A versatile method for systematic conformational searches: Application to CheY

Abstract

A novel molecular structure prediction method, the Z Method, is described. It provides a versatile platform for the development and use of systematic, grid-based conformational search protocols, in which statistical information (i.e., rotamers) can also be included. The Z Method generates trial structures by applying many changes of the same type to a single starting structure, thereby sampling the conformation space in an unbiased way. The method, implemented in the CHARMM program as the Z Module, is applied here to an illustrative model problem in which rigid, systematic searches are performed in a 36-dimensional conformational space that describes the relative positions of the ten secondary structural elements of the protein CheY. A polar hydrogen representation with an implicit solvation term (EEF1) is used to evaluate successively larger fragments of the protein generated in a hierarchical build-up procedure. After a final refinement stage, and a total computational time of about two-and-a-half days on AMD Opteron processors, the prediction is within 1.56 Å of the native structure. The errors in the predicted backbone dihedral angles are found to approximately cancel. Monte Carlo and simulated annealing trials on the same or smaller versions of the problem, using the same atomic model and energy terms, are shown to result in less accurate predictions. Although the problem solved here is a limited one, the findings illustrate the utility of systematic searches with atom-based models for macromolecular structure prediction and the importance of unbiased sampling in structure prediction methods.

Optimization Bias in Energy-Based Structure Prediction

“…By contrast, the current study has examined the possibility of errors in energy-based predictions due to biases introduced by differences in the extent of local sampling around conformers being compared in a search. The work was motivated in part by observations made in prior studies using systematic searches, 13,17,19,20 in which the best results were obtained when structures were generated “in parallel” — i.e. from a common starting structure, rather than in a serial, chain-like manner, 37,38 as is commonly done in Monte Carlo-based structure prediction methods.…”

“…The “parallel-generation” approach to conformational search mentioned above, described as the Z method in previous work, 19 avoids optimization bias by applying similar types and numbers of changes to a single common starting structure, so that the degree of optimization of the generated structures is essentially the same. However, the current analysis also demonstrates that, even in parallel-generation searches, optimization bias can be introduced if the procedure is not carried out properly — for example, if the energies of structures generated with different grid spacings in separate stages of a search protocol or regions of conformational space are directly compared, without the appropriate corrections.…”

“…Failure to restore the original, unminimized structure at each grid point in these cases will result in predictions that tend to favor the structures generated later in the search, which are, in effect, more highly optimized. 19 (The studies here restored the original structure at each grid point. )…”

“…Using the Z module facility in the CHARMM program, a series of searches with the EEF1 solvation function were carried out for the protein CheY, by varying 36 dihedral angles in the loops between the 10 secondary structural elements (five α helices and five β strands), whose internal structure was fixed, as in previous work. 19 Here, the searches were conducted only locally about the native structure of the protein. For each series of calculations, the search used a single grid spacing, S .…”

“…The current work is essentially an examination of this assumption, motivated in part by the success of systematic, “parallel-generation” searches for structure prediction, 13,16–19 in which optimization bias is largely avoided. In the main part of the paper, a formalism is developed for describing the bias that is introduced by the unequal sampling of spherically symmetric wells in an energy-based prediction.…”