The dynamical Matryoshka model: 1. Incoherent neutron scattering functions for lipid dynamics in bilayers

Abstract

Fluid lipid bilayers are the building blocks of biological membranes. Although there is a large amount of experimental data using inconsistent quasi-elastic neutron scattering (QENS) techniques to study membranes, very little theoretical works have been developed to study the local dynamics of membranes. The main objective of this work is to build a theoretical framework to study and describe the local dynamics of lipids and derive analytical expressions of inconsistent diffusion functions (ISF) for QENS. As results, we developed the dynamical Matryoshka model which describes the local dynamics of lipid molecules in membrane layers as a nested hierarchical convolution of three motional processes: (i) individual motions described by the vibrational motions of H-atoms; (ii) internal motions including movements of the lipid backbone, head groups and tails, and (iii) molecule movements of the lipid molecule as a whole. The analytical expressions of the ISF associated with these movements are all derived. For use in analyzing the QENS experimental data, we also derived an analytical expression for the aggregate ISF of the Matryoshka model which involves an elastic term plus three inelastic terms of well-separated time scales and whose amplitudes and rates are functions of the lipid motions. And as an illustrative application, we used the aggregated ISF to analyze the experimental QENS data on a lipid sample of multilamellar bilayers of DMPC (1,2-dimyristoyl-\textit{sn}-glycero-3-phosphocholine). It is clear from this analysis that the dynamical Matryoshka model describes very well the experimental data and allow extracting the dynamical parameters of the studied system.

The dynamical Matryoshka model: 3. Diffusive nature of the atomic motions contained in a new dynamical model for deciphering local lipid dynamics

“…This suggests that the local atomic motions of the tails are faster than those of the head groups. This is in good agreement with the Matryoshka model [21], where it was necessary to ascribe the contribution of the tail groups to the fast motions in order to fully account for the EISFs and QISFs of the current samples. Since the Matryoshka model was established independently of the width analysis of Lorentzian functions described in this paper, this agreement further enhances the validity of the Matryoshka model.…”

“…In a previous QENS study on the bilayers of dipalmitoyl-phosphatidylcholine (DPPC) with and without deuteration of its tail group, the same tendency has been observed [29]. The EISF/QISF analysis by the Matryoshka model on the same samples has shown that the diffusion radius of the head group (d54DMPC MLB135) on the membrane plane is larger than that of the whole molecule [21,22]. Together with this finding, the present results imply that the head group of DMPC takes more time to explore the available space than the tail group.…”

“…Details of sample preparations, QENS experiments, and the analysis of the QENS spectra are described in the accompanying papers [21,22]. Briefly, the following samples were used for neutron experiments:…”

“…Based on the dynamical models above, a new theoretical model named Matryoshka model has been presented in the accompanying papers [21,22], where the dynamic structure factor S(Q, ω) is analytically expressed by directly incorporating the scattering functions of various motions that lipid molecules undergo in addition to the decomposition of all the possible motions into three classes, i.e. slow, intermediate, and fast motions.…”

“…This has enabled the detailed investigation of the geometry of motions in lipid molecules placed in various physicochemical environments. On the other hand, although the diffusive nature of the motions classified as the slow, intermediate and fast motions in the Matryoshka model is theoretically characterized through a series of analytical equations of relaxation rates of each of these motions [21], it has not yet been experimentally characterized. In the present paper, this aspect of each of the three types of motions are reported and discussed.…”