A combined molecular/continuum-modeling approach to predict the small-angle neutron scattering of curved membranes

This paper develops a framework to compute the small-angle neutron scattering (SANS) from highly curved, dynamically fluctuating, and potentially inhomogeneous membranes. This method is needed to compute the scattering from nanometer-scale membrane domains that couple to curvature, as predicted by molecular modeling. The detailed neutron scattering length density of a small planar bilayer patch is readily available via molecular dynamics simulation. A mathematical, mechanical transformation of the planar scattering length density is developed to predict the scattering from curved bilayers. By simulating a fluctuating, curved, surface-continuum model, long time- and length-scales can be reached while, with the aid of the planar-to-curved transformation, the molecular features of the scattering length density can be retained. A test case for the method is developed by constructing a coarse-grained lipid vesicle following a protocol designed to relieve both the osmotic stress inside the vesicle and the lipid-number stress between the leaflets. A question was whether the hybrid model would be able to replicate the scattering from the highly deformed inner and outer leaflets of the small vesicle. Matching the scattering of the full (molecular vesicle) and hybrid (continuum vesicle) models indicated that the inner and outer leaflets of the full vesicle were expanded laterally, consistent with previous simulations of the Martini forcefield that showed thinning in small vesicles. The vesicle structure is inconsistent with a zero-tension leaflet deformed by a single set of elastic parameters, and the results show that this is evident in the scattering. The method can be applied to translate observations of any molecular model's neutron scattering length densities from small patches to large length and timescales.

Laterally Resolved Small-Angle Scattering Intensity from Lipid Bilayer Simulations: An Exact and a Limited-Range Treatment

When combined, molecular simulations and small-angle scattering experiments are able to provide molecular-scale resolution of structure. Separately, scattering experiments provide only intermingled pair correlations between atoms, while molecular simulations are limited by model quality and the relatively short time scales that they can access. Their combined strength relies on agreement between the experimental spectra and those computed by simulation. To date, computing the neutron spectra from a molecular simulation of a lipid bilayer is straightforward only if the structure is approximated by laterally averaging the in-plane bilayer structure. However, this neglects all information about lateral heterogeneity, e.g., clustering of components in a lipid mixture. This paper presents two methods for computing the scattering intensity of simulated bilayers with in-plane heterogeneity, enabling a full treatment of both the transverse and lateral bilayer structure for the first time. The first method, termed the Dirac Brush, computes the exact spectra including spurious artifacts resulting from using information from neighboring periodic cells to account for the long-range structure of the bilayer. The second method, termed PFFT, applies a mean-field treatment in the field far from a scattering element, resulting in a correlation range that can be tuned (eliminating correlations with neighboring periodic images), but with computational cost that prohibits obtaining the exact (Dirac Brush) spectra. Following their derivation, the two methods are applied to a coarse-grained molecular simulation of a bilayer inhomogeneity, demonstrating the contributions of lateral correlations to the resulting spectra.