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

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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.