Sumudu P. Leelananda

Multibody coarse‐grained potentials for native structure recognition and quality assessment of protein models

Multibody potentials have been of much interest recently because they take into account three dimensional interactions related to residue packing and capture the cooperativity of these interactions in protein structures. Our goal was to combine long range multibody potentials and short range potentials to improve recognition of native structure among misfolded decoys. We optimized the weights for four‐body nonsequential, four‐body sequential, and short range potentials to obtain optimal model ranking results for threading and have compared these data against results obtained with other potentials (26 different coarse‐grained potentials from the Potentials ‘R’Us web server have been used). Our optimized multibody potentials outperform all other contact potentials in the recognition of the native structure among decoys, both for models from homology template‐based modeling and from template‐free modeling in CASP8 decoy sets. We have compared the results obtained for this optimized coarse‐grained potentials, where each residue is represented by a single point, with results obtained by using the DFIRE potential, which takes into account atomic level information of proteins. We found that for all proteins larger than 80 amino acids our optimized coarse‐grained potentials yield results comparable to those obtained with the atomic DFIRE potential. Proteins 2011;

The importance of slow motions for protein functional loops

Loops in proteins that connect secondary structures such as alpha-helix and beta-sheet, are often on the surface and may play a critical role in some functions of a protein. The mobility of loops is central for the motional freedom and flexibility requirements of active-site loops and may play a critical role for some functions. The structures and behaviors of loops have not been studied much in the context of the whole structure and its overall motions, especially how these might be coupled. Here we investigate loop motions by using coarse-grained structures (C(α) atoms only) to solve the motions of the system by applying Lagrange equations with elastic network models to learn about which loops move in an independent fashion and which move in coordination with domain motions, faster and slower, respectively. The normal modes of the system are calculated using eigen-decomposition of the stiffness matrix. The contribution of individual modes and groups of modes is investigated for their effects on all residues in each loop by using Fourier analyses. Our results indicate overall that the motions of functional sets of loops behave in similar ways as the whole structure. But overall only a relatively few loops move in coordination with the dominant slow modes of motion, and these are often closely related to function.

Free energies for coarse-grained proteins by integrating multibody statistical contact potentials with entropies from elastic network models.

We propose a novel method of calculation of free energy for coarse grained models of proteins by combining our newly developed multibody potentials with entropies computed from elastic network models of proteins. Multi-body potentials have been of much interest recently because they take into account three dimensional interactions related to residue packing and capture the cooperativity of these interactions in protein structures. Combining four-body non-sequential, four-body sequential and pairwise short range potentials with optimized weights for each term, our coarse-grained potential improved recognition of native structure among misfolded decoys, outperforming all other contact potentials for CASP8 decoy sets and performance comparable to the fully atomic empirical DFIRE potentials. By combing statistical contact potentials with entropies from elastic network models of the same structures we can compute free energy changes and improve coarse-grained modeling of protein structure and dynamics. The consideration of protein flexibility and dynamics should improve protein structure prediction and refinement of computational models. This work is the first to combine coarse-grained multibody potentials with an entropic model that takes into account contributions of the entire structure, investigating native-like decoy selection.

Exploration of the relationship between topology and designability of conformations

Protein structures are evolutionarily more conserved than sequences, and sequences with very low sequence identity frequently share the same fold. This leads to the concept of protein designability. Some folds are more designable and lots of sequences can assume that fold. Elucidating the relationship between protein sequence and the three-dimensional (3D) structure that the sequence folds into is an important problem in computational structural biology. Lattice models have been utilized in numerous studies to model protein folds and predict the designability of certain folds. In this study, all possible compact conformations within a set of two-dimensional and 3D lattice spaces are explored. Complementary interaction graphs are then generated for each conformation and are described using a set of graph features. The full HP sequence space for each lattice model is generated and contact energies are calculated by threading each sequence onto all the possible conformations. Unique conformation giving minimum energy is identified for each sequence and the number of sequences folding to each conformation (designability) is obtained. Machine learning algorithms are used to predict the designability of each conformation. We find that the highly designable structures can be distinguished from other non-designable conformations based on certain graphical geometric features of the interactions. This finding confirms the fact that the topology of a conformation is an important determinant of the extent of its designability and suggests that the interactions themselves are important for determining the designability.

