College 8 Seminar | Stochastic models for joint elastic and inelastic scattering data analysis of fluctuating membranesfacility

Membranes are ubiquitous in biological and synthetic systems. Developing analytical tools to investigate their structure and dynamics is key to understanding their physicochemical properties, and in the case of biological membranes how they fulfill their function. In that context, scattering methods (of either x-rays or neutrons) play a unique role because they enable one to characterize structures in situ in their natural environment with nanometer resolution.

In general, different models are used to analyze the elastic and inelastic scattering of membranes. Typically, small-angle scattering (SAXS or SANS) of membranes is often analyzed with one-dimensional scattering-length density profiles. And neutron spin-echo (NSE) data measured on the same systems are often analyzed using stretched exponentials, inspired by theoretical results about bending fluctuations of two-dimensional films. This situation prevents one from building on the structure inferred from SAXS/SAS to unravel the dynamics hidden in the NSE data.

This presentation focuses on a mathematical model developed to jointly analyze elastic and inelastic scattering data of fluctuating membranes within a single theoretical framework. The model builds on a non-homogeneously clipped time-dependent Gaussian random field. The approach is illustrated with the analysis of SAXS/SANS/NSE data measured on vesicles prepared from phospholipids extracted from porcine brain tissues [1]. The parameters inferred on the entire data set are the lengths of the chain and the head of the molecules that make up the membrane, the amplitude and lateral sizes of the bending deformations, the thickness fluctuation, and a single parameter characterizing the dynamics. The model is afterwards generalized to allow for the presence of protein-like inclusions in the membrane, and it is used to analyze SAXS/SANS/NSE of red blood cell membranes, of which transmembrane proteins constitute 25% of the volume [2].

[1] C.J. Gommes, P. Dubey, A. Stadler, B. Wu, O. Czakkel, L. Porcar, S. Jacksch, S. Frielinghaus, O. Holderer. Gaussian model of fluctuating membrane and its scattering properties. Phys. Rev. E 2024, 110, 034608; [2] C. J. Gommes, O. Matsarskaia, J. M. Pusterla, I. Graf von Westarp, B. Wu, O. Czakkel, A. M. Stadler. Model for small-angle scattering analysis of membranes with protein-like inclusions. J. Appl. Cryst. 2025, 58, 1571.