Small-amplitude protein conformational dynamics: Second-order analytic relation between cartesian coordinates and dihedral angles

An analytic expression for protein atomic displacements in Cartesian coordinate space (CCS) against small changes in dihedral angles is derived. To study time-dependent dynamics of a native protein molecule in CCS from dynamics in the internal coordinate space (ICS), it is necessary to convert small changes of internal coordinate variables to Cartesian coordinate variables. When we are interested in molecular motion, six degrees of freedom for translational and rotational motion of the molecule must be eliminated in this conversion, and this conversion is achieved by requiring the Eckart condition to hold. In this article, only dihedral angles are treated as independent internal variables (i.e., bond angles and bond lengths are fixed), and Cartesian coordinates of atoms are given analytically by a second-order Taylor expansion in terms of small deviations of variable dihedral angles. Coefficients of the first-order terms are collected in the K matrix obtained previously by Noguti and Go (1983) (see ref. 2). Coefficients of the second-order terms, which are for the first time derived here, are associated with the (newly termed) L matrix. The effect of including the resulting quadratic terms is compared against the precise numerical treatment using the Eckart condition. A normal mode analysis (NMA) in the dihedral angle space (DAS) of the protein bovine pancreatic trypsin inhibitor (BPTI) has been performed to calculate shift of mean atomic positions and mean square fluctuations around the mean positions. The analysis shows that the second-order terms involving the L matrix have significant contributions to atomic fluctuations at room temperature. This indicates that NMA in CCS involves significant errors when applied for such large molecules as proteins. These errors can be avoided by carrying out NMA in DAS and by considering terms up to second order in the conversion of atomic motion from DAS to CCS. © 1995 by John Wiley & Sons, Inc.     

T-Analyst: a program for efficient analysis of protein conformational changes by torsion angles

T-Analyst is a user-friendly computer program for analyzing trajectories from molecular modeling. Instead of using Cartesian coordinates for protein conformational analysis, T-Analyst is based on internal bond-angle-torsion coordinates in which internal torsion angle movements, such as side-chain rotations, can be easily detected. The program computes entropy and automatically detects and corrects angle periodicity to produce accurate rotameric states of dihedrals. It also clusters multiple conformations and detects dihedral rotations that contribute hinge-like motions. Correlated motions between selected dihedrals can also be observed from the correlation map. T-Analyst focuses on showing changes in protein flexibility between different states and selecting representative protein conformations for molecular docking studies. The program is provided with instructions and full source code in Perl.     

Finite-state and reduced-parameter representations of protein backbone conformations

This article studies the representation of protein backbone conformations using a finite number of values for the backbone dihedral angles. We develop a combinatorial search algorithm that guarantees finding the global minima of functions over the configuration space of discrete protein conformations, and use this procedure to fit finite-state models to the backbones of globular proteins. It is demonstrated that a finite-state representation with a reasonably small number of states yields either a small root-mean-square error or a small dihedral angle deviation from the native structure, but not both at the same time. The problem can be resolved by introducing limited local optimization in each step of the combinatorial search. In addition, it is shown that acceptable approximation is achieved using a single dihedral angle as an independent variable in local optimization. Results for 11 proteins demonstrate the advantages and shortcomings of both the finite-state and reduced-parameter approximations of protein backbone conformations. © 1994 by John Wiley & Sons, Inc.     

Realistic sampling of amino acid geometries for a multipolar polarizable force field

The Quantum Chemical Topological Force Field (QCTFF) uses the machine learning method kriging to map atomic multipole moments to the coordinates of all atoms in the molecular system. It is important that kriging operates on relevant and realistic training sets of molecular geometries. Therefore, we sampled single amino acid geometries directly from protein crystal structures stored in the Protein Databank (PDB). This sampling enhances the conformational realism (in terms of dihedral angles) of the training geometries. However, these geometries can be fraught with inaccurate bond lengths and valence angles due to artefacts of the refinement process of the X‐ray diffraction patterns, combined with experimentally invisible hydrogen atoms. This is why we developed a hybrid PDB/nonstationary normal modes (NM) sampling approach called PDB/NM. This method is superior over standard NM sampling, which captures only geometries optimized from the stationary points of single amino acids in the gas phase. Indeed, PDB/NM combines the sampling of relevant dihedral angles with chemically correct local geometries. Geometries sampled using PDB/NM were used to build kriging models for alanine and lysine, and their prediction accuracy was compared to models built from geometries sampled from three other sampling approaches. Bond length variation, as opposed to variation in dihedral angles, puts pressure on prediction accuracy, potentially lowering it. Hence, the larger coverage of dihedral angles of the PDB/NM method does not deteriorate the predictive accuracy of kriging models, compared to the NM sampling around local energetic minima used so far in the development of QCTFF. © 2015 The Authors. Journal of Computational Chemistry Published by Wiley Periodicals, Inc.     

