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.