Orientation-dependent Potential Research Articles

Automated simulation-based membrane protein refinement into cryo-EM data

The resolution revolution has increasingly enabled single-particle cryogenic electron microscopy (cryo-EM) reconstructions of previously inaccessible systems, including membrane proteins—a category that constitutes a disproportionate share of drug targets. We present a protocol for using density-guided molecular dynamics simulations to automatically refine atomistic models into membrane protein cryo-EM maps. Using adaptive force density-guided simulations as implemented in the GROMACS molecular dynamics package, we show how automated model refinement of a membrane protein is achieved without the need to manually tune the fitting force ad hoc. We also present selection criteria to choose the best-fit model that balances stereochemistry and goodness of fit. The proposed protocol was used to refine models into a new cryo-EM density of the membrane protein maltoporin, either in a lipid bilayer or detergent micelle, and we found that results do not substantially differ from fitting in solution. Fitted structures satisfied classical model-quality metrics and improved the quality and the model-to-map correlation of the x-ray starting structure. Additionally, the density-guided fitting in combination with generalized orientation-dependent all-atom potential was used to correct the pixel-size estimation of the experimental cryo-EM density map. This work demonstrates the applicability of a straightforward automated approach to fitting membrane protein cryo-EM densities. Such computational approaches promise to facilitate rapid refinement of proteins under different conditions or with various ligands present, including targets in the highly relevant superfamily of membrane proteins.

Molecular rotations in matter-wave interferometry

We extend the theory of matter-wave interferometry of point-like particles to non-spherical objects by taking the orientational degrees of freedom into account. In particular, we derive the grating transformation operator, that maps the impinging state onto the outgoing state, for a general, orientation-dependent interaction potential between the grating and the molecule. The grating operator is then worked out for the diffraction of symmetric top molecules from standing light waves, and the resulting interference pattern is calculated in the near-field. This allows us to identify a signature of the orientational degrees of freedom in near-field matter-wave experiments.

Computational design of enzyme-ligand binding using a combined energy function and deterministic sequence optimization algorithm.

Enzyme amino-acid sequences at ligand-binding interfaces are evolutionarily optimized for reactions, and the natural conformation of an enzyme-ligand complex must have a low free energy relative to alternative conformations in native-like or non-native sequences. Based on this assumption, a combined energy function was developed for enzyme design and then evaluated by recapitulating native enzyme sequences at ligand-binding interfaces for 10 enzyme-ligand complexes. In this energy function, the electrostatic interaction between polar or charged atoms at buried interfaces is described by an explicitly orientation-dependent hydrogen-bonding potential and a pairwise-decomposable generalized Born model based on the general side chain in the protein design framework. The energy function is augmented with a pairwise surface-area based hydrophobic contribution for nonpolar atom burial. Using this function, on average, 78% of the amino acids at ligand-binding sites were predicted correctly in the minimum-energy sequences, whereas 84% were predicted correctly in the most-similar sequences, which were selected from the top 20 sequences for each enzyme-ligand complex. Hydrogen bonds at the enzyme-ligand binding interfaces in the 10 complexes were usually recovered with the correct geometries. The binding energies calculated using the combined energy function helped to discriminate the active sequences from a pool of alternative sequences that were generated by repeatedly solving a series of mixed-integer linear programming problems for sequence selection with increasing integer cuts.

Formation of double glass in binary mixtures of anisotropic particles: Dynamic heterogeneities in rotations and displacements

We study glass behavior in a mixture of elliptic and circular particles in two dimensions at low temperatures using an orientation-dependent Lennard-Jones potential. The ellipses have a mild aspect ratio (∼1.2) and tend to align at low temperatures, while the circular particles play the role of impurities disturbing the ellipse orientations at a concentration of 20%. These impurities have a size smaller than that of the ellipses and attract them in the homeotropic alignment. As a result, the coordination number around each impurity is mostly 5 or 4 in glassy states. We realize double glass, where both the orientations and the positions are disordered but still hold mesoscopic order. We find a strong heterogeneity in the flip motions of the ellipses, which sensitively depends on the impurity clustering. In our model, a small fraction of the ellipses still undergo flip motions relatively rapidly even at low temperatures. In contrast, the nonflip rotations (with angle changes not close to ±π) are mainly caused by the cooperative configuration changes involving many particles. Then, there arises a long-time heterogeneity in the nonflip rotations closely correlated with the dynamic heterogeneity in displacements.

