Victor M. Anisimov

Determination of Electrostatic Parameters for a Polarizable Force Field Based on the Classical Drude Oscillator

A procedure to determine the electrostatic parameters has been developed for a polarizable empirical force field based on the classical Drude oscillator model. Atomic charges and polarizabilities for a given molecule of interest were derived from restrained fitting to quantum-mechanical electrostatic potentials (ESP) calculated at the B3LYP/ cc-pVDZ or B3LYP/aug-cc-pVDZ levels on grid points located on concentric Connolly surfaces. The determination of the atomic polarizabilities requires a series of perturbed ESP maps, each one representing the electronic response of the molecule in the presence of a background charge placed on Connolly surfaces primarily along chemical bonds and lone pairs. Reference values for the partial atomic charges were taken from the CHARMM27 additive all-atom force field, and those for the polarizabilities were based on adjusted Millers ahp atomic polarizability values. The fitted values of atomic polarizabilities were scaled to reflect the reduced polarization expected for the condensed media and/or to correct for the systematic underestimation of experimental molecular polarizabilities by B3LYP calculations. Following correction of the polarizabilities, the atomic charges were adjusted to reproduce gas-phase dipole moments. The developed scheme has been tested on a set of small molecules representing functional moieties of nucleic acids. The derived electrostatic parameters have been successfully applied in a preliminary polarizable molecular dynamics simulation of a DNA octamer in a box of water with sodium counterions. Thus, this study confirms the feasibility of the use of a polarizable force field based on a classical Drude model for simulations of biomolecules in the condensed phase.

Additive and classical drude polarizable force fields for linear and cyclic ethers

Empirical force field parameters consistent with the CHARMM additive and classical Drude based polarizable force fields are presented for linear and cyclic ethers. Initiation of the optimization process involved validation of the aliphatic parameters based on linear alkanes and cyclic alkanes. Results showed the transfer to cyclohexane to yield satisfactory agreement with target data; however, in the case of cyclopentane direct transfer of the Lennard-Jones parameters was not sufficient due to ring strain, requiring additional optimization of these parameters for this molecule. Parameters for the ethers were then developed starting with the available aliphatic parameters, with the nonbond parameters for the oxygens optimized to reproduce both gas- and condensed-phase properties. Nonbond parameters for the polarizable model include the use of an anisotropic electrostatic model on the oxygens. Parameter optimization emphasized the development of transferable parameters between the ethers of a given class. The ether models are shown to be in satisfactory agreement with both pure solvent and aqueous solvation properties, and the resulting parameters are transferable to test molecules. The presented force field will allow for simulation studies of ethers in condensed phase and provides a basis for ongoing developments in both additive and polarizable force fields for biological molecules.

ISOEFF98. A program for studies of isotope effects using Hessian modifications

A new program for calculations of isotope effects has been developed. It requires only force constants for substrate and transition state as the external data. All other calculational steps are integrated into the program. ISOEFF98 has features of Hessian modification and scale factor optimization. The first of these allows studies of isotope effect changes upon weakening or strengthening of internal coordinates. The second feature allows fitting of the calculated isotope effect to the experimental value by scaling of molecular frequencies.

Development of CHARMM Polarizable Force Field for Nucleic Acid Bases Based on the Classical Drude Oscillator Model

A polarizable force field for nucleic acid bases based on the classical Drude oscillator model is presented. Parameter optimization was performed to reproduce crystallographic geometries, crystal unit cell parameters, heats of sublimation, vibrational frequencies and assignments, dipole moments, molecular polarizabilities and quantum mechanical base-base and base-water interaction energies. The training and validation data included crystals of unsubstituted and alkyl-substituted adenine, guanine, cytosine, uracil, and thymine bases, hydrated crystals, and hydrogen bonded base pairs. Across all compounds, the RMSD in the calculated heats of sublimation is 4.1%. This equates to an improvement of more than 2.5 kcal/mol in accuracy compared to the nonpolarizable CHARMM27 force field. However, the level of agreement with experimental molecular volume decreased from 1.7% to 2.1% upon moving from the nonpolarizable to the polarizable model. The representation of dipole moments is significantly improved with the Drude polarizable force field. Unlike in additive force fields, there is no requirement for the gas-phase dipole moments to be overestimated, illustrating the ability of the Drude polarizable force field to treat accurately differently dielectric environments and indicating the improvements in the electrostatic model. Validation of the model was performed on the basis of the calculation of the gas-phase binding enthalpies of base pairs obtained via potential of mean force calculations; the additive and polarizable models both performed satisfactorily with average differences of 0.2 and 0.9 kcal/mol, respectively, and rms differences of 1.3 and 1.7 kcal/mol, respectively. Overall, considering the number of significant improvements versus the additive CHARMM force field, the incorporation of explicit polarizability into the force field for nucleic acid bases represents an additional step toward accurate computational modeling of biological systems.

