Spontaneous Curvature C0 Research Articles

Phase interfaces within different vesicle shapes

Liquid droplets on flat surfaces generally exhibit a contact angle in a range from 0 to , but the two-phase interface within a vesicle membrane is very fascinating due to the involved force balance along three bending interfaces. Giant lipid vesicles encapsulated with the poly(ethylene glycol)/dextran aqueous two-phase system are established recently, and the phase interfaces within vesicle membrane are very interesting as experimentally observed. The developed theoretical framework by a combination of the Helfrich curvature elastic theory for vesicle membranes and self-consistent field theory for polymers has been extended to explore aqueous two phases within vesicles. The intrinsic contact angle that represents the material parameter, is introduced to describe this phase interfaces within vesicles, especially the transitions from complete wetting to partial wetting, from partial wetting to complete dewetting. The dependence of intrinsic contact angles on the parameters, such as the interaction strengths between the polymers and between the membrane and polymer , the volume fraction , impermeability of the membrane to the enclosed polymers and membrane spontaneous curvature c0, are thoroughly investigated, as well as these wetting/dewetting transitions are extensively discussed in the present study.

Mechanism behind the Beauty: The Golden Ratio Appeared in the Shape of Red Blood Cells

AbstractIn the past two decades, a rigorous solution for the shape of human red blood cell (RBC) with a negative spontaneous curvature c0 has been derived with the Helfrich model under the condition that both the osmotic pressure Δp and tensile stress λ are equal to zero. By fitting the experimentally observed shape of RBC, c0R0 has been predicted to be –1.62, theminus golden ratio, where R0 is the radius of a sphere which has the same surface area as RBC. In this paper, we verify this prediction by comparing experimental data with an analytical equation describing the relation between volume and surface area. Furthermore, it is also found ρmax /ρB ≈ 1.6 with ρmax the maximal radius and ρB the characteristic radius of RBC, showing an approximate beautiful golden cross section of RBC. On the basis of a complete numerical calculation, we propose a mechanism behind the beauty of the minus golden ratio that c0R0 results from the balance between the minimization of the surface area and the requirement of adequate deformability of RBC to allow it passing through the spleen, the so called “physical fitness test”.

Nanotubes from asymmetrically decorated vesicles

Hydrodynamic nanotube extrusion is used to characterize chitosan-decorated vesicles, which are more robust to pH and salt shocks and exhibit specific behavior under osmotic pressure if compared to their bare homologues. The vesicle attached to a micro-rod is submitted to a flow. Above a threshold velocity, we observe the extrusion of a lipidic nanotube. We study how it grows and relaxes when the flow is stopped. We find that extrusion forces for decorated vesicles are weaker than for bare vesicles. We interpret these results using a model that introduces the spontaneous curvature due to asymmetric adsorption of chitosan on the external leaflet of the bilayer, which allows us to calculate the stationary length of the tube versus the flow velocity and to estimate the spontaneous curvature c0.

A relationship between membrane properties forms the basis of a selectivity mechanism for vesicle self-reproduction.

Self-reproduction and the ability to regulate their composition are two essential properties of terrestrial biotic systems. The identification of non-living systems that possess these properties can therefore contribute not only to our understanding of their functioning but also hint at possible prebiotic processes that led to the emergence of life. Growing lipid vesicles have been previously established as having the capacity to self-reproduce. Here it is demonstrated that vesicle self-reproduction can occur only at selected values of vesicle properties. We treat as an example a simple vesicle with membrane elastic properties defined by a membrane bending modulus kappa and spontaneous curvature C0, whose volume variation depends on the membrane hydraulic permeability Lp and whose membrane area doubles in time Td. Vesicle self-reproduction is described as a process in which a growing vesicle first transforms its shape from a sphere into a budded shape of two spheres connected by a narrow neck, and then splits into two spherical daughter vesicles. We show that budded vesicle shapes can be reached only under the condition that Td Lpkappa C0(4)> or =1.85. Thus, in a growing vesicle population containing vesicles of different composition, only the vesicles for which this condition is fulfilled can increase their number in a self-reproducing manner. The obtained results also suggest that at times much longer than Td the number of vesicles with their properties near the "edge" in the system parameter space defined by the minimum value of the product Td Lpkappa C0(4), will greatly exceed the number of any other vesicles.

Budding of crystalline domains in fluid membranes.

