Empirical Potential Function for Simplified Protein Models: Combining Contact and Local Sequence-Structure Descriptors

An effective potential function is critical for protein structure prediction and folding simulation. Simplified protein models such as those requiring only $C_\alpha$ or backbone atoms are attractive because they enable efficient search of the conformational space. We show residue specific reduced discrete state models can represent the backbone conformations of proteins with small RMSD values. However, no potential functions exist that are designed for such simplified protein models. In this study, we develop optimal potential functions by combining contact interaction descriptors and local sequence-structure descriptors. The form of the potential function is a weighted linear sum of all descriptors, and the optimal weight coefficients are obtained through optimization using both native and decoy structures. The performance of the potential function in test of discriminating native protein structures from decoys is evaluated using several benchmark decoy sets. Our potential function requiring only backbone atoms or $C_\alpha$ atoms have comparable or better performance than several residue-based potential functions that require additional coordinates of side chain centers or coordinates of all side chain atoms. By reducing the residue alphabets down to size 5 for local structure-sequence relationship, the performance of the potential function can be further improved. Our results also suggest that local sequence-structure correlation may play important role in reducing the entropic cost of protein folding.Comment: 20 pages, 5 figures, 4 tables. In press, Protein

Potential function of simplified protein models for discriminating native proteins from decoys: Combining contact interaction and local sequence-dependent geometry

An effective potential function is critical for protein structure prediction and folding simulation. For simplified models of proteins where coordinates of only $C_\alpha$ atoms need to be specified, an accurate potential function is important. Such a simplified model is essential for efficient search of conformational space. In this work, we present a formulation of potential function for simplified representations of protein structures. It is based on the combination of descriptors derived from residue-residue contact and sequence-dependent local geometry. The optimal weight coefficients for contact and local geometry is obtained through optimization by maximizing margins among native and decoy structures. The latter are generated by chain growth and by gapless threading. The performance of the potential function in blind test of discriminating native protein structures from decoys is evaluated using several benchmark decoy sets. This potential function have comparable or better performance than several residue-based potential functions that require in addition coordinates of side chain centers or coordinates of all side chain atoms.Comment: 4 pages, 2 figures, Accepted by 26th IEEE-EMBS Conference, San Francisc

Orientation-dependent backbone-only residue pair scoring functions for fixed backbone protein design

<p>Abstract</p> <p>Background</p> <p>Empirical scoring functions have proven useful in protein structure modeling. Most such scoring functions depend on protein side chain conformations. However, backbone-only scoring functions do not require computationally intensive structure optimization and so are well suited to protein design, which requires fast score evaluation. Furthermore, scoring functions that account for the distinctive relative position and orientation preferences of residue pairs are expected to be more accurate than those that depend only on the separation distance.</p> <p>Results</p> <p>Residue pair scoring functions for fixed backbone protein design were derived using only backbone geometry. Unlike previous studies that used spherical harmonics to fit 2D angular distributions, Gaussian Mixture Models were used to fit the full 3D (position only) and 6D (position and orientation) distributions of residue pairs. The performance of the 1D (residue separation only), 3D, and 6D scoring functions were compared by their ability to identify correct threading solutions for a non-redundant benchmark set of protein backbone structures. The threading accuracy was found to steadily increase with increasing dimension, with the 6D scoring function achieving the highest accuracy. Furthermore, the 3D and 6D scoring functions were shown to outperform side chain-dependent empirical potentials from three other studies. Next, two computational methods that take advantage of the speed and pairwise form of these new backbone-only scoring functions were investigated. The first is a procedure that exploits available sequence data by averaging scores over threading solutions for homologs. This was evaluated by applying it to the challenging problem of identifying interacting transmembrane alpha-helices and found to further improve prediction accuracy. The second is a protein design method for determining the optimal sequence for a backbone structure by applying Belief Propagation optimization using the 6D scoring functions. The sensitivity of this method to backbone structure perturbations was compared with that of fixed-backbone all-atom modeling by determining the similarities between optimal sequences for two different backbone structures within the same protein family. The results showed that the design method using 6D scoring functions was more robust to small variations in backbone structure than the all-atom design method.</p> <p>Conclusions</p> <p>Backbone-only residue pair scoring functions that account for all six relative degrees of freedom are the most accurate and including the scores of homologs further improves the accuracy in threading applications. The 6D scoring function outperformed several side chain-dependent potentials while avoiding time-consuming and error prone side chain structure prediction. These scoring functions are particularly useful as an initial filter in protein design problems before applying all-atom modeling.</p

Knowledge-based energy functions for computational studies of proteins

This chapter discusses theoretical framework and methods for developing knowledge-based potential functions essential for protein structure prediction, protein-protein interaction, and protein sequence design. We discuss in some details about the Miyazawa-Jernigan contact statistical potential, distance-dependent statistical potentials, as well as geometric statistical potentials. We also describe a geometric model for developing both linear and non-linear potential functions by optimization. Applications of knowledge-based potential functions in protein-decoy discrimination, in protein-protein interactions, and in protein design are then described. Several issues of knowledge-based potential functions are finally discussed.Comment: 57 pages, 6 figures. To be published in a book by Springe

MESSM: a framework for protein threading by neural networks and support vector machines

Protein threading, which is also referred to as fold recognition, aligns a probe amino acid sequence onto a library of representative folds of known structure to identify a structural similarity. Following the threading technique of the structural profile approach, this research focused on developing and evaluating a new framework - Mixed Environment Specific Substitution Mapping (MESSM) - for protein threading by artificial neural networks (ANNs) and support vector machines (SVMs). The MESSM presents a new process to develop an efficient tool for protein fold recognition. It achieved better efficiency while retained the effectiveness on protein prediction. The MESSM has three key components, each of which is a step in the protein threading framework. First, building the fold profile library-given a protein structure with a residue level environmental description, Neural Networks are used to generate an environment-specific amino acid substitution (3D-1D) mapping. Second, mixed substitution mapping--a mixed environment-specific substitution mapping is developed by combing the structural-derived substitution score with sequence profile from well-developed amino acid substitution matrices. Third, confidence evaluation--a support vector machine is employed to measure the significance of the sequence-structure alignment. Four computational experiments are carried out to verify the performance of the MESSM. They are Fischer, ProSup, Lindahl and Wallner benchmarks. Tested on Fischer, Lindahl and Wallner benchmarks, MESSM achieved a comparable performance on fold recognition to those energy potential based threading models. For Fischer benchmark, MESSM correctly recognise 56 out of 68 pairs, which has the same performance as that of COBLATH and SPARKS. The computational experiments show that MESSM is a fast program. It could make an alignment between probe sequence (150 amino acids) and a profile of 4775 template proteins in 30 seconds on a PC with IG memory Pentium IV. Also, tested on ProSup benchmark, the MESSM achieved alignment accuracy of 59.7%, which is better than current models. The research work was extended to develop a threading score following the threading technique of the contact potential approach. A TES (Threading with Environment-specific Score) model is constructed by neural networks