Anharmonic force field and spectroscopic constants of silene: an ab initio study

High-level ab initio calculations with large basis sets are reported for silene, H₂C=SiH₂. Correlated harmonic force fields are obtained from coupled cluster CCSD(T) calculations with the cc-pVQZ basis (cc-pVTZ for H) while the anharmonic force fields are computed at the MP2/TZ2Pf level. There is excellent agreement with the available experimental data, in particular the equilibrium geometry and the fundamental vibrational frequencies. Many other spectroscopic constants are predicted for the C _{2 v} isotopomers of silene. Received: 27 May 1998 / Accepted: 23 July 1998 / Published online: 9 October 1998     

Dynamics of the transmembrane domain of the ErbB-2 receptor

The structure and dynamics of the ErbB-2 transmembrane domain have been examined using molecular dynamics techniques both in vacuum and within an explicit hydrated L-α-dilauroyl-phosphatidyl-ethanolamine environment. In-vacuum simulations show that a highly cooperative structural transition occurs frequently within the α-helical transmembrane domain which converts to local π-helices. We show that the α-helix alteration does not depend upon the force field or initial side-chain conformations but is intimately related to the sequence. The membrane-like environment does not prevent the structural transition in the helix but slows down the peptide dynamics indicating that the appearance of a π-bulge is not an artifact of the vacuum approximation. The consequences of π-helix formation could be very huge for the ErbB-2 receptor which is involved in numerous human cancers and also for other membrane proteins wherein similar local structures are also observed experimentally. Received: 9 May 1998 / Accepted: 3 September 1998 / Published online: 17 December 1998     

Generalized extended empirical bond-order dependent force fields including nonbond interactions

We present a general approach for describing chemical processes (bond breaking and bond formation) in materials using force fields (FF) that properly describe multiple bonds at small distances while describing nonbond (Coulomb and van der Waals) interactions at long distances. This approach is referred to as the generalized extended empirical bond-order dependent FF. In this paper we use the Brenner empirical bond-order dependent FF for the short-range interactions and report applications on the energetics and structures of graphite crystal, dynamics of molecular crystals, and distortions of bucky tubes. Received: 7 August 1998 / Accepted: 26 October 1998 / Published online: 16 March 1999     

Molecular dynamics simulations of the isolated domain 1 of annexin I

Annexin molecules consist of a symmetrical arrangement of four domains of identical folds but very different sequences. Nuclear magnetic resonance (NMR) experiments on the isolated domains of annexin I in aqueous solution have indicated that domain 1 retains its native structure whereas domain 2 unfolds. Therefore these two domains constitute interesting models for comparative simulations of structural stability using molecular dynamics. Here we present the preliminary results of molecular dynamics simulations of the isolated domain 1 in explicit water at 300 K, using two different simulation protocols. For the first, domain 1 was embedded in a 46 ? cubic box of water. A group-based non-bonded cut-off of 9 ? with a 5–9 ? non-bonded switching function was used and a 2 fs integration step. Bonds containing hydrogens were constrained with the SHAKE algorithm. These conditions led to unfolding of the domain within 400 ps at 300 K. In the second protocol, the domain was embedded in a 62 ? cubic box of water. An atom-based non-bonded cut-off of 8–12 ? using a force switching function for electrostatics and a shifting function for van der Waals interactions were used with a 1 fs integration step. This second protocol led to a native-like conformation of the domain in accord with the NMR data which was stable over the whole trajectory (∼2 ns). A small, but well-defined relaxation of the structure, from that observed for the same domain in the entire protein, was observed. This structural relaxation is described and methodological aspects are discussed. Received: 10 May 1998 / Accepted: 4 August 1998 / Published online: 2 November 1998     

Poisson-Boltzmann calculations versus molecular dynamics simulations for calculating the electrostatic potential of a solvated peptide

We performed a very long molecular dynamics simulation of a peptide in explicit water molecules and ions and averaged the electrostatic potential caused by peptide, water and ions at eight points in the vicinity of the peptide. These electrostatic potential values were directly compared to the potential calculated by solving the non-linear Poisson-Boltzmann equation for the system, which describes the solvent using continuum electrostatics. We analyze the contribution of dielectric constant, conformational flexibility and solvation effects on the electrostatic potential at these eight points. Received: 24 April 1998 / Accepted: 4 August 1998 / Published online: 23 November 1998     

Information about the biologically relevant properties of Clostridium pasteurianum rubredoxin obtained from modeling and dynamics simulations of molecular variants

