Showing papers in "Journal of Computational Chemistry in 2003"

Energies, structures, and electronic properties of molecules in solution with the C-PCM solvation model.

Abstract: The conductor-like solvation model, as developed in the framework of the polarizable continuum model (PCM), has been reformulated and newly implemented in order to compute energies, geometric structures, harmonic frequencies, and electronic properties in solution for any chemical system that can be studied in vacuo Particular attention is devoted to large systems requiring suitable iterative algorithms to compute the solvation charges: the fast multipole method (FMM) has been extensively used to ensure a linear scaling of the computational times with the size of the solute A number of test applications are presented to evaluate the performances of the method

A point-charge force field for molecular mechanics simulations of proteins based on condensed-phase quantum mechanical calculations.

Abstract: Molecular mechanics models have been applied extensively to study the dynamics of proteins and nucleic acids. Here we report the development of a third-generation point-charge all-atom force field for proteins. Following the earlier approach of Cornell et al., the charge set was obtained by fitting to the electrostatic potentials of dipeptides calculated using B3LYP/cc-pVTZ//HF/6-31G** quantum mechanical methods. The main-chain torsion parameters were obtained by fitting to the energy profiles of Ace-Ala-Nme and Ace-Gly-Nme di-peptides calculated using MP2/cc-pVTZ//HF/6-31G** quantum mechanical methods. All other parameters were taken from the existing AMBER data base. The major departure from previous force fields is that all quantum mechanical calculations were done in the condensed phase with continuum solvent models and an effective dielectric constant of e = 4. We anticipate that this force field parameter set will address certain critical short comings of previous force fields in condensed-phase simulations of proteins. Initial tests on peptides demonstrated a high-degree of similarity between the calculated and the statistically measured Ramanchandran maps for both Ace-Gly-Nme and Ace-Ala-Nme di-peptides. Some highlights of our results include (1) well-preserved balance between the extended and helical region distributions, and (2) favorable type-II poly-proline helical region in agreement with recent experiments. Backward compatibility between the new and Cornell et al. charge sets, as judged by overall agreement between dipole moments, allows a smooth transition to the new force field in the area of ligand-binding calculations. Test simulations on a large set of proteins are also discussed. © 2003 Wiley Periodicals, Inc. J Comput Chem 24: 1999–2012, 2003

Optimized Slater-type basis sets for the elements 1-118.

Abstract: Seven different types of Slater type basis sets for the elements H (Z = 1) up to E118 (Z = 118), ranging from a double zeta valence quality up to a quadruple zeta valence quality, are tested in their performance in neutral atomic and diatomic oxide calculations. The exponents of the Slater type functions are optimized for the use in (scalar relativistic) zeroth-order regular approximated (ZORA) equations. Atomic tests reveal that, on average, the absolute basis set error of 0.03 kcal/mol in the density functional calculation of the valence spinor energies of the neutral atoms with the largest all electron basis set of quadruple zeta quality is lower than the average absolute difference of 0.16 kcal/mol in these valence spinor energies if one compares the results of ZORA equation with those of the fully relativistic Dirac equation. This average absolute basis set error increases to about 1 kcal/mol for the all electron basis sets of triple zeta valence quality, and to approximately 4 kcal/mol for the all electron basis sets of double zeta quality. The molecular tests reveal that, on average, the calculated atomization energies of 118 neutral diatomic oxides MO, where the nuclear charge Z of M ranges from Z = 1-118, with the all electron basis sets of triple zeta quality with two polarization functions added are within 1-2 kcal/mol of the benchmark results with the much larger all electron basis sets, which are of quadruple zeta valence quality with four polarization functions added. The accuracy is reduced to about 4-5 kcal/mol if only one polarization function is used in the triple zeta basis sets, and further reduced to approximately 20 kcal/mol if the all electron basis sets of double zeta quality are used. The inclusion of g-type STOs to the large benchmark basis sets had an effect of less than 1 kcal/mol in the calculation of the atomization energies of the group 2 and group 14 diatomic oxides. The basis sets that are optimized for calculations using the frozen core approximation (frozen core basis sets) have a restricted basis set in the core region compared to the all electron basis sets. On average, the use of these frozen core basis sets give atomic basis set errors that are approximately twice as large as the corresponding all electron basis set errors and molecular atomization energies that are close to the corresponding all electron results. Only if spin-orbit coupling is included in the frozen core calculations larger errors are found, especially for the heavier elements, due to the additional approximation that is made that the basis functions are orthogonalized on scalar relativistic core orbitals.