Statistical Contact Potentials in Protein Coarse-Grained Modeling: From Pair to Multi-body Potentials

The basic concepts of coarse-graining protein structures led to the introduction of empirical statistical potentials in protein computations. We review the history of the development of statistical contact potentials in computational biology and discuss the common features and differences between various pair contact potentials. Potentials derived from the statistics of non-bonded contacts in protein structures from the Protein Data Bank (PDB) are compared with potentials developed for threading purposes based on the optimization of the selection of the native structures among decoys. The energy of transfer of amino acids from water to a protein environment is discussed in detail. We suggest that a next generation of statistical contact potentials should include the effects of residue packing in proteins to improve predictions of protein native three-dimensional structures. We review existing multi-body potentials that have been proposed in the literature, including our own recent four-body potentials. We show how these are related to amino acid substitution matrices.

Predicting Designability of Small Proteins from Graph Features of Contact Maps.

Highly designable structures can be distinguished based on certain geometric graphical features of the interactions, confirming the fact that the topology of a protein structure and its residue-residue interaction network are important determinants of its designability. The most designable structures and least designable structures obtained for sets of proteins having the same number of residues are compared. It is shown that the most designable structures predicted by the graph features of the contact diagrams are more densely packed, whereas the poorly designable structures are more open structures or structures that are loosely packed. Interestingly enough, it can also be seen that the highly designable identified are also common structural motifs found in nature.

Volumes and surface areas: geometries and scaling relationships between coarse- grained and atomic structures.

Computing volumes and surface areas of molecular structures is generally considered to be a solved problem, however, comparisons presented in this review show that different ways of computing surface areas and volumes can yield dramatically different values. Volumes and surface areas are the most basic geometric properties of structures, and estimating these becomes especially important for large scale simulations when individual components are being assembled in protein complexes or drugs being fitted into proteins. Good approximations of volumes and surfaces are derived from Delaunay tessellations, but these values can differ significantly from those from the rolling ball approach of Lee and Richards (3V webserver). The origin of these differences lies in the extended parts and the less well packed parts of the proteins, which are ignored in some approaches. Even though surface areas and volumes from the two approaches differ significantly, their correlations are high. Atomic models have been compared, and the poorly packed regions of proteins are found to be most different between the two approaches. The Delaunay complexes have been explored for both fully atomic and for coarse-grained representations of proteins based on only C(α) atoms. The scaling relationships between the fully atomic models and the coarse-grained model representations of proteins are reported, and the lines fit yield simple relationships for the surface areas and volumes as a function of the number of protein residues and the number of heavy atoms. Further, the atomic and coarse-grained values are strongly correlated and simple relationships are reported.

Incorporating Protein Topology Information in Similarity Matrices for Improved Sequence Matching (A Fold-Specific Scoring System)

Sequence matching is an important tool for much of biology. It is important for discovering information such as functional and evolutionary relationships. Functions for a large fraction of the genes identified today are unknown and gene annotation projects rely upon sequence matching.Substitution matrices such as BLOSUM are widely used to find the sequence similarities. However, these matrices do not take into account structural information of proteins and treat all proteins classes the same. It is reasonable to hypothesize that use of structural information can lead to improvements in sequence matching. We have used CATH topologies where protein structures are clustered at 35% sequence identity. In the multiple sequence alignments, the number of times one amino acid is substituted by another is counted in order to obtain mutability matrices for each topology. These data are then combined with BLOSUM62 with a range of weight coefficients to obtain perturbed BLOSUM matrices for each topology.A set of 27 sequence-dissimilar (less than 25% similarity) structurally-similar pairs of proteins that belong to unique CATH topologies were used as the test dataset.The sequence matching scores for all the sequence pairs in the test set along with scores for all the cross sequence pairs were calculated separately using (1) the BLOSUM62 matrix and (2) the corresponding new matrix for the topology of each sequence pair. Z-scores were used to compare the results obtained from the original BLOSUM and the perturbed matrices.Improved sequence matching scores are obtained for 59% of the test cases.