Rubredoxins are small electron transfer proteins containing one iron atom at their active site. The rubredoxin from the anaerobic bacterium Clostridium pasteurianum has been subjected to molecular dynamics studies starting from the minimized solvated structure. The results of the simulations have been compared with identical ones carried out with selected mutated forms of the protein obtained by molecular modeling. Surface residues, which are highly conserved among rubredoxins and close to the cysteine ligands, can be replaced by glutamates, i.e. long chain carboxylates. The main structural consequence is a shift of the protein backbone bearing conserved aromatic residues. Reciprocally, substitution of the aromatic residue closest to the iron atom shifts the cysteine-containing peptide fragments. These observations have been related to the changes in electron transfer and redox properties previously measured for this set of rubredoxin molecular variants. Received: 16 May 1998 / Accepted: 4 August 1998 / Published online: 2 November 1998     

Study of flexible joints and permanent bends in DNA fragments by brownian dynamics simulations

The use of Brownian dynamics simulations to investigate the presence of structural (kinks) and dynamic (bulges) anomalies in short DNA stretches is analyzed in connection with a string-of-beads model. A scaling method to choose the hydrodynamic translational and rotational parameters of the beads is proposed and tested on straight, kinked and bulged DNA fragments 17 nm long. The model reproduces the rigid-body rotational diffusion for the straight DNA and for the fluorescence polarization anisotropy decay of the kinked and bulged DNAs the model predicts a different behavior which is found experimentally. Received: 24 March 1998 / Accepted: 3 September 1998 / Published online: 23 November 1998     

Conformational free energy surface of the linear DPDPE peptide: cost of pre-organization for disulfide bond formation

We have calculated the free energy differences between four conformers of the linear form of the opioid pentapeptide DPDPE in aqueous solution. The conformers are Cyc, representing the structure adopted by the linear peptide prior to disulfide bond formation, β _C and β _E , two slightly different β-turns previously identified in unconstrained molecular dynamics simulations, and Ext, an extended structure. Our simulations indicate that β _E is the most stable of the studied conformers of linear DPDPE in aqueous solution, with β _C , Cyc and Ext having free energies higher by 2.3, 6.3, and 28.2 kcal/mol, respectively. The free energy differences of 4.0 kcal/mol between β _C and Cyc, and 6.3 kcal/mol between β _E and Cyc, reflect the cost of pre-organizing the linear peptide into a conformation conducive for disulfide bond formation. Such a conformational change is a pre-requisite for the chemical reaction of S–S bond formation to proceed. The relatively low population of the cyclic-like structure agrees qualitatively with observed lower potency and different receptor specificity of the linear form relative to the cyclic peptide, and with previous unconstrained simulation results. Free energy component analysis indicates that the moderate stability difference of 4.0–6.3 kcal/mol between the β-turns and the cyclic-like structure results from cancellation of two large opposing effects. In accord with intuition, the relaxed β-turns have conformational strain 43–45 kcal/mol lower than the Cyc structure. However, the cyclic-like conformer interacts with water about 39 kcal/mol strongly than the open β-turns. Our simulations are the first application of the recently developed multidimensional conformational free energy thermodynamic integration (CFTI) protocol to a solvated system, with fast convergence of the free energy obtained by fixing all flexible dihedrals. Additionally, the availability of the CFTI multidimensional free energy gradient leads to a new decomposition scheme, giving the contribution of each fixed dihedral to the overall free energy change and providing additional insight into the microscopic mechanisms of the studied processes. Received: 20 April 1998 / Accepted: 9 September 1998 / Published online: 7 December 1998     

The generalized hybrid orbital method for combined quantum mechanical/molecular mechanical calculations: formulation and tests of the analytical derivatives

 Hybrid quantum mechanical (QM) and molecular mechanical (MM) potentials are becoming increasingly important for studying condensed-phase systems but one of the outstanding problems in the field has been how to treat covalent bonds between atoms of the QM and MM regions. Recently, we presented a generalized hybrid orbital (GHO) method that was designed to tackle this problem for hybrid potentials using semiempirical QM methods [Gao et al. (1998) J Phys Chem A 102: 4714–4721]. We tested the method on some small molecules and showed that it performed well when compared to the purely QM or MM potentials. In this article, we describe the formalism for the determination of the GHO energy derivatives and then present the results of more tests aimed at validating the model. These tests, involving the calculation of the proton affinities of some model compounds and a molecular dynamics simulation of a protein, indicate that the GHO method will prove useful for the application of hybrid potentials to solution-phase macromolecular systems. Received: 4 October 1999 / Accepted: 18 December 1999 / Published online: 5 June 2000     

