Abstract: Herein we will focus on the use of quantum mechanics (QM) in drug design (DD) to solve disparate problems from scoring protein–ligand poses to building QM QSAR models. Through the variational principle of QM we know that we can obtain a more accurate representation of molecular systems than classical models, and while this is not a matter of debate, it still has not been shown that the expense of QM approaches is offset by improved accuracy in DD applications. Objectively validating the improved applicability and performance of QM over classical-based models in DD will be the focus of research in the coming years along with research on the conformational sampling problem as it relates to protein–ligand complexes.

Authors: Kaushik Raha, Martin B. Peters, Bing Wang, Ning Yu, Andrew M. Wollacott, Lance M. Westerhoff, and Kenneth M. Merz Jr.

Reference: Drug Discovery Today. 2007, 12:17-18, 725-731. (see link for full paper).

Abstract: A critical evaluation of the performance of X-ray refinement protocols using various energy functions is presented using the bovine pancreatic trypsin inhibitor (BPTI) protein. The four potential energy functions we explored include: (1) fully quantum mechanical calculations; (2) one based on an incomplete molecular mechanics (MM) energy function employed in the Crystallography and NMR System (CNS) with empirical parameters developed by Engh and Huber (EH), which lacks electrostatic and attractive van der Waals terms; (3) one based on a complete MM energy function (AMBER ff99 parameter set); and (4) the same as 3, with the addition of a Generalized Born (GB) implicit solvation term. The R, R free, real space R values of the refined structures and deviations from the original experimental structure were used to assess the relative performance. It was found that at 1 Å resolution the physically based energy functions 1, 3, and 4 performed better than energy function 2, which we attribute to the better representation of key interactions, particularly electrostatics. The observed departures from the experimental structure were similar for the refinements with physically based energy functions and were smaller than the structure refined with EH. A test refinement was also performed with the reflections truncated at a high-resolution cutoff of 2.5 Å and with random perturbations introduced into the initial coordinates, which showed that low-resolution refinements with physically based energy functions held the structure closer to the experimental structure solved at 1 Å resolution than the EH-based refinements.

Authors: Ning Yu, Xue Li, Guanglei Cui, Seth A. Hayik, and Kenneth M. Merz, Jr.

Reference: Prot. Sci. 2006, 15, 2773-2784. (see link for full paper).

Abstract: In recent years, a lot of attention has been focused on the electronic properties of DNA. With recent advances in linear scaling quantum mechanics there are now new tools available to enhance our understanding of the electronic properties of DNA among other biomolecules. Using both explicit solvent models and implicit (continuum) solvent models, the electronic characteristics of a dodecamer duplex DNA have been fully studied using both divide and conquer (D&C), semi-empirical quantum mechanics and non-D&C semi-empirical quantum mechanics. According to the AM1 Hamiltonian, 3.5 electrons (0.3 electron/base pair) are transferred from the duplex to the solvent. According to the density of state (DOS) analysis, in vacuo DNA has a band gap of 1 eV showing that in the absence of solvent, the DNA may exhibit similar properties to those of a semiconductor. Upon increasing solvation (2.5–5.5 Å), the band gap ranges from 3 eV to 6 eV. For the implicit solvent model, the band gap continues this widening trend to 7 eV. Therefore, upon solvation and in the absence of dopants, the DNA should begin to loose its conductive properties. Finally, when one considers the energy and localization of the frontier orbitals (HOMO and LUMO), solvent has a stabilizing effect on the DNA system. The energy of the HOMO drops from 15 eV in vacuo to 2 eV for 5.5 Å of water to −8 eV for the implicit solvent model. Similarly, the LUMO drops from 16 eV for in vacuo to 9 eV for 5.5 Å of water to −1 eV for the implicit model. Beyond the importance of the computed results on the materials properties of DNA, the present work also shows that the behavior of intercalators will be affected by the electronic properties of DNA. This could have an impact on our understanding of how DNA based drugs interact with DNA and on the design of new DNA based small molecule drugs.

Authors: Lance M. Westerhoff and Kenneth M. Merz, Jr.

Reference: J. Mol. Graph. Mod. 2006, 24(6), 440-455. (see link for full paper).

Abstract: Recent studies have shown that semiempirical methods (e.g., PM3 and AM1) for zinc-containing compounds are unreliable for modeling structures containing zinc ions with ligand environments similar to those observed in zinc metalloenzymes. To correct these deficiencies a reparameterization of zinc at the PM3 level was undertaken. In this effort we included frequency corrected B3LYP/6-311G* zinc metalloenzyme ligand environments along with previously utilized experimental data. Average errors for the heats of formation have been reduced from 46.9 kcal/mol (PM3) to 14.2 kcal/mol for this new parameter set, termed ZnB for Zinc, Biological. In addition, the new parameter sets predict geometries for the Bacillus fragilis active site model and other zinc metalloenzyme mimics that are qualitatively in agreement with high-level ab initio results, something existing parameter sets failed to do.

Authors: Edward N. Brothers, Dimas Suarez, David W. Deerfield, and Kenneth M. Merz, Jr.

Reference: J. Comp. Chem. 2004, 25(14), 1677-1692. (see link for full paper).

