An Analysis of the Interactions between Nucleic Acid Bases: Hydrogen-Bonded Base Pairs

Efficient and accurate density-based prediction of macromolecular polarizabilities

Accurately and efficiently predicting macromolecules' polarizabilities is an open problem. In this work, we employ a few simple density-based quantities from the information-theoretic approach (ITA) to predict polarizability of proteins. We first build quantitative structure/property relationships between molecular polarizabilities and ITA quantities. We then verify the broad applicability of ITA quantities for polarizability prediction for inorganic, organic, and biological systems with both localized and delocalized electronic structure. As a proof-of-concept application, we predict the molecular polarizabilities of complex proteins. Based on the linear regression equations for 20 natural amino acid residues, 400 dipeptides, and 8000 tripeptides, one then predicts the molecular polarizability of a larger peptide or even a protein once the molecular wavefunction is obtained. Because it is extremely costly to determine the wavefunction for a macromolecule like a protein, we propose to combine the ITA with the linear-scaling generalized energy-based fragmentation (GEBF) method to predict the macromolecular polarizability. In GEBF, the total molecular polarizability is obtained as a linear combination of the corresponding quantities from a series of small subsystems. We can predict them based on the subsystem wavefunction and linear regression equations rather than compute them from the nearly-intractable coupled-perturbed Hartree-Fock or Kohn-Sham equations for the whole macromolecule. Computational results showcase that the GEBF-ITA protocol should be an inexpensive yet accurate theoretical tool for predicting macromolecular polarizabilities.

A Density Functional Theory and Information-Theoretic Approach Study of Interaction Energy and Polarizability for Base Pairs and Peptides

Using density functional theory (DFT) and the information-theoretic approach (ITA) quantities to appreciate the energetics and properties of biopolymers is still an unaccomplished and ongoing task. To this end, we studied the building blocks of nucleic acid base pairs and small peptides. For base pairs, we have dissected the relative importance of energetic components by using two energy partition schemes in DFT. Our results convincingly show that the exchange-correlation effect predominantly governs the molecular stability of base pairs while the electrostatic potential plays a minor but indispensable role, and the steric effect is trivial. Furthermore, we have revealed that simple density-based ITA functions are in good relationships with molecular polarizabilities for a series of 30 hydrogen-bonded base pairs and all 20 natural α-amino acids, 400 dipeptides, and 8000 tripeptides. Based on these lines, one can easily predict the molecular polarizabilities of larger peptides, even proteins as long as the total molecular wavefunction is available, rather than solving the computationally demanding coupled-perturbed Hartree–Fock (CPHF) equation or its DFT counterpart coupled-perturbed Kohn–Sham (CPKS) equation.

New insights in chemical reactivity from quantum chemical topology

Based on the quantum chemical topology of the modified electron localization function ELF_x , an efficient and robust mechanistic methodology designed to identify the favorable reaction pathway between two reactants is proposed. We first recall and reshape how the supermolecular interaction energy can be evaluated from only three distinct terms, namely the intermolecular coulomb energy, the intermolecular exchange-correlation energy and the intramolecular energies of reactants. Thereafter, we show that the reactivity between the reactants is driven by the first-order variation in the coulomb intermolecular energy defined in terms of the response to changes in the number of electrons. Illustrative examples with the formation of the dative bond B-N involved in the BH₃ NH₃ molecule and the typical formation of the hydrogen bond in the canonical water dimer are presented. For these selected systems, our approach unveils a noticeable mimicking of E_dual onto the DFT intermolecular interaction energy surface calculated between the both reactants. An automated reaction-path algorithm aimed to determine the most favorable relative orientations when the two molecules approach each other is also outlined.

Partitioning of interaction-induced nonlinear optical properties of molecular complexes. I. Hydrogen-bonded systems

Interaction-induced electronic and vibrational (hyper)polarizabilities were decomposed into different interaction types (electrostatic, exchange, induction and dispersion).