Detailed analysis of grid-based molecular docking: A case study of CDOCKER-A CHARMm-based MD docking algorithm.

Abstract: The influence of various factors on the accuracy of protein-ligand docking is examined. The factors investigated include the role of a grid representation of protein-ligand interactions, the initial ligand conformation and orientation, the sampling rate of the energy hyper-surface, and the final minimization. A representative docking method is used to study these factors, namely, CDOCKER, a molecular dynamics (MD) simulated-annealing-based algorithm. A major emphasis in these studies is to compare the relative performance and accuracy of various grid-based approximations to explicit all-atom force field calculations. In these docking studies, the protein is kept rigid while the ligands are treated as fully flexible and a final minimization step is used to refine the docked poses. A docking success rate of 74% is observed when an explicit all-atom representation of the protein (full force field) is used, while a lower accuracy of 66-76% is observed for grid-based methods. All docking experiments considered a 41-member protein-ligand validation set. A significant improvement in accuracy (76 vs. 66%) for the grid-based docking is achieved if the explicit all-atom force field is used in a final minimization step to refine the docking poses. Statistical analysis shows that even lower-accuracy grid-based energy representations can be effectively used when followed with full force field minimization. The results of these grid-based protocols are statistically indistinguishable from the detailed atomic dockings and provide up to a sixfold reduction in computation time. For the test case examined here, improving the docking accuracy did not necessarily enhance the ability to estimate binding affinities using the docked structures.

Deriving effective mesoscale potentials from atomistic simulations.

Abstract: We demonstrate how an iterative method for potential inversion from distribution functions developed for simple liquid systems can be generalized to polymer systems. It uses the differences in the potentials of mean force between the distribution functions generated from a guessed potential and the true distribution functions to improve the effective potential successively. The optimization algorithm is very powerful: convergence is reached for every trial function in few iterations. As an extensive test case we coarse-grained an atomistic all-atom model of polyisoprene (PI) using a 13:1 reduction of the degrees of freedom. This procedure was performed for PI solutions as well as for a PI melt. Comparisons of the obtained force fields are drawn. They prove that it is not possible to use a single force field for different concentration regimes. © 2003 Wiley Periodicals, Inc. J Comput Chem 13: 1624–1636, 2003

An improvement of the resolution of the identity approximation for the formation of the Coulomb matrix

Abstract: A straightforward modification of the resolution of the identity (RI) approximation to the Coulomb interaction is described. In the limit of basis sets that are dominated by high angular momentum functions the observed speedups in realistic test systems reach a factor of 2 compared to the standard RI algorithm, and a factor of up to 300 compared to the standard algorithm to form the Coulomb matrix. More moderate savings on the order of 0-20% are obtained for the more commonly used smaller basis sets. A series of test calculations is reported to illustrate the efficiency of the algorithm.

