Quantum mechanics approaches to drug research in the era of structural chemogenomics

The rapid growth of the available crystallographic information about proteins and binding pockets creates remarkable opportunities for enriching the drug research pipelines with computational prediction of novel protein–ligand interactions. While ab initio quantum mechanical (QM) approaches are known to provide unprecedented accuracy in structure‐based binding energy calculations, they are limited to only small systems of dozens of atoms. In the structural chemogenomics era, it is critical that new approaches are developed that enable application of QM methodologies to noncovalent interactions in systems as large as protein–ligand complexes and conformational ensembles. This perspective highlights recent advances towards bridging the gap between high‐accuracy and high‐volume computations in drug research. © 2013 Wiley Periodicals, Inc.     

Theoretical calculations of physico-chemical and spectroscopic properties of bioinorganic systems: current limits and perspectives

In the last decade, we have witnessed substantial progress in the development of quantum chemical methodologies. Simultaneously, robust solvation models and various combined quantum and molecular mechanical (QM/MM) approaches have become an integral part of quantum chemical programs. Along with the steady growth of computer power and, more importantly, the dramatic increase of the computer performance to price ratio, this has led to a situation where computational chemistry, when exercised with the proper amount of diligence and expertise, reproduces, predicts, and complements the experimental data. In this perspective, we review some of the latest achievements in the field of theoretical (quantum) bioinorganic chemistry, concentrating mostly on accurate calculations of the spectroscopic and physico-chemical properties of open-shell bioinorganic systems by wave-function (ab initio) and DFT methods. In our opinion, the one-to-one mapping between the calculated properties and individual molecular structures represents a major advantage of quantum chemical modelling since this type of information is very difficult to obtain experimentally. Once (and only once) the physico-chemical, thermodynamic and spectroscopic properties of complex bioinorganic systems are quantitatively reproduced by theoretical calculations may we consider the outcome of theoretical modelling, such as reaction profiles and the various decompositions of the calculated parameters into individual spatial or physical contributions, to be reliable. In an ideal situation, agreement between theory and experiment may imply that the practical problem at hand, such as the reaction mechanism of the studied metalloprotein, can be considered as essentially solved.     

Molecular dynamics simulations of proteins and peptides: from folding to drug design

Computer simulations of proteins, lipids and nucleic acids at equilibrium have become essentially routine. However, the fact remains that complete sampling of conformational space continues to be a bottle-neck in the field. The challenge for the future is to overcome such problems and use computational approaches to understand recognition and spontaneous self-organization in biomolecular systems (folding, aggregation and assembly of complexes), processes that cannot be directly observed experimentally. In this review, examples illustrating the extent to which simulations can be used to understand these phenomena in biomolecular systems will be presented along with examples of methodological developments to increase our