Understanding the dielectric properties of liquid amides from a polarizable force field.

The role played by electronic polarization in the dielectric properties of liquid N-methyl acetamide (NMA) is examined using molecular dynamics simulations with a polarizable force field based on classical Drude oscillators. The model presented is the first force field shown to reproduce the anomalously large dielectric constant of liquid NMA. Details of the molecular polarizability are found to be important. For instance, all elements of the polarizability tensor, rather then just the trace, impact on the condensed phase properties. Two factors related to electronic polarizability are found to contribute to this large dielectric constant. First is the significant enhancement of the mean amide molecular dipole magnitude, which is 50% larger in the liquid than in the gas phase. Second is the consequent strong hydrogen bonding between molecular neighbors that enhances the orientational alignment of the molecular dipoles. Polarizable models of amide compounds that have two (acetamide) and zero (N,N-dimethyl acetamide) polar hydrogen-bond donor atoms are also investigated. Experimentally, the neat liquid dielectric constants at 373 K are 100 for NMA, 66 for acetamide and 26 for N,N-dimethyl acetamide. The polarizable models replicate this trend, predicting a dielectric constant of 92+/-5 for NMA, 66+/-3 for acetamide and 23+/-1 for N,N-dimethyl acetamide.

Quantum mechanical binding free energy calculation for phosphopeptide inhibitors of the Lck SH2 domain

The accurate and efficient calculation of binding free energies is essential in computational biophysics. We present a linear‐scaling quantum mechanical (QM)‐based end‐point method termed MM/QM‐COSMO to calculate binding free energies in biomolecular systems, with an improved description of entropic changes. Molecular dynamics trajectories are re‐evaluated using a semiempirical Hamiltonian and a continuum solvent model; translational and rotational entropies are calculated using configurational integrals, and internal entropy is calculated using the harmonic oscillator approximation. As an application, we studied the binding of a series of phosphotyrosine tetrapeptides to the human Lck SH2 domain, a key component in intracellular signal transduction, modulation of which can have therapeutic relevance in the treatment of cancer, osteoporosis, and autoimmune diseases. Calculations with molecular mechanics Poisson–Boltzmann, and generalized Born surface area methods showed large discrepancies with experimental data stemming from the enthalpic component, in agreement with an earlier report. The empirical force field‐based solvent interaction energy scoring function yielded improved results, with average unsigned error of 3.6 kcal/mol, and a better ligand ranking. The MM/QM‐COSMO method exhibited the best agreement both for absolute (average unsigned error = 0.7 kcal/mol) and relative binding free energy calculations. These results show the feasibility and promise of a full QM‐based end‐point method with an adequate balance of accuracy and computational efficiency.

LocalSCF method for semiempirical quantum-chemical calculation of ultralarge biomolecules.

A linear-scaling semiempirical method, LocalSCF, has been proposed for the quantum-chemical calculations of ultralarge molecular systems by treating the large-scale molecular task as a variational problem. The method resolves the self-consistent field task through the finite atomic expansion of weakly nonorthogonal localized molecular orbitals. The inverse overlap matrix arising from the nonorthogonality of the localized orbitals is approximated by preserving the first-order perturbation term and applying the second-order correction by means of a penalty function. This allows for the separation of the orbital expansion procedure from the self-consistent field optimization of linear coefficients, thereby maintaining the localized molecular orbital size unchanged during the refinement of linear coefficients. Orbital normalization is preserved analytically by the variation of virtual degrees of freedom, which are orthogonal to the initial orbitals. Optimization of linear coefficients of localized orbitals is performed by a gradient procedure. The computer program running on a commodity personal computer was applied to the GroEL-GroES chaperonin complex containing 119,273 atoms.

