Numerical Geometry of Map and Model Assessment

We are describing best practices and assessment strategies for the atomic interpretation of cryo-electron microscopy (cryo-EM) maps. Multiscale numerical geometry strategies in the Situs package and in secondary structure detection software are currently evolving due to the recent increases in cryo-EM resolution. Criteria that aim to predict the accuracy of fitted atomic models at low (worse than 8 angstrom) and medium (4-8 angstrom) resolutions remain challenging. However, a high level of confidence in atomic models can be achieved by combining such criteria. The observed errors are due to map-model discrepancies and due to the effect of imperfect global docking strategies. Extending the earlier motion capture approach developed for flexible fitting, we use simulated fiducials (pseudoatoms) at varying levels of coarse-graining to track the local drift of structural features. We compare three tracking approaches: naive vector quantization, a smoothly deformable model, and a tessellation of the structure into rigid Voronoi cells, which are fitted using a multi-fragment refinement approach. The lowest error is an upper bound for the (small) discrepancy between the crystal structure and the EM map due to different conditions in their structure determination. When internal features such as secondary structures are visible in medium-resolution EM maps, it is possible to extend the idea of point-based fiducials to more complex geometric representations such as helical axes, strands, and skeletons. We propose quantitative strategies to assess map-model pairs when such secondary structure patterns are prominent

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

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)

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

Molecular dynamics simulations on the Tre1 G protein-coupled receptor: Exploring the role of the arginine of the NRY motif in Tre1 structure

Abstract Background: The arginine of the D/E/NRY motif in Rhodopsin family G protein-coupled receptors (GPCRs) is conserved in 96% of these proteins. In some GPCRs, this arginine in transmembrane 3 can form a salt bridge with an aspartic acid or glutamic acid in transmembrane 6. The Drosophila melanogaster GPCR Trapped in endoderm-1 (Tre1) is required for normal primordial germ cell migration. In a mutant form of the protein, Tre1sctt, eight amino acids RYILIACH are missing, resulting in a severe disruption of primordial germ cell development. The impact of the loss of these amino acids on Tre1 structure is unknown. Since the missing amino acids in Tre1sctt include the arginine that is part of the D/E/NRY motif in Tre1, molecular dynamics simulations were performed to explore the hypothesis that these amino acids are involved in salt bridge formation and help maintain Tre1 structure. Results: Structural predictions of wild type Tre1 (Tre1+) and Tre1sctt were subjected to over 250 ns of molecular dynamics simulations. The ability of the model systems to form a salt bridge between the arginine of the D/E/NRY motif and an aspartic acid residue in transmembrane 6 was analyzed. The results indicate that a stable salt bridge can form in the Tre1+ systems and a weak salt bridge or no salt bridge, using an alternative arginine, is likely in the Tre1sctt systems. Conclusions: The weak salt bridge or lack of a salt bridge in the Tre1sctt systems could be one possible explanation for the disrupted function of Tre1sctt in primordial germ cell migration. These results provide a framework for studying the importance of the arginine of the D/E/NRY motif in the structure and function of other GPCRs that are involved in cell migration, such as CXCR4 in the mouse, zebrafish, and chicken

Computation of protein geometry and its applications: Packing and function prediction

This chapter discusses geometric models of biomolecules and geometric constructs, including the union of ball model, the weigthed Voronoi diagram, the weighted Delaunay triangulation, and the alpha shapes. These geometric constructs enable fast and analytical computaton of shapes of biomoleculres (including features such as voids and pockets) and metric properties (such as area and volume). The algorithms of Delaunay triangulation, computation of voids and pockets, as well volume/area computation are also described. In addition, applications in packing analysis of protein structures and protein function prediction are also discussed.Comment: 32 pages, 9 figure

Structural aspects of molecular recognition

This thesis describes the design, implementation and application of a novel docking algorithm. Chapter 1 reviews some important facts about proteins and protein structure. Several molecular recognition systems are examined in detail. This Chapter also reviews a representative set of recent protein/protein docking methods and discusses their relative merits. Chapter 2 sets out the aims of the new docking algorithm, called DAPMatch, and gives full details of its implementation on a parallel architecture computer. The testing of the algorithm is also discussed. Subsequent chapters describe the application of the DAPMatch algorithm to a number of docking problems. DAPMatch is used to reconstruct the known structures of three antibody/lysozyme complexes, using the unbound structure of lysozyme. For the first time a model of the D1.3 antibody is used as a target molecule for a docking algorithm. These results are presented in Chapter 3 and analysed in detail to demonstrate their significance; non-native solutions are also examined. Chapter 4 describes the practical use of the DAPMatch algorithm in a modelling situation, to construct a hypothetical structure for the high molecular weight epidermal growth factor complex. Chapter 5 describes the adaptation of the DAPMatch algorithm to investigate α-helix/α-helix docking, and presents the results obtained. Chapter 6 explains the conclusions that were derived from this work, and suggests possible future enhancements to the algorithm