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.

本文开发了一个框架来计算来自高度弯曲、动态波动和可能不均匀的膜的小角度中子散射 (SANS)。正如分子建模所预测的那样，需要这种方法来计算耦合到曲率的纳米级膜域的散射。通过分子动力学模拟可以很容易地获得小型平面双层贴片的详细中子散射长度密度。开发了平面散射长度密度的数学机械变换来预测弯曲的散射双层。通过模拟波动的、弯曲的、表面连续模型，可以达到长时间和长度尺度，同时借助平面到曲线的转换，可以保留散射长度密度的分子特征。该方法的测试案例是通过构建粗粒脂质囊泡来开发的，该协议旨在缓解囊泡内的渗透压力和小叶之间的脂质数压力。一个问题是混合模型是否能够复制来自小囊泡高度变形的内部和外部小叶的散射。匹配完整（分子囊泡）和混合（连续囊泡）模型的散射表明，完整囊泡的内外小叶横向扩张，与之前的马提尼力场模拟一致，显示小囊泡变薄。囊泡结构与由一组弹性参数变形的零张力小叶不一致，结果表明这在散射中很明显。该方法可用于将任何分子模型的中子散射长度密度的观察结果从小块转化为大长度和时间尺度。