Abstract: Sodium is very important as a counterion in biology. However, when used with the most common semiempirical Hamiltonians, such as AM1 or PM3, sodium is modeled as a point charge that can accept no electron density, called a "sparkle". To better model sodium, we derived two sets of sodium parameters, which treat sodium on the same footing as other atoms parametrized in semiempirical methods. One set is compatible with the AM1 parameter set, while the second is compatible with PM3. These parameters were derived using a modified genetic algorithm with a diverse set of 71 compounds. The average unsigned error for the heats of formation was 10.3 kcal/mol for AM1 and 10.5 kcal/mol for PM3.

Authors: Edward N. Brothers and Kenneth M. Merz, Jr.

Reference: J. Phys. Chem. B. 2002, 106(10), 2779-2785. (see link for full paper).

Abstract: We present a detailed analysis of the performance of the semiempirical divide and conquer method as compared with standard semiempirical MO calculations. The influence of different subsetting schemes involving dual buffer regions on the magnitude of the errors in energies and computational cost of the calculations are discussed. In addition, the results of geometry optimizations on several protein systems (453 to 4088 atoms) driven by a quasi-Newton algorithm are also presented. These results indicate that the divide and conquer approach gives reliable energies and gradients and suggest that protein geometry optimization using semiempirical methods can be routinely feasible using current computational resources.

Authors: Arjan van der Vaart, Dimas Suárez, and Kenneth M. Merz, Jr.

Reference: J. Chem. Phys. 2000, 113(23), 10512-10523. (see link for full paper).

Abstract: A linear-scaling revolution is occurring in quantum chemistry. This development is allowing for the first time the routine examination of large molecular assembles (e.g., proteins and DNA in water) using electronic structure methods. One of these approaches is the divide and conquer method and, in this article, we review the implementation of this approach for semiempirical Hamiltonians. This is then followed by brief reviews of three application areas. First, we will discuss the charge distribution of biological molecules in solution as described by quantum mechanics. In particular, the role polarization and charge transfer plays in affecting the charge distribution of proteins will be discussed. Next, we will examine the energetic consequences of charge transfer and polarization on biomolecular solvation. The final section will describe the computation of solvation free energies using a combined divide and conquer/Poisson-Boltzmann approach. The application of linear scaling quantum mechanical methods to biology is only just beginning, but the future is very bright, and it is our opinion that quantum mechanics will have a profound influence on our understanding of biological systems in the coming years.

Authors: Arjan van der Vaart, Valentin Gogonea, Steven L. Dixon, and Kenneth M. Merz, Jr.

Reference: J. Comp. Chem. 2000, 21(16), 1494-1504. (see link for full paper).

Abstract: In this paper we report a method for solving the Schrödinger equation for large molecules in solution which involved merging a linear scaling divide and conquer (D&C) semiempirical algorithm with the Poisson-Boltzmann (PB) equation. We then assess the performance of our self-consistent reaction field (SCRF) approach by comparing our D&C-PB calculations for a set of 29 neutral and 36 charged molecules with those obtained by ab initio GVB and DFT (B3LYP) methods, Cramer and Truhlar's semiempirical generalized-Born SM5 model, and with the experimental solvation free energies. Furthermore, we show that our SCRF method can be used to perform fully quantum mechanical calculations of proteins in solution in a reasonable amount of time on a modern workstation. We believe that all electrostatic interactions in biological systems require a quantum mechanical description in order to obtain an accurate representation. Thus, our new SCRF method should have an impact on the computational study of physical and chemical phenomena occurring in proteins and nucleic acids, which are, in general, strongly influenced by electrostatic interactions. Moreover, this may lead to novel insights into classic problems like protein folding or drug design.

Authors: Valentin Gogonea and Kenneth M. Merz, Jr.

Reference: J. Phys. Chem. A. 1999, 103(26), 5171-5188. (see link for full paper).

Abstract: A detailed review of the semiempirical divide-and-conquer (D&C) method is given, including a new approach to subsetting, which involves dual buffer regions. Comparisons are drawn between this method and other semiempirical macromolecular schemes. D&C calculations are carried out using a basic 32 Mbyte memory workstation on a variety of peptide systems, including proteins containing up to 1960 atoms. Aspects of storage and SCF convergence are addressed, and parallelization of the D&C algorithm is discussed.

Authors: Steven L. Dixon and Kenneth M. Merz, Jr.

Reference: J. Chem. Phys. 1997, 107(3), 879-893. (see link for full paper).

Abstract: Details are provided for the implementation of a density matrix divide-and-conquer approximation into the framework of molecular orbital theory on nonperiodic systems. Originally developed for density functional theory, the divide-and-conquer procedure is one of the most promising in a growing list of techniques that exhibit linear scaling with respect to the number of basis functions in the system. The key to linear scaling is the division of the electronic structure calculation into a series of calculations over a set of small, overlapping subsystems. A semiempirical molecular orbital program designed around the divide-and-conquer approach has been written and a number of tests are carried out on polyglycine structures in order to evaluate its performance. For the systems examined, linear scaling is indeed observed, and the accuracy of the calculations can be controlled quite readily by the manner in which the system is divided into its component subsystems. For very large structures, the expense associated with the computation of two-center interactions will ultimately dominate the calculation, and quadratic scaling will become apparent. Techniques to linearize this aspect of the calculation are investigated and discussed.

Authors: Steven L. Dixon and Kenneth M. Merz, Jr.

Reference: J. Chem. Phys. 1996, 104(17), 6643-6649. (see link for full paper).