Orientation-dependent ionization potential of CuPc and energy level alignment at C60/CuPc interface

The electronic structure evolution of interfaces of fullerene (C60) with copper phthalocyanine (CuPc) on highly oriented pyrolytic graphite (HOPG) and on native silicon oxide has been investigated with ultraviolet photoemission spectroscopy and inverse photoemission spectroscopy. The LUMO edge of C60 was found to be pinned at the interface with CuPc on SiO2. A substantial difference in the electron affinity of CuPc on the two substrates was observed as the orientation of CuPc is lying flat on HOPG and standing up on SiO2. The ionization potential and electron affinity of C60 were not affected by the orientation of CuPc due to the spherical symmetry of C60 molecules. We observed band bending in C60 on the standing-up orientation of CuPc molecules, while the energy levels of C60 on the flat-lying orientation of CuPc molecules were observed to be flat. The observation points to a dependence of photoexcited charge transfer on the relative molecular orientation at the interface.

GOAP: A Generalized Orientation-Dependent, All-Atom Statistical Potential for Protein Structure Prediction

An accurate scoring function is a key component for successful protein structure prediction. To address this important unsolved problem, we develop a generalized orientation and distance-dependent all-atom statistical potential. The new statistical potential, generalized orientation-dependent all-atom potential (GOAP), depends on the relative orientation of the planes associated with each heavy atom in interacting pairs. GOAP is a generalization of previous orientation-dependent potentials that consider only representative atoms or blocks of side-chain or polar atoms. GOAP is decomposed into distance- and angle-dependent contributions. The DFIRE distance-scaled finite ideal gas reference state is employed for the distance-dependent component of GOAP. GOAP was tested on 11 commonly used decoy sets containing 278 targets, and recognized 226 native structures as best from the decoys, whereas DFIRE recognized 127 targets. The major improvement comes from decoy sets that have homology-modeled structures that are close to native (all within ∼4.0 Å) or from the ROSETTA ab initio decoy set. For these two kinds of decoys, orientation-independent DFIRE or only side-chain orientation-dependent RWplus performed poorly. Although the OPUS-PSP block-based orientation-dependent, side-chain atom contact potential performs much better (recognizing 196 targets) than DFIRE, RWplus, and dDFIRE, it is still ∼15% worse than GOAP. Thus, GOAP is a promising advance in knowledge-based, all-atom statistical potentials. GOAP is available for download at http://cssb.biology.gatech.edu/GOAP.

Straley Model of Biaxial Nematics Extended

In 1974 Straley [Phys. Rev. A 10, 1881 (1974)] presented the mean-field model of interacting particles similar to hard rectangular blocks. The orientation-dependent potential was built from the four basic functions composed from the standard rotation matrix elements with j = 2. As there is only one basic function composed from the standard rotation matrix elements with j = 3, it is interesting to find out whether it has any influence on the known phase diagrams. We show that the j = 3 term can enlarge the biaxial nematic phase range. The article also discusses an extension of the Romano model mimicking shape amphiphilicity [Phys. Lett. A 333, 110 (2004)]. It is showed that the j = 3 interaction term can create the tetrahedral phase with the second order transition to the isotropic phase. What is more, the first order transition from the biaxial nematic phase to the isotropic phase or to the tetrahedral phase is predicted. Finally, the possible presence of the j = 3 term in other theories is discussed.

A novel side-chain orientation dependent potential derived from random-walk reference state for protein fold selection and structure prediction.

BackgroundAn 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.MethodologyWe 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.SignificanceRW 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.

A Computer Simulation Study of Stick−Slip Transitions in Water Films Confined between Model Hydrophilic Surfaces. 1. Monolayer Films

The shear behavior of monolayer water films confined in a slit-like pore between hydrophilic walls is simulated in the quasistatic regime using the grand canonical Monte Carlo technique. Each wall is represented as a hexagonal lattice of force sites that interact with water through an orientation-dependent hydrogen-bonding potential. When the walls are in registry, the water oxygen atoms form either a crystal- or fluid-like structure, depending on the period of the wall's lattice. In both cases, however, the monolayer structure is orientationally disordered. Both the crystal- and fluid-like monolayers prove to be capable of experiencing well-defined stick-slip transitions, with the largest yield stress occurring in the crystal-like case. Beyond the yield point, the crystal-like monolayers "melt", but their structure and molecular motion differ in many respects from those characteristic of normal fluids.

Inelastic Neutron Scattering and Molecular Dynamics Determination of the Interaction Potential in LiquidCD4

Anisotropic interactions of liquid CD4 are studied in detail by comparison of inelastic neutron Brillouin scattering data with molecular dynamics simulations using up to four different models of the methane site-site potential. We demonstrate that the experimental dynamic structure factor S(Q,omega) acts as a highly discriminating quantity for possible interaction schemes. In particular, the Q evolution of the spectra enables a selective probing of the short- and medium-range features of the anisotropic potentials. We show that the preferential configuration of methane dimers at liquid densities can thus be discerned by analyzing the orientation-dependent model potential curves, in light of the experimental and simulation results.

