Conformational searching

The analysis of potential energy surfaces may be of importance for both molecular-mechanical and quantum-mechanical computations. However, due to the fact that thousands of structures instead of only one need to be optimized, the methods briefly described here are only routinely used with force field calculations 35-1. 

Molecular dynamics involves the calculation of the time dependent movement of each atom in a molecule[39]. Generally, the forces determined by empirical force fields are used in combination with Newton s laws of motion (Eqs. 2.11, 2.12). 

In the random (or stochastic or Monte Carlo) search method one starts with a stable conformer and generates new initial configurations either by randomly chang- 

For a 1, pair of atoms with n 4, the minimum allowed distance is initially set equal to the sum of the van der Waals radii of the atoms, and the maximum allowed distance is temporarily set equal to some large number (say, 100 A). These maximum allowed distances are then reduced using the triangle inequality ag + doE where A, E, and G are any three nuclei. (To see the validity of this relation, just join A, E, and G to form a triangle.) One repeatedly examines all possible sets of three nuclei and lowers each AE maximum-allowed distance that does not satisfy Uae ag + ge where u denotes the upper bound (maximum allowed value). The preceding triangle inequality can be written as ae d E- One therefore repeatedly examines all trios of nuclei and raises any lower-bound distances /ag that do not satisfy AG AE ge- 

Using the molecular dynamics approach for simulated annealing, after the atomic positions have evolved for several hundred time steps, one cools the system a bit by multiplying each velocity component by a scale factor that is slightly less than one. After another several hundred time steps, one again reduces the velocity components. This is repeated until the temperature is very low, typically 50 K. 

Unfortunately, the minimum found by the DEM is not always the global minimum. Hence a two-step procedure has been proposed in which one first uses the DEM to locate a minimum and then searches the coordinate space in the region of this minimum. By confining the second search to the region near the DEM minimum, one greatly reduces the ranges of variables that must be searched [S. Nakamura et al.. 

8374 (1995)].TTie DEM is a very promising method that is undergoing further refinement. 

Simulated annealing is widely used to refine biomolecular structures found from X-ray crystallography or NMR. 

For any of the search methods used, all conformers found should be verified to be local minima, rather than saddle points, by calculating their vibrational frequencies and checking that these are all real. 

A 2012 review of protein structure prediction noted that so far no success has been achieved in predicting protein structures solely by finding the conformations of lowest free energy, due to the difficulty of accurately modeling intra-protein and protein-solute 

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Figure 4.49 reprinted with permission from Pranata J and W L Jorgensen. Computational Studies on FK506 Conformational Search and Molecular Dynamics Simulations in Water. The Journal of the American Chemical Society 113 9483-9493. 1991 American Chemical Society. 

The input to a minimisation program consists of a set of initial coordinates for the system. The initial coordinates may come from a variety of sources. They may be obtained from an experimental technique, such as X-ray crystallography or NMR. In other cases a theoretical method is employed, such as a conformational search algorithm. A combination of experimenfal and theoretical approaches may also be used. For example, to study the behaviour of a protein in water one may take an X-ray structure of the protein and immerse it in a solvent bath, where the coordinates of the solvent molecules have been obtained from a Monte Carlo or molecular dynamics simulation. 

Tree representation of the conformation search problem for hexane. Unlike the tree in Figure 9.4 the path gth from the root node to any of the terminal nodes is constant. 

Flow chart steps Jbllowed by a random conformational search. 

A comparison of fine different conformational searching algorithms. (Data from [Saunders et at 1990].)... 

Judson R S, W P Jaeger, A M Treasurywala and M L Peterson 1993. Conformational Searching Methods for Small Molecules. 2. Genetic Algorithm Approach. Journal of Computational Chemistry 14 1407-1414. 

Method and a Genetic Algorithm for Conformational Searching. Journal of Computational... 

All of the conformational search methods that were described in Sections 9.2-9.7 have bee used at some stage to explore the conformational space of small pephdes. Here we wi describe some of the methods designed specifically for tackling the problem for peptide and proteins. 

The amount of computation necessary to try many conformers can be greatly reduced if a portion of the structure is known. One way to determine a portion of the structure experimentally is to obtain some of the internuclear distances from two-dimensional NMR experiments, as predicted by the nuclear Over-hauser effect (NOE). Once a set of distances are determined, they can be used as constraints within a conformation search. This has been particularly effective for predicting protein structure since it is very difficult to obtain crystallographic structures of proteins. It is also possible to define distance constraints based on the average bond lengths and angles, if we assume these are fairly rigid while all conformations are accessible. 

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