Isomer combinatorics for acyclic conjugated polyenes: enumeration and beyond

A combinatorial approach to fully conjugated acyclic polyenes (C _N H _{N +2}) is considered with a view to the extension of standard enumeration techniques to treat a widened range of chemically interesting features. As a first step, enumerations are made respecting: placement of single and double bonds, the occurrence of cis/trans isomers, and the degree (and type) of “radicality” of such conjugated networks. As a further extension, several structural (graph-theoretic) invariants averaged over various types of isomer classes and sub-classes are made, and then these invariants are utilized to estimate several physicochemical properties averaged over these same classes or sub-classes. The properties currently so considered are heats of formation, indices of refraction, and magnetic susceptibilities. Finally, the asymptotic behaviors of isomer counts and isomer properties in the many-atom limit is elaborated. Received: 10 August 1998 / Accepted: 17 November 1998 / Published online: 16 March 1999     

Solution conformations of structured peptides: continuum electrostatics versus distance-dependent dielectric functions

To compare different implicit solvent potentials, the folding thermodynamics of the helical peptide RN24 and the β-hairpin peptide BH8 are studied by molecular dynamics simulation with adaptive umbrella sampling. As the potential energy functions, the analytical continuum solvent (ACS) potential and three simplified variants, termed EPSR₁, EPSR₄, and EPSR₁₀, are used. The ACS potential is a combination of the standard CHARMM force field for the internal energy (bonds, angles, dihedrals) and the van der Waals energy with the analytical continuum electrostatic (ACE) potential and a non-polar solvation potential. The EPSR potentials differ from the ACS potential by the use of Coulomb's law with a distance-dependent dielectric function to calculate the electrostatic energy. With the ACS potential, quantitative agreement with experiment is obtained for the helix propensity (RN24: 62% calculated vs 50–60% experiment) and the β-hairpin propensity (BH8: 33% calculated vs 19–37% experiment) of the peptides. During the simulations with the EPSR potentials, no significant formation of secondary structure is observed. It is shown that the preference for coil conformations over conformations with secondary structure by the EPSR potentials is due to an overestimation of the energy of salt bridge formation, independent of the magnitude of the Coulomb energy relative to the other energy terms. Possible improvements of the distance-dependent dielectric functions which may permit their application to the simulation of peptide folding, are discussed. Received: 11 July 1998 / Accepted: 22 September 1998 / Published online: 17 December 1998     

Derivation of class II force fields: V. Quantum force field for amides,peptides, and related compounds

As the field of biomolecular structure advances, there is an ever-growing need for accurate modeling of molecular energy surfaces to simulate and predict the properties of these important systems. To address this need, a second generation amide force field for use in simulations of small organics as well as proteins and peptides has been derived. The critical question of what accuracy can be expected from calculations in general, and with this class II force field in particular, is addressed for structural, dynamic, and energetic properties. The force field is derived from a recent methodology we have developed that involves the systematic use of quantum mechanical observables. Systematic ab initio calculations were carried out for numerous configurations of 17 amide and related compounds. Relative energies and first and second derivatives of the energy of 638 structures of these compounds resulted in 140,970 ab initio quantum mechanical observables. The class II peptide quantum mechanical force field (QMFF), containing 732 force constants and reference values, was parameterized against these observables. A major objective of this work is to help establish the role of anharmonicity and coupling in improving the accuracy of molecular force fields, as these terms have not yet become an agreed upon standard in the ever more extensive simulations being used to probe biomolecular properties. This has been addressed by deriving a class I harmonic diagonal force field (HDFF), which was fit to the same energy surface as the QMFF, thus providing an opportunity to quantify the effects of these coupling and anharmonic contributions. Both force field representations are assessed in terms of their ability to fit the observables. They have also been tested by calculating the properties of 11 stationary states of these amide molecules. Optimized structures, vibrational frequencies, and conformational energies obtained from the quantum calculations and from both the QMFF and the HDFF are compared. Several strained and derivatized compounds including urea, formylformamide, and butyrolactam are included in these tests to assess the range of applicability (transferability) of the force fields. It was found that the class II coupled anharmonic force field reproduced the structures, energies, and vibrational frequencies significantly more faithfully than the class I harmonic diagonal force field. An important measure, rms energy deviation, was found to be 1.06 kcal/mol with the class II force field, and 2.30 kcal/mol with the harmonic diagonal force field. These deviations represent the error in relative configurational energy differences for strained and distorted structures calculated with the force fields compared with quantum mechanics. This provides a measure of the accuracy that might be expected in applications where strain may be important such as calculating the energy of a system as it approaches a (rotational) barrier, in ligand binding to a protein, or effects of introducing substituents into a molecule that may induce strain. Similar results were found for structural properties. Protein dynamics is becoming of ever-increasing interest, and, to simulate dynamic properties accurately, the dynamic behavior of model compounds needs to be well accounted for. To this end, the ability of the class I and class II force fields to reproduce the vibrational frequencies obtained from the quantum energy surface was assessed. An rms deviation of 43 cm⁻¹ was achieved with the coupled anharmonic force field, as compared to 105 cm⁻¹ with the harmonic diagonal force field. Thus, the analysis presented here of the class II force field for the amide functional group demonstrates that the incorporation of anharmonicity and coupling terms in the force field significantly improves the accuracy and transferability with regard to the simulation of structural, energetic, and dynamic properties of amides. © 1998 John Wiley & Sons, Inc. J Comput Chem 19: 430–458, 1998     