Generalized born model with a simple smoothing function

Abstract: Based on recent developments in generalized Born (GB) theory that employ rapid volume integration schemes (M. S. Lee, F. R. Salabury, Jr., and C. L. Brooks III, J Chem Phys 2002, 116, 10606) we have recast the calculation of the self-electrostatic solvation energy to utilize a simple smoothing function at the dielectric boundary. The present GB model is formulated in this manner to provide consistency with the Poisson-Boltzmann (PB) theory previously developed to yield numerically stable electrostatic solvation forces based on finite-difference methods (W. Im, D. Beglov, and B. Roux, Comp Phys Commun 1998, 111, 59). Our comparisons show that the present GB model is indeed an efficient and accurate approach to reproduce corresponding PB solvation energies and forces. With only two adjustable parameters--a(0) to modulate the Coulomb field term, and a(1) to include a correction term beyond Coulomb field--the PB solvation energies are reproduced within 1% error on average for a variety of proteins. Detailed analysis shows that the PB energy can be reproduced within 2% absolute error with a confidence of about 95%. In addition, the solvent-exposed surface area of a biomolecule, as commonly used in calculations of the nonpolar solvation energy, can be calculated accurately and efficiently using the simple smoothing function and the volume integration method. Our implicit solvent GB calculations are about 4.5 times slower than the corresponding vacuum calculations. Using the simple smoothing function makes the present GB model roughly three times faster than GB models, which attempt to mimic the Lee-Richards molecular volume.

Development of polyphosphate parameters for use with the AMBER force field

Abstract: Accurate force fields are essential for reproducing the conformational and dynamic behavior of condensed-phase systems. The popular AMBER force field has parameters for monophosphates, but they do not extend well to polyphorylated molecules such as ADP and ATP. This work presents parameters for the partial charges, atom types, bond angles, and torsions in simple polyphosphorylated compounds. The parameters are based on molecular orbital calculations of methyldiphosphate and methyltriphosphate at the RHF/6-31+G* level. The new parameters were fit to the entire potential energy surface (not just minima) with an RMSD of 0.62 kcal/mol. This is exceptional agreement and a significant improvement over the current parameters that produce a potential surface with an RMSD of 7.8 kcal/mol to that of the ab initio calculations. Testing has shown that the parameters are transferable and capable of reproducing the gas-phase conformations of inorganic diphosphate and triphosphate. Also, the parameters are an improvement over existing parameters in the condensed phase as shown by minimizations of ATP bound in several proteins. These parameters are intended for use with the existing AMBER 94/99 force field, and they will permit users to apply AMBER to a wider variety of important enzymatic systems.

Geometry optimization with QM/MM, ONIOM, and other combined methods. I. Microiterations and constraints.

Abstract: Hybrid energy methods such as QM/MM and ONIOM, that combine different levels of theory into one calculation, have been very successful in describing large systems. Geometry optimization methods can take advantage of the partitioning of these calculations into a region treated at a quantum mechanical (QM) level of theory and the larger, remaining region treated by an inexpensive method such as molecular mechanics (MM). A series of microiterations can be employed to fully optimize the MM region for each optimization step in the QM region. Cartesian coordinates are used for the MM region and are chosen so that the internal coordinates of the QM region remain constant during the microiterations. The coordinates of the MM region are augmented to permit rigid body translation and rotation of the QM region. This is essential if any atoms in the MM region are constrained, but it also improves the efficiency of unconstrained optimizations. Because of the microiterations, special care is needed for the optimization step in the QM region so that the system remains in the same local valley during the course of the optimization. The optimization methodology with microiterations, constraints, and step-size control are illustrated by calculations on bacteriorhodopsin and other systems.

Packing optimization for automated generation of complex system's initial configurations for molecular dynamics and docking.

Abstract: Molecular Dynamics is a powerful methodology for the comprehension at molecular level of many chemical and biochemical systems. The theories and techniques developed for structural and thermodynamic analyses are well established, and many software packages are available. However, designing starting configurations for dynamics can be cumbersome. Easily generated regular lattices can be used when simple liquids or mixtures are studied. However, for complex mixtures, polymer solutions or solid adsorbed liquids (for example) this approach is inefficient, and it turns out to be very hard to obtain an adequate coordinate file. In this article, the problem of obtaining an adequate initial configuration is treated as a "packing" problem and solved by an optimization procedure. The initial configuration is chosen in such a way that the minimum distance between atoms of different molecules is greater than a fixed tolerance. The optimization uses a well-known algorithm for box-constrained minimization. Applications are given for biomolecule solvation, many-component mixtures, and interfaces. This approach can reduce the work of designing starting configurations from days or weeks to few minutes or hours, in an automated fashion. Packing optimization is also shown to be a powerful methodology for space search in docking of small ligands to proteins. This is demonstrated by docking of the thyroid hormone to its nuclear receptor.

