New statistical potentials for improved protein structure prediction

This dissertation presents a new scheme to derive four-body contact potentials as a way to consider protein interactions in a more cooperative model. These new four-body contact potentials, noted as SET1 four-body contact potentials (sequential information included), show important gains in threading. SET2 four-body contact potentials (non-sequential information included) have also been developed to supplement SET1 by including spatial information. In addition to SET1 and SET2, we also include the short-range conformational energies introduced by us previously in threading. The combination of these different potentials shows significant improvement in threading tests of some decoy sets. Protein packing is an important aspect of computational structural biology. Icosahedron is chosen as an ideal model to fit the protein packing clusters from a set of protein structures. A theoretical description of packing patterns and packing regularities of icosahedron has been proposed. We find that the order parameter (orientation function) measuring the angular overlap of directions in coordination clusters with directions of the icosahedron is 0.91, which is a significant improvement in comparison with the value 0.82 for the order parameter with the face-centered cubic (fcc) lattice. Close packing tendencies and patterns of residue packing in proteins is considered in detail and a theoretical description of these packing regularities is proposed. Protein motion is another important field. The elastic network interpolation (ENI) model has been used to generate conformational transition intermediates of adenylate kinase (AK) based only C alpha atoms. We construct the atomistic intermediates by grafting all the other atoms except C alpha from the open form AK and then performing CHARMM energy minimization to remove steric conflicts and optimize the intermediate structures. We compare the free energy profiles for all intermediates from both CHARMM force field and statistical energy functions. And we find CHARMM total free energies can successfully captures the two energy minima representing the open form AK and the closed form AK, however the free energies from statistical energy functions can detect the energy minimum representing the semi-closed intermediate with LID domain closed and NMP domain open and the local energy minimum representing the closed form AK

Knowledge-based potentials in protein fold recognition

An accurate potential function is essential for protein folding problem and structure prediction. Two different types of potential energy functions are currently in use. The first type is based on the law of physics and second type is referred to as statistical potentials or knowledge based potentials.  In the latter type, the energy function is extracted from statistical analysis of experimental data of known protein structures. By increasing the amount of three dimensional protein structures, this approach is growing rapidly.There are various forms of knowledge based potentials depending on how statistics are calculated and how proteins are modeled. In this review, we explain how the knowledge based potentials are extracted by using known protein structures and briefly compare many of the potentials in theory

Protein folding using contact maps

We present the development of the idea to use dynamics in the space of contact maps as a computational approach to the protein folding problem. We first introduce two important technical ingredients, the reconstruction of a three dimensional conformation from a contact map and the Monte Carlo dynamics in contact map space. We then discuss two approximations to the free energy of the contact maps and a method to derive energy parameters based on perceptron learning. Finally we present results, first for predictions based on threading and then for energy minimization of crambin and of a set of 6 immunoglobulins. The main result is that we proved that the two simple approximations we studied for the free energy are not suitable for protein folding. Perspectives are discussed in the last section.Comment: 29 pages, 10 figure

Limitations of Ab Initio Predictions of Peptide Binding to MHC Class II Molecules

Successful predictions of peptide MHC binding typically require a large set of binding data for the specific MHC molecule that is examined. Structure based prediction methods promise to circumvent this requirement by evaluating the physical contacts a peptide can make with an MHC molecule based on the highly conserved 3D structure of peptide:MHC complexes. While several such methods have been described before, most are not publicly available and have not been independently tested for their performance. We here implemented and evaluated three prediction methods for MHC class II molecules: statistical potentials derived from the analysis of known protein structures; energetic evaluation of different peptide snapshots in a molecular dynamics simulation; and direct analysis of contacts made in known 3D structures of peptide:MHC complexes. These methods are ab initio in that they require structural data of the MHC molecule examined, but no specific peptide:MHC binding data. Moreover, these methods retain the ability to make predictions in a sufficiently short time scale to be useful in a real world application, such as screening a whole proteome for candidate binding peptides. A rigorous evaluation of each methods prediction performance showed that these are significantly better than random, but still substantially lower than the best performing sequence based class II prediction methods available. While the approaches presented here were developed independently, we have chosen to present our results together in order to support the notion that generating structure based predictions of peptide:MHC binding without using binding data is unlikely to give satisfactory results

Assessing the structure of proteins and protein complexes through physical and statistical approaches

