Implicit two-phase solvation model as a tool to assess conformation and energetics of proteins in membrane-mimetic media

 A heterogeneous implicit membrane-mimetic model is applied to simulations of membrane proteins. The model employs atomic solvation parameters for gas–water and gas–cyclohexane transfer. It is used to analyze structure, energetics, and orientation with respect to the bilayer of two polypeptides with different modes of membrane binding – hydrophobic segment of human glycophorin A (GpA) and cytotoxin II from Naja naja oxiana snake venom (CTX). The native state of GpA represents a transmembrane (TM) α helix, while CTX is a water-soluble protein, which is able to interact with the cell membrane. The conformational space of the polypeptides was explored in Monte Carlo simulations. The results show that the most stable conformers of GpA represent a TM α helix. They are additionally stabilized by an applied TM voltage. The results also show that CTX inserts with its three loops, does not cross the hydrophobic layer, and stays partially immersed in the membrane. This agrees well with the experimental data, thus confirming the validity of the solvation model. Received: 13 June 2000 / Accepted: 15 September 2000 / Published online: 19 January 2001     

Prediction of DNA far-IR absorption spectra based on normal mode analysis

 We present a computational method which couples normal mode analysis in internal coordinates of a molecule with very far IR spectroscopy. The analytical expression for the dependence of IR absorption on frequency incorporates frequencies and optical activities of each normal mode. In order to predict far-IR spectra of a molecule we evaluate the optical activity of each normal mode. This optical activity is determined by the vibration amplitude of the dipole moment produced by a normal mode. We calculated normal modes of DNA double-helical fragments (dA)₁₂ · (dT)₁₂ and (dA-dT)₆ · (dA-dT)₆ and evaluated their optical activities. These were found to be very sensitive to the DNA base-pair sequence. The positions of the resonance peaks in the calculated absorption spectrum of (dA)₁₂ · (dT)₁₂ are in a good agreement with those obtained by Fourier transform IR spectroscopy (Powell JW et al. 1987 Phys Rev A 35: 3929–3939). Received: 20 June 2000 / Accepted: 5 January 2001/ Published online: 3 May 2001     

Compacting local protein folds with a “hybrid protein model”

 The “hybrid protein model” is a fuzzy model for compacting local protein structures. It learns a nonredundant database encoded in a previously defined structural alphabet composed of 16 protein blocks (PBs). The hybrid protein is composed of a series of distributions of the probability of observing the PBs. The training is an iterative unsupervised process that for every fold to be learnt consists of looking for the most similar pattern present in the hybrid protein and modifying it slightly. Finally each position of the hybrid protein corresponds to a set of similar local structures. Superimposing those local structures yields an average root mean square of 3.14 ?. The significant amino acid characteristics related to the local structures are determined. The use of this model is illustrated by finding the most similar folds between two cytochromes P450. Received: 13 June 2000 / Accepted: 18 September 2000 / Published online: 19 January 2001     

Transition structure selectivity in enzyme catalysis: a QM/MM study of chorismate mutase

Two different transition structures (TSs) have been located and characterized for the chorismate conversion to prephenate in Bacillus subtilis chorismate mutase by means of hybrid quantum-mechanical/molecular-mechanical (QM/MM) calculations. GRACE software, combined with an AM1/CHARMM24/TIP3P potential, has been used involving full gradient relaxation of the position of ca. 3300 atoms. These TSs have been connected with their respective reactants and products by the intrinsic reaction coordinate (IRC) procedure carried out in the presence of the protein environment, thus obtaining for the first time a realistic enzymatic reaction path for this reaction. Similar QM/MM computational schemes have been applied to study the chemical reaction solvated by ca. 500 water molecules. Comparison of these results together with gas phase calculations has allowed understanding of the catalytic efficiency of the protein. The enzyme stabilizes one of the TSs (TS_OHout) by means of specific hydrogen bond interactions, while the other TS (TS_OHin) is the preferred one in vacuum and in water. The enzyme TS is effectively more polarized but less dissociative than the corresponding solvent and gas phase TSs. Electrostatic stabilization and an intramolecular charge-transfer process can explain this enzymatically induced change. Our theoretical results provide new information on an important enzymatic transformation and the key factors responsible for efficient selectivity are clarified. Received: 25 March 2000 / Accepted: 7 August 2000 / Published online: 23 November 2000     