Crystalline domains embedded in fluid membrane vesicles are studied by Monte Carlo simulations of dynamically triangulated surfaces and by scaling arguments. A budding transition from a caplike state to a budded shape is observed for increasing spontaneous curvature C0 of the crystalline domain as well as increasing line tension lambda. The location of the budding transition is determined as a function of C0, lambda, and the radius R(A) of the crystalline domain. In contrast to previous theoretical predictions, it is found that budding occurs at a value of the spontaneous curvature C0, that is always a decreasing function of the domain size R(A). Several characteristic scaling regimes are predicted. The distribution of five- and sevenfold disclinations as the budding transition is approached is determined, and the dynamics of the generation of defects is studied.

Effect of Added Salt and Poly(ethylene glycol) on the Phase Behavior of a Balanced AOT−Water−Oil System

The phase behavior of AOT−water−NaCl−poly(ethylene glycol) (PEG; Mw = 20 000)−isooctane mixtures at equal volumes of water and oil has been systematically explored as a function of AOT, NaCl, and PEG concentrations. The effect of adding PEG is in many respects similar to that of adding salt although the changes are less pronounced. Each additive, taken separately, shifts the phase behavior to higher temperature, promotes the formation of bicontinuous microemulsions, and induces a lamellar-to-bicontinuous microemulsion phase transition. The simultaneous presence of both additives enhances the effect of salt. These phase behavior results suggest that the two variables salt and PEG act in the same direction on the spontaneous curvature C0, the bending rigidity κ, and the Gaussian bending modulus κ of the AOT monolayer.

Spontaneous Curvature-Induced Rayleigh-like Instability in Swollen Cylindrical Micelles

We study a Rayleigh-like instability of an oil in water cylindrical “droplet” in the presence of excess surfactant. The surfactant monolayer is modeled by an interfacial bending energy with a nonvanishing spontaneous curvature C0. We find that, even when surfactant reduces the interfacial tension to a vanishingly small value, the bending energy with spontaneous curvature can destabilize the cylinder if its radius R is greater than C0-1. The cylinder deforms into “beads” which can eventually break up into spherical droplets whose radius we predict. Unlike in the classical Rayleigh case, we find that the total interfacial area is usually increasing. Using our theory, we discuss the kinetics of the transition from a microemulsion phase of swollen cylindrical micelles to a droplet phase, following a sudden increase in the spontaneous curvature parameter.

Surfactant film bending elasticity in microemulsions: Structure and droplet polydispersity

The surfactant film bending elasticity can be described by a spontaneous curvature C0 and two elastic constants K and K̄ associated with the mean curvature and the Gaussian curvature, respectively. These parameters are very important in the determination of the structure of the dispersions stabilized by the surfactant (droplets or sponge-like structures). We have studied ternary mixtures of oil, water, and nonionic surfactants of different chain lengths. Depending on the temperature, the microemulsions are in equilibrium with excess oil (o/w structure), excess water (w/o), or both excess oil and water (bicontinuous). We present neutron scattering data from which we determine the microemulsion structure and, in the case of droplet structures, of the droplet polydispersity. These results, in combination with those from earlier experiments using ellipsometry, are used to estimate K̄.

Shape equations of the axisymmetric vesicles.

Based on the same bending energy of the spontaneous curvature model, three shape equations for axisymmetric vesicles are derived from different variational methods. They are degenerate for the spherical vesicle, while for the cylindrical vesicle, two of them are the same. They all have a special toroidal solution, Clifford tori, but the constraints on the Lagrange multipliers DELTAP and lambda and the spontaneous curvature c0 are different. We consider the physical mode of variation and introduce an arbitrary parameter for the axisymmetric action; we get the shape equation in terms of this parameter from it. When this parameter is identified as the parameter rho, it reduces to the same equation that is from the general shape equation.

DETERMINATION OF SPONTANEOUS CURVATURE AND INTERNAL PRESSURE OF VESICLES AND RED CELLS BY THEIR SHAPE AND THE FLEXOELECTRIC EFFECT OF MEMBRANE

Three geometric relations for vesicle equilibrium within the Helfrich elasticity model have been derived. The relations can serve to determine the spontaneous curvature c0 and cell internal pressure −Δp=pin−pext from the vesicle shape. In analogy with the theory of the flexoelectric effect of nematic liquid crystals we have also obtained a relation between c0 and the membrane potential. By applying these predictions to the human red blood cell (RBC) shape measured by Evans and Fung we found good agreement of the calculated potential with measured values previously given by other biologists by direct impaling RBC with a microelectrode. The calculated value of the internal pressure is discussed by comparison with previous works.