Molecular restraints

The problems that occur when one tries to estimate affinity in terms of component terms do not arise when perturbation methods are used with simulations in order to compute potentials of mean force or free energies for molecular transformations simulations use a simple physical force field and thereby implicitly include all component terms discussed earlier. We have used the molecular transformation approach to compute binding affinities from these first principles [14]. The basic approach had been introduced in early work, in which we studied the affinity of xenon for myoglobin [11]. The procedure was to gradually decrease the interactions between xenon atom and protein, and compute the free energy change by standard perturbation methods, cf. (10). An (issential component is to impose a restraint on the... 

In our implementation of SMD, modified versions of VMD and Sigma communicate with each other using a customized, lightweight protocol. Sigma sends atomic positions resulting from each molecular dynamics time step to VMD for display. When the user specifies restraints on parts of the displayed model, VMD sends them to Sigma, where they are converted into potential-well restraints added to the force field [21]. 

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 ... 

Note MM-i- is derived from the public domain code developed by Dr. Norm an Allinger, referred to as M.M2( 1977), and distributed by the Quantum Chemistry Program Exchange (QCPE). The code for MM-t is not derived from Dr. Allin ger s present version of code, which IS trademarked MM2 . Specifically. QCMPOlO was used as a starting point Ibr HyperChem MM-t code. The code was extensively modified and extended over several years to include molecular dynamics, switching functuins for cubic stretch terms, periodic boundary conditions, superimposed restraints, a default (additional) parameter scheme, and so on. 

These molecular dynamics restraints are stored with the IIIX file and are relained as long as ihe Named Seleclions are slill active (structural changes not made to molecular systemli or the restraints are still rec iiested via the Restraint Forces dialog box. 

Ortiz A R, A Kolinski and J Skolnick 1998. Fold Assembly of Small Proteins Using Monte C Simulations Driven by Restraints Derived from Multiple Sequence Alignments. Jourru Molecular Biology 277 419-446. 

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. 

You can often use experimental data, such as Nuclear Overhauser Effect (NOE) signals from 2D NMR studies, as restraints. NOE signals give distances between pairs of hydrogens in a molecule. Use these distances to limit distances during a molecular mechanics geometry optimization or molecular dynamics calculation. Information on dihedral angles, deduced from NMR, can also limit a conformational search. 

You usually remove restraints during the final phases of molecular dynamics simulations and geometry optimizations. 

The HyperChem Reference manual and Getting Started discuss the sequence of steps to perform a molecular mechanics calculation. These steps include choosing a force field, force field options, and possible restraints. 

You can restrain atoms during molecular mechanics or quantum mechanics calculations. Choosing restraints, via the Restraint Forces dialog box, applies additional harmonic forces—which you specify, to interatomic distances, angles, or dihedrals that you have set up as named selections. 

You can add restraints to any molecular mechanics calculation (single point, optimization or dynamics). These might be NMR restraints, for example, or any situation where a length, angle, or torsion is known or pre-defined. Restraints with large force constants result in high frequency components in a molecular dynamics calculation and can result in instability under some circumstances. 

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. 

A molecular dynamics force field is a convenient compilation of these data (see Chapter 2). The data may be used in a much simplified fonn (e.g., in the case of metric matrix distance geometry, all data are converted into lower and upper bounds on interatomic distances, which all have the same weight). Similar to the use of energy parameters in X-ray crystallography, the parameters need not reflect the dynamic behavior of the molecule. The force constants are chosen to avoid distortions of the molecule when experimental restraints are applied. Thus, the force constants on bond angle and planarity are a factor of 10-100 higher than in standard molecular dynamics force fields. Likewise, a detailed description of electrostatic and van der Waals interactions is not necessary and may not even be beneficial in calculating NMR strucmres. 

In the second step, the spatial restraints and the CHARMM22 force field tenns enforcing proper stereochemistry [80,81] are combined into an objective function. The general form of the objective function is similar to that in molecular dynamics programs such as CHARMM22 [80]. The objective function depends on the Cartesian coordinates of —10,000 atoms (3D points) that form a system (one or more molecules) ... 

Figure 5 Optimization of the objective function in Modeller. Optimization of the objective function (curve) starts with a random or distorted model structure. The iteration number is indicated below each sample structure. The first approximately 2000 iterations coiTespond to the variable target function method [82] relying on the conjugate gradients technique. This approach first satisfies sequentially local restraints, then slowly introduces longer range restraints until the complete objective function IS optimized. In the remaining 4750 iterations, molecular dynamics with simulated annealing is used to refine the model [83]. CPU time needed to generate one model is about 2 mm for a 250 residue protein on a medium-sized workstation.

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. 

Crystallographic refinement is a procedure which iteratively improves the agreement between structure factors derived from X-ray intensities and those derived from a model structure. For macro molecular refinement, the limited diffraction data have to be complemented by additional information in order to improve the parameter-to-observation ratio. This additional information consists of restraints on bond lengths, bond angles, aromatic planes, chiralities, and temperature factors. 

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. 

DG was primarily developed as a mathematical tool for obtaining spahal structures when pairwise distance information is given [118]. The DG method does not use any classical force fields. Thus, the conformational energy of a molecule is neglected and all 3D structures which are compatible with the distance restraints are presented. Nowadays, it is often used in the determination of 3D structures of small and medium-sized organic molecules. Gompared to force field-based methods, DG is a fast computational technique in order to scan the global conformational space. To get optimized structures, DG mostly has to be followed by various molecular dynamic simulation. 

The first step in the DG calculations is the generation of the holonomic distance matrix for aU pairwise atom distances of a molecule [121]. Holonomic constraints are expressed in terms of equations which restrict the atom coordinates of a molecule. For example, hydrogen atoms bound to neighboring carbon atoms have a maximum distance of 3.1 A. As a result, parts of the coordinates become interdependent and the degrees of freedom of the molecular system are confined. The acquisition of these distance restraints is based on the topology of a model structure with an arbitrary, but energetically optimized conformation. 

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