New analytic approximation to the standard molecular volume definition and its application to generalized Born calculations.

Abstract: In a recent article (Lee, M. S.; Salsbury, F. R. Jr.; Brooks, C. L., III. J Chem Phys 2002, 116, 10606), we demonstrated that generalized Born (GB) theory provides a good approximation to Poisson electrostatic solvation energy calculations if one uses the same definitions of molecular volume for each. In this work, we present a new and improved analytic method for reproducing the Lee-Richards molecular volume, which is the most common volume definition for Poisson calculations. Overall, 1% errors are achieved for absolute solvation energies of a large set of proteins and relative solvation energies of protein conformations. We also introduce an accurate SASA approximation that uses the same machinery employed by our GB method and requires a small addition of computational cost. The combined methodology is shown to yield an efficient and accurate implicit solvent representation for simulations of biopolymers.

About the calculation of exchange coupling constants in polynuclear transition metal complexes.

Abstract: The application of theoretical methods based on the density functional theory with hybrid functionals provides good estimates of the exchange coupling constants for polynuclear transition metal complexes. The accuracy is similar to that previously obtained for dinuclear compounds. We present test calculations on simple model systems based on H · · · He and CH2 · · · He units to compare with Hartree–Fock and multiconfigurational results. Calculations for complete, nonmodeled polynuclear transition metal complexes yield coupling constants in very good agreement with available experimental data. © 2003 Wiley Periodicals, Inc. J Comput Chem 24: 982–989, 2003

A Partition Function Algorithm for Nucleic Acid Secondary Structure Including Pseudoknots

Abstract: Nucleic acid secondary structure models usually exclude pseudoknots due to the difficulty of treating these nonnested structures efficiently in structure prediction and partition function algorithms. Here, the standard secondary structure energy model is extended to include the most physically relevant pseudoknots. We describe an O(N^5) dynamic programming algorithm, where N is the length of the strand, for computing the partition function and minimum energy structure over this class of secondary structures. Hence, it is possible to determine the probability of sampling the lowest energy structure, or any other structure of particular interest. This capability motivates the use of the partition function for the design of DNA or RNA molecules for bioengineering applications.

Exploring potential energy surfaces for chemical reactions: An overview of some practical methods

Abstract: Potential energy surfaces form a central concept in the application of electronic structure methods to the study of molecular structures, properties, and reactivities. Recent advances in tools for exploring potential energy surfaces are surveyed. Methods for geometry optimization of equilibrium structures, searching for transition states, following reaction paths and ab initio molecular dynamics are discussed. For geometry optimization, topics include methods for large molecules, QM/MM calculations, and simultaneous optimization of the wave function and the geometry. Path optimization methods and dynamics based techniques for transition state searching and reaction path following are outlined. Developments in the calculation of ab initio classical trajectories in the Born-Oppenheimer and Car-Parrinello approaches are described.

nMoldyn: a program package for a neutron scattering oriented analysis of molecular dynamics simulations.

Abstract: We present a new implementation of the program nMoldyn, which has been developed for the computation and decomposition of neutron scattering intensities from Molecular Dynamics trajectories (Comp. Phys. Commun 1995, 91, 191-214). The new implementation extends the functionality of the original version, provides a much more convenient user interface (both graphical/interactive and batch), and can be used as a tool set for implementing new analysis modules. This was made possible by the use of a high-level language, Python, and of modern object-oriented programming techniques. The quantities that can be calculated by nMoldyn are the mean-square displacement, the velocity autocorrelation function as well as its Fourier transform (the density of states) and its memory function, the angular velocity autocorrelation function and its Fourier transform, the reorientational correlation function, and several functions specific to neutron scattering: the coherent and incoherent intermediate scattering functions with their Fourier transforms, the memory function of the coherent scattering function, and the elastic incoherent structure factor. The possibility to compute memory function is a new and powerful feature that allows to relate simulation results to theoretical studies.