A theoretical study of substituent effects on the structure of isolated and condensed three-membered rings. A comparison between radicals and parent hydrocarbons

Substituent effects on the structure of radicals and parent hydrocarbons formed by isolated or condensed three-membered rings have been investigated by Hartree-Fock, post-Hartree-Fock and density functional methods. The trends of structural parameters computed for the hydrocarbon systems are in agreement with available experimental data. Substituent effects can be rationalized in terms of interactions between localized orbitals obtained by natural bond analysis. The effects are even larger in free radicals and can be analyzed using the same model. Received: 13 March 1998 / Accepted: 13 July 1998 / Published online: 9 October 1998     

Molecular dynamics simulation in aqueous solution of N-methylazetidinone as a model of β-lactam antibiotics

In this article, we analyze the results of a molecular dynamics simulation in aqueous solution of the N-methylazetidinone molecule, often used to model β-lactam antibiotics. The radial distribution functions (RDFs) corresponding to the most interesting atoms, in terms of reactivity, are presented. We focus our study on the effect of a polar environment on the molecule. The solvent structure around the system is compared to the structure of β-lactam-water complexes, as obtained in a previous study of reaction mechanisms for the neutral and alkaline hydrolyses of N-methylazetidinone. Two types of complexes have been considered which are related to different hydrolysis mechanisms having similar energy barriers at the rate-limiting step of the reaction path. In the first type, the β-lactam-water interaction takes place through the oxygen carbonyl atom and there is agreement between the maxima of the RDFs obtained here and the ab initio structure of the complexes previously reported. In the second type, the interaction takes place through the nitrogen atom and we do not predict a coordination layer around the β-lactam nitrogen atom. The results suggest that in aqueous solution hydrolysis of the carbonyl group is the most probable starting point for the overall hydrolysis reaction. Some discussion on the use of cluster models to represent the solvent effect is included. Received: 29 July 1998 / Accepted: 13 October 1998 / Published online: 1 February 1999     

SAC-CI general-R study of the ionization spectrum of HCl

The valence ionization spectrum of HCl is studied by symmetry-adapted-cluster configuration-interaction general-R and SD-R methods. The general-R method describes well the peak positions and intensities of seven satellite lines observed below the double ionization threshold. The twinning shake-up states due to the (4σ)⁻¹ state and the Rydberg states of HCl⁺ are correctly reproduced. Received: 26 June 1998 / Accepted: 9 September 1998 / Published online: 8 February 1999     

The saddle point of the nucleophilic substitution reaction Cl− + CH3Cl: results of large-scale coupled cluster calculations

On the basis of large-scale coupled cluster calculations including connectedz triple substitutions in a perturbative way, the geometrical parameters of the D _{3 h} saddle point of the Walden inversion reaction Cl⁻ + CH₃Cl′→ ClCH₃ + Cl′⁻ are predicted to be R _s (C—Cl) = 2.301 ? and r _s (C—H) = 1.069 ?. The barrier height with respect to the reactants is recommended to be 11.5 ± 1.0 kJ mol⁻¹. Connected triple substitutions lower the barrier height by almost a factor of 2, but have very little influence on the geometric structure of the saddle point. Received: 26 June 1998 / Accepted: 15 July 1998 / Published online: 28 September 1998     

