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Development of a polarizable force field for proteins via ab initio quantum chemistry: first generation model and gas phase tests.

We present results of developing a methodology suitable for producing molecular mechanics force fields with explicit treatment of electrostatic polarization for proteins and other molecular system of biological interest. The technique allows simulation of realistic-size systems. Employing high-level ab initio data as a target for fitting allows us to avoid the problem of the lack of detailed experimental data. Using the fast and reliable quantum mechanical methods supplies robust fitting data for the resulting parameter sets. As a result, gas-phase many-body effects for dipeptides are captured within the average RMSD of 0.22 kcal/mol from their ab initio values, and conformational energies for the di- and tetrapeptides are reproduced within the average RMSD of 0.43 kcal/mol from their quantum mechanical counterparts. The latter is achieved in part because of application of a novel torsional fitting technique recently developed in our group, which has already been used to greatly improve accuracy of the peptide conformational equilibrium prediction with the OPLS-AA force field.1 Finally, we have employed the newly developed first-generation model in computing gas-phase conformations of real proteins, as well as in molecular dynamics studies of the systems. The results show that, although the overall accuracy is no better than what can be achieved with a fixed-charges model, the methodology produces robust results, permits reasonably low computational cost, and avoids other computational problems typical for polarizable force fields. It can be considered as a solid basis for building a more accurate and complete second-generation model.

Algorithms↗

Complex autocorrelation function and energy spectrum by classical trajectory calculations.

A quasiclassical method which enables evaluation of complex autocorrelation function from classical trajectory calculations is proposed. The method is applied for two highly excited nonlinearly coupled harmonic oscillators in regimes prevailed either by regular or chaotic classical motions. A good agreement of classical and quantum autocorrelation functions is found within short (Ehrnfest) time limit. Fourier transforms of the autocorrelation functions provide moderate resolved energy spectra, where classical and quantum results nearly coincide. The actual energy levels are obtained from approximate short-time autocorrelation functions with the help of filter diagonalization. This study is a follow up to our previous work [P. Zdanska and N. Moiseyev, J. Chem. Phys. 115, 10608 (2001)], where the complex autocorrelation has been obtained up to overall phase factors of recurrences.

Algorithms↗

Interacting classical dimers on the square lattice.

We study a model of close-packed dimers on the square lattice with a nearest neighbor interaction between parallel dimers. This model corresponds to the classical limit of quantum dimer models [D. S. Rokhsar and S. A. Kivelson, Phys. Rev. Lett. 61, 2376 (1988)]. By means of Monte Carlo and transfer matrix calculations, we show that this system undergoes a Kosterlitz-Thouless transition separating a low temperature ordered phase where dimers are aligned in columns from a high temperature critical phase with continuously varying exponents. This is understood by constructing the corresponding Coulomb gas, whose coupling constant is computed numerically. We also discuss doped models and implications on the finite-temperature phase diagram of quantum dimer models.

Journal Article↗

Cooperative hydrogen bonding effects are key determinants of backbone amide proton chemical shifts in proteins.

A computational methodology for backbone amide proton chemical shift (delta(H)) predictions based on ab initio quantum mechanical treatment of part of the protein is presented. The method is used to predict and interpret 13 delta(H) values in protein G and ubiquitin. The predicted amide-amide delta(H) values are within 0.6 ppm of experiment, with a root-mean-square deviation (RMSD) of 0.3 ppm. We show that while the hydrogen bond geometry is the most important delta(H)-determinant, longer-range cooperative effects of extended hydrogen networks make significant contributions to delta(H). We present a simple model that accurately relates the protein structure to delta(H).

Amino Acid Sequence↗

A computational analysis of ordering in ABCHN at the nematic-isotropic transition.

A computational analysis of ordering in the nematogenic compound 4-alkenyl bicyclohexylnitrile has been carried out based on quantum mechanics and intermolecular forces. The evaluation of atomic charge and dipole moment at each atomic center has been carried out using the complete neglect differential overlap (CNDO/2) method. Modified Rayleigh-Schrodinger perturbation theory along with a multicentered- multipole expansion method has been employed to evaluate long-range intermolecular interactions, while a '6-exp' potential function has been assumed for short-range interactions. The total interaction energy values obtained through these computations were used to calculate the probability of each configuration at room temperature (300 K), the nematic-isotropic transition temperature (364.7 K) and above transition temperature (450 K) using the Maxwell-Boltzmann formula. The various possible configurations during the different modes (i.e., stacking, in-plane and terminal) of interactions have been studied in terms of variation of probability due to small departures from the most probable configurations. An attempt has been made to analyze the characteristic features of liquid crystallinity in terms of their relative order with molecular parameters introduced in this paper.