Implementation of a general multireference configuration interaction procedure with analytic gradients in a semiempirical context using the graphical unitary group approach.

Abstract: The graphical unitary group approach has been applied in an efficient implementation of a general multireference configuration interaction (MRCI) method for use with small active molecular orbital spaces in a semiempirical framework. Gradients can be computed analytically for molecular orbitals from a closed-shell or a half-electron open-shell Hartree-Fock calculation. CPU times for single point energy and gradient calculations are reported. The code allows MRCI geometry optimizations of large molecules, as illustrated for the singlet ground state and the four lowest triplet states of fullerene C76. © 2003 Wiley Periodicals, Inc. J Comput Chem 6: 714–726, 2003

Solvent viscosity dependence of the folding rate of a small protein: Distributed computing study

Abstract: By using distributed computing techniques and a supercluster of more than 20,000 processors we simulated folding of a 20-residue Trp Cage miniprotein in atomistic detail with implicit GB/SA solvent at a variety of solvent viscosities (gamma). This allowed us to analyze the dependence of folding rates on viscosity. In particular, we focused on the low-viscosity regime (values below the viscosity of water). In accordance with Kramers' theory, we observe approximately linear dependence of the folding rate on 1/gamma for values from 1-10(-1)x that of water viscosity. However, for the regime between 10(-4)-10(-1)x that of water viscosity we observe power-law dependence of the form k approximately gamma(-1/5). These results suggest that estimating folding rates from molecular simulations run at low viscosity under the assumption of linear dependence of rate on inverse viscosity may lead to erroneous results.

Stochastic proximity embedding

Abstract: We introduce stochastic proximity embedding (SPE), a novel self-organizing algorithm for producing meaningful underlying dimensions from proximity data. SPE attempts to generate low-dimensional Euclidean embeddings that best preserve the similarities between a set of related observations. The method starts with an initial configuration, and iteratively refines it by repeatedly selecting pairs of objects at random, and adjusting their coordinates so that their distances on the map match more closely their respective proximities. The magnitude of these adjustments is controlled by a learning rate parameter, which decreases during the course of the simulation to avoid oscillatory behavior. Unlike classical multidimensional scaling (MDS) and nonlinear mapping (NLM), SPE scales linearly with respect to sample size, and can be applied to very large data sets that are intractable by conventional embedding procedures. The method is programmatically simple, robust, and convergent, and can be applied to a wide range of scientific problems involving exploratory data analysis and visualization.

Modeling zinc in biomolecules with the self consistent charge-density functional tight binding (SCC-DFTB) method: Applications to structural and energetic analysis

Abstract: Parameters for the zinc ion have been developed in the self-consistent charge density functional tight-binding (SCC-DFTB) framework. The approach was tested against B3LYP calculations for a range of systems, including small molecules that contain the typical coordination environment of zinc in biological systems (cysteine, histidine, glutamic/aspartic acids, and water) and active site models for a number of enzymes such as alcohol dehydrogenase, carbonic anhydrase, and aminopeptidase. The SCC-DFTB approach reproduces structural and energetic properties rather reliably (e.g., total and relative ligand binding energies and deprotonation energies of ligands and barriers for zinc-assisted proton transfers), as compared with B3LYP/6-311+G** or MP2/6-311+G** calculations.

Chemical information from the source function.

