Structure determination molecular dynamics

Nuclear relaxation in paramagnetic complexes occurs due to the time dependent terms in the nuclear spin Hamiltonian. The amount of relaxation effect is dependent on the intensity of electron-nuclear interaction and the rate at which this interaction is interrupted. Thus the relaxation rates of ligand nuclei are determined by the two factors, namely, molecular structure and molecular dynamics in solution. Thus the relaxation rates of ligand nuclei shed light on molecular structure and dynamics in solution. 

Isothermal-isobaric molecular dynamics simulations of the a, p and 5 modifications have been carried out over the temperature range 4.2 - 553 K, using a force field developed for RDX, together with charges derived from ab initio calculations (Sorescu et al. 99ib). These gave results in close agreement with the experimentally determined crystal structures. Another molecular dynamics study (Kohno et al. 

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.

Our work is targeted to biomolecular simulation applications, where the objective is to illuminate the structure and function of biological molecules (proteins, enzymes, etc) ranging in size from dozens of atoms to tens of thousands of atoms today, with the desire to increase this limit to millions of atoms in the near future. Such molecular dynamics (MD) simulations simply apply Newton s law to each atom in the system, with the force on each atom being determined by evaluating the gradient of the potential field at each atom s position. The potential includes contributions from bonding forces. 

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 moleculai dynarrdcs is usually used in which additional terms, called penalty functions, are added tc the potential energy function. These extra terms have the effect of penalising conformations... 

For a conformation in a relatively deep local minimum, a room temperature molecular dynamics simulation may not overcome the barrier and search other regions of conformational space in reasonable computing time. To overcome barriers, many conformational searches use elevated temperatures (600-1200 K) at constant energy. To search conformational space adequately, run simulations of 0.5-1.0 ps each at high temperature and save the molecular structures after each simulation. Alternatively, take a snapshot of a simulation at about one picosecond intervals to store the structure. Run a geometry optimization on each structure and compare structures to determine unique low-energy conformations. 

In principle, we could find the minimum-energy crystal lattice from electronic structure calculations, determine the appropriate A-body interaction potential in the presence of lattice defects, and use molecular dynamics methods to calculate ab initio dynamic macroscale material properties. Some of the problems associated with this approach are considered by Wallace [1]. Because of these problems it is useful to establish a bridge between the micro-... 

The initial coordinates r(0) are usually obtained from experimentally determined molecular structures, mainly from X-ray crystallography and NMR experiments. Alternatively, the initial coordinates can be based on computer models generated by a variety of modeling techniques (see Chapters 14 and 15). Note, however, that even the experimentally determined strucmres must often undergo some preparation steps before they can be used as initial structures in a dynamic simulation. 

Modeling in NMR Structure Determination B. Molecular Dynamics Simulated Annealing... 

Another principal difficulty is that the precise effect of local dynamics on the NOE intensity cannot be determined from the data. The dynamic correction factor [85] describes the ratio of the effects of distance and angular fluctuations. Theoretical studies based on NOE intensities extracted from molecular dynamics trajectories [86,87] are helpful to understand the detailed relationship between NMR parameters and local dynamics and may lead to structure-dependent corrections. In an implicit way, an estimate of the dynamic correction factor has been used in an ensemble relaxation matrix refinement by including order parameters for proton-proton vectors derived from molecular dynamics calculations [72]. One remaining challenge is to incorporate data describing the local dynamics of the molecule directly into the refinement, in such a way that an order parameter calculated from the calculated ensemble is similar to the measured order parameter. 

Molecular modeling is an indispensable tool in the determination of macromolecular structures from NMR data and in the interpretation of the data. Thus, state-of-the-art molecular dynamics simulations can reproduce relaxation data well [9,96] and supply a model of the motion in atomic detail. Qualitative aspects of correlated backbone motions can be understood from NMR structure ensembles [63]. Additional data, in particular residual dipolar couplings, improve the precision and accuracy of NMR structures qualitatively [12]. 

CM Clore, AT Bifinger, M Karplus, AM Gronenborn. Application of molecular dynamics with mterproton distance restraints to 3D protein structure determination. J Mol Biol 191 523-551, 1986. 

MI Sutcliffe, CM Dobson, RE Oswald. Solution structure of neuronal bungarotoxm determined by two-dimensional NMR spectroscopy Calculation of tertiary structure using systematic homologous model building, dynamical simulated annealing, and restrained molecular dynamics. Biochemistry 31 2962-2970, 1992. 

Fig. 4. Optimized toroidal structures (a) torus and (b) torus C24o Pentagons and heptagons are shaded. The diameters of the tube of the stable torus determined by optimization using molecular dynamics with Stillinger-Weber poiemial[211, is 8.8 A. The diameter of the hole is 7.8 A, which is quite close to the diameter of fullerence Qy.

J. D. Weeks, D. Chandler, H. C. Andersen. Role of repulsive forces in determining the equilibrium structure of simple liquids. J Chem Phys 54 5237, 1971. R. L. Rowley, M. W. Schuck, J. Perry. A direct method for determination of chemical potential with molecular dynamics simulations. 2. Mixtures. Mol Phys 55 125, 1995. 

More detailed aspects of protein function can be obtained also by force-field based approaches. Whereas protein function requires protein dynamics, no experimental technique can observe it directly on an atomic scale, and motions have to be simulated by molecular dynamics (MD) simulations. Also free energy differences (e.g. between binding energies of different protein ligands) can be characterised by MD simulations. Molecular mechanics or molecular dynamics based approaches are also necessary for homology modelling and for structure refinement in X-ray crystallography and NMR structure determination. 

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