Small-angle scattering (SAS) is a powerful technique for characterizing nanoscale structures by analyzing how photons or neutrons scatter from a sample. While widely used to characterize materials and biomolecules such as proteins, RNA, and lipids, extracting structural parameters from scattering profiles remains challenging. This process typically requires domain expertise and relies on fitting experimental scattering profiles to approximate mathematical models (analytical models). Of particular interest is resolving the real space structure of lipid nanoparticle (LNP)s. LNPs are used to deliver mRNA in Covid vaccines and are candidate delivery vehicles for many emerging biotherapeutics.

A machine learning framework is developed to directly infer structural parameters from the scattering length-weighted pair distance distribution function (PDDF), p(r). The PDDF is obtained directly from the SAS data by inverse Fourier transform (IFT) of the scattering curve I(Q) under appropriate conditions. A synthetic dataset of computed p(r) functions and their corresponding structural parameters was generated and used to train a machine learning model. p(r) functions are computed from analytical models as well as numerical simulations of model LNPs of varying size, composition, and structure. The effects of contrast variation (such as afforded by deuteration) are included to enable simultaneous resolution of multiple I(Q) measurements with varying contrast.

A variational autoencoder (VAE) was trained to recover key structural parameters, including particle radius, shell dimensions, internal structure and possible bleb structures directly from the IFT of the SAS. The model jointly performs classification of structure type (e.g., solid or hollow sphere, bleb, internal structure), regression of underlying geometric parameters, and reconstruction of the p(r) curve. By sampling the latent space, the model also estimates uncertainty in its parameter predictions. This framework captures the underlying structure of p(r) curves in a low-dimensional latent space and enables confidence-aware inference.

Our framework enables exploration of how features in p(r) curves reflect underlying physical structures, assesses the model’s generalization across diverse structural types, and provides a fast and flexible alternative to traditional model-based fitting, laying the groundwork for data-driven structural analysis in SAS-based studies.

Afnan Pathan

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