Abstract: The source function, which enables one to equate the value of the electron density at any point within a molecule to a sum of atomic contributions, has been applied to a number of cases. The source function is a model-independent, quantitative measure of the relative importance of an atom's or group's contribution to the density at any point in a system, and it represents a potentially interesting tool to provide chemical information. It is shown that the source contribution from H to the electron density rho(b) at the bond critical point in HX diatomics decreases with increasing X's electronegativity, and that this decrease is a result of significant changes in the Laplacian distribution within the H-basin. It is also demonstrated that the source function from Li to rho(b) in LiX diatomics is a more sensitive index of atomic transferability than it is the lithium atomic energy or population. The observed changes are such as to ensure a constant percentage source contribution from Li to rho(b) throughout the LiX series, rather than a constant source as one would expect in the limit of perfect atomic transferability. Application of the source function to planar lithium clusters has revealed that the source function clearly discriminates between a nonnuclear electron density maximum and a maximum associated to a nucleus, on the basis of the relative weight of the source contributions from the basin associated to the maximum and from the remaining basins in the cluster. The source function has also allowed for a classification of hydrogen bonds in terms of characteristic source contributions to the density at the H-bond critical point from the H involved in the H-bond, the H-donor D, and the H-acceptor A. The source contribution from the H appears as the most distinctive marker of the H-bond strength, being highly negative for isolated H-bonds, slightly negative for polarized assisted H-bonds, close to zero for resonance-assisted H-bonds, and largely positive for charge-assisted H-bonds. The contributions from atoms other than H, D, and A strongly increase with decreasing H-bond strength, consistently with the parallel increased electrostatic character of the interaction. The correspondence between the classification provided by the Electron Localization Function topologic approach and by the source function has been highlighted. It is concluded that the source function represents a practical tool to disclose the local and nonlocal character of the electron density distributions and to quantify such a locality and nonlocality in terms of a physically sound and appealing chemical partitioning.

Ab initio quality one‐electron properties of large molecules: Development and testing of molecular tailoring approach

Abstract: The development of a linear-scaling method, viz. “molecular tailoring approach” with an emphasis on accurate computation of one-electron properties of large molecules is reported. This method is based on fragmenting the reference macromolecule into a number of small, overlapping molecules of similar size. The density matrix (DM) of the parent molecule is synthesized from the individual fragment DMs, computed separately at the Hartree–Fock (HF) level, and is used for property evaluation. In effect, this method reduces the O(N3) scaling order within HF theory to an n·O(N′3) one, where n is the number of fragments and N′, the average number of basis functions in the fragment molecules. An algorithm and a program in FORTRAN 90 have been developed for an automated fragmentation of large molecular systems. One-electron properties such as the molecular electrostatic potential, molecular electron density along with their topography, as well as the dipole moment are computed using this approach for medium and large test chemical systems of varying nature (tocopherol, a model polypeptide and a silicious zeolite). The results are compared qualitatively and quantitatively with the corresponding actual ones for some cases. This method is also extended to obtain MP2 level DMs and electronic properties of large systems and found to be equally successful. © 2003 Wiley Periodicals, Inc. J Comput Chem 24: 484–495, 2003

Exact rotamer optimization for protein design

Abstract: Computational methods play a central role in the rational design of novel proteins. The present work describes a new hybrid exact rotamer optimization (HERO) method that builds on previous dead-end elimination algorithms to yield dramatic performance enhancements. Measured on experimentally validated physical models, these improvements make it possible to perform previously intractable designs of entire protein core, surface, or boundary regions. Computational demonstrations include a full core design of the variable domains of the light and heavy chains of catalytic antibody 48G7 FAB with 74 residues and 10^(128) conformations, a full core/boundary design of the β1 domain of protein G with 25 residues and 10^(53) conformations, and a full surface design of the β1 domain of protein G with 27 residues and 10^(60) conformations. In addition, a full sequence design of the β1 domain of protein G is used to demonstrate the strong dependence of algorithm performance on the exact form of the potential function and the fidelity of the rotamer library. These results emphasize that search algorithm performance for protein design can only be meaningfully evaluated on physical models that have been subjected to experimental scrutiny. The new algorithm greatly facilitates ongoing efforts to engineer increasingly complex protein features.

Ground and excited state CASPT2 geometry optimizations of small organic molecules.