Determining the correct state of a protein or a protein complex is of paramount importance for current medical and pharmaceutical research. The stable conformation of such systems depend on two processes called protein folding and protein-protein interaction. In the course of the last 50 years, both processes have been fruitfully studied. Yet, a complete understanding is still not reached, and the accuracy and the efficiency of the approaches for studying these problems is not yet optimal. This thesis is devoted to devising physical and statistical methods for recognizing the native state of a protein or a protein complex. The studies will be mostly based on BACH, a knowledge-based potential originally designed for the discrimination of native structures in protein folding problems. BACH method will be analyzed and extended: first, a new method to account for protein-solvent interaction will be presented. Then, we will describe an extension of BACH aimed at assessing the quality of protein complexes in protein-protein interaction problems. Finally, we will present a procedure aimed at predicting the structure of a complex based on a hierarchy of approaches ranging from rigid docking up to molecular dynamics in explicit solvent. The reliability of the approaches we propose will be always benchmarked against a selection of other state-of-the-art scoring functions which obtained good results in CASP and CAPRI competitions

Protein structure prediction: improving and automating knowledge-based approaches

This work presents a computational approach to improve the automatic prediction of protein structures from sequence. Its main focus was twofold. An automated method for guiding the modeling process was first developed. This was tested and found to be state of the art in the CASP4 structure prediction contest in 2000. The second focus was the development of a novel divide and conquer algorithm for modeling flexible loops in proteins. Implementation of the search procedure and subsequent ranking is presented. The results are again compared with state of the art methods

Mass & secondary structure propensity of amino acids explain their mutability and evolutionary replacements

Why is an amino acid replacement in a protein accepted during evolution? The answer given by bioinformatics relies on the frequency of change of each amino acid by another one and the propensity of each to remain unchanged. We propose that these replacement rules are recoverable from the secondary structural trends of amino acids. A distance measure between high-resolution Ramachandran distributions reveals that structurally similar residues coincide with those found in substitution matrices such as BLOSUM: Asn Asp, Phe Tyr, Lys Arg, Gln Glu, Ile Val, Met → Leu; with Ala, Cys, His, Gly, Ser, Pro, and Thr, as structurally idiosyncratic residues. We also found a high average correlation (\overline{R} R = 0.85) between thirty amino acid mutability scales and the mutational inertia (I X ), which measures the energetic cost weighted by the number of observations at the most probable amino acid conformation. These results indicate that amino acid substitutions follow two optimally-efficient principles: (a) amino acids interchangeability privileges their secondary structural similarity, and (b) the amino acid mutability depends directly on its biosynthetic energy cost, and inversely with its frequency. These two principles are the underlying rules governing the observed amino acid substitutions. © 2017 The Author(s)

A Novel Side-Chain Orientation Dependent Potential Derived from Random-Walk Reference State for Protein Fold Selection and Structure Prediction

An accurate potential function is essential to attack protein folding and structure prediction problems. The key to developing efficient knowledge-based potential functions is to design reference states that can appropriately counteract generic interactions. The reference states of many knowledge-based distance-dependent atomic potential functions were derived from non-interacting particles such as ideal gas, however, which ignored the inherent sequence connectivity and entropic elasticity of proteins.We developed a new pair-wise distance-dependent, atomic statistical potential function (RW), using an ideal random-walk chain as reference state, which was optimized on CASP models and then benchmarked on nine structural decoy sets. Second, we incorporated a new side-chain orientation-dependent energy term into RW (RWplus) and found that the side-chain packing orientation specificity can further improve the decoy recognition ability of the statistical potential.RW and RWplus demonstrate a significantly better ability than the best performing pair-wise distance-dependent atomic potential functions in both native and near-native model selections. It has higher energy-RMSD and energy-TM-score correlations compared with other potentials of the same type in real-life structure assembly decoys. When benchmarked with a comprehensive list of publicly available potentials, RW and RWplus shows comparable performance to the state-of-the-art scoring functions, including those combining terms from multiple resources. These data demonstrate the usefulness of random-walk chain as reference states which correctly account for sequence connectivity and entropic elasticity of proteins. It shows potential usefulness in structure recognition and protein folding simulations. The RW and RWplus potentials, as well as the newly generated I-TASSER decoys, are freely available in http://zhanglab.ccmb.med.umich.edu/RW

