Conformation sampling MCSS

A successful application of GA to conformation sampling is, for example, as a part of flexible docking [12-14], It should be noted, however, that none of the three sampling methods discussed above, MD, MC, and GA, was shown to outperform the other two in any general way. In fact, a comparison of the three methods in the context of flexible docking showed similar efficiency for all three [12], although specific advantages are likely to exist for particular apphcations. 

Although MC is an underutilized tool in the field of computational molecular biophysics, there are beneficial features that can be exploited, especially in conjunction with implicit solvent models. Specifically, MC has the potential of accessing length scales that are inaccessible to MD in complex phenomena like peptide aggregation or conformational sampling of intrinsically disordered proteins. 

The literature is full of examples of many types of conformational sampling algorithms [17-20]. Some of the principal ones are the model building approach [21], genetic algorithms [22, 23], the Monte Carlo (MC) [24] and simulated annealing [25] protocols. 

The ESMC method in the form of the multicanonical MC has been used to simulate conformations of oligopeptides by Hansmann and Okamoto [42,44,45]. These studies were aimed at determining the canonical properties of the molecules and searching for the low-energy conformations. Therefore, only approximate multicanonical functions, for example, with no convergence check on these functions, were used in the conformational sampling. It was reported that, for the small polypeptides studied, about... 

While numerous works of Monte Carlo simulations were carried out for the study of the clay-water system, especially in terms of clay swelling and interlayer cation solvation, molecular dynamics (MD) has only recently been used. While MC has an advantage in conformation sampling in the entire system in equilibrium by its stochastic method, MD is more suited to the dynamical or diffusion properties of the chemical system. Here, several examples of using MD techniques on clay minerals are reviewed for understanding the current activities in this field. 

A critical issue in statistical conformational sampling is the reliability and accuracy of the samples. In order to ensure the reliability of the statistical sampling of a particular conformational state, the relevant conformational region must be sampled sufficiently. A measure of the accuracy of statistical results is the variances of the samples. In order for the statistical results to be accurate, several independent samples have to be taken and the variances of the results calculated from these samples must be within given tolerances. Conformational sampling using the standard MC or MD procedures does not always meet the requirements of reliability and accuracy in all problems. Therefore, efforts have to be made to improve upon the basic sampling procedures in order to obtain satisfactory results. 

With conventional (i.e., canonical) conformational sampling methods such as MC and MD, each simulation produces information about the molecular system at only one temperature. Therefore, in order to obtain the complete information about the molecular system at all ranges of temperature, many simulations have to be carried out at different temperatures. This is a bit wasteful of computational labor. In fact, from each simulation with the standard sampling methods, much more information about the molecular system can be obtained. Specifically, the sampled density of states at energy level , W E), is related to the density of energy states of the molecular system, (E), by the relationship... 

In Chapter 2, a brief discussion of statistical mechanics was presented. Statistical mechanics provides, in theory, a means for determining physical properties that are associated with not one molecule at one geometry, but rather, a macroscopic sample of the bulk liquid, solid, and so on. This is the net result of the properties of many molecules in many conformations, energy states, and the like. In practice, the difficult part of this process is not the statistical mechanics, but obtaining all the information about possible energy levels, conformations, and so on. Molecular dynamics (MD) and Monte Carlo (MC) simulations are two methods for obtaining this information... 

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... 

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