Abstract: A method for computing second-order multiconfigurational perturbation theory (CASPT2) energy gradients numerically has been implemented and applied to a range of elementary organic chromophores, including 1,3 butadiene, acrolein, and two protonated Schiff bases. Geometries of ground and excited states—as well as conical intersections—are compared with the corresponding CASSCF structures, illustrating the effect of including the correction for dynamical electron correlation. It is shown that the differences between the two methods are not readily categorized, but that, while individual changes in bond lengths can be quite large (∼0.01–0.02 A), the natures and CASPT2 energetics of the structures remain similar. Exceptions to this tend to be systems that have a strong ionic character and that are not well described at the CASSCF level. Basis set effects (double- vs. triple-ζ) were examined for a limited number of examples, and found to be quite dramatic at both levels of theory. © 2003 Wiley Periodicals, Inc. J Comput Chem 24: 298–309, 2003

Improved third-order Møller–Plesset perturbation theory

Abstract: Based on a partitioning of the total correlation energy into contributions from parallel- and antiparallel-spin pairs of electrons, a modified third-order Moller-Plesset (MP) perturbation theory is developed. The method, termed SCS-MP3 (SCS for spin-component-scaled) continues previous work on an improved version of MP2. A benchmark set of 32 isogyric reaction energies, 11 atomization energies, and 11 stretched geometries is used to assess to performance of the model in comparison to the standard quantum chemical approaches MP2, MP3, and QCISD(T). It is found, that the new method performs significantly better than usual MP2/MP3 and even outperforms the more costly QCISD method. Opposite to the usual MP series, the SCS third-order correction uniformly improves the results. Dramatic enhancements are especially observed for the more difficult atomization energies, some of the stretched geometries, and reaction and ionization energies involving transition metal compounds where the method seems to be competitive or even superior to the widely used density functional approaches. Further tests performed for other complex systems (biradicals, C(20) isomers, transition states) demonstrate that the SCS-MP3 model yields often results of QCISD(T) accuracy. The uniformity with which the new approach improves for very different correlation problems indicates significant robustness, and suggests it as a valuable quantum chemical method of general use.

Calculation of the water-cyclohexane transfer free energies of neutral amino acid side-chain analogs using the OPLS all-atom force field.

Abstract: We calculated the free energy of solvation of the neutral analogs of 18 amino acid side-chains (not including glycine and proline) using the OPLS all-atom force field in TIP4P water, SPC water, and cyclohexane by molecular dynamics simulation and thermodynamic integration. The average unsigned errors in the free energies of solvation in TIP4P, SPC, and cyclohexane are 4.4, 4.9, and 2.1 kJ/mol respectively. Most of the calculated hydration free energies are not favorable enough compared to experiment. The largest errors are found for tryptophan, histidine, glutamic acid, and glutamine. The average unsigned errors in the free energy of transfer from TIP4P to cyclohexane and from SPC to cyclohexane are 4.0 and 4.1 kJ/mol, respectively. The largest errors, of more than 7.5 kJ/mol, are found for histidine, glutamine, and glutamatic acid.

Ab initio quality properties for macromolecules using the ADMA approach.

Abstract: We describe new developments of an earlier linear scaling algorithm for ab initio quality macromolecular property calculations based on the adjustable density matrix assembler (ADMA) approach. In this approach, a large molecule is divided into fuzzy fragments, for which quantum chemical calculations can easily be done using moderate-size "parent molecules" that contain all the local interactions within a selected distance. If greater accuracy is required, a larger distance is chosen. With the present extension of this approximation, properties of the large molecules, like the electron density, the electrostatic potential, dipole moments, partial charges, and the Hartree-Fock energy are calculated. The accuracy of the method is demonstrated with test cases of medium size by comparing the ADMA results with direct quantum chemical calculations.

Tork: Conformational analysis method for molecules and complexes.

Abstract: A conformational search method for organic molecules and bimolecular complexes is presented. The method, termed Tork, uses normal-mode analysis in bond-angle-torsion coordinates and focuses on a key subset of torsional coordinates to identify natural molecular motions that lead the initial conformation to new energy minima. New conformations are generated via distortion along these modes and their pairwise combinations, followed by energy minimization. For complexes, special treatment is accorded to the six coordinates that specify the position and orientation of one molecule relative to the other. Tests described here show that Tork is highly efficient for cyclic, acyclic, and mixed single molecules, as well as for host-guest complexes.

Parameterization of charge model 3 for AM1, PM3, BLYP, and B3LYP.

