Electronic structure properties of solvated biomolecules: A quantum approach for macromolecular characterization

Specific Reaction Parametrization of the AM1/d Hamiltonian for Phosphoryl Transfer Reactions: H, O, and P Atoms

A semiempirical AM1/d Hamiltonian is developed to model phosphoryl transfer reactions catalyzed by enzymes and ribozymes for use in linear-scaling calculations and combined quantum mechanical/molecular mechanical simulations. The model, designated AM1/d-PhoT, is parametrized for H, O, and P atoms to reproduce high-level density-functional results from a recently constructed database of quantum calculations for RNA catalysis ( http://theory.chem.umn.edu/Database/QCRNA ), including geometries and relative energies of minima, transition states and reactive intermediates, dipole moments, proton affinities, and other relevant properties. The model is tested in the gas phase and in solution using a QM/MM potential. The results indicate that the method provides significantly higher accuracy than MNDO/d, AM1, and PM3 methods and, for the transphosphorylation reactions, is in close agreement with the density-functional calculations at the B3LYP/6-311++G(3df,2p) level with a reduction in computational cost of 3-4 orders of magnitude. The model is expected to have considerable impact on the application of semiempirical QM/MM methods to transphosphorylation reactions in solution, enzymes, and ribozymes and to ultimately facilitate the design of improved next-generation multiscale quantum models.

“One-into-Many” Model: An Approach on DFT Based Reactivity Descriptor to Predict the Regioselectivity of Large Systems

The present work consists of the development of a new model (named "one-into-many") to predict the regioselectivity of large chemical and biological systems. Large chemical and biological systems with multiple reactive sites are proposed to be broken into small fragments having at least one reactive site in each fragment. The environment around each reactive site is mimicked by incorporating a buffer zone. Local reactivity descriptor (i.e., local hardness), originally proposed by Berkowitz et al. (J. Am.Chem. Soc. 1985, 107, 6811) and later implemented by Langenaeker et al. (J. Phys. Chem. 1995, 99, 6424), is evaluated for each reactive site adopting a new modified approach (i.e., without neglecting kinetic energy and exchange energy parts). When the model is applied to predict the regioselectivity (toward an electrophilic attack) of the base pairs in DNA (PDB ID: 1BNA) (Proc. Natl. Acad. Sci. U.S.A. 1981, 78, 2179) the generated results are found to be satisfactory in most cases.

Hybrid boundary element and finite difference method for solving the nonlinear Poisson-Boltzmann equation

A hybrid approach for solving the nonlinear Poisson-Boltzmann equation (PBE) is presented. Under this approach, the electrostatic potential is separated into (1) a linear component satisfying the linear PBE and solved using a fast boundary element method and (2) a correction term accounting for nonlinear effects and optionally, the presence of an ion-exclusion layer. Because the correction potential contains no singularities (in particular, it is smooth at charge sites) it can be accurately and efficiently solved using a finite difference method. The motivation for and formulation of such a decomposition are presented together with the numerical method for calculating the linear and correction potentials. For comparison, we also develop an integral equation representation of the solution to the nonlinear PBE. When implemented upon regular lattice grids, the hybrid scheme is found to outperform the integral equation method when treating nonlinear PBE problems. Results are presented for a spherical cavity containing a central charge, where the objective is to compare computed 1D nonlinear PBE solutions against ones obtained with alternate numerical solution methods. This is followed by examination of the electrostatic properties of nucleic acid structures.