Near-degeneracy corrections for second-order perturbation theory: comparison of two approaches

 We compare two approximate perturbation schemes which were developed recently to deal with the (quasi)degeneracy problem in many-body perturbation theory. We conclude that although the two methods were introduced on quite different theoretical grounds, their performances are quite similar, and present an improvement over traditional perturbation theory. Both methods are cheap in computation time, but cannot compete in accuracy with more sophisticated schemes such as complete-active-space perturbation theory or dressed particle theories. Received: 1 August 2000 / Accepted: 2 August 2000 / Published online: 19 January 2001     

Stabilization centers and protein stability

The well-balanced stability of protein structures allows large-scale fluctuations, which are indispensable in many biochemical functions, ensures the long-term persistence of the equilibrium structure and it regulates the degradation of proteins to provide amino acids for biosynthesis. This balance is studied in the present work with two sets of proteins by analyzing stabilization centers, defined as certain clusters of residues involved in cooperative long-range interactions. One data set contains 56 proteins, which belong to 16 families of homologous proteins, derived from organisms of various physiological temperatures. The other set is composed of 31 major histocompatibility complex (MHC)–peptide complexes, which represent peptide transporters complexed with peptide ligands that apparently contribute to the stabilization of the MHC proteins themselves. We show here that stabilization centers, which had been identified as special clusters of residues that protect the protein structure, evolved to serve also as regulators of function – related degradation of useless protein as part of protein housekeeping. Received: 25 August 2000 / Accepted: 6 September 2000 / Published online: 21 December 2000     

Electrochemical behaviour of a Cu/CuSe microelectrode and its application in detecting temporal and spatial localisation of copper(II) fluxes along Olea europaea roots

The electrochemical behaviour of a Cu/CuSe electrode was studied in order to define its selectivity towards cupric ions, Nerstian response, limit of detection and response time. The chalcogenide electrode was prepared by cathodic deposition of Se and subsequent formation of a thin layer of CuSe on a copper substrate. A Cu/CuSe microelectrode was prepared using copper wire 75 μm in diameter. The dimensions and response time (<0.5 s) allowed use of this electrode in the “vibrating probe method” with the aim of measuring net influxes as well as effluxes of copper(II) ions in Olea europaea roots. The electrode potential was measured along the root at a distance of 5 μm from the surface for 5 s, and then again for 5 s at a distance of 55 μm, moving the microelectrode with respect to the root surface by steps with a frequency of 0.1 Hz. The potentials measured at the two extremes of vibration were then converted to copper(II) concentrations. Substitution of these values in Fick's law yields the flux, assuming the diffusion constant D for copper ions in aqueous solutions. The results enabled us to detect copper(II) fluxes as small as 0.05 pmol cm⁻² s⁻¹. Copper(II) influx showed marked spatial and temporal features: it was highest at about 1.5 mm from the root apex and exhibited an oscillatory pattern in time. Received: 29 September 1999 / Accepted: 11 January 2000     

Deciphering globular protein sequence–structure relationships: from observation to prediction