Bridged Bicyclo Compounds↗

Implementation of the bisection sampling method in path integral simulations.

A bisection sampling method is implemented in the framework of a quantized classical path algorithm to include nuclear quantum effects in path integral simulations. The present study examines the convergence of these calculations on two model systems with respect to the number of beads used in the polymer chain and the number of configurations both in free-particle sampling and in classical configuration sampling. The results will be useful for future studies of kinetic isotope effects in enzymatic reactions.

Algorithms↗

Non-Markovian theory of open systems in classical limit.

A fully classical limit of the recently published quantum-classical approximation [A. A. Neufeld, J. Chem. Phys. 119, 2488 (2003)] is obtained and analyzed. The resulting kinetic equations are capable of describing the evolution of an open system on the entire time axis, including the short-time non-Markovian stage, and are valid beyond linear response regime. We have shown, that proceeding to the classical mechanics limit we restrict the class of allowed correlations between an open system and a canonical bath, so that the initial conditions and the relaxation operator has to be appropriately modified (projected). Disregard of the projection may lead to unphysical behavior, since mechanism of the decay of some correlations is essentially of quantum-mechanical nature, and is not correctly described by classical mechanics. The projection (quantum correction to the kinetics) is particularly important for the non-Markovian regime of relaxation towards canonical equilibrium. The conformity of the developed method to the conventional approaches is demonstrated using a model of Brownian motion (heavy particle in the bath of light ones), for which the obtained non-Markovian equations are reduced to the standard Fokker-Planck equation in phase space.

Computer Simulation↗

Fe/C interactions during SWNT growth with C2 feedstock molecules: A quantum chemical molecular dynamics study.

We are presenting the first quantum chemical molecular dynamics (QM/MD) model simulations for iron catalyzed single-walled carbon nanotube (SWNT) growth based on the density functional tight binding (DFTB) quantum chemical potential. As model systems, open-ended (10,10) armchair tube fragments were selected with 0, 10, and 20 Fe atoms attached in 1,4-positions on the open rims, and ensembles of randomly oriented C2 molecules were included to simulate carbon plasma feedstock molecules. Isokinetic trajectories at 1500 K to 3000 K show that divalent Fe increases the number of coordination partners with carbon and/or Fe, depending on the Fe concentration. Fe/C interactions weaken the tube sidewall due to electron transfer from Fe into antibonding carbon orbitals, and C2 addition occurs mainly in an Fe-C2-Fe bridge addition mechanism, while growth of polyyne chains characteristic for high-temperature carbon systems is suppressed in the presence of Fe on the rims of the growing SWNT. Our findings are the first quantum chemical evidence for the importance of intermetallic interactions during SWNT growth.

Carbon↗

The application of stereolithography to the fabrication of accurate molecular models.

The process of stereolithography, which automatically fabricates plastic models from designs created in certain computer-aided design programs, has been applied to the production of accurate plastic molecular models. Atomic coordinates obtained from quantum mechanical calculations and from neutron diffraction data were used to locate spheres in the I-DEAS CAD program with radii proportional to the appropriate van der Waals radii. The sterolithography apparatus was used to build the models using a photosensitive liquid resin, resulting in hard plastic models that accurately represent the computed or experimental input structures. Three examples are given to illustrate how the models can be used to interpret experimental structure-activity data for systems of biological importance or host-guest chemistry: (1) Interpretation of kinetic data for the formation of a stable blocking complex between amiloride analogs and the epithelial sodium channel, (2) interpretation of binding and neural activity data for the interaction of certain amino acids and their analogs at the L-alanine taste receptor of the channel catfish, and (3) interpretation of shape selectivity and rate acceleration in cyclodextrin catalysis using models of the neutron diffraction structure of beta-cyclodextrin and of the transition state for the cleavage of phenyl acetate by the secondary hydroxyl oxygen of beta-cyclodextrin.

Acrylates↗

Oxidation of methionine residues in aqueous solutions: free methionine and methionine in granulocyte colony-stimulating factor.

