Conformation search Monte Carlo

Figure 4 Conformational search Monte Carlo method (left) and Molecular Dynamics method (right).

Random search of an energy surface (see conformational search, deterministic search, Monte Carlo search, molecular dynamics). 

Conformational search Scanning of a potential energy surface. Only deterministic methods (that is point-by-point searches) are fully reliable. However, these are in practice, due to the enormous computational effort, hardly ever possible. The methods currently used include random search methods (stochastic search, e.g., Monte Carlo methods) and molecular dynamics (see Potential energy surface, Deterministic search, Monte Carlo search, Stochastic search. Molecular dynamics, and Scanning an energy surface). 

A similar algorithm has been used to sample the equilibrium distribution [p,(r )] in the conformational optimization of a tetrapeptide[5] and atomic clusters at low temperature.[6] It was found that when g > 1 the search of conformational space was greatly enhanced over standard Metropolis Monte Carlo methods. In this form, the velocity distribution can be thought to be Maxwellian. 

A molecular dynamics simulation samples the phase space of a molecule (defined by the position of the atoms and their velocities) by integrating Newton s equations of motion. Because MD accounts for thermal motion, the molecules simulated may possess enough thermal energy to overcome potential barriers, which makes the technique suitable in principle for conformational analysis of especially large molecules. In the case of small molecules, other techniques such as systematic, random. Genetic Algorithm-based, or Monte Carlo searches may be better suited for effectively sampling conformational space. 

Mon te Carlo simulation s arc com mori ly used to com pute ih c average Ihcrmodyri am ic properties of a molecule or a system of molecules, and have been employed extensively in the study of the structure an d et uilihriiim properties of liquids an d solution s. Monte Carlo mcLhods have also been used to conduct conformation al search es tin der ri on -et uilibrium con dilion s. 

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. 

A particular advantage of the low-mode search is that it can be applied to botli cyclic ajic acyclic molecules without any need for special ring closure treatments. As the low-mod> search proceeds a series of conformations is generated which themselves can act as starting points for normal mode analysis and deformation. In a sense, the approach is a system ati( one, bounded by the number of low-frequency modes that are selected. An extension of th( technique involves searching random mixtures of the low-frequency eigenvectors using Monte Carlo procedure. 

Monte Carlo searching becomes more difficult for large molecules. This is because a small change in the middle of the molecule can result in a large displacement of the atoms at the ends of the molecule. One solution to this problem is to hold bond lengths and angles fixed, thus changing conformations only, and to use a small maximum displacement. 

Monte Carlo search methods are stochastic techniques based on the use of random numbers and probability statistics to sample conformational space. The name Monte Carlo was originally coined by Metropolis and Ulam [4] during the Manhattan Project of World War II because of the similarity of this simulation technique to games of chance. Today a variety of Monte Carlo (MC) simulation methods are routinely used in diverse fields such as atmospheric studies, nuclear physics, traffic flow, and, of course, biochemistry and biophysics. In this section we focus on the application of the Monte Carlo method for... 

In performing a Monte Carlo sampling procedure we let the dice decide, again and again, how to proceed with the search process. In general, a Monte Carlo search consists of two steps (1) generating a new trial conformation and (2) deciding whether the new confonnation will be accepted or rejected. 

To overcome the limitations of the database search methods, conformational search methods were developed [95,96,109]. There are many such methods, exploiting different protein representations, objective function tenns, and optimization or enumeration algorithms. The search algorithms include the minimum perturbation method [97], molecular dynamics simulations [92,110,111], genetic algorithms [112], Monte Carlo and simulated annealing [113,114], multiple copy simultaneous search [115-117], self-consistent field optimization [118], and an enumeration based on the graph theory [119]. 

R Abagyan, M Totrov. Biased probability Monte Carlo conformational searches and electrostatic calculations for peptides and proteins. I Mol Biol 235 983-1002, 1994. 

We have added a companion option to PBUILD, PRANDOM which eases considerably the problem of finding good conformations of a polymer segment. PRANDOM automatically selects all of the polymer backbone and/or side chain bonds and will randomly select rotations for each bond. In a few minutes, one can not only build a polymer fragment, but also set up a Monte-Carlo search of its conformational space. However, even this cannot solve the problems for large models (pentamer or larger), again due to the number of bonds to be rotated. 

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