Careful comparison of proteins sharing a same fold but only low or no sequence identity should allow a better understanding of the coding of three-dimensional structures by amino acid sequences. It has already been shown that positions of a given fold occupied mainly by hydrophobic residues in the different proteins of a structural family share very specific physical properties and participate in stabilization of the protein domain. They probably also play a crucial role in the very first steps of folding [ Poupon A, Mornon J.-P (1999) FEBS Lett. 452: 283–289; Mirny LA, Shaknovich EI (1999) J. Mol. Biol. 291: 177–196]. To further understand the sequence–structure relationship, we studied the correlation between allowed mutations at a given three-dimensional position and some of its physical properties. The different amino acids were divided in three groups (hydrophobic, nonpolar or weakly polar and polar or charged), and a correlation was established between the occupation rate of each group at a given position in the fold and the burying, the side-chain dispersion, the interposition distances and the ability to form a network of directly interacting residues. The results are then applied to predict some solvent accessibility. We show that this property can be accurately predicted for about 70% of the residues, providing precious information concerning the corresponding three-dimensional structures. The results are used to predict other structural features, as secondary structures, compactness or long-range interactions between residues remote in sequence. This information will allow the number of possible structures for a given sequence to be reduced considerably, simplifying the ab initio modelling problem to a level where it might be solved by computing methods. Received: 7 October 2000 / Accepted: 5 January 2001 / Published online: 3 April 2001     

Intramolecular coupling study on nonlinear optical signals

 In this contribution, we have introduced intramolecular coupling in order to study possible modifications in the topology of the resonances associated with the four-wave mixing signal emerging as a consequence of incorporating the permanent dipole moments when the rotating-wave approximation is not included. Received: 17 September 1999 / Accepted: 9 March 2000 / Published online: 21 June 2000     

A reexamination of virial coefficients of the Lennard-Jones fluid

The fourth-order virial coefficients have been calculated exactly to five decimal places for pure fluids of the Lennard-Jones potential at many points in the phase diagram. The calculations were performed through direct evaluation of the integrals, or diagrams, which make up the density expansion of the radial distribution function: included were the standard fast Fourier transform method of evaluating the simply connected diagrams and the evaluation of the bridge diagram for the fourth order in density by expansion in Legendre polynomials. The polynomial-order dependence of the bridge diagram calculation and the range dependence of the simply connected diagrams of the fourth order are found to have more significance than was thought from previous studies, especially in the low-temperature range. This result was confirmed by direct evaluation of the diagrams which construct the virial coefficients, as given by Rowlinson, Barker, and coworkers. This calculation confirmed that numerical convergence has not been achieved at the precision levels previously reported in the literature. These differences, though minor at higher temperatures, can be seen to be more significant at the lower temperature ranges. Received: 31 July 2000 / Accepted: 18 September 2000 / Published online: 21 December 2000     

An improved iterative solution to solve the electrostatic problem in the polarizable continuum model

 We present a discrete iterative interpolation scheme (DIIS) to improve the convergence rate of electrostatic calculations in the polarizable continuum model (PCM) to describe solvent effects on molecular solutes. The electrostatic calculations may easily become the bottleneck of the calculation when the solute size is large. For large molecules iterative procedures turn out to be computationally more convenient than matrix inversion or closure methods. The DIIS scheme is compared here to another iterative procedure (DAMP) and to the biconjugate gradient (BCG) method. The comparisons show that DIIS leads to a sizeable saving of computational time for the C-PCM and IEF-PCM methods (average 40%) compared to DAMP, and more than 50% with respect to the BCG method. Received: 5 October 2000 / Accepted: 13 November 2000 / Published online: 19 January 2001     

Extracting parameters for base-pair level models of DNA from molecular dynamics simulations

 A method is described to extract a complete set of sequence-dependent energy parameters for a rigid base-pair model of DNA from molecular dynamics (MD) simulations. The method is properly consistent with equilibrium statistical mechanics and leads to effective inertia parameters for the base-pair units as well as stacking and stiffness parameters for the base-pair junctions. We give explicit formulas that yield a complete set of base-pair model parameters in terms of equilibrium averages that can be estimated from a time series generated in an MD simulation. The expressions to be averaged depend strongly both on the choice of coordinates used to describe rigid-body orientations and on the choice of strain measures at each junction. Received: 12 July 2000 / Accepted: 5 January 2001 / Published online: 3 May 2001     