The free energy barriers and a mechanism of the oxidation of the amino acid methionine in water and in granulocyte colony-stimulating factor (G-CSF) are analyzed via combined quantum mechanical and molecular mechanical (QM/MM) methods, constrained molecular dynamics, and committor probability calculations. The computed free energy barrier of free methionine amino acid is very close to the measured value (14.7 +/- 1.2 versus 15.5 +/- 0.02 kcal/mol). The reaction coordinate was found to be the difference between the O-O bond of H2O2 and the S-O bond, where the S is the sulfur atom of the methionine residue. It was confirmed by computing the committor probability distribution and the distribution of constrained forces that this coordinate is not coupled to the activation of other degrees of freedom. The computed free energies of the oxidation of methionine residues in G-CSF indicate that the protein environment has insignificant effects on the reaction barriers of oxidation. This result further validates our proposal that the access of solvent to methionine sites, as measured by the two-shell water coordination number, governs the kinetics of the oxidation reaction of methionine groups in a protein molecule. We also found that the number of hydrogen bonds between the distal oxygen of H2O2 and the water molecules near the methionine increases along the reaction coordinate as oxidation progresses, indicating that the charge separation developed during the oxidation by H2O2 is stabilized by specific interactions with water molecules, such as hydrogen bonding.

Granulocyte Colony-Stimulating Factor↗

High-performance selective excitation pulses for solid- and liquid-state NMR spectroscopy.

Computer-optimized selective pulses are routinely used in solution-state NMR spectroscopy. At the same time, their utility and importance for solid-state applications has yet to be fully realized. We suggest a new computational approach that makes the design of soft selective pulses with desired properties relatively straightforward. By applying this technique to the generic selective excitation problem, we have arrived at a family of high performance selective excitation pulses, dubbed E-Family, that allows more flexibility and better performance than analogous pulses previously reported in the literature. The new pulses have been successfully tested in both solid- and solution-state NMR experiments. A theoretical treatment of the effects of chemical shift anisotropy (CSA) on the selective excitation in magic-angle spinning (MAS) experiments in solids is presented. The set of heuristics that comprise our new strategy were incorporated into a general NMR simulation program SPINEVOLUTION.

Anisotropy↗

Excited-state properties and environmental effects for protonated schiff bases: a theoretical study.

Complete active space self-consistent field (CASSCF), multireference configuration interaction (MRCI), density functional theory (DFT), time dependent DFT (TDDFT) and the singles and doubles coupled-cluster (CC2) methodologies have been used to study the ground state and excited states of protonated and neutral Schiff bases (PSB and SB) as models for the retinal chromophore. Systems with two to four conjugated double bonds are investigated. Geometry relaxation effects are studied in the excited pipi* state using the aforementioned methods. Taking the MRCI results as reference we find that CASSCF results are quite reliable even though overshooting of geometry changes is observed. TDDFT does not reproduce bond alternation well in the pipi* state. CC2 takes an intermediate position. Environmental effects due to solvent or protein surroundings have been studied in the excited states of the PSBs and SBs using a water molecule and solvated formate as model cases. Particular emphasis is given to the proton transfer process from the PSB to its solvent partner in the excited state. It is found that its feasibility is significantly enhanced in the excited state as compared to the ground state, which means that a proton transfer could be initiated already at an early step in the photodynamics of PSBs.

Computer Simulation↗

Low- and high-spin iron (II) complexes studied by effective crystal field method combined with molecular mechanics.

A computational method targeted to Werner-type complexes is developed on the basis of quantum mechanical effective Hamiltonian crystal field (EHCF) methodology (previously proposed for describing electronic structure of transition metal complexes) combined with the Gillespie-Kepert version of molecular mechanics (MM). It is a special version of the hybrid quantum/MM approach. The MM part is responsible for representing the whole molecule, including ligand atoms and metal ion coordination sphere, but leaving out the effects of the d-shell. The quantum mechanical EHCF part is limited to the metal ion d-shell. The method reproduces with reasonable accuracy geometry and spin states of the Fe(II) complexes with monodentate and polydentate aromatic ligands with nitrogen donor atoms. In this setting a single set of MM parameters set is shown to be sufficient for handling all spin states of the complexes under consideration.

Journal Article↗

Dynamics of flexible cycloalkanes. Ab initio and DFT study of the conformational energy hypersurface of cyclononane.