Quantum descriptors for biological macromolecules from linear-scaling electronic structure methods

The characterization of electrostatic and chemical properties at the surface of biological macromolecules is of interest in elucidating the fundamental biological structure-function relationships as well as in problems of rational drug design. This paper presents a set of macromolecular quantum descriptors for the characterization of biological macromolecules in solution that can be obtained with modest computational cost from linear-scaling semi-empirical quantum/solvation methods. The descriptors discussed include: solvent-polarized electrostatic surface potential maps, equilibrated atomic charges, Fukui reactivity indices, approximate local hardness maps, and relative proton potentials. These properties are applied to study the conformational dependence of the electrostatic surface potential of the solvated phosphate-binding protein mutant (T141D), the regioselectivity of the zinc finger domains of HIV-1 nucleocapsid (NC) protein, and the order of pKa values of acidic residues in turkey ovomucoid third domain (OMTKY3) and of the zinc-binding residues in the carboxyl terminal zinc finger of NC. In all cases, insight beyond that obtainable from purely classical models is gained and can be used to rationalize the experimental observations. The macromolecular quantum descriptors presented here greatly extend the arsenal of tools for macromolecular characterization and offer promise in applications to modern structure-based drug design.

A quantum mechanical study on phosphotyrosyl peptide binding to the SH2 domain of p56lck tyrosine kinase with insights into the biochemistry of intracellular signal transduction events

A study on the interaction between a phosphotyrosyl peptide with the SH2 domain of Lck kinase has been undertaken with the aid of semiempirical linear-scaling quantum mechanical methods. The structure of this complex has been solved at atomic resolution and, hence, it represents the ideal candidate for studying the charge deformation effects induced by the phosphopeptide on the binding site. Substantial changes in the charge of amino acid residues located in the binding pocket of the protein are observed upon ligand binding. More specifically, our quantum chemical calculations indicate that H-bonds involving charged side-chains are subject to consistent charge deformation effects whereas those forming salt bridges are unaffected by ligand binding. Furthermore, ligand binding has the effect of changing both the magnitude and direction of the protein's macrodipole, which rotates approximately 150 degrees with respect that of the unliganded protein. This suggests that a change in the polarization state of the protein might acts as a switch during the transmission of intracellular signals. The binding energy calculated with the aid of the COSMO solvation model corresponds to about -200 kcal/mol, most of which is attributed to the interaction of the phosphotyrosine head with the amino acid chains located in the binding site of the SH2 domain.

Ab initioquality properties for macromolecules using the ADMA approach

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.

Ab initio quality one-electron properties of large molecules: development and testing of molecular tailoring approach

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(N(3)) 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.

Fast approximate methods for calculating nucleic acid base pair interaction energies

Interaction enthalpies for six base pairs have been computed at a variety of efficient levels of electronic structure theory and compared to experiment. In addition to previously defined levels of theory, modified Hamiltonians with adjusted parameters in hybrid Hartree-Fock/density functionals and semiempirical neglect-of-diatomic-differential-overlap models were examined. Of the pure and hybrid density functional levels, mPWPW91/MIDI! performed most satisfactorily, as judged by comparison not only to the available experimental data, but also to data from more robust electronic structure methods for 22 additional base pairs. The low computational cost of the mPWPW91/MIDI! model was further exploited in an investigation of various base trimers, tetramers, and one base pentamer. A carefully reparameterized semiempirical model, PM3(BP), was able to achieve similar levels of accuracy at a still greater savings in terms of computational effort.

The treatment of solvation by a generalized Born model and a self-consistent charge-density functional theory-based tight-binding method

We present a model to calculate the free energies of solvation of small organic compounds as well as large biomolecules. This model is based on a generalized Born (GB) model and a self-consistent charge-density functional theory-based tight-binding (SCC-DFTB) method with the nonelectrostatic contributions to the free energy of solvation modeled in terms of solvent-accessible surface areas (SA). The parametrization of the SCC-DFTB/GBSA model has been based on 60 neutral and six ionic molecules composed of H, C, N, O, and S, and spanning a wide range of chemical groups. Effective atomic radii as parameters have been obtained through Monte Carlo Simulated Annealing optimization in the parameter space to minimize the differences between the calculated and experimental free energies of solvation. The standard error in the free energies of solvation calculated by the final model is 1.11 kcal mol(-1). We also calculated the free energies of solvation for these molecules using a conductor-like screening model (COSMO) in combination with different levels of theory (AM1, SCC-DFTB, and B3LYP/6-31G*) and compared the results with SCC-DFTB/GBSA. To assess the efficiency of our model for large biomolecules, we calculated the free energy of solvation for a HIV protease-inhibitor complex containing 3,204 atoms using the SCC-DFTB/GBSA and the SCC-DFTB/COSMO models, separately. The computed relative free energies of solvation are comparable, while the SCC-DFTB/GBSA model is three to four times more efficient, in terms of computational cost.