Influence of ligand binding on the conformation of Torpedo californica acetylcholinesterase

With the aim of identifying structural changes in acetylcholinesterase, induced by ligand binding, we use a completely automatic procedure to analyse the differences between the backbone conformation of the free enzyme and those in eight complexes of Torpedo californica acetylcholinesterase, with various quaternary ammonium ligands, and with the protein inhibitor fasciculin. In order to discriminate between structural changes due to ligand binding and those arising from model imprecision, we also examine protein–ligand and protein–water contacts. Except for the peptide flip in the complex with huperzine A, the backbones of other complexes with quaternary ammonium ligands display negligible changes relative to the free enzyme. Another exception is the complex with the bisquaternary ammonium ligand decamethonium, where several loops display above average deformations, but only two, those spanning residues 334–348 and residues 277–304, seem to move as a result of ligand binding. Movement of the ω loop (residues 61–95) is detected only in the complex with the protein fasciculin. Received: 21 July 2000 / Accepted: 18 September 2000 / Published online: 28 February 2001     

Ab initio structure predictions using a hierarchical approach applied to 434 cro and the Drosophila homeodomain

A discrete-state ab initio protein structure prediction procedure is presented, based on the assumption that some proteins fold in an hierarchical way, where the early folding of independent units precedes and helps complete structure formation. It involves a first step predicting, by means of threading algorithms and local structure prediction methods, the location of autonomous protein subunits presenting favorable local and tertiary interactions. The second step consists of predicting the structure of these units by Monte Carlo simulated annealing using several database-derived potentials. In a last step, these predicted structures are used as starting conformations of additional simulations, keeping these structures frozen and including the complete protein sequence. This procedure is applied to two small DNA-binding proteins, 434 cro and the Drosophila melanogaster homeodomain that contain 65 and 47 residues, respectively, and is compared to the nonhierarchical procedure where the whole protein is predicted in a single run. The best predicted structures were found to present root-mean-square deviations relative to the native conformation of 2.7 ? in the case of the homeodomain and of 3.9 ? for 434 cro; these structures thus represent low-resolution models of the native structures. Strikingly, not only the helices were correctly predicted but also intervening turn motifs. Received: 6 July 2000 / Accepted: 8 September 2000 / Published online: 21 December 2000     

Analysis of the RGD sequence in protein structures: comparison to the conformations of the RGDW and DRGDW peptides determined by molecular dynamics simulations

Geometric properties of the RGD sequence in a data set of protein crystal and NMR structures deposited in the Protein Data Bank were examined to identify structural characteristics that are related to cell adhesion activity. Interatomic distances and dihedral angles are examined. These geometric measures are then used in an analysis of the conformations of the RGDW and _DRGDW peptides obtained from molecular dynamics simulations (Stote RH, et al. (2000) J Phys ChemB 104:1624). This analysis leads to the suggestion that differences in the accessible conformations contribute to the difference in biological activity between the RGDW and the _DRGDW peptides. Received: 15 August 2000 / Accepted: 4 October 2000 / Published online: 21 March 2001     

A generalized Langevin dynamics approach to model solvent dynamics effects on proteins via a solvent-accessible surface. The carboxypeptidase A inhibitor protein as a model