FPDock: Protein–protein docking using flower pollination algorithm

Proteins play their vital role in biological systems through interaction and complex formation with other biological molecules. Indeed, abnormalities in the interaction patterns affect the proteins’ structure and have detrimental effects on living organisms. Research in structure prediction gains its gravity as the functions of proteins depend on their structures. Protein–protein docking is one of the computational methods devised to understand the interaction between proteins. Metaheuristic algorithms are promising to use owing to the hardness of the structure prediction problem. In this paper, a variant of the Flower Pollination Algorithm (FPA) is applied to get an accurate protein–protein complex structure. The algorithm begins execution from a randomly generated initial population, which gets flourished in different isolated islands, trying to find their local optimum. The abiotic and biotic pollination applied in different generations brings diversity and intensity to the solutions. Each round of pollination applies an energy-based scoring function whose value influences the choice to accept a new solution. Analysis of final predictions based on CAPRI quality criteria shows that the proposed method has a success rate of 58% in top10 ranks, which in comparison with other methods like SwarmDock, pyDock, ZDOCK is better. Source code of the work is available at: https://github.com/Sharon1989Sunny/_FPDock_.     

Applications of Pattern Recognition in Drug Discovery

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Solution structure of the aqueous model peptide N-methylacetamide

Classical molecular dynamics simulations of aqueous N-methylacetamide (NMA) have been performed across a concentration range at 308 K. This peptidic fragment molecule is a useful model for investigating water/peptide hydrogen bond competition. The simulations predict considerable NMA self-association even at low concentrations with a concentration-dependent increase in the ratio of branched to linear clusters. Water-mediated NMA contacts are a feature of this regime, manifested by an unexpected increase in the number of short NMA oxygen contacts arising from water bridge motifs. In contrast, bulk water structure is significantly disrupted by the addition of even small quantities of NMA. With increases in NMA concentration water molecules become progressively more isolated, forming dimers and trimers hydrogen-bonded to NMA. The mixture in this concentration regime may therefore offer a minimal model system for certain structural properties of interior water buried in protein cavities and hydrogen-bonded to mainchain peptide groups.     

From secondary structure to three-dimensional structure: Improved dihedral angle probability distribution function for use with energy searches for native structures of polypeptides and proteins

An improved scheme to help in the prediction of protein structure is presented. This procedure generates improved starting conformations of a protein suitable for energy minimization. Trivariate gaussian distribution functions for the π, ψ, and χ¹ dihedral angles have been derived, using conformational data from high resolution protein structures selected from the Protein Data Bank (PDB). These trivariate probability functions generate initial values for the π, ψ, and χ¹ dihedral angles which reflect the experimental values found in the PDB. These starting structures speed the search of the conformational space by focusing the search mainly in the regions of native proteins. The efficiency of the new trivariate probability distributions is demonstrated by comparing the results for the α-class polypeptide fragment, the mutant Antennapedia (C39 → S) homeodomain (2HOA), with those from two reference probability functions. The first reference probability function is a uniform or flat probability function and the second is a bivariate probability function for π and ψ. The trivariate gaussian probability functions are shown to search the conformational space more efficiently than the other two probability functions. The trivariate gaussian probability functions are also tested on the binding domain of Streptococcal protein G (2GB1), an α/β class protein. Since presently available energy functions are not accurate enough to identify the most native-like energy-minimized structures, three selection criteria were used to identify a native-like structure with a 1.90-Å rmsd from the NMR structure as the best structure for the Antennapedia fragment. Each individual selection criterion (ECEPP/3 energy, ECEPP/3 energy-plus-free energy of hydration, or a knowledge-based mean field method) was unable to identify a native-like structure, but simultaneous application of more than one selection criterion resulted in a successful identification of a native-like structure for the Antennapedia fragment. In addition to these tests, structure predictions are made for the Antennapedia polypeptide, using a Pattern Recognition-based Importance-Sampling Minimization (PRISM) procedure to predict the backbone conformational state of the mutant Antennapedia homeodomain. The ten most probable backbone conformational state predictions were used with the trivariate and bivariate gaussian dihedral angle probability distributions to generate starting structures (i.e., dihedral angles) suitable for energy minimization. The final energy-minimized structures show that neither the trivariate nor the bivariate gaussian probability distributions are able to overcome the inaccuracies in the backbone conformational state predictions to produce a native-like structure. Until highly accurate predictions of the backbone conformational states become available, application of these dihedral angle probability distributions must be limited to problems, such as homology modeling, in which only a limited portion of the backbone (e.g., surface loops) must be explored. © 1996 John Wiley & Sons, Inc.     