Computational studies of darunavir into HIV-1 protease and DMPC bilayer: necessary conditions for effective binding and the role of the flaps

Human immunodeficiency virus type 1 protease (HIV-1 PR) is one of the main targets toward AIDS therapy. We have selected the potent drug darunavir and a weak inhibitor (fullerene analog) as HIV-1 PR substrates to compare protease's conformational features upon binding. Molecular dynamics (MD), molecular mechanics Poisson-Boltzmann surface area (MM-PBSA), and quantum-mechanical (QM) calculations indicated the importance of the stability of HIV-1 PR flaps toward effective binding: a weak inhibitor may induce flexibility to the flaps, which convert between closed and semiopen states. A water molecule in the darunavir-HIV-1 PR complex bridged the two flap tips of the protease through hydrogen bonding (HB) interactions in a stable structure, a feature that was not observed for the fullerene-HIV-1 PR complex. Additionally, despite that van der Waals interactions and nonpolar contribution to solvation favored permanent fullerene entrapment into the cavity, these interactions alone were not sufficient for effective binding; enhanced electrostatic interactions as observed in the darunavir-complex were the crucial component of the binding energy. An alternative pathway to the usual way of a ligand to access the cavity was also observed for both compounds. Each ligand entered the binding cavity through an opening between the one flap of the protease and a neighboring loop. This suggested that access to the cavity is not necessarily regulated by flap opening. Darunavir exerts its biological action inside the cell, after crossing the membrane barrier. Thus, we also initiated a study on the interactions between darunavir and the DMPC bilayer to reveal that the drug was accommodated inside the bilayer in conformations that resembled its structure into HIV-1 PR, being stabilized via HBs with the lipids and water molecules.

COMPUTATION OF LARGE SYSTEMS WITH AN ECONOMIC BASIS SET: AB INITIO CALCULATIONS OF BIOLOGICAL NUCLEIC ACID BASE PAIRS

We show that an economic basis set, in which the polarization functions are considered only for oxygen and nitrogen atoms of strong electronegativity, can be used to determine reliable structures of nucleic acid base pairs. Mulliken charge analysis and the HOMO-LUMO gap in single-point energy calculations using standard basis sets on the geometric structures optimized with the economic basis set found reasonable agreements with the ones of standard calculations. This study is expected to provide a general guideline for basis set selection in the computation of large biological systems being performed with considerable high accuracy, using a low cost computation resource.

Noncanonical hydrogen bonding in nucleic acids. Benchmark evaluation of key base-phosphate interactions in folded RNA molecules using quantum-chemical calculations and molecular dynamics simulations

RNA molecules are stabilized by a wide range of noncanonical interactions that are not present in DNA. Among them, the recently classified base-phosphate (BPh) interactions belong to the most important ones. Twelve percent of nucleotides in the ribosomal crystal structures are involved in BPh interactions. BPh interactions are highly conserved and provide major constraints on RNA sequence evolution. Here we provide assessment of the energetics of BPh interactions using MP2 computations extrapolated to the complete basis set of atomic orbitals and corrected for higher-order electron correlation effects. The reference computations are compared with DFT-D and DFT-D3 approaches, the SAPT method, and the molecular mechanics force field. The computations, besides providing the basic benchmark for the BPh interactions, allow some refinements of the original classification, including identification of some potential doubly bonded BPh patterns. The reference computations are followed by analysis of some larger RNA fragments that consider the context of the BPh interactions. The computations demonstrate the complexity of interaction patterns utilizing the BPh interactions in real RNA structures. The BPh interactions are often involved in intricate interaction networks. We studied BPh interactions of protonated adenine that can contribute to catalysis of hairpin ribozyme, the key BPh interaction in the S-turn motif of the sarcin-ricin loop, which may predetermine the S-turn topology and complex BPh patterns from the glmS riboswitch. Finally, the structural stability of BPh interactions in explicit solvent molecular dynamics simulations is assessed. The simulations well preserve key BPh interactions and allow dissection of structurally/functionally important water-meditated BPh bridges, which could not be considered in earlier bioinformatics classification of BPh interactions.

Rapid evaluation of the binding energies in hydrogen-bonded amide-thymine and amide-uracil dimers in gas phase

The binding energies and the equilibrium hydrogen bond distances as well as the potential energy curves of 48 hydrogen-bonded amide-thymine and amide-uracil dimers are evaluated from the analytic potential energy function established in our lab recently. The calculation results show that the potential energy curves obtained from the analytic potential energy function are in good agreement with those obtained from MP2/6-311+G** calculations by including the BSSE correction. For all the 48 dimers, the analytic potential energy function yields the binding energies of the MP2/6-311+G** with BSSE correction within the error limits of 0.50 kcal/mol for 46 dimers, only two differences are larger than 0.50 kcal/mol and the largest one is only 0.60 kcal/mol. The analytic potential energy function produces the equilibrium hydrogen bond distances of the MP2/6-311+G** with BSSE correction within the error limits of 0.050 Å for all the 48 dimers. The analytic potential energy function is further applied to four more complicated hydrogen-bonded amide-base systems involving amino acid side chain and β-sheet. The values of the binding energies and equilibrium hydrogen bond distances obtained from the analytic potential energy function are also in good agreement with those obtained from MP2 calculations with the BSSE correction. These results demonstrate that the analytic potential energy function can be used to evaluate the binding energies in hydrogen-bonded amide-base dimers quickly and accurately.

