A novel generic method for prediction of spectral line shapes from Molecular Dynamics modelling: Application to EPR

近几十年来的技术进步导致光谱仪灵敏度的提高，使其能够准确测量分子动力学和结构。电子顺磁共振（EPR）光谱就是一个例子。自旋标记是一种特殊设计的化学“试剂”，携带一个稳定的未配对电子。它们可以被引入到复杂的分子系统中，以报告主体分子的有序性和动力学。自旋标记在磁场中的取向对这种线形有显著的影响，因此可以研究分子的迁移率、动力学和取向。第二个例子涉及由四极核动力学产生的线形，例如NMR光谱中的2 H核自旋，其在固态下特别有用，例如生物膜相行为的研究。分析分子运动所产生的谱线形状需要大量的建模和数值模拟，这是40多年来一直备受关注的研究课题。近年来，计算机能力的巨大增长导致了分子动力学（MD）模拟作为预测复杂化学系统动力学的工具的使用增加。为了建立计算机建模和实验之间的紧密联系，希望拥有一个通用的和强大的方法，将允许预测的谱线形状的MD模拟的结果。目前用于从MD模拟线形的方法是基于所谓的数值传播技术，其中计算的动力学基本上重复以考虑系统的量子力学自旋状态的变化。为了实现统计平均，传播必须在数字上执行大量的次数。因此，这种计算通常非常耗时，并且不能保证稳定的解决方案。这种情况进一步复杂化的可能性存在的几个模式的运动相互独立，必须确定和他们的贡献分别模拟。这是不足为奇的，有没有通用的MD-EPR模拟套件，但更广泛的研究社区。代替直接遵循已经计算的MD轨迹，更有效的方法将是使用智能数学工具，其允许在谱线形状中直接利用来自MD的信息。事实上，这可以借助著名的随机刘维尔方程（SLE）来实现，该方程包含描述分子随机动力学的数学术语。然而，应用这种方法的困难在于，这些数学术语不是先验已知的。该建议将克服这一困难，通过使用MD模拟的结果的真实的分子结构，以重建这样的动力学项在SLE方程的自旋状态，通过解决逆问题，即确定从其解决方案的运动方程。所需的条款，然后用来完成SLE方程，因此计算光谱线的形状直接从它的解决方案。新方法将主要用于EPR光谱学。它将被严格测试并应用于当前感兴趣的重要局部分子系统（例如脂质系统和自旋标记蛋白质）。然而，将开发的方法是通用的，可转移的EPR光谱。因此，它可以用于例如NMR光谱分析。我们将扩展的模拟方法预测NMR谱线的形状所产生的分子运动的核自旋使用的情况下，2 H NMR光谱。这项建议的成果将以方便用户的免费软件形式提供给国际科学界。

Technological advances over recent decades have led to improvements in sensitivity of spectrometers allowing them to accurately measure molecular dynamics and structure. An example is Electron Paramagnetic Resonance (EPR) spectroscopy with spin labels, specially designed chemical "agents" that carry a stable unpaired electron. They can be introduced into complex molecular systems in order to report on the order and dynamics of the host molecules. The orientation of the spin label in the magnetic field has a dramatic effect on this line shape and therefore molecular mobility, dynamics and orientations can be studied. A second example concerns the line shapes arising from the dynamics of quadrupolar nucleus, e.g. 2H nuclear spin in NMR spectroscopy that is particular informative in the solid state, e.g. the study of biological membrane phase behavior. Analysis of spectral lines shapes arising from molecular motions requires extensive modelling and numerical simulation, topics which have been of high research interest for more than 40 years. The huge recent growth in computer power has led to an increase in the use of molecular dynamics (MD) simulations as a tool to predict the dynamics of complex chemical systems. In order to establish a tight link between computer modelling and experiment it is desirable to possess a generic and robust method that will allow prediction of spectral lines shapes from the results of MD simulations. Current approaches for simulation of line shapes from MD are based on so-called numerical propagation techniques where the calculated dynamics is essentially repeated to account for the changes in the Quantum Mechanical spin states of the system. In order to achieve statistical averaging the propagation has to be performed numerically a large number of times. As a result, such calculations are generally very time consuming and do not guarantee a stable solution. The situation is complicated further by the possibility of the presence of several modes of motion independent from each other that have to be identified and their contributions simulated separately. It is unsurprising that there is no general MD-EPR simulation suite yet available to the wider research community. Instead of directly following MD trajectories already calculated a more efficient approach would be to use smart mathematical tools that allow the information from MD to be utilised directly in the spectral line shapes. In fact this can be achieved with the help of the famous Stochastic Liouville equation (SLE) for the spin states which contains the mathematical terms that describe the stochastic dynamics of a molecule. The difficulty in applying this method, however, is that these mathematical terms are not known a priori. This proposal will overcome this difficulty by using the results of MD simulations of real molecular structures in order to re-construct such dynamics terms in the SLE equation for the spin states by solving the inverse problem, namely determining the equation of motion from its solution. The terms required are then used to complete the SLE equation and hence calculate the spectral line shapes directly from its solution. The new method will be developed primarily for EPR spectroscopy. It will be rigorously tested and applied to important topical molecular systems of current interest (e.g. lipid systems and spin labelled proteins). However, the methodology that will be developed is general and transferable beyond EPR spectroscopy. Thus it can be adopted for instance in analysis of NMR spectra. We will extend the simulation approach for predicting NMR spectral line shapes arising from molecular motions of the nuclear spin using the case of 2H NMR spectroscopy. The output of this proposal will be made available to the international scientific community in the form of user-friendly free software.