Structural refinement restrained molecular dynamics

Recently, Lindorff-Larsen el al.uo included the order parameter (S 2) in the target function, and refined an ubiquitin X-ray structure by restrained molecular dynamics (Section 6.4) to obtain an NMR structure ensemble (Section 6.5) from the trajectories. They simulated the values of RDCs (Section 9.1) and side chain scalar coupling from the calculated ensemble to confirm that the method can determine the protein three-dimensional structure and dynamic structure simultaneously. The simulated values were in good agreement with the corresponding measurement data. The simulation accuracy was improved from the preliminary calculated structure without the order parameters. The approach is typically important, because they tried to link the ensemble with a dynamic structure directly. 

K. Perturbations to NMR DNA chemical shifts and 24 intermolecular NOEs identified the 5 -ApG and 5 -GpT steps as the principle intercalation sites and allowed a structural model to be refined using NOE-restrained molecular dynamics (Figure 6a and b). 

A particularly important application of molecular dynamics, often in conjunction with the simulated annealing method, is in the refinement of X-ray and NMR data to determine the three-dimensional structures of large biological molecules such as proteins. The aim of such refinement is to determine the conformation (or conformations) that best explain the experimental data. A modified form of molecular dynamics called restrained molecular dynamics is usually used in which additional terms, called penalty junctions, are added to the potential energy function. These extra terms have the effect of penalising conformations... 

Jack and Levitt introduced molecular modelling techniques into the refinement in the form of an energy minimisation step (using a force field function) that was performed alternately with the least-squares refinement [Jack and Levitt 1978]. This approach was shown to give convergence to better structures. More recently, restrained molecular dynamics methods were introduced by Brunger, Kuriyan and Karplus [Brunger et al. 1987]. These methods have had a dramatic impact on the refinement of X-ray and NMR structure of proteins. 

As mentioned above, the cross peak intensities from NOESY spectra taken at long mixing times caimot be related in a simple and direct way to distances between two protons due to spin diffusion effects that mask the actual proton distances. A possibiUty to extract such information is provided by relaxation matrix analysis that accounts for all dipolar interactions of a given proton and hence takes spin diffusion effects explicitly into consideration. Several computational procedures have been developed which iteratively back-calculate an experimental NOESY spectrum, starting from a certain molecular model that is altered in many cycles of the iteration process to fit best the experimental NOESY data. In each cycle, the calculated structures are refined by restrained molecular dynamics and free energy minimization [42,43]. 

Recent developments in molecular dynamics techniques allow consideration of values and NOE restraints as an ensemble property (Lindorff-Larsen et al. 2005 Richter et al. 2007). The obtained ensembles represent a more realistic view of these flexible molecules in solution than those calculated with conventional NMR structure refinement methods. The dynamically restrained ensembles occupy a considerably larger conformational space than the conventionally calculated ones, and reproduce independent NMR parameters (e.g., chemical shifts) much better. 

Differences between the refined results for the average atomic positions and their mean-square fluctuations and those obtained from the molecular dynamics trajectory are due to errors introduced by the refinement procedure. The overall rms error in atomic positions ranged from 0.24 to 0.29 A for slightly different restrained and unrestrained refinement procedures.197 The errors in backbone positions (0.10 to 0.20 A) are less than those for sidechain atoms (0.28 to 0.33 A rms). These backbone errors, though small, are comparable to the rms deviation of 0.21 A between the positions of the backbone atoms in the refined experimental structures of oxymyoglobin and carboxy-... 

This section covers ab initio and density functional theory (DFT), semi-empirical and empirical, and molecular mechanics and molecular dynamics methods. For gas-phase structure determinations, a refinement to the use of ab initio calculations the SARACEN (Structure Analysis Restrained by Ab initio Calculations for Electron diffractioN) method, and other relevant theoretical and computational chemistry techniques, including quantitative structure-activity/property relationship (QSAR/QSPR) models for prediction of biological activity and physicochemical properties, are also covered. 

Figure 7 Three-dimensional structure of DNA hairpin d(GCGAAGC) determined using NMR data obtained on a C- and N-labeled molecule. NOE, dihedral, and RDC restrains were applied to refine the structure using molecular dynamics simulations using AMBER 7.0 software package.

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