How does modification of adenine by hydroxyl radical influence the stability and the nature of stacking interactions in adenine-cytosine complex?

This study reports on ab initio calculations of adenine-cytosine complexes in two different context alignments appearing in B-DNA. The influence of adenine modification by hydroxyl radical on the stability of the complexes is also discussed. The analysis was performed on over 40 crystallographic structures for each of the sequence contexts. In most cases, modification of adenine by hydroxyl radical leads to less negative intermolecular interaction energies. The issue of the influence of alteration of structural base step parameters on the stability of modified and unmodified adenine-cytosine complexes is also addressed. Analysis of the dependence of intermolecular interaction energy on base step parameters reveals that for twist and shift modification of adenine by hydroxyl radical leads to quite different interaction energy profiles in comparison with unmodified complexes. In order to elucidate the physical origins of this phenomenon, i.e. to analyze how the modification of adenine by hydroxyl radical is reflected in the change of intermolecular interaction energy components, a variational-perturbational decomposition scheme was applied at the MP2/aug-cc-pVDZ level of theory.

Theoretical insights into the nature of intermolecular interactions in cytosine dimer

In this study we discuss stacking interactions in cytosine dimer in conformations appearing in B-DNA crystals. The variational-perturbational scheme was applied for decomposition of the intermolecular interaction energy at the MP2 level of theory. The significant influence of the mutual orientation of cytosine monomers was observed not only on the total intermolecular interaction energy but also on its components: Different components of intermolecular interaction energy depend in different manner on parameters describing mutual orientation of cytosine monomers.

Numerically stable optimized effective potential method with balanced Gaussian basis sets

A solution to the long-standing problem of developing numerically stable optimized effective potential (OEP) methods based on Gaussian basis sets is presented by introducing an approach consisting of an exact exchange OEP method with an accompanying construction and balancing scheme for the involved auxiliary and orbital Gaussian basis sets that is numerically stable and that properly represents an exact exchange Kohn-Sham method. The method is a purely analytical method that does not require any numerical grid, scales like Hartree-Fock or B3LYP procedures, is straightforward to implement, and is easily generalized to take into account orbital-dependent density functionals other than the exact exchange considered in this work. Thus, the presented OEP approach opens the way to the development and application of novel orbital-dependent exchange-correlation functionals. It is shown that adequately taking into account the continuum part of the Kohn-Sham orbital spectrum is crucial for numerically stable Gaussian basis set OEP methods. Moreover, it is mandatory to employ orbital basis sets that are converged with respect to the used auxiliary basis representing the exchange potential. OEP calculations in the past often did not meet the latter requirement and therefore may have led to erroneously low total energies.

An analysis of the electrostatic interaction between nucleic acid bases

Results from several commonly used approximate methods of evaluating electrostatic interactions have been compared to the rigorous, nonexpanded electrostatic energies at both uncorrelated and correlated levels of theory. We examined a number of energy profiles for both hydrogen bonded and stacked configurations of the nucleic acid base pairs. We found that the penetration effects play an extremely important role and the expanded electrostatic energies are significantly underestimated with respect to the ab initio values. Apart from the inability to reproduce the magnitudes of the ab initio electrostatic energy, there are other problems with the available approximate electrostatic models. For example, the distributed multipole analysis, one of the most advanced methods, is extremely sensitive to the basis set and level of theory used to evaluate the multipole moments. Detailed ab initio results are provided that other researchers could use to test their approximate models.

Computation of large systems with an economic basis set: Structures and reactivity indices of nucleic acid base pairs from density functional theory

We show here that an economic basis set can describe nucleic acid base pairs involving the hydrogen bond interactions in density functional calculations. The economic basis set in which the polarization function is added only to oxygen and nitrogen atoms of strong electronegativity can predict reliable geometric structures and dipole moment of nucleic acid base pairs, comparable to those obtained from the basis set of 6-31G* in B3LYP calculations. Combining single point calculations with the standard basis set on the geometric structures optimized by the economic basis set, the present approach has predicted accurate natural bond orbital charge, binding energy, electronegativity, hardness, softness, and electrophilicity index. The principle for basis selection presented in this study can be regarded as a general guideline in the computation of large biological systems with considerably high accuracy and low computational expense.

