Relating the structure factors of two-dimensional materials in planar and spherical geometries

Modulated and spiral surface patterns on deformable lipid vesicles

We investigate the behavior of two-dimensional systems that exhibit a transition between homogeneous and spatially inhomogeneous phases, which have spherical topology, and whose mechanical properties depend on the local value of the order parameter. One example of such a system is multicomponent lipid bilayer vesicles, which serve as a model to study cellular membranes. Under certain conditions, such bilayers separate into coexisting liquid-ordered and liquid-disordered regions. When arranged into the shape of small vesicles, this phase coexistence can result in spatial patterns that are more complex than the basic two-domain configuration encountered in typical bulk systems. The difference in bending rigidity between the liquid-ordered and liquid-disordered regions couples the shape of the vesicle to the local composition. We show that this interplay gives rise to a rich phase diagram that includes homogeneous, separated, and axisymmetric modulated phases that are divided by regions of spiral patterns in the surface morphology.

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.

Simulation Best Practices for Lipid Membranes [Article v1.0]

We establish a reliable and robust standardization of settings for practical molecular dynamics (MD) simulations of pure and mixed (single- and multi-component) lipid bilayer membranes. In lipid membranes research, particle-based molecular simulations are a powerful tool alongside continuum theory, lipidomics, and model, in vitro, and in vivo experiments. Molecular simulations can provide precise and reproducible spatiotemporal (atomic- and femtosecond-level) information about membrane structure, mechanics, thermodynamics, kinetics, and dynamics. Yet the simulation of lipid membranes can be a daunting task, given the uniqueness of lipid membranes relative to conventional liquid-liquid and solid-liquid interfaces, the immense and complex thermodynamic and statistical mechanical theory, the diversity of multiscale lipid models, limitations of modern computing power, the difficulty and ambiguity of simulation controls, finite size effects, competitive continuum simulation alternatives, and the desired application, including vesicle experiments and biological membranes. These issues can complicate an essential understanding of the field of lipid membranes, and create major bottlenecks to simulation advancement. In this article, we clarify these issues and present a consistent, thorough, and user-friendly framework for the design of state-of-the-art lipid membrane MD simulations. We hope to allow early-career researchers to quickly overcome common obstacles in the field of lipid membranes and reach maximal impact in their simulations.