Abstract: We have recently developed a new Class IV charge model for calculating partial atomic charges in molecules. The new model, called Charge Model 3 (CM3), was parameterized for calculations on molecules containing H, Li, C, N, O, F, Si, S, P, Cl, and Br by Hartree-Fock theory and by hybrid density functional theory (DFT) based on the modified Perdew-Wang density functional with several basis sets. In the present article we extend CM3 to semiempirical molecular orbital theory, in particular Austin Model 1 (AM1) and Parameterized Model 3 (PM3), and to the popular BLYP and B3LYP DFT and hybrid DFT methods, respectively. For the BLYP extension, we consider the 6-31G(d) basis set, and for the B3LYP extension, we consider three basis sets: 6-31G(d), 6-31+G(d), and MIDI!6D. We begin with the previous CM3 strategy, which involves 34 parameters for 30 pairs of elements. We then refine the model to improve the charges in compounds that contain N and O. This modification, involving two new parameters, leads to improved dipole moments for amides, bifunctional H, C, N, O compounds, aldehydes, ketones, esters, and carboxylic acids; the improvement for compounds not containing N results from obtaining more physical parameters for carbonyl groups when the O=C-N conjugation of amides is addressed in the parameterization. In addition, for the PM3 method, we added an additional parameter to improve dipole moments of compounds that contain bonds between C and N. This additional parameter leads to improved accuracy in the dipole moments of aromatic nitrogen heterocycles with five-membered rings.

Using PC clusters to evaluate the transferability of molecular mechanics force fields for proteins.

Abstract: The transferability of molecular mechanics parameters derived for small model systems to larger biopolymers such as proteins can be difficult to assess. Even for small peptides, molecular dynamics simulations are typically too short to sample structures significantly different than initial conformations, making comparison to experimental data questionable. We employed a PC cluster to generate large numbers of native and non-native conformations for peptides with experimentally measured structural data, one predominantly helical and the other forming a β-hairpin. These atomic-detail sets do not suffer from slow convergence, and can be used to rapidly evaluate important force field properties. In this case a suspected bias toward α-helical conformations in the ff94 and ff99 force fields distributed with the AMBER package was verified. The sets provide critical feedback not only on force field transferability, but may also predict modifications for improvement. Such predictions were used to modify the ff99 parameter set, and the resulting force field was used to test stability and folding of model peptides. Structural behavior during molecular dynamics with the modified force field is found to be very similar to expectations, suggesting that these basis sets of conformations may themselves have significant transferability among force fields. We continue to improve and expand this data set and plan to make it publicly accessible. The calculations involved in this process are trivially parallel and can be performed using inexpensive personal computers with commodity components. © 2002 Wiley Periodicals, Inc. J Comput Chem 24: 21–31, 2003

Rigid-Body Dynamics in the Isothermal-Isobaric Ensemble: A Test on the Accuracy and Computational Efficiency

Abstract: We have developed a time-reversible rigid-body (rRB) molecular dynamics algorithm in the isothermal- isobaric (NPT) ensemble. The algorithm is an extension of rigid-body dynamics (Matubayasi and Nakahara, J Chem Phys 1999, 110, 3291) to the NPT ensemble on the basis of non-Hamiltonian statistical mechanics (Martyna, G. J. et al., J Chem Phys 1994, 101, 4177). A series of MD simulations of water as well as fully hydrated lipid bilayer systems have been undertaken to investigate the accuracy and efficiency of the algorithm. The rRB algorithm was shown to be superior to the state-of-the-art constraint-dynamics algorithm SHAKE/RATTLE/ROLL, with respect to computational efficiency. However, it was revealed that both algorithms produced accurate trajectories of molecules in the NPT as well as NVT ensembles, as long as a reasonably short time step was used. A couple of multiple time-step (MTS) integration schemes were also examined. The advantage of the rRB algorithm for computational efficiency increased when the MD simulation was carried out using MTS on parallel processing computer systems; total computer time for MTS-MD of a lipid bilayer using 64 processors was reduced by about 40% using rRB instead of SHAKE/RATTLE/ROLL.