A generalized Langevin dynamics (GLD) scheme is derived for (bio)macromolecules having internal structure, arbitrary shapes and a size larger than solvent molecules (i.e. proteins). The concept of solvent-accessible surface area (SASA) is used to incorporate solvent effects via external forces thereby avoiding its explicit molecular representation. A simulation algorithm is implemented in the GROMOS molecular dynamics (MD) program including random forces and memory effects, while solvation effects enter via derivatives of the surface area. The potato carboxypeptidase inhibitor (PCI), a small protein, is used to numerically test the approach. This molecule has N- and C-terminal tails whose structure and fluctuations are solvent dependent. A 1-ns MD trajectory was analyzed in depth. X-ray and NMR structures are used in conjunction with MD simulations with and without explicit solvent to gauge the quality of the results. All the analyses showed that the GLD simulation approached the results obtained for the MD simulation with explicit simple-point-charge-model water molecules. The SASAs of the polar atoms show a natural exposure towards the solvent direction. A FLS solvent simulation was completed in order to sense memory effects. The approach and results presented here could be of great value for developing alternatives to the use of explicit solvent molecules in the MD simulation of proteins, expanding its use and the time-scale explored. Received: 2 February 2000 / Revised: 12 March 2000 / Accepted: 26 May 2000 / Published online: 2 November 2000     

Relativistic Gaussian basis sets for the elements K – Uuo

A series of energy-minimized relativistic Gaussian basis sets for the elements with atomic numbers 19–118 is presented. The basis sets have been derived at the self-consistent field level as weighted average energies of the respective electronic configurations. A spherical Gaussian charge distribution has been used to model the nucleus. The basis sets are constructed as interleaving dual family sets with shared exponents within each family. The quality of the basis sets is better than double zeta. Received: 7 July 2000 / Accepted: 21 September 2000 / Published online: 21 December 2000     

A fast algorithm to compute atomic charges based on the topology of the electron density

This work proposes a novel algorithm to compute atomic charges as defined by the theory of “atoms in molecules” (AIM). Using the divergence theorem it is possible to express the 3D volume integral over an atomic basin purely in terms of 2D surface integrals. Hence, it can be proven that an atomic charge is equal to the flux of the electric field of the whole molecule through the atom's complete boundary. This boundary consists of the interatomic surfaces and the so-called outeratomic surface, which is the open side of the atom. When fine-tuned the algorithm can generate atomic charges in the order of minutes without introducing any approximations. Moreover, the problem of the geometrical cusp occurring in atomic basins and that of multiple intersections is also eliminated. The computational overhead of computing the electric field (which is analytical) is compensated by the gain in computing time by eliminating one dimension of quadrature. The proposed algorithm opens an avenue to invalidate the oft-quoted drawback that AIM charges are computationally expensive. We explain the details of the implementation in MORPHY01 and illustrate the novel algorithm with a few examples. Received: 1 June 2000 / Accepted: 4 October 2000 / Published online: 23 January 2001     

Effective modeling of intrinsic and environmental effects on the structure and electron plaramagnetic resonance parameters of nitroxides by an integrated quantum mechanical/molecular mechanics/polarizable continuum model approach

 Experimental and density functional theory geometries have been used to extend the AMBER force field to nitroxides. An optimum set of transferable atomic charges for the calculation of electrostatic interactions both in vacuo and in aqueous solution has been obtained by averaging the charges obtained by a restrained electrostatic potential fitting of representative compounds. Besides reliable structural data, our implementation allows the computation of accurate spectromagnetic properties by single-point B3LYP computations on geometries optimized at the AMBER level. Solvent shifts in aqueous solution can be reproduced quantitatively by a mixed model in which specific solvent effects are described by two water molecules strongly coordinated to the nitroxide oxygen, while bulk effects are described by the polarizable continuum model. Received: 17 September 1999 / Accepted: 3 February 2000 / Published online: 29 June 2000     

Inexpensive and accurate predictions of optical excitations in transition-metal complexes: the TDDFT/PBE0 route

Time-dependent density functional theory (TDDFT) is applied to calculate vertical excitation energies of three representative transition metal complexes. The computational model (PBE0) is obtained by combining the Perdew-Burke-Erzenrhof (PBE) generalized gradient functional with a predetermined amount of exact exchange. Our results show that the TDDFT/PBE0 model represents a cheap and reliable tool for the computation of optical excitations for transition metal complexes. Received: 8 August 2000 / Accepted: 7 September 2000 / Published online: 23 November 2000