Core and peripheral connectivity based cluster analysis over PPI network

A number of methods have been proposed in the literature of protein–protein interaction (PPI) network analysis for detection of clusters in the network. Clusters are identified by these methods using various graph theoretic criteria. Most of these methods have been found time consuming due to involvement of preprocessing and post processing tasks. In addition, they do not achieve high precision and recall consistently and simultaneously. Moreover, the existing methods do not employ the idea of core-periphery structural pattern of protein complexes effectively to extract clusters. In this paper, we introduce a clustering method named CPCA based on a recent observation by researchers that a protein complex in a PPI network is arranged as a relatively dense core region and additional proteins weakly connected to the core. CPCA uses two connectivity criterion functions to identify core and peripheral regions of the cluster. To locate initial node of a cluster we introduce a measure called DNQ (Degree based Neighborhood Qualification) index that evaluates tendency of the node to be part of a cluster. CPCA performs well when compared with well-known counterparts. Along with protein complex gold standards, a co-localization dataset has also been used for validation of the results.     

Force field development for organic molecules: Modifying dihedral and 1–n pair interaction parameters

We comprehensively illustrate a general process of fitting all‐atom molecular mechanics force field (FF) parameters based on quantum mechanical calculations and experimental thermodynamic data. For common organic molecules with free dihedral rotations, this FF format is comprised of the usual bond stretching, angle bending, proper and improper dihedral rotation, and 1–4 scaling pair interactions. An extra format of 1–n scaling pair interaction is introduced when a specific intramolecular rotation is strongly hindered. We detail how the preferred order of fitting all intramolecular FF parameters can be determined by systematically generating characteristic configurations. The intermolecular Van der Waals parameters are initially taken from the literature data but adjusted to obtain a better agreement between the molecular dynamics (MD) simulation results and the experimental observations if necessary. By randomly choosing the molecular configurations from MD simulation and comparing their energies computed from FF parameters and quantum mechanics, the FF parameters can be verified self‐consistently. Using an example of a platform chemical 3‐hydroxypropionic acid, we detail the comparison between the new fitting parameters and the existing FF parameters. In particular, the introduced systematic approach has been applied to obtain the dihedral angle potential and 1–n scaling pair interaction parameters for 48 organic molecules with different functionality. We suggest that this procedure might be used to obtain better dihedral and 1–n interaction potentials when they are not available in the current widely used FF. © 2014 Wiley Periodicals, Inc.     

Simulations of the temperature dependence of amide I vibration

For spectroscopic studies of peptide and protein thermal denaturation it is important to single out the contribution of the solvent to the spectral changes from those originated in the molecular structure. To obtain insights into the origin and size of the temperature solvent effects on the amide I spectra, combined molecular dynamics and density functional simulations were performed with the model N-methylacetamide molecule (NMA). The computations well reproduced frequency and intensity changes previously observed in aqueous NMA solutions. An empirical correction of vacuum frequencies in single NMA molecule based on the electrostatic potential of the water molecules provided superior results to a direct density functional average obtained for a limited number of solute-solvent clusters. The results thus confirm that the all-atom quantum and molecular mechanics approach captures the overall influence of the temperature dependent solvent properties on the amide I spectra and can improve the accuracy and reliability of molecular structural studies.     

