Metropolis Monte Carlo search method

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... 

Simulated annealing is a global, multivariate optimization technique based on the Metropolis Monte Carlo search algorithm. The method starts from an initial random state, and walks through the state space associated with the problem of interest by generating a series of small, stochastic steps. An objective function maps each state into a value in EH that measures its fitness. In the problem at hand, a state is a unique -membered subset of compounds from the n-membered set, its fitness is the diversity associated with that set, and the step is a small change in the composition of that set (usually of the order of 1-10% of the points comprising the set). While downhill transitions are always accepted, uphill transitions are accepted with a probability that is inversely proportional to... 

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. 

The effective use of temperature as a control factor in the Metropolis Monte Carlo process is the most important factor for the success of simulated annealing method. This has inspired an attempt to exploit temperature in a new way. Von Freyberg [21] has proposed a Simulated Shocking protocol for the efficient search for conformations of polypeptides. In this protocol, the temperature jumps between a very low (T = 5 K) and very high temperature... 

In a random search, one can move from one region of the energy-surface to a completely unconnected region in a single step. A commonly applied method is the Metropolis Monte Carlo scheme that starts with a minimized conformation A of a molecule. Then a random move on the energy-landscape is carried out (e.g. torsion angles are rotated by a random amount) and the structure is minimized. The potential energy of the output structure B is evaluated. If < Epot (A), the new conformation is accepted. 

Molecular model-building (conformational search) methods fall into two general classes systematic and random. - Systematic methods search all possible combinations of torsional angles, whereas random methods usually involve a Monte Carlo (with Metropolis sampling ) or molecular dynamics trajectory. Both approaches attempt to search large areas of conformational space and eventually converge on the desired conformation or structure. Dis-... 

---