Assessment of Semiempirical Quantum Mechanical Methods for the Evaluation of Protein Structures

Structural Predictive Model of Presenilin-2 Protein and Analysis of Structural Effects of Familial Alzheimer's Disease Mutations

Alzheimer's disease manifests itself in brain tissue by neuronal death, due to aggregation of β-amyloid, produced by senile plaques, and hyperphosphorylation of the tau protein, which produces neurofibrillary tangles. One of the genetic markers of the disease is the gene that translates the presenilin-2 protein, which has mutations that favor the appearance of the disease and has no reported crystallographic structure. In view of this, protein modeling is performed using prediction and structural refinement tools followed by an energetic and stereochemical characterization for its validation. For the simulation, four reported mutations are chosen, which are Met239Ile, Met239Val, Ser130Leu, and Thr122Arg, all associated with various functional responses. From a theoretical analysis, a preliminary bioinformatic study is made to find the phosphorylation patterns in the protein and the hydropathic index according to the polarity and chemical environment. Molecular visualization was carried out with the Chimera 1.14 software, and the theoretical calculation with the hybrid quantum mechanics/molecular mechanics system from the semi-empirical method, with Spartan18 software and an AustinModel1 basis. These relationships allow for studying the system from a structural approach with the determination of small distance changes, potential surfaces, electrostatic maps, and angle changes, which favor the comparison between wild-type and mutant systems. With the results obtained, it is expected to complement experimental data reported in the literature from models that would allow us to understand the effects of the selected mutations.

Novel phosphatidylinositol 4-kinases III beta (PI4KIIIβ) inhibitors discovered by virtual screening using free energy models

Herein, the LASSBio Chemical Library is presented as a valuable source of compounds for screening to identify hits suitable for subsequent hit-to-lead optimization stages. A feature of the LASSBio Chemical Library worth highlighting is the fact that it is a smart library designed by medicinal chemists with pharmacological activity as the main priority. The great majority of the compounds part of this library have shown in vivo activity in animal models, which is an indication that they possess overall favorable bioavailability properties and, hence, adequate pharmacokinetic profiles. This, in turn, is supported by the fact that approximately 85% of the compounds are compliant with Lipinski's rule of five and ca. 95% are compliant with Veber's rules, two important guidelines for oral bioavailability. In this work it is presented a virtual screening methodology combining a pharmacophore-based model and an empirical Gibbs free energy-based model for the ligand-protein interaction to explore the LASSBio Chemical Library as a source of new hits for the inhibition of the phosphatidylinositol 4-kinase IIIβ (PI4KIIIβ) enzyme, which is related to the development of viral infections (including enteroviruses, SARS coronavirus, and hepatitis C virus), cancers and neurological diseases. The approach resulted in the identification of two hits, LASSBio-1799 (7) and LASSBio-1814 (10), which inhibited the target enzyme with IC₅₀ values of 3.66 μM and IC₅₀ and 6.09 μM, respectively. This study also enabled the determination of the structural requirements for interactions with the active site of PI4KIIIβ, demonstrating the importance of both acceptor and donor hydrogen bonding groups for forming interactions with binding site residues Val598 and Lys549.

Semiempirical Quantum Mechanical Methods for Noncovalent Interactions for Chemical and Biochemical Applications

Semiempirical (SE) methods can be derived from either Hartree-Fock or density functional theory by applying systematic approximations, leading to efficient computational schemes that are several orders of magnitude faster than ab initio calculations. Such numerical efficiency, in combination with modern computational facilities and linear scaling algorithms, allows application of SE methods to very large molecular systems with extensive conformational sampling. To reliably model the structure, dynamics, and reactivity of biological and other soft matter systems, however, good accuracy for the description of noncovalent interactions is required. In this review, we analyze popular SE approaches in terms of their ability to model noncovalent interactions, especially in the context of describing biomolecules, water solution, and organic materials. We discuss the most significant errors and proposed correction schemes, and we review their performance using standard test sets of molecular systems for quantum chemical methods and several recent applications. The general goal is to highlight both the value and limitations of SE methods and stimulate further developments that allow them to effectively complement ab initio methods in the analysis of complex molecular systems.

Enhanced semiempirical QM methods for biomolecular interactions

Recent successes and failures of the application of 'enhanced' semiempirical QM (SQM) methods are reviewed in the light of the benefits and backdraws of adding dispersion (D) and hydrogen-bond (H) correction terms. We find that the accuracy of SQM-DH methods for non-covalent interactions is very often reported to be comparable to dispersion-corrected density functional theory (DFT-D), while computation times are about three orders of magnitude lower. SQM-DH methods thus open up a possibility to simulate realistically large model systems for problems both in life and materials science with comparably high accuracy.