Scalar Coupling Constants—Their Analysis and Their Application for the Elucidation of Structures

Since their discovery in the early fifties, scalar/coupling constants have been of great interest to the NMR spectroscopist. Their impact on structure determination by NMR spectroscopy is founded on the fact that the size of the coupling constant is directly related to molecular conformation. Today, for most chemical substances the parameters for the Karplus relationship, which relates the vicinial (3-bond) coupling constant to the dihedral angle, have been determined. In addition to proton–proton distances, the application of coupling constants in modern conformational analysis is indispensable. In the study of larger molecules which are of current interest, more and more involved experiments are necessary in order to overcome signal overlap and increasing line widths. A large number of experimental techniques for the determination of coupling constants has been developed; however, for this reason the choice of the most appropriate experiment to use has become more difficult. This decision must be made carefully to maximize instrument usage and obtain the largest number of couplings with the greatest accuracy possible. Many of the computer programs used in structure calculations can directly apply coupling constant restraints, similar to proton–proton distances developed from NOEs. Therefore, not only is the quality of the structure improved, but the molecular motions (internal dynamics) are better described. In this article, we review the techniques that exist today with particular attention paid to helping the non-expert to choose the appropriate experiment for the problem at hand. In addition, the use of coupling constants in computer simulations are discussed.     

Theoretical studies of transplantation antigens: Predicted conformation and structure-function relationship of the murine MHC class i antigen H-2Kb

Despite the elucidation of the primary sequences of a number of transplantation antigens from human and murine sources, no tertiary structure has yet been determined. In an attempt to determine a theoretically-stable spatial conformation for the heavy chain and the β₂-microglobulin, which constitute the murine class I transplantation antigen H-2K^b, a computer program has been used. This program, developed by us, searches for the preferred conformations of proteins, under an energy criterion, through variation of the dihedral angles Φ,Ψ,χ,₁. A stable conformation of the complex formed by both chains was then obtained, also under an energy criterion, by means of a molecular interactions program developed in this laboratory. The information obtained from the resulting structure (spatial distribution of the residues and helical content), together with complementary information from the hydrophilicity and recognition profiles of the heavy chain, suggest that the sequence regions 63–72 and 129–139 constitute the alloantigenic determinants of H2K^b. The fact that the 63–72 region is an alloantigenic determinant has been confirmed by the use of a synthetic peptide 61–69, which elicits specific T and B cell immune responses against the H-2K^b molecule.     

Influence of the presence of small gas molecules in the structure of comblike polyacrylates: a Monte Carlo study

A theoretical strategy has been developed to study the motion of small molecules through ordered polymeric systems. The strategy, which has been incorporated into a computer program denoted MCDP/2, is especially useful to study comblike polymers organized in biphasic arrangements. This is because it is based on a configurational bias Monte Carlo algorithm, which is more efficient than conventional methods to study dense systems. The MCDP/2 program has been used to investigate the influence of CH(4) and CO(2) gas molecules in the structure of isotactic poly(octadecyl acrylate), a typical comblike polymer. For this purpose, the pure polymer and different molecular systems constituted by several gas molecules dissolved in the polymer matrix have been simulated. Results indicated that the structural relaxation of the polymer is not coupled to the motion of gas molecules. The importance of these results in the field of molecular modeling of transport properties in comblike polymers is discussed.     

Morphology and crystal structure of the poly(ethylene oxide)–hydroquinone molecular complex

