetric flip-flops. Symmetric flip-flop leads to a steady state of the membrane with an effective temperature higher than that of the equilibrium membrane and an effective surface tension lower than that of the equilibrium membrane. Asymmetric flip-flop leads to transient conformational changes in the membrane in the form of bud or blister formation, depending on the flip rate.

Membrane tension lowering induced by protein activity

Using videomicroscopy we present measurements of the fluctuation spectrum of giant vesicles containing bacteriorhodopsin pumps. When the pumps are activated, we observe a significant increase of the fluctuations in the low wave vector region, which we interpret as due to a lowering of the effective tension of the membrane.

Fluctuation spectrum of quasispherical membranes with force-dipole activity

The fluctuation spectrum of a quasispherical vesicle with active membrane proteins is calculated. The activity of the proteins is modeled as the proteins pushing on their surroundings giving rise to nonlocal force distributions. Both the contributions from the thermal fluctuations of the active protein densities and the temporal noise in the individual active force distributions of the proteins are taken into account. The noise in the individual force distributions is found to become significant at short wavelengths.