Recent advances toward a general purpose linear-scaling quantum force field

There is need in the molecular simulation community to develop new quantum mechanical (QM) methods that can be routinely applied to the simulation of large molecular systems in complex, heterogeneous condensed phase environments. Although conventional methods, such as the hybrid quantum mechanical/molecular mechanical (QM/MM) method, are adequate for many problems, there remain other applications that demand a fully quantum mechanical approach. QM methods are generally required in applications that involve changes in electronic structure, such as when chemical bond formation or cleavage occurs, when molecules respond to one another through polarization or charge transfer, or when matter interacts with electromagnetic fields. A full QM treatment, rather than QM/MM, is necessary when these features present themselves over a wide spatial range that, in some cases, may span the entire system. Specific examples include the study of catalytic events that involve delocalized changes in chemical bonds, charge transfer, or extensive polarization of the macromolecular environment; drug discovery applications, where the wide range of nonstandard residues and protonation states are challenging to model with purely empirical MM force fields; and the interpretation of spectroscopic observables. Unfortunately, the enormous computational cost of conventional QM methods limit their practical application to small systems. Linear-scaling electronic structure methods (LSQMs) make possible the calculation of large systems but are still too computationally intensive to be applied with the degree of configurational sampling often required to make meaningful comparison with experiment.

In this work, we present advances in the development of a quantum mechanical force field (QMFF) suitable for application to biological macromolecules and condensed phase simulations. QMFFs leverage the benefits provided by the LSQM and QM/MM approaches to produce a fully QM method that is able to simultaneously achieve very high accuracy and efficiency. The efficiency of the QMFF is made possible by partitioning the system into fragments and self-consistently solving for the fragment-localized molecular orbitals in the presence of the other fragment’s electron densities. Unlike a LSQM, the QMFF introduces empirical parameters that are tuned to obtain very accurate intermolecular forces. The speed and accuracy of our QMFF is demonstrated through a series of examples ranging from small molecule clusters to condensed phase simulation, and applications to drug docking and protein–protein interactions. In these examples, comparisons are made to conventional molecular mechanical models, semiempirical methods, ab initio Hamiltonians, and a hybrid QM/MM method. The comparisons demonstrate the superior accuracy of our QMFF relative to the other models; nonetheless, we stress that the overarching role of QMFFs is not to supplant these established computational methods for problems where their use is appropriate. The role of QMFFs within the toolbox of multiscale modeling methods is to extend the range of applications to include problems that demand a fully quantum mechanical treatment of a large system with extensive configurational sampling.

Parametrization of an Orbital-Based Linear-Scaling Quantum Force Field for Noncovalent Interactions

We parametrize a linear-scaling quantum mechanical force field called mDC for the accurate reproduction of nonbonded interactions. We provide a new benchmark database of accurate ab initio interactions between sulfur-containing molecules. A variety of nonbond databases are used to compare the new mDC method with other semiempirical, molecular mechanical, ab initio, and combined semiempirical quantum mechanical/molecular mechanical methods. It is shown that the molecular mechanical force field significantly and consistently reproduces the benchmark results with greater accuracy than the semiempirical models and our mDC model produces errors twice as small as the molecular mechanical force field. The comparisons between the methods are extended to the docking of drug candidates to the Cyclin-Dependent Kinase 2 protein receptor. We correlate the protein-ligand binding energies to their experimental inhibition constants and find that the mDC produces the best correlation. Condensed phase simulation of mDC water is performed and shown to produce O-O radial distribution functions similar to TIP4P-EW.

QM and QM/MM simulations of proteins

Molecular dynamics simulations of biomolecules have matured into powerful tools of structural biology. In addition to the commonly used empirical force field potentials, quantum mechanical descriptions are gaining popularity for structure optimization and dynamic simulations of peptides and proteins. In this chapter, we introduce methodological developments such as the QM/MM framework and linear-scaling QM that make efficient calculations on large biomolecules possible. We identify the most common scenarios in which quantum descriptions of peptides and proteins are employed, such as structural refinement, force field development, treatment of unusual residues, and predicting spectroscopic and exited state properties. The benefits and shortcomings of QM potentials, in comparison to classical force fields, are discussed, with special emphasis on the sampling problems of protein conformational space. Finally, recent examples of QM/MM calculations in light-sensitive membrane proteins illustrate typical applications of the reviewed methods.

A variational linear-scaling framework to build practical, efficient next-generation orbital-based quantum force fields

We introduce a new hybrid molecular orbital/density-functional modified divide-and-conquer (mDC) approach that allows the linear-scaling calculation of very large quantum systems. The method provides a powerful framework from which linear-scaling force fields for molecular simulations can be developed. The method is variational in the energy, and has simple, analytic gradients and essentially no break-even point with respect to the corresponding full electronic structure calculation. Furthermore, the new approach allows intermolecular forces to be properly balanced such that non-bonded interactions can be treated, in some cases, to much higher accuracy than the full calculation. The approach is illustrated using the second-order self-consistent charge density-functional tight-binding model (DFTB2). Using this model as a base Hamiltonian, the new mDC approach is applied to a series of water systems, where results show that geometries and interaction energies between water molecules are greatly improved relative to full DFTB2. In order to achieve substantial improvement in the accuracy of intermolecular binding energies and hydrogen bonded cluster geometries, it was necessary to extend the DFTB2 model to higher-order atom-centered multipoles for the second-order self-consistent intermolecular electrostatic term. Using generalized, linear-scaling electrostatic methods, timings demonstrate that the method is able to calculate a water system of 3000 atoms in less than half of a second, and systems of up to one million atoms in only a few minutes using a conventional desktop workstation.

