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-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.

中文翻译：

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动力学 Matryoshka 模型：1. 双层脂质动力学的非相干中子散射函数

流体脂质双层是生物膜的组成部分。尽管有大量使用不一致准弹性中子散射 (QENS) 技术来研究膜的实验数据，但很少有理论工作用于研究膜的局部动力学。这项工作的主要目标是建立一个理论框架来研究和描述脂质的局部动力学，并推导出 QENS 不一致扩散函数 (ISF) 的分析表达式。作为结果，我们开发了动力学 Matryoshka 模型，该模型将膜层中脂质分子的局部动力学描述为三个运动过程的嵌套层次卷积：（i）由 H 原子的振动运动描述的个体运动；(ii) 内部运动，包括脂质骨架的运动，头部基团和尾部，以及（iii）整个脂质分子的分子运动。与这些运动相关的 ISF 的分析表达式都是派生出来的。为了用于分析 QENS 实验数据，我们还推导出了 Matryoshka 模型的总 ISF 的解析表达式，该模型涉及一个弹性项加上三个分离良好的时间尺度的非弹性项，其振幅和速率是脂质运动的函数。作为说明性应用，我们使用聚集的 ISF 分析了 DMPC（1,2-二肉豆蔻酰基- 我们还推导出了 Matryoshka 模型的总 ISF 的解析表达式，它涉及一个弹性项加上三个分离良好的时间尺度的非弹性项，其振幅和速率是脂质运动的函数。作为说明性应用，我们使用聚集的 ISF 分析了 DMPC（1,2-二肉豆蔻酰基- 我们还推导出了 Matryoshka 模型的总 ISF 的解析表达式，它涉及一个弹性项加上三个分离良好的时间尺度的非弹性项，其振幅和速率是脂质运动的函数。作为说明性应用，我们使用聚集的 ISF 分析了 DMPC（1,2-二肉豆蔻酰基-sn-甘油-3-磷酸胆碱）。从这个分析中可以清楚地看出，动态套娃模型很好地描述了实验数据，并允许提取所研究系统的动态参数。