Reconstructing protein structure from solvent exposure using tabu search

BACKGROUND: A new, promising solvent exposure measure, called half-sphere-exposure (HSE), has recently been proposed. Here, we study the reconstruction of a protein's C(α )trace solely from structure-derived HSE information. This problem is of relevance for de novo structure prediction using predicted HSE measure. For comparison, we also consider the well-established contact number (CN) measure. We define energy functions based on the HSE- or CN-vectors and minimize them using two conformational search heuristics: Monte Carlo simulation (MCS) and tabu search (TS). While MCS has been the dominant conformational search heuristic in literature, TS has been applied only a few times. To discretize the conformational space, we use lattice models with various complexity. RESULTS: The proposed TS heuristic with a novel tabu definition generally performs better than MCS for this problem. Our experiments show that, at least for small proteins (up to 35 amino acids), it is possible to reconstruct the protein backbone solely from the HSE or CN information. In general, the HSE measure leads to better models than the CN measure, as judged by the RMSD and the angle correlation with the native structure. The angle correlation, a measure of structural similarity, evaluates whether equivalent residues in two structures have the same general orientation. Our results indicate that the HSE measure is potentially very useful to represent solvent exposure in protein structure prediction, design and simulation

Beyond rotamers: a generative, probabilistic model of side chains in proteins.

RIGHTS : This article is licensed under the BioMed Central licence at http://www.biomedcentral.com/about/license which is similar to the 'Creative Commons Attribution Licence'. In brief you may : copy, distribute, and display the work; make derivative works; or make commercial use of the work - under the following conditions: the original author must be given credit; for any reuse or distribution, it must be made clear to others what the license terms of this work are.BACKGROUND: Accurately covering the conformational space of amino acid side chains is essential for important applications such as protein design, docking and high resolution structure prediction. Today, the most common way to capture this conformational space is through rotamer libraries - discrete collections of side chain conformations derived from experimentally determined protein structures. The discretization can be exploited to efficiently search the conformational space. However, discretizing this naturally continuous space comes at the cost of losing detailed information that is crucial for certain applications. For example, rigorously combining rotamers with physical force fields is associated with numerous problems. RESULTS: In this work we present BASILISK: a generative, probabilistic model of the conformational space of side chains that makes it possible to sample in continuous space. In addition, sampling can be conditional upon the protein's detailed backbone conformation, again in continuous space - without involving discretization. CONCLUSIONS: A careful analysis of the model and a comparison with various rotamer libraries indicates that the model forms an excellent, fully continuous model of side chain conformational space. We also illustrate how the model can be used for rigorous, unbiased sampling with a physical force field, and how it improves side chain prediction when used as a pseudo-energy term. In conclusion, BASILISK is an important step forward on the way to a rigorous probabilistic description of protein structure in continuous space and in atomic detail

Potentials of Mean Force for Protein Structure Prediction Vindicated, Formalized and Generalized

Understanding protein structure is of crucial importance in science, medicine and biotechnology. For about two decades, knowledge based potentials based on pairwise distances -- so-called "potentials of mean force" (PMFs) -- have been center stage in the prediction and design of protein structure and the simulation of protein folding. However, the validity, scope and limitations of these potentials are still vigorously debated and disputed, and the optimal choice of the reference state -- a necessary component of these potentials -- is an unsolved problem. PMFs are loosely justified by analogy to the reversible work theorem in statistical physics, or by a statistical argument based on a likelihood function. Both justifications are insightful but leave many questions unanswered. Here, we show for the first time that PMFs can be seen as approximations to quantities that do have a rigorous probabilistic justification: they naturally arise when probability distributions over different features of proteins need to be combined. We call these quantities reference ratio distributions deriving from the application of the reference ratio method. This new view is not only of theoretical relevance, but leads to many insights that are of direct practical use: the reference state is uniquely defined and does not require external physical insights; the approach can be generalized beyond pairwise distances to arbitrary features of protein structure; and it becomes clear for which purposes the use of these quantities is justified. We illustrate these insights with two applications, involving the radius of gyration and hydrogen bonding. In the latter case, we also show how the reference ratio method can be iteratively applied to sculpt an energy funnel. Our results considerably increase the understanding and scope of energy functions derived from known biomolecular structures

Model quality assessment using distance constraints from alignments

Given a set of alternative models for a specific protein sequence, the model quality assessment (MQA) problem asks for an assignment of scores to each model in the set. A good MQA program assigns these scores such that they correlate well with real quality of the models, ideally scoring best that model which is closest to the true structure. In this paper, we present a new approach for addressing the MQA problem. It is based on distance constraints extracted from alignments to templates of known structure, and is implemented in the Undertaker [9] program for protein structure prediction. One novel feature is that we extract non-contact constraints as well as contact constraints. We describe how the distance constraint extraction is done and we show how they can be used to address the MQA problem. We have compared our method on CASP7 targets and the results show that our method is at least comparable with the best MQA methods that were assessed at CASP7 [7]. We also propose a new evaluation measure, Kendall's τ, that is more interpretable than conventional measures used for evaluating MQA methods (Pearson's r and Spearman's ρ). We show clear examples where Kendall's τ agrees much more with our intuition of a correct MQA and we therefore propose that Kendall's τ be used for future CASP MQA assessments