Ab initio calculations of dispersion coefficients for nucleic acid base pairs

The results of ab initio calculations of two- and three-body dispersion coefficients for the four most important nucleic acid bases are reported. The isotropic as well as anisotropic coefficients were found by using the time-dependent Hartree-Fock approach and the aug-cc-pVDZ basis set. Single and double excitation coupled-cluster theory with noniterative treatment of triple excitations [CCSD(T)] was used to find the values of static polarizabilities which were subsequently used to estimate the values of the CCSD(T) dispersion coefficients. A comparison of these estimated CCSD(T) dispersion coefficients with coefficients found by using empirical approaches based on atomic contributions revealed that the latter are not reliable.

Critical examination of the supermolecule density functional theory calculations of intermolecular interactions

The results of calculations employing twelve different combinations of exchange and correlation functionals are compared with results of ab initio calculations for two different configurations of the water dimer and three different configurations of the thymine-adenine complex. None of the density functional theory (DFT) treatments could properly reproduce the results of coupled-cluster calculations for all configurations examined. The DFT approaches perform well when the interaction energy is dominated by the electrostatic component and the dispersion energy is less important. Two mechanisms that compensate for the missing dispersion component were identified. The first one is the decrease of the magnitude of the intermolecular exchange-repulsion and the second one is the increase of the magnitude of the attractive deformation energy. For some functionals both effects are observed together, but for some other ones only the second effect occurs. The three correlation functionals that were examined were found to make only very small contributions to the deformation energy. The examination of angular and distance dependence of the interactions shows that the currently available DFT approaches are not suitable for developing intermolecular potential energy surfaces. They could however be used to find global minima on potential energy surfaces governed by intermolecular electrostatic interactions. Additional single point ab initio calculations are recommended as the means of validating optimized structures.

Accurate interaction energies of hydrogen-bonded nucleic acid base pairs

Hydrogen-bonded nucleic acids base pairs substantially contribute to the structure and stability of nucleic acids. The study presents reference ab initio structures and interaction energies of selected base pairs with binding energies ranging from -5 to -47 kcal/mol. The molecular structures are obtained using the RI-MP2 (resolution of identity MP2) method with extended cc-pVTZ basis set of atomic orbitals. The RI-MP2 method provides results essentially identical with the standard MP2 method. The interaction energies are calculated using the Complete Basis Set (CBS) extrapolation at the RI-MP2 level. For some base pairs, Coupled-Cluster corrections with inclusion of noniterative triple contributions (CCSD(T)) are given. The calculations are compared with selected medium quality methods. The PW91 DFT functional with the 6-31G basis set matches well the RI-MP2/CBS absolute interaction energies and reproduces the relative values of base pairing energies with a maximum relative error of 2.6 kcal/mol when applied with Becke3LYP-optimized geometries. The Becke3LYP DFT functional underestimates the interaction energies by few kcal/mol with relative error of 2.2 kcal/mol. Very good performance of nonpolarizable Cornell et al. force field is confirmed and this indirectly supports the view that H-bonded base pairs are primarily stabilized by electrostatic interactions.

Molecular Interactions of Nucleic Acid Bases. A Review of Quantum-Chemical Studies

Ab initio quantum-chemical calculations with inclusion of electron correlation significantly contributed to our understanding of molecular interactions of DNA and RNA bases. Some of the most important findings are introduced in the present overview: structures and energies of hydrogen bonded base pairs, nature of base stacking, interactions between metal cations and nucleobases, nonplanarity of isolated nucleobases and other monomer properties, tautomeric equilibria of nucleobases, out-of-plane hydrogen bonds and amino acceptor interactions. The role of selected molecular interactions in nucleic acids is discussed and representative examples where these interactions occur are given. Also, accuracy of density functional theory, semiempirical methods, distributed multipole analysis and empirical potentials is commented on. Special attention is given to our very recent reference calculations on base stacking and H-bonding. Finally, we briefly comment on the relationship between advanced ab initio quantum-chemical methods and large-scale explicit solvent molecular dynamics simulations of nucleic acids.