Simulations of Interacting Membranes in the Soft Confinement Regime

Abstract

The liquid crystalline model biomembrane system consisting of a stack of interacting membranes is studied in the realistic soft confinement regime by the newly developed Fourier Monte Carlo simulation technique. In this regime experiment and simulations show that the functional form of the fluctuation pressure is more nearly exponential rather than the power law valid for the hard confinement regime. The simulations provide quantitative improvement over perturbation theory. It is shown that the harmonic theory that is routinely used to interpret x-ray scattering line shapes is valid. Stacks of lipid bilayers (see Fig. 1) are model systems for biomembranes that are much studied for two reasons. First, such stacks diffract fairly well and this facilitates determination of the structure of individual membranes, which is of primary interest in biophysics. However, these stacks are not crystals with the long-range order that is assumed in traditional biophysical analysis, but smectic liquid crystals with quasi-long-range order. Therefore, quantitative use of the scattering intensity for structure determination requires correction for the fluctuations endemic in such systems [1]. A harmonic theory [2,3] that predicts power law tails in the scattering line shapes fits membrane data very well [4,5], but the anharmonicities that are inherent in realistic potentials have remained a concern for quantitative interpretation [6,7], even though a renormalization group analysis suggested that such effects are small [8].Stacks of bilayers are also much studied because they provide ideal environments to study fundamental interactions between bilayers, especially since the range of interbilayer distances a can be systematically varied by applying osmotic pressure P [9]. The corresponding theory [10] is an approximate first-order perturbation theory that again relies on harmonic assumptions, such as the normality of the probability distribution function of the interbilayer spacing. While this theory has been a valuable guide, it is too inaccurate to extract fundamental interbilayer interactions from P(a) data.Both these issues are addressed using Monte Carlo simulations with realistic intermembrane potentials for the biologically relevant regime where the interbilayer water spacing a is of order 5-30 Å and each membrane is flexible with bending modulus K c ≃ 10-25k B T. In this regime, called the soft confinement regime [10], it is usually supposed that the primary interbilayer interactions for dipolar lipids are the attractive van der Waals (vdW) potential and the mysterious, but easily measured, repulsive hydration potential, where z is the local distance between two membranes [11]. These interactions are significantly anharmonic, to the extent that the potential of a membrane midway between two neighboring membranes (at the dashed positions in Fig. 1) may have a maximum instead of a minimum. The contrasting regime, sometimes called the hard confinement regime, consists of only excluded volume or steric interactions betwe...

Bending Rigidities and Interdomain Forces in Membranes with Coexisting Lipid Domains

“…For large solvent layer thickness, the nonpairwise additive effects in the latter case become negligible and the van der Waals interaction potential for the two cases follows exactly the same separation dependence. Due to the divergence of the van der Waals potential for a / 0, the 1/a 2 term is cut off for a < 1 Å (38). In experiments, the collapse of chargeneutral bilayers due to van der Waals forces is avoided by very short-range steric interactions established by McIntosh et al (61) that occur at significantly higher osmotic pressures than those relevant for the experiments presented here (see also Fig.…”

Lipid bilayer structure

“…The Luzzati thickness is given by D B = V L /A, where for DPPC the lipid volume is accurately determined to be V L = 1232±2Å 3 per molecule [5]. Snapshot of a Monte Carlo simulation of eight liquid crystalline bilayers (in black) with fluctuating water spacings (in white) [20]. The mesoscale Monte Carlo simulation incorported bilayer bending energy and van der Waals and hydration force interactions between the bilayers (see McIntosh review -next paper).…”

Diffuse scattering provides material parameters and electron density profiles of biomembranes

“…Electron density profiles ͑z͒ ͑electrons/ Å 3 ͒ along the z direction perpendicular to DOPC bilayers at 30°C. The bilayer is symmetric with center at z = 0; a full water region is shown and the beginning of a second bilayer at z =40 Å. actions between bilayers [12,26] with the aid of Monte Carlo simulations [27].…”