Static electric properties of LiH: explicitly correlated coupled cluster calculations

Explicitly correlated MBPT-R12 and coupled cluster [up to CCSD(T)-R12] methods have been used in calculations of various (vibrationless) electrical properties for the LiH molecule, including the dipole and quadrupole moments, dipole and quadrupole polarizability tensors, dipole hyperpolarizability tensors, and the second dipole hyperpolarizability tensors. Generally, with extension of the basis set the R12 method did not lead to faster convergence for the calculated properties towards the basis limit. Nevertheless, R12 calculations serve as useful indicators to judge the reliability of the results, and substantially help in determining the accuracy. Results obtained with the 11s8p6d5f/9s8p6d5f basis and CCSD(T)-R12 calculated within this work should be close to the basis set limit. Received: 8 June 1998 / Accepted: 23 July 1998 / Published online: 7 October 1998     

Implementation of the IMOMM methodology for performing combined QM/MM molecular dynamics simulations and frequency calculations

A technique for implementing the integrated molecular orbital and molecular mechanics (IMOMM) methodology developed by Maseras and Morokuma that is used to perform combined quantum mechanics/molecular mechanics (QM/MM) molecular dynamics simulations, frequency calculations and simulations of macromolecules including explicit solvent is presented. Although the IMOMM methodology is generalized to any coordinate system, the implementation first described by Maseras and Morokuma requires that the QM and MM gradients be transformed into internal coordinates before they are added together. This coordinate transformation can be cumbersome for macromolecular systems and can become ill-defined during the course of a molecular dynamics simulation. We describe an implementation of the IMOMM method in which the QM and MM gradients are combined in the cartesian coordinate system, thereby avoiding potential problems associated with using the internal coordinate system. The implementation can be used to perform combined QM/MM molecular dynamics simulations and frequency calculations within the IMOMM framework. Finally, we have examined the applicability of thermochemical data derived from IMOMM framework. Finally, we have examined the applicability of thermochemical data derived from IMOMM frequency calculations. Received: 11 May 1998 / Accepted: 14 August 1998 / Published online: 16 November 1998     

Argon-matrix-isolation Raman spectra and density functional study of 1,3-butadiene conformers

s-trans, s-cis and gauche conformers of 1,3-butadiene have been studied using density functional theory and the coupled-cluster method using double substitutions (CCD). Matrix isolation Raman and IR data for the minor conformer were obtained and are used in combination with the theoretical results to resolve earlier ambiguities in vibrational assignments. Based on high-quality Hessians, new harmonic stretching force constants are reported for the carbon backbone of s-trans-1,3-butadiene. For the minor conformer the best unscaled root mean square error of the calculated frequencies for the s-cis and gauche geometries are 17.5 cm⁻¹ and 7.4 cm⁻¹, respectively, primarily due to a better agreement of the gauche results for the vibrations at 983 cm⁻¹, 596 cm⁻¹ and 470 cm⁻¹ which depend strongly on the torsional angle. Although this points towards the gauche form rather than the s-cis form, the calculated transition dipole moment directions at the CCD/6-311G(d,p) level confirm the earlier conclusion that the minor conformer has C _{2 v} symmetry in the matrix. It is concluded that either the better agreement between the frequencies calculated for the gauche form and the observed values is coincidental, or that the molecule is indeed nonplanar in the matrix and tunnels very rapidly between the two mirror-image forms (or its lowest vibrational level lies above the barrier). Received: 1 July 1998 / Accepted: 26 October 1998 / Published online: 15 February 1999     

Prediction of 13C NMR chemical shifts in substituted naphthalenes

The prediction of the ¹³C NMR signals for derivatives of naphthalene has been investigated using mathematical modeling techniques. Two empirical multiple regression models which utilize the field, resonance, and Charton's steric parameters together with molar refractivity were developed, one for α- and the other for β-substituted naphthalene derivatives. In the α case the model had a correlation coefficient of observed versus predicted line positions of r = 0.973 with a standard deviation of 2.2 ppm while in the β case r = 0.979 with the standard deviation being 2.3 ppm. The database consisted of 3152 signals from 394 naphthalene derivatives. We also report the use of the Taft steric parameter in place of the Charton steric parameter in the above- mentioned prediction equations. Received: 19 June 1998 / Accepted: 20 October 1998 / Published online: 16 March 1999