Restrained dynamics

The additional penalty function that is added to the empirical potential energy function in restrained dynamics X-ray refinement has the form ... 

You can include geometric restraints—for interatomic distances, bond angles, and torsion angles—in any molecular dynamics calculation or geometry optim i/.ation. Here are some applications of restrain ts ... 

You usually rern ove restrain ts diirin g th e final ph ases of m olccti lar dynamics situ tilatious and gcom etry optimizations. 

Example If a drug molecule interacts with a receptor molecule through hydrogen bonds, then yon might restrain the distance between the donor and acceptor atoms involved in the hydrogen bonds. During a molecular dynamics simulation, these atoms would slay near an ideal value, while the rest of the molecular system fully relaxes. 

Example Molecular dynamics simulations of selected portions of proteins can demonstrate the motion of an amino acid sequence while fixing the terminal residues. These simulations can probe the motion of an alpha helix, keeping the ends restrained, as occurs n atiirally m transmembrane proteins. You can also investigate the conformations of loops with fixed endpoints. 

The first molecular dynamics simulations of a lipid bilayer which used an explicit representation of all the molecules was performed by van der Ploeg and Berendsen in 1982 [van dei Ploeg and Berendsen 1982]. Their simulation contained 32 decanoate molecules arranged in two layers of sixteen molecules each. Periodic boundary conditions were employed and a xmited atom force potential was used to model the interactions. The head groups were restrained using a harmonic potential of the form ... 

Solving Protein Structures Using Restrained Molecular Dynamics and Simulated Annealing... 

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... 

In a related way, ensemble molecular dynamics derives a pharmacophore using restrained molecular dynamics for a collection of molecules. A force field model is set up so that none of the atoms in each molecule sees the atoms in ainy other molecule. This enables the molecules to be overlaid in space. A restraint term is included in the potential, which forces the appropriate atoms or functional groups to be overlaid in space. 

The default restraints are appropriate for molecular dynamics calculations where larger force constants would create undesirable high frequency motions but much larger force constants may be desired for restrained geometry optimization. 

In many cases, it is also helpful to have the path repel itself so that the transition pathway is self-avoiding. An acmal dynamic trajectory may oscillate about a minimum energy configuration prior to an activated transition. In the computed restrained, selfavoiding path, there will be no clusters of intermediates isolated in potential energy minima and no loops or redundant segments. The self-avoidance restraint reduces the wasted effort in the search for a characteristic reaction pathway. The constraints and restraints are essential components of the computational protocol. 

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. 2.47 The (P)-2.5-helical structure of N.N -linked oligoureas as determined by NMR meaurements in pyridine-c/5. (A) Stereo-view along the helix axis of a low energy conformer of nonamer 178 generated by restrained molecular dynamics calculations. (Adapted from [274]). The helix is characterized by (i) a rigid +)-SYnclinal arrangement around the C(a)-...

Methods for simulating restrained x>ray refinement data from molecular dynamics trajectories. 

If all nuclei are assigned and the spectral parameters for the conformational analysis are extracted, a conformation is calculated - usually by distance geometry (DG) or restrained molecular dynamics calculations (rMD). A test for the quality of the conformation, obtained using the experimental restraints, is its stability in a free MD run, i.e. an MD without experimental restraints. In this case, explicit solvents have to be used in the MD calculation. An indication of more than one conformation in fast equilibrium can be found if only parts of the final structure are in agreement with experimental data [3]. Relaxation data and heteronuclear NOEs can also be used to elucidate internal dynamics, but this is beyond the scope of this article. 

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