The multidimensional Potential Energy Hypersurface (PEHS) for the cyclononane molecule was comprehensively investigated at the Hartree-Fock (HF), and Density Functional Theory (DFT) levels of theory. Second-order Møller-Plesset perturbation theory (MP2) optimizations were also carried out to confirm the low-energy conformations. The previously reported Geometrical Algorithm to Search Conformational Space (GASCOS) has been used to generate the starting geometries for the conformational analysis. The GASCOS algorithm combined with ab initio and DFT optimization permits searching of the potential energy hypersurface for all minimum-energy conformations as well as transition structures connecting the low-energy forms. The search located all previously reported structures together with 11 transition states, some of which were not found by earlier searching techniques. Altogether, 16 geometries (five low-energy conformations and 11 transition states) were found to be important for a description of the conformational features of cyclononane. RB3LYP/aug-cc-pVTZ//RB3LYP/6-31G(d) calculations suggest a conformational mixture between the twist boat-chair and twist chair-boat conformations as the preferred forms. In addition only the twist chair-chair conformation with 1.52 kcal/mol above the global minimum should contribute somewhat to the equilibrium mixture of conformations. Our results allow us to form a concise idea about the internal intricacies of the 9D vector space describing the conformation of cyclononane as well as the associated conformational potential energy hypersurface of nine independent variables.

Computer Simulation↗

Prediction of spectroscopic constants for diatomic molecules in the ground and excited states using time-dependent density functional theory.

Spectroscopic constants of the ground and next seven low-lying excited states of diatomic molecules CO, N2, P2, and ScF were computed using the density functional theory SAOP/ATZP model, in conjunction with time-dependent density functional theory (TD-DFT) and a recently developed Slater type basis set, ATZP. Spectroscopic constants, including the equilibrium distances r(e), harmonic vibrational frequency omega(e), vibrational anharmonicity omega(e)x(e), rotational constant B(e), centrifugal distortion constant D(e), the vibration-rotation interaction constant alpha(e), and the vibrational zero-point energy E(n)0 were generated in an effort to establish a reliable database for electron spectroscopy. By comparison with experimental values and a similar model with an established larger Slater-type basis set, et-QZ3P-xD, it was found that this model provides reliably accurate results at reduced computational costs, for both the ground and excited states of the molecules. The over all errors of all eight lowest lying electronic states of the molecules under study using the effective basis set are r(e)(+/-4%), omega(e)(+/-5% mostly without exceeding +/-20%), omega(e)x(e)(+/-5% mostly without exceeding 20%, much more accurate than a previous study on this constant of +/-30%), B(e)(+/-8%), D(e)(+/-10%), alpha(e)(+/-10%), and E(n)0(+/-10%). The accuracy obtained using the ATZP basis set is very competitive to the larger et-QZ3P-xD basis set in particular in the ground electronic states. The overall errors in r(e), omega(e)x(e), and alpha(e) in the ground states were given by +/-0.7, +/-10.1, and +/-8.4%, respectively, using the efficient ATZP basis set, which is competitive to the errors of +/-0.5, +/-9.2, and +/-9.1%, respectively for those constants using the larger et-QZ3P-xD basis set. The latter basis set, however, needs approximately four times of the CPU time on the National Supercomputing Facilities (Australia). Due to the efficiency of the model (TD-DFT, SAOP and ATZP), it will be readily applied to study larger molecular systems.

Carbon Monoxide↗

On the suitability of strictly localized orbitals for hybrid QM/MM calculations.

In the QM/MM method we have developed (LSCF/MM), the QM and the MM parts are held together by means of strictly localized bonding orbitals (SLBOs). Generally these SLBOs are derived from localized bond orbitals (LBOs) that undergo tails deletion, resulting in a nonpredictable change of their properties. An alternative set of SLBOs is provided by the extremely localized molecular orbitals (ELMOs) approach, where the orbitals are rigorously localized on some prefixed atoms without tails on the other atoms of the molecule. A comparative study of SLBOs arising from various localization schemes and ELMOs is presented to test the reliability and the transferability of these functions within the Local Self-Consistent Field (LSCF) framework. Two types of chemical bonds were considered: C--C and C--O single bonds. The localized functions are obtained on the ethane and the methanol molecules, and are tested on beta-alanine and diethyl ether molecules. Moreover, the various protonation forms of beta-alanine have been investigated to illustrate how well the polarity variation of the chemical bond can be handled throughout a chemical process. At last, rotation energy profiles around C--C and C--O bonds are reproduced for butane and fluoromethanol. Energetic, geometric, as well as electronic factors all indicate that ELMO functions are much more transferable from one molecule to another, leading to results closer to the usual SCF reference than any other calculations involving any other localized orbitals. When the shape of the orbital is the most important factor then ELMO functions will perform as well as any other localized orbital.

Butanes↗