GPU Linear Algebra Libraries and GPGPU Programming for Accelerating MOPAC Semiempirical Quantum Chemistry Calculations

In this study, we present some modifications in the semiempirical quantum chemistry MOPAC2009 code that accelerate single-point energy calculations (1SCF) of medium-size (up to 2500 atoms) molecular systems using GPU coprocessors and multithreaded shared-memory CPUs. Our modifications consisted of using a combination of highly optimized linear algebra libraries for both CPU (LAPACK and BLAS from Intel MKL) and GPU (MAGMA and CUBLAS) to hasten time-consuming parts of MOPAC such as the pseudodiagonalization, full diagonalization, and density matrix assembling. We have shown that it is possible to obtain large speedups just by using CPU serial linear algebra libraries in the MOPAC code. As a special case, we show a speedup of up to 14 times for a methanol simulation box containing 2400 atoms and 4800 basis functions, with even greater gains in performance when using multithreaded CPUs (2.1 times in relation to the single-threaded CPU code using linear algebra libraries) and GPUs (3.8 times). This degree of acceleration opens new perspectives for modeling larger structures which appear in inorganic chemistry (such as zeolites and MOFs), biochemistry (such as polysaccharides, small proteins, and DNA fragments), and materials science (such as nanotubes and fullerenes). In addition, we believe that this parallel (GPU-GPU) MOPAC code will make it feasible to use semiempirical methods in lengthy molecular simulations using both hybrid QM/MM and QM/QM potentials.

A reliable docking/scoring scheme based on the semiempirical quantum mechanical PM6-DH2 method accurately covering dispersion and H-bonding: HIV-1 protease with 22 ligands

In this study, we introduce a fast and reliable rescoring scheme for docked complexes based on a semiempirical quantum mechanical PM6-DH2 method. The method utilizes a PM6-based Hamiltonian with corrections for dispersion energy and hydrogen bonds. The total score is constructed as the sum of the PM6-DH2 interaction enthalpy, the empirical force field (AMBER) interaction entropy, and the sum of the deformation (PM6-DH2, SMD) and the desolvation (SMD) energies of the ligand. The main advantage of the procedure is the fact that we do not add any empirical parameter for either an individual component of the total score or an individual protein-ligand complex. This rescoring method is applied to a very challenging system, namely, the HIV-1 protease with a set of ligands. As opposed to the conventional DOCK procedure, the PM6-DH2 rescoring based on all of the terms distinguishes between binders and nonbinders and provides a reliable correlation of the theoretical and experimental binding free energies. Such a dramatic improvement, resulting from the PM6-DH2 rescoring of all the complexes, provides a valuable yet inexpensive tool for rational drug discovery and de novo ligand design.

A Transferable H-Bonding Correction for Semiempirical Quantum-Chemical Methods

Semiempirical methods could offer a feasible compromise between ab initio and empirical approaches for the calculation of large molecules with biological relevance. A key problem for attempts in this direction is the rather bad performance of current semiempirical methods for noncovalent interactions, especially hydrogen-bonding. On the basis of the recently introduced PM6-DH method, which includes empirical corrections for dispersion (D) and hydrogen-bond (H) interactions, we have developed an improved and transferable H-bonding correction for semiempirical quantum chemical methods. The performance of the improved correction is evaluated for PM6, AM1, OM3, and SCC-DFTB (enhanced by standard empirical dispersion corrections) with several test sets for noncovalent interactions and is shown to reach the quality of current DFT-D approaches for these types of problems.

Importance of dispersion and electron correlation in ab initio protein folding

Dispersion is well-known to be important in biological systems, but the effect of electron correlation in such systems remains unclear. In order to assess the relationship between the structure of a protein and its electron correlation energy, we employed both full system Hartree-Fock (HF) and second-order Møller-Plesset perturbation (MP2) calculations in conjunction with the Polarizable Continuum Model (PCM) on the native structures of two proteins and their corresponding computer-generated decoy sets. Because of the expense of the MP2 calculation, we have utilized the fragment molecular orbital method (FMO) in this study. We show that the sum of the Hartree-Fock (HF) energy and force field (LJ6)-derived dispersion energy (HF + LJ6) is well correlated with the energies obtained using second-order Møller-Plesset perturbation (MP2) theory. In one of the two examples studied, the correlation energy as well as the empirical dispersive energy term was able to discriminate between native and decoy structures. On the other hand, for the second protein we studied, neither the correlation energy nor dispersion energy showed discrimination capabilities; however, the ab initio MP2 energy and the HF+LJ6 both ranked the native structure correctly. Furthermore, when we randomly scrambled the Lennard-Jones parameters, the correlation between the MP2 energy and the sum of the HF energy and dispersive energy (HF+LJ6) significantly drops, which indicates that the choice of Lennard-Jones parameters is important.