Predicting multibody assembly of proteins

textThis thesis addresses the multi-body assembly (MBA) problem in the context of protein assemblies. [...] In this thesis, we chose the protein assembly domain because accurate and reliable computational modeling, simulation and prediction of such assemblies would clearly accelerate discoveries in understanding of the complexities of metabolic pathways, identifying the molecular basis for normal health and diseases, and in the designing of new drugs and other therapeutics. [...] [We developed] F²Dock (Fast Fourier Docking) which includes a multi-term function which includes both a statistical thermodynamic approximation of molecular free energy as well as several of knowledge-based terms. Parameters of the scoring model were learned based on a large set of positive/negative examples, and when tested on 176 protein complexes of various types, showed excellent accuracy in ranking correct configurations higher (F² Dock ranks the correcti solution as the top ranked one in 22/176 cases, which is better than other unsupervised prediction software on the same benchmark). Most of the protein-protein interaction scoring terms can be expressed as integrals over the occupied volume, boundary, or a set of discrete points (atom locations), of distance dependent decaying kernels. We developed a dynamic adaptive grid (DAG) data structure which computes smooth surface and volumetric representations of a protein complex in O(m log m) time, where m is the number of atoms assuming that the smallest feature size h is [theta](r[subscript max]) where r[subscript max] is the radius of the largest atom; updates in O(log m) time; and uses O(m)memory. We also developed the dynamic packing grids (DPG) data structure which supports quasi-constant time updates (O(log w)) and spherical neighborhood queries (O(log log w)), where w is the word-size in the RAM. DPG and DAG together results in O(k) time approximation of scoring terms where k << m is the size of the contact region between proteins. [...] [W]e consider the symmetric spherical shell assembly case, where multiple copies of identical proteins tile the surface of a sphere. Though this is a restricted subclass of MBA, it is an important one since it would accelerate development of drugs and antibodies to prevent viruses from forming capsids, which have such spherical symmetry in nature. We proved that it is possible to characterize the space of possible symmetric spherical layouts using a small number of representative local arrangements (called tiles), and their global configurations (tiling). We further show that the tilings, and the mapping of proteins to tilings on arbitrary sized shells is parameterized by 3 discrete parameters and 6 continuous degrees of freedom; and the 3 discrete DOF can be restricted to a constant number of cases if the size of the shell is known (in terms of the number of protein n). We also consider the case where a coarse model of the whole complex of proteins are available. We show that even when such coarse models do not show atomic positions, they can be sufficient to identify a general location for each protein and its neighbors, and thereby restricts the configurational space. We developed an iterative refinement search protocol that leverages such multi-resolution structural data to predict accurate high resolution model of protein complexes, and successfully applied the protocol to model gp120, a protein on the spike of HIV and currently the most feasible target for anti-HIV drug design.Computer Science

Computational Methods in Biomolecules:Study of Hydrophilic Interactions in Protein Folding & Constant-pH Molecular Simulation of pH Sensitive Lipid MORC16

Water molecules play a significant role in biological process and are directly involved with bio-molecules and organic compounds and ions. Recent research has focused on the thermal dynamics and kinetics of water molecules in solution, including experimental (infrared spectroscopy and Raman spectroscopy) and computational (Quantum Mechanics and Molecular Dynamics) approaches. The reason that water molecules are so unique, why they have such a profound influence on bio-activity, why water molecules show some anomalies compared to other small molecules, and where and how water molecules exert their influence on solutes are some of the areas under study. We studied some properties of hydrogen bond networks, and the relationship of these properties with solutes in water. Molecular dynamics simulation, followed by an analysis of “water bridges”, which represent protein-water interaction have been carried out on folded and unfolded proteins. Results suggest that the formation of transient water bridges within a certain distance helps to consolidate the protein, possibly in transition states, and may help further guide the correct folding of proteins from these transition states. This is supporting evidence that a hydrophilic interaction is the driving force of protein folding. Biological membranes are complex structures formed mostly by lipids and proteins. For this reason the lipid bilayer has received much attention, through computation and experimental studies in recent years. In this dissertation, we report results of a newly designed pH sensitive lipid MORC16, through all-atom and coarse-grained models. The results did not yield a MORC16 amphiphile which flips its conformation in response to protonation. This may be due to imperfect force field parameters for this lipid, an imperfect protonation definition, or formation of hydrogen bond does not responsible for conformation flip in our models. Despite this, some insights for future work were obtained