MD Simulations and NMR Relaxation Parameters

The fundamentals of NMR relaxation theory have been presented in many places [6-9], and there is no space here to give more than a taste of whaf is involved. The rate of ref urn of a spin system to equilibrium is determined by the time-dependent magnetic fields experienced at each atomic nucleus, arising from molecular motions. The ability of this stochastic, fluctuating field fo induce spin 

Department of Molecular Biology, The Scripps Research Institute, La Jolla, CA 92037, USA 

Annual Reports in Computational Chemistry, Vol. 4 ISSN 1574-1400, DOI 10.1016/S1574-1400(08)00008-X 

This general subject has been covered in earlier reviews [10,11]. Here, we summarize recent (and significant) progress made possible by faster computers and longer simulations, and by improvements in protein force fields. 

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Briischweiler and coworkers use MD simulations to calculate order parameters and to compare them with model-free parameters obtained in NMR relaxation measurements. They present a more accurate method... 

MD simulations provide a detailed insight in the behavior of molecular systems in both space and time, with ranges of up to nanometers and nanoseconds attainable for a system of the size of a CYP enzyme in solution. However, MD simulations are based on empirical molecular mechanics (MM) force field descriptions of interactions in the system, and therefore depend directly on the quality of the force field parameters (92). Commonly used MD programs for CYPs are AMBER (93), CHARMM (94), GROMOS (95), and GROMACS (96), and results seem to be comparable between methods (also listed in Table 2). For validation, direct comparisons between measured parameters and parameters calculated from MD simulations are possible, e.g., for fluorescence (97) and NMR (cross-relaxation) (98,99). In many applications where previously only energy minimization would be applied, it is now common to perform one or several MD simulations, as Ludemann et al. and Winn et al. (100-102) performed in studies of substrate entrance and product exit. 

We want to stress that NMR relaxation, in many cases, depends on very complex processes and is difficult to describe by theoretical models. Thus, MD simulations is required for a proper interpretation. The MD simulations can be used, for example, to clarify obscure features and to offer interpretations of the parameters as well as to suggest modifications to the theoretical models. 

In the past, comparisons between NMR relaxation and MD simulations have concentrated on internal motions, since these often involve sub-nanosecond time scales that could be examined with limited computer resources. In this approach, overall rotational motion is removed by an rms fitting procedure (for example, on backbone atoms in regular secondary structure), and computing time-correlation functions from the result. Typical results are shown in the upper panel of Figure 8.1 similar plots have been presented many times before [4,12,10,11]. Many backbone vectors are like Thr 49, and decay in less than 0.1 ns to a plateau value which can be identified as the order parameter for that vector. Most regions of regular secondary structure resemble this, although there can be exceptions, and there is potentially important information in the decay rates and plateau values that are obtained. 

In NMR experiments, n is typically a backbone N-H bond vector, and dioc(n,2) is computed as a function of R2(n)/Ri(n) (or related quantities, such as (2R2 — Ri)/Ri)/ where Ri and R2 are longitudinal and transverse relaxation rates [48,47]. In this way, the local diffusion constants become a key intermediate quantity that can be estimated from both NMR experiments and from simulations in this respect, they play much the same role here as the model-free parameters and Tg play in the analysis of internal motions by MD. 

Ryde and coworkers use NMR relaxation data to estimate conformational entropy changes and analyze the results against trajectories from long MD simulations in attempt to generate an order-parameter-to-entropy dictionaiy , which they find to depend more on the studied protein and sampling frequency than the force field they use making the transferability of such dictionaiy rather poor but still useful within the same protein. 

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