Membrane Bending Rigidity Research Articles

Nonequilibrium size distributions of fluid membrane vesicles

We investigate nonequilibrium behavior of polydisperse ensembles of fluid membrane vesicles by means of a diffusive Boltzmann transport equation that incorporates vesicle diffusion and reactions between vesicles. This approach is used to study time evolutions of size distributions of initially monodisperse vesicle ensembles. We investigate various nonequilibrium paths that ensembles of vesicles may follow during the equilibration process. Depending on the initial size distribution of vesicles, the thermodynamic equilibrium may be reached either via a fusional growth of vesicles, or via their fissional decay. In the former case, typical vesicle size grows as $R(t)\ensuremath{\sim}{t}^{1/2}$ until it saturates to its equilibrium value, whereas in the latter case we find that vesicle size decays in a finite time proportional to $[R(0){]}^{1/3},$ where $R(0)$ is the initial vesicle size. The latter behavior is related to the length scale dependence of membrane bending and saddle splay rigidity.

Spin relaxation by collective director fluctuations and molecular diffusion in lamellar phases. Continuum theory of relaxation anisotropy and dispersion

The orientation and frequency dependence of nuclear spin relaxation rates can provide detailed information about the amplitudes and rates of collective orientational fluctuations (director fluctuations) in liquid crystals. In particular, the low-frequency spin relaxation rates from a lamellar phase reflect the membrane bending rigidity and the intermembrane forces. This information is contained in three spectral density functions Jn(ω), n=0,1,2. We have recently presented a continuum-mechanical theory for the second-order spectral density J1(ω). Here we extend the theory to the fourth-order spectral densities J0(ω) and J2(ω), which dominate the transverse relaxation rate in the parallel and perpendicular configurations. These spectral densities have previously been considered in connection with director fluctuations in nematic phases, neglecting the elastic and hydrodynamic anisotropy of the phase. In lamellar phases, this anisotropy plays a crucial role and must be retained in the relaxation theory. Director fluctuations can be induced by elastic distortion modes as well as by molecular translational diffusion. In a lamellar phase, these independent processes give rise to qualitatively different spin relaxation behavior. In particular, J0(0) and J2(0) diverge in the limit of quenched disorder. The theoretical results presented here are directly applicable to spin relaxation data from a variety of lamellar systems, including phospholipid bilayers and sterically stabilized dilute lamellar phases. An analysis of published H2 and P31 relaxation data from phospholipid bilayer phases is presented, leading to a qualitatively different picture from what has previously been deduced in terms of a free membrane theory.

Diffusion on a flexible surface

The self-diffusion of a particle on a flexible surface, such as a fluid bilayer membrane or a macroscopic interface, is analyzed theoretically in order to relate the macroscopic diffusion coefficient DM, describing displacements in a laboratory-fixed plane, to the intrinsic surface diffusion coefficient DS and to the configurational statistics of the surface. An exact result for DM is obtained for a rapidly fluctuating surface. For a static surface, rigorous bounds on DM are established and an effective medium approximation is derived that should remain accurate for strongly disordered surfaces. With the aid of these results, classical self-diffusion measurements can be used to study the configuration, bending rigidity, and interactions of flexible membranes and interfaces.

Evidence of entropic contribution to “hydration” forces between membranes Part II. Temperature dependence of the “hydration” force: a small angle neutron scattering study

The temperature dependence of structural parameters of 1,2-dimiristoyl-sn-glycero-phosphatidylcholine (DMPC) and 1,2-dipalmitoyl-sn-glycero-phosphatidylcholine (DPPC) membranes in D 2O (1% w/w of lipid) has been studied via neutron small-angle scattering. A new approach was used to determine the intermembrane distance d w. The repeat distance d was determined from the position of diffraction peaks from multilamellar membranes in solution. The thickness of membranes d L was calculated from small-angle scattering with single vesicles. The intermembrane distance d w was determined as the difference between d and d L. Repeat and intermembrane distances increase considerably with temperature increase at T > 65°C. However, the lipid bilayer thickness decreases continuously with the increase of temperature. The integral intensities of the diffraction peaks decrease considerably. It is shown here that the temperature dependence of the intermembrane distance can be explained by the increase of entropic forces due to an increase of protrusion-like thermal fluctuations of the membrane surface and membrane undulations. The membrane undulations increase due to the decrease of membrane bending rigidity. Considerable changes in the bending rigidity with temperature cannot be explained only by the reduction of the bilayer thickness. The increase of protrusion amplitude with temperature increase results in a dramatic decrease of the bending rigidity.

Oil-Water Interface in the Widom Model: Is It Smooth, Rough or Crumpled?