New deformed model of α-decay half-lives with a microscopic potential

The \ensuremath{\alpha}-decay half-lives of deformed nuclei are investigated in a new version of the density-dependent cluster model. By the multipole expansion method, the deformation- and orientation-dependent double-folding potential is derived to calculate the \ensuremath{\alpha}-decay width through a deformed Coulomb barrier. We perform systematic calculations for the ground-state \ensuremath{\alpha} transitions of even-even nuclei with $Z=52\ensuremath{-}104$. The theoretical results are in good agreement with the experimental data. This is, to our knowledge, the first deformed calculation of \ensuremath{\alpha}-decay half-lives within the framework of microscopic double-folding potentials. A unified description of \ensuremath{\alpha}-decay half-lives of both spherical and deformed nuclei is obtained by the microscopic potentials.

Anomalous Orientation-Dependent Effective Pair Interaction among Histidine and Other Amino Acid Residues in Metalloproteins: Breakdown of the Hydropathy Scale Index

Hydropathy scale is widely used to obtain a measure of the effective interaction between any two amino acid residues in proteins and is based on the assumption that attraction between two hydrophobic groups and repulsion between hydrophilic groups (in water) can be translated straightforwardly to protein environment. Here we employ a recently developed statistical mechanical approach combined with the Protein Data Bank to obtain both distance- and orientation-dependent potential of mean force (ODPMF). This allowed us to explore effective pair potential among many amino acid residues and to examine the validity of the hydropathy scale in modeling the interaction among amino acid residues. We find that in some cases, like Phe-Phe and Lys-Lys, the hydropathy scale approach is largely obeyed. However, we also observe many unexpected pair interactions which defy the trend given by published hydropathy scales. An example of the former is the arginine-arginine (Arg-Arg) pair interaction which is found to be strongly and surprisingly attractive at short separation, even though it is the most hydrophilic residue. Here the head-to-head (see text) interaction is also stabilized. Tryptophan residues also exhibit strong attractive interaction. Equally important, we find strong influence of metal in determining effective interaction among the amino acid residues. It is the behavior of the histidine (His) which is found to be the most unusual. It exhibits a strong attractive interaction with itself which gets significantly enhanced in metalloproteins. These results highlight the important (sometime hidden) role of metals in protein structure and folding.

Orientation-dependent potential of mean force for protein folding

We present a solvent-implicit minimalistic model potential among the amino acid residues of proteins, obtained by using the known native structures [deposited in the Protein Data Bank (PDB)]. In this model, the amino acid side chains are represented by a single ellipsoidal site, defined by the group of atoms about the center of mass of the side chain. These ellipsoidal sites interact with other sites through an orientation-dependent interaction potential which we construct in the following fashion. First, the site-site potential of mean force (PMF) between heavy atoms is calculated [following F. Melo and E. Feytsman, J. Mol. Biol. 267, 207 (1997)] from statistics of their distance separation obtained from crystal structures. These site-site potentials are then used to calculate the distance and the orientation-dependent potential between side chains of all the amino acid residues (AAR). The distance and orientation dependencies show several interesting results. For example, we find that the PMF between two hydrophobic AARs, such as phenylalanine, is strongly attractive at short distances (after the obvious repulsive region at very short separation) and is characterized by a deep minimum, for specific orientations. For the interaction between two hydrophilic AARs, such a deep minimum is absent and in addition, the potential interestingly reveals the combined effect of polar (charge) and hydrophobic interactions among some of these AARs. The effectiveness of our potential has been tested by calculating the Z-scores for a large set of proteins. The calculated Z-scores show high negative values for most of them, signifying the success of the potential to identify the native structure from among a large number of its decoy states.

Analysis of anisotropic side-chain packing in proteins and application to high-resolution structure prediction.

pi-pi, Cation-pi, and hydrophobic packing interactions contribute specificity to protein folding and stability to the native state. As a step towards developing improved models of these interactions in proteins, we compare the side-chain packing arrangements in native proteins to those found in compact decoys produced by the Rosetta de novo structure prediction method. We find enrichments in the native distributions for T-shaped and parallel offset arrangements of aromatic residue pairs, in parallel stacked arrangements of cation-aromatic pairs, in parallel stacked pairs involving proline residues, and in parallel offset arrangements for aliphatic residue pairs. We then investigate the extent to which the distinctive features of native packing can be explained using Lennard-Jones and electrostatics models. Finally, we derive orientation-dependent pi-pi, cation-pi and hydrophobic interaction potentials based on the differences between the native and compact decoy distributions and investigate their efficacy for high-resolution protein structure prediction. Surprisingly, the orientation-dependent potential derived from the packing arrangements of aliphatic side-chain pairs distinguishes the native structure from compact decoys better than the orientation-dependent potentials describing pi-pi and cation-pi interactions.