DFT study of B-like conformations of deoxydinucleoside monophosphates containing Gua and/or Cyt and their complexes with Na+ cation.

Abstract B-like minimum energy conformations of deoxydinucleoside monophosphate anions (dD-MPs) containing Gua and/or Cyt and their Na+ complexes have been studied by the DFT PW91PW91/DZVP method. The optimized geometry of the dDMPs is in close agreement with experimental observations and the obtained minimum energy conformations are consistent with purine-purine, purine-pyrimidine, and pyrimidine-purine arrangements in crystals of B-DNA duplexes. All the studied systems are characterized by pyramidalization of the amino groups, which participate in the formation of unusual hydrogen bond between the carbonyl oxygen of the second base in the dGpdC, dCpdG dDMPs, and their Na+ complexes. In all the obtained structures the bases assume a nearly parallel disposition to each other and this effect is independent on the degree of their spatial superposition. From this it is concluded that the parallel disposition of the bases in the B-like single-stranded conformations is dictated by the sugar-phosphate backbone. Correspondingly, the base-base interactions attain a secondary role in the formation of these spatial structures. The formation of a weak C6-H6…O5′ hydrogen bond between cytosine and the phosphate oxygen is reported, in agreement with experimental observations.

Computational and experimental studies of the interaction between phospho-peptides and the C-terminal domain of BRCA1

The C-terminal domain of BRCA1(BRCT) is involved in the DNA repair pathway by recognizing the pSXXF motif in interacting proteins. It has been reported that short peptides containing this motif bind to BRCA1(BRCT) in the micromolar range with high specificity. In this work, the binding of pSXXF peptides has been studied computationally and experimentally in order to characterize their interaction with BRCA1(BRCT). Elucidation of the contacts that drive the protein–ligand interaction is critical for the development of high affinity small-molecule BRCA1 inhibitors. Molecular dynamics (MD) simulations revealed the key role of threonine at the peptide P+2 position in providing structural rigidity to the ligand in the bound state. The mutation at P+1 had minor effects. Peptide extension at the N-terminal position with the naphthyl amino acid exhibited a modest increase in binding affinity, what could be explained by the dispersion interaction of the naphthyl side-chain with a hydrophobic patch. Three in silico end-point methods were considered for the calculation of binding free energy. The Molecular Mechanics Poisson–Boltzmann Surface Area and the Solvated Interaction Energy methods gave reasonable agreement with experimental data, exhibiting a Pearlman predictive index of 0.71 and 0.78, respectively. The MM-quantum mechanics-surface area method yielded improved results, which was characterized by a Pearlman index of 0.78. The correlation coefficients were 0.59, 0.61 and 0.69, respectively. The ability to apply a QM level of theory within an end-point binding free energy protocol may provide a way for a consistent improvement of accuracy in computer-aided drug design.

Post Hartree-Fock Studies of the Canonical Watson-Crick DNA Base Pairs: Molecular Structure and the Nature of Stability

Abstract Gas-phase gradient optimization was carried out on the canonical Watson-Crick DNA base pairs using the second-order Møller-Plesset perturbation method at the 6–31G(d) and 6- 31G(d,p) basis sets. It is detected that full geometry optimization at the MP2 level leads to an intrinsically nonplanar propeller-twisted and buckled geometry of G-C and A-T base pairs; while HF and DFT methods predict perfect planar or almost planar geometry of the base pairs. Supposedly the nonplanarity of the pairs is caused by pyramidalization of the amino nitrogen atoms, which is underestimated by the HF and DFT methods. This justifies the importance of geometry optimization at the MP2 level for obtaining reliable prediction of the charge distribution, molecular dipole moments and geometrical structure of the base pairs. The Morokuma-Kitaura and the Reduced Variational Space methods of the decomposition for molecular HF interaction energies were used for investigation of the hydrogen bonding in the Watson-Crick base pairs. It is shown that the HF stability of the hydrogen-bonded DNA base pairs originates mainly from electrostatic interactions. At the same time, the calculated magnitude of the second order intramolecular correlation correction to the Coulomb energy showed that electron correlation reduces the contribution of the electrostatic term to the attractive interaction for the A-T and G-C base pairs. Polarization, charge transfer and dispersion interactions also make considerable contribution to the attraction energy of bases.