An ab initio theoretical study of electronic structure and properties of 2'-deoxyguanosine in gas phase and aqueous media

Molecular geometries of two structural forms of 2'-deoxyguanosine (keto-N9R and keto-N7R, R = the sugar moiety) considering both the C2'-endo and C3'-endo conformations of the sugar ring and those of the complexes of these species with two water molecules each were optimized employing the ab initio RHF procedure. A mixed basis set consisting of the 6-311+G* basis set for the nitrogen atom of the amino group and the 4-31G basis set for all the other atoms was used. The RHF calculations were followed by correlation correction of the total energy at the MP2 level. Both the structural forms of 2'-deoxyguanosine were solvated using the polarized continuum model (PCM) of the self-consistent reaction field (SCRF) theory and the corresponding RHF optimized geometries at the RHF and MP2 levels. Geometry optimization was also performed in aqueous media using the Onsager model at the RHF level using the above-mentioned mixed basis set, and subsequently, using the reoptimized geometries, single-point MP2 calculations were performed. It is found that both the keto-N9R and keto-N7R forms of 2'-deoxyguanosine as well as their complexes with two water molecules each would occur, particularly at the water-air interface. Though the normal Watson-Crick-type base pairing would not be possible with the keto-N7R form of 2'-deoxyguanosine(G*), two other (G*-C and G*-T) base pairing schemes may occur with this form of the nucleoside, which may cause mutation. The present calculated geometry of the keto-N9R form of the anti-conformation of 2'-deoxyguanosine including the dihedral angle chi(CN) agree satisfactorily with the available crystallographic results. The present results also agree satisfactorily with those obtained by other authors earlier for the keto-N9R form of 2'-deoxyguanosine using B3LYP and MP2 methods employing the 6-31G* basis set. Using transition state calculations, it is shown that tautomerism of guanine and other similar molecules where the tautomers would coexist would be facilitated by the occurrence of the H(+) and OH(-) fragments of water molecules. Further, this coexistence of the two tautomers appears to make the C8 carbon atom located between the N7 and N9 nitrogen atoms susceptible to attack by the OH(-) group. Thus, an explanation is obtained for the efficient formation of the reaction product 8-hydroxy-2'-deoxyguanosine, which serves as a biomarker for oxidative damage to DNA in biological systems.

Molecular dynamics simulation of nucleic acids: successes, limitations, and promise

In the last five years we have witnessed a significant increase in the number publications describing accurate and reliable all-atom molecular dynamics simulations of nucleic acids. This increase has been facilitated by the development of fast and efficient methods for treating the long-range electrostatic interactions, the availability of faster parallel computers, and the development of well-validated empirical molecular mechanical force fields. With these technologies, it has been demonstrated that simulation is not only capable of consistently reproducing experimental observations of sequence specific fine structure of DNA, but also can give detailed insight into prevalent problems in nucleic acid structure, ion association and specific hydration of nucleic acids, polyadenine tract bending, and the subtle environmental dependence of the A-DNA-B-DNA duplex equilibrium. Despite the advances, there are still issues with the methods that need to be resolved through rigorous controlled testing. In general, these relate to deficiencies of the underlying molecular mechanical potentials or applied methods (such as the imposition of true periodicity in Ewald simulations and the need for energy conservation), and significant limits in effective conformational sampling. In this perspective, we provide an overview of our experiences, provide some cautionary notes, and provide recommendations for further study in molecular dynamics simulation of nucleic acids.