A physical reference state unifies the structure-derived potential of mean force for protein folding and binding.

Extracting knowledge-based statistical potential from known structures of proteins is proved to be a simple, effective method to obtain an approximate free-energy function. However, the different compositions of amino acid residues at the core, the surface, and the binding interface of proteins prohibited the establishment of a unified statistical potential for folding and binding despite the fact that the physical basis of the interaction (water-mediated interaction between amino acids) is the same. Recently, a physical state of ideal gas, rather than a statistically averaged state, has been used as the reference state for extracting the net interaction energy between amino acid residues of monomeric proteins. Here, we find that this monomer-based potential is more accurate than an existing all-atom knowledge-based potential trained with interfacial structures of dimers in distinguishing native complex structures from docking decoys (100% success rate vs. 52% in 21 dimer/trimer decoy sets). It is also more accurate than a recently developed semiphysical empirical free-energy functional enhanced by an orientation-dependent hydrogen-bonding potential in distinguishing native state from Rosetta docking decoys (94% success rate vs. 74% in 31 antibody-antigen and other complexes based on Z score). In addition, the monomer potential achieved a 93% success rate in distinguishing true dimeric interfaces from artificial crystal interfaces. More importantly, without additional parameters, the potential provides an accurate prediction of binding free energy of protein-peptide and protein-protein complexes (a correlation coefficient of 0.87 and a root-mean-square deviation of 1.76 kcal/mol with 69 experimental data points). This work marks a significant step toward a unified knowledge-based potential that quantitatively captures the common physical principle underlying folding and binding. A Web server for academic users, established for the prediction of binding free energy and the energy evaluation of the protein-protein complexes, may be found at http://theory.med.buffalo.edu.

Monte Carlo studies of self-assembled monolayers using simple generalized models. II. A two-site molecular model

A simple two-site molecular model is suggested for computer simulation of self-assembled monolayers (SAMs) formed by long-chain functionalized molecules on the surface of solid substrates. In this model, one force site, placed at the functional headgroup, is responsible for the interaction of the headgroup with the periodic substrate field and the other headgroups. The second force site, positioned in the middle of the molecule, describes the chain–substrate and chain–chain interactions. For the latter interaction, a Gay–Berne–Pechukas orientation-dependent potential is used. The parameters of the model potentials are chosen so as to mimic the interactions in alkanethiol/Au(111) SAMs. The phase and structural behavior of the model system is explored using the Monte Carlo technique as a function of temperature, coverage, and the magnitude of surface corrugation. Simulations reveal a commensurate–incommensurate solid-phase transition preceding two-dimensional melting. At incomplete coverages, a two-phase region is observed, in which the usual crystalline phase characteristic of saturation coverage coexists with a low-density translationally disordered phase. The surface-aligned “striped” phase observed in STM experiments [G. E. Poirier and E. D. Pylant, Science 272, 1154 (1996)] can only be modeled at low temperatures assuming head-to-head dimerization of the molecules.

Semi-empirical investigation of the angular dependence of the interaction energy between two ground-state oxygen molecules

An orientation-dependent intermolecular potential for two ground-state O 2 molecules has been determined using a modified Kihara potential function based on molecular charge-distribution contours, observed second virial coefficients and long-range electrostatic quadrupolar and dispersion interactions. Good agreement with experimental predictions and ab initio calculations has been displayed.

Statistical-mechanical calculations for nematic liquid crystals

A molecular theory of liquid crystals is developed within the framework of statistical mechanics for classical liquids. Coupled Bogoliubov-Born-Green-Kirkwood-Yvon (BBGKY) equations are derived and solved for anisotropic systems of molecules interacting via a pairwise, orientation-dependent potential. Solutions representing isotropic and nematic phases are obtained. Among the quantities calculated are the temperature- and density-dependent orientational order parameters. Besides serving as a prototype calculation, what is presented here also provides a theoretical background in which the mean-field approximation can better be understood.

Thermodynamic perturbation theory for simple polar fluids. II

The study of polar fluids begun in a previous paper is continued. Calculations for the Stockmayer potential are extended to include the term of order μ6, where μ is the dipole moment. The effects of higher-order terms are then approximated by means of a simple Padé extrapolation procedure, and the liquid-gas coexistence curve is located in this approximation. An orientation-independent but temperature-dependent potential that is thermodynamically equivalent to an arbitrary orientation-dependent potential is introduced and used to assess the lowest-order thermodynamic effects that result from the presence of quadrupole and octupole terms in the pair-potential. Several values of quadrupole and octupole moments representative of a dipolar molecule (HCl) as well as linear molecules (N2, O2 and CO2, for which μ=0) are considered.

Scattering of High-Velocity Neutral Particles by an Orientation Dependent Potential

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