Trie interface in trie two-dimensional Ising model with only nearest-neighbour ferromagnetic interactions is known ta be rougir at ail temperatures T > o. Trie Widom model for temary microemulsions is, effectively, a spin-1/2 Ising model with, Dot Orly nearest-neighbour ferromagnetic interactions, but aise specific farther-neighbour antiferromagnetic interactions. We investigate trie effects of these farther-neighbour interactions m the Widom model on the roughening properties of the interface by carrymg eut Monte Carlo simulations. Temary microemulsions are three component mixtures where amphiphilic molecules act as surfactants between oil and water iii. Several lattice models of these systems bave been pro- posed and are similar in spirit to trie lattice gas model for trie liquid-gas transition (2). To our knowledge, trie Widom model (3) is trie simplest among trie lattice models of ternary microemulsions. This is, effectively, a spin-1/2 Ising model with not only nearest-neighbour ferromagnetic interactions, but also with farther neighbour antiferromagnetic interactions of specific type descnbed below. Trie farther-neighbour interactions arise from Widom's prescrip- tion for incorporating trie bending rigidity of trie amphiphilic membrane (a monolayer) formed by trie surfactants at the oil-water interface (4). Trie interface between trie up-spm and down- spin domains in trie two-dimensional Ising model with only nearest-neighbour interactions is known to be rougir at ail non-zero temperatures. Trie atm of this communication is to study trie effects of trie farther-neighbour antiferromagnetic interactions m trie Widom model on trie roughening properties of trie interface. In contrast to trie earlier series expansion study for trie three dimensional Widom model by Kahng et ai. (5) we carry out Monte Carlo Simulation of trie two dimensional Widom model. In trie Widom model trie amphiphilic molecules, as well as trie molecules of oit and water, are assumed to be located on trie nearest-neighbour bonds of a simple cubic lattice. Classical Ising spins are put at each of trie lattice sites and one uses trie convention that each bond between nearest-neighbour (+ +) spin pairs is occupied by a molecule of oil, that between (--) spin pairs is occupied by a molecule of water, and that between anti-parallel nearest-neighbour spin pairs is occupied by a surfactant. Trie Hamiltonian of trie system m ternis of trie Ising spin

Influence of bilayer fluctuations on the steric interactions between polymer-grafted bilayers

Abstract We propose a mechanism, through which the low membrane bending rigidity changes the steric polymer repulsion between polymer-grafted bilayers. We calculate the energy of a polymer chain trapped between two thermally undulating surfaces. The proposed treatment is in terms of de Gennes' theory of fluctuations in liquid crystals, later developed by Helfrich for membranes. We show that the confinement energy of the polymer increases due to membrane fluctuations. Also, the repulsive forces between soft polymer-grafted bilayers can extend further from the surface than the height of the polymer layer.

Bending tensions and the bending rigidity of fluid membranes

It is shown theoretically that the lateral tension associated with bending may in erect reduce the elastic resistance to curvature of fluid membranes. In particular, the spontaneous curvature of surfactant monolayers gives rise to a reduction of the bending rigidity

Static and dynamic rigidities of normal and sickle erythrocytes. Major influence of cell hemoglobin concentration.

Static and dynamic deformabilities of erythrocytes are important determinants of microcirculatory blood flow. To determine the influence of increased cellular hemoglobin concentration on these properties, we quantitated static and dynamic deformabilities of isolated subpopulations of oxygenated normal and sickle erythrocytes with defined cell densities using micromechanical manipulations of individual cells. The rheological properties measured to characterize static deformability were membrane extensional rigidity and bending rigidity. To characterize dynamic deformability of the cells, we measured the time constants for rapid elastic recovery from extensional and bending deformations. The extensional rigidity of sickle cells increased with increasing cell hemoglobin concentration while that of normal cells was independent of the state of cell hydration. Moreover, sickle cells were found to exhibit inelastic behavior at much lower cell hemoglobin concentrations than normal cells. In contrast, the dynamic rigidity of both normal and sickle cells was increased to the same extent at elevated hemoglobin concentrations. Moreover, this increase in dynamic rigidity with increasing cellular dehydration was much more pronounced than that seen for static rigidity. Both the increased static and dynamic rigidities of the dehydrated sickle cells could be greatly improved by hydrating the cells. This suggests that increased bulk hemoglobin concentration, which is perhaps inordinately increased adjacent to the membrane, plays a major role in regulating the rigidity of sickle cells. In addition, irreversible membrane changes also appear to accompany cell dehydration in vivo, resulting in increased membrane shear rigidity and plastic flow. We expect that the marked increases in rigidity of dehydrated sickle cells observed here may have a major influence on the dynamics of their circulation in the microvasculature.

Bending elastic modulus of red blood cell membrane derived from buckling instability in micropipet aspiration tests

Observation of cell membrane buckling and cell folding in micropipette aspiration experiments was used to evaluate the bending rigidity of the red blood cell membrane. The suction pressure required to buckle the membrane surface initially was found to be about one-half to two-thirds of the pressure that caused the cell to fold and move up the pipet. A simple analytical model for buckling of a membrane disk supported at inner and outer radii correlates well with the observed buckling pressures vs. pipet radii. The buckling pressure is predicted to increase in inverse proportion to the cube of the pipet radius; also, the buckling pressure depends inversely on the radial distance to the toroidal rim of the cell, normalized by the pipet radius. As such, the pressure required to buckle the membrane with 1 X 10(-4) cm diam pipet would be about four times greater than with a 2 X 10(-4) cm pipet. This is the behavior observed experimentally. Based on analysis of the observed buckling data, the membrane bending or curvature elastic modulus is calculated to be 1.8 X 10(-12) dyn-cm.