Introduction

Probability Grid Monte Carlo (PGMC) is a method developed for predicting the conformations of peptides and proteins by searching their torsional degrees of freedom. The PGMC method combines two of the best features from other torsion-space conformational search methods which have been developed to study peptide conformations; Monte Carlo importance sampling and grid searching. Like the importance sampling method of Lambert and Scheraga[56], the method described here assigns probabilities to different conformations, and conformations are generated according to those probabilities, rather than completely at random or through an exhaustive search of all possibilities. However, unlike Lambert and Scheraga, our probabilities are derived to work within the framework of a grid search method, i.e., only discrete values are chosen for the dihedral angles. There are two primary advantages to using discrete values for dihedral angles, rather than sampling from a continuum: the conformational space is reduced to a finite number of possible conformations per dihedral angle and the probabilities can be generated to reflect known distributions more accurately. In addition, the method is easily extended to sidechain () dihedrals. Because no functional form is necessary to specify the probabilities, grids can be developed for any necessary dimensionality. They range from one-dimensional grids for small sidechains to five-dimensional grids for arginine.

Grid searches have been employed in many conformational studies, such as those designed to predict protein loop structures[57] and those employed in the study of organic molecules[58]. The conformational space in a grid method is still large, as each dihedral can assume 360/ conformations, where is the grid spacing. Therefore, these methods usually employ sophisticated schemes for eliminating combinations which cause steric overlap. The PGMC method, in contrast, implicitly includes a great deal of steric information through the use of probability grids: probabilities are assigned to different protein backbone () and sidechain () dihedrals according to their distributions in known protein structures. Conformations with significant steric overlap are not found in nature and, therefore, have extremely low probabilities of being sampled.

The Probability Grid Monte Carlo method has evolved into a general tool for protein modeling. Its conformational search methodology has been adapted to several problems in addition to the study of peptide conformations. The first of these is the prediction of all-atom conformations of proteins from C coordinates, discussed in Chapter 5. The second is the study of loop conformations in proteins, as applied to immunoglobulin hypervariable loops in Chapter 6. Both of these methods use the fundamental PGMC algorithms in conjunction with geometric constraints: the C coordinates or the loop endpoints, respectively. The results from both of these applications are encouraging: the C-based modeling gives results comparable to or better than other published methods, while the loop modeling is nearly as good as other methods, even though they employ surface-area corrections in order to choose more native-like conformations. Success in these modeling studies indicates that the method can be applied to cases where experimental information is lacking, such as the conformational states of small peptides.