The occurrence of a molecular complex between poly(ethylene oxide) (PEO) and p‐dihydroxybenzene (hydroquinone) has been determined using different experimental techniques such as differential scanning calorimetry (DSC), wide‐angle X‐ray diffraction (WAXD), and Fourier transform infrared spectroscopy (FTIR). From DSC investigations, an ethylene oxide/hydroquinone molar ratio of 2/1 was deduced. During the heating, the molecular complex undergoes a peritectic reaction and spontaneously transforms into a liquid phase and crystalline hydroquinone (incongruent melting). A triclinic unit cell (a = 1.17 nm, b = 1.20 nm, c = 1.06 nm, α = 78°, β = 64°, γ = 115°), containing eight ethylene oxide (EO) monomers and four hydroquinone molecules, has been determined from the analysis of the X‐ray diffraction fiber patterns of stretched and spherulitic films. The PEO chains adopt a helical conformation with four monomers per turn, which is very similar to the 7₂ helix of the pure polymer. A crystal structure is proposed on the basis of molecular packing considerations and X‐ray diffraction intensities. It consists of a layered structure with an alternation of PEO and small molecules layers, both layers being stabilized by an array of hydrogen bonds. The morphology of PEO–HYD crystals was studied by small angle X‐ray scattering and DSC. As previously shown for the PEO–resorcinol complex, PEO–HYD samples crystallize with a lamellar thickness corresponding to fully extended or integral folded chains. The relative proportion of lamellae with different thicknesses depends on the crystallization temperature and time. Finally, the observed morphologies are discussed in terms of intermolecular interactions and chain mobility. © 1999 John Wiley & Sons, Inc. J Polym Sci B: Polym Phys 37: 1197–1208, 1999     

CAMWI: Detecting protein complexes using weighted clustering coefficient and weighted density

Detection of protein complexes is very important to understand the principles of cellular organization and function. Recently, large protein–protein interactions (PPIs) networks have become available using high-throughput experimental techniques. These networks make it possible to develop computational methods for protein complex detection. Most of the current methods rely on the assumption that protein complex as a module has dense structure. However complexes have core-attachment structure and proteins in a complex core share a high degree of functional similarity, so it expects that a core has high weighted density. In this paper we present a Core-Attachment based method for protein complex detection from Weighted PPI Interactions using clustering coefficient and weighted density. Experimental results show that the proposed method, CAMWI improves the accuracy of protein complex detection.     

Glycan Reader: automated sugar identification and simulation preparation for carbohydrates and glycoproteins

Understanding how glycosylation affects protein structure, dynamics, and function is an emerging and challenging problem in biology. As a first step toward glycan modeling in the context of structural glycobiology, we have developed Glycan Reader and integrated it into the CHARMM-GUI, http://www.charmm-gui.org/input/glycan. Glycan Reader greatly simplifies the reading of PDB structure files containing glycans through (i) detection of carbohydrate molecules, (ii) automatic annotation of carbohydrates based on their three-dimensional structures, (iii) recognition of glycosidic linkages between carbohydrates as well as N-/O-glycosidic linkages to proteins, and (iv) generation of inputs for the biomolecular simulation program CHARMM with the proper glycosidic linkage setup. In addition, Glycan Reader is linked to other functional modules in CHARMM-GUI, allowing users to easily generate carbohydrate or glycoprotein molecular simulation systems in solution or membrane environments and visualize the electrostatic potential on glycoprotein surfaces. These tools are useful for studying the impact of glycosylation on protein structure and dynamics.     

Synthesis and structural studies of 16-ferrocenemethyl-estra-1,3,5(10)-triene-3,17β-diol and its interaction with human serum albumin by fluorescence spectroscopy and in silico docking approaches

16-Ferrocenylmethyl-estra-1,3,5(10)-triene-3,17β-diol crystallizes in a triclinic unit cell and P1 space group. It contains four crystallographic independent molecules in the unit, representing four different conformers of the ferrocene–hormone conjugate. It provides evidence of a low rotational barrier around C₁₉–C₂₀ and the existence of alpha and beta conformers. The four conformers are interconnected by hydrogen bonds through hydroxyl groups of rings A and D. Density functional theory studies show the rotational barrier energy to be 4.96 Kcal/mol and the preferred conformer has a dihedral angle φ2 (defined as C₁₆–C₁₉–C₂₀–C₂₁) of 85.79°. This angle represents the conformer with the lowest steric strains. Docking studies between the subject compound and human serum albumin (HSA) showed that the most likely binding pocket of HSA is drug-binding site 2. Quenching fluorescence spectroscopy was used to study HSA–ferrocene conjugate interaction and results showed that the complex formation was static and dominated by van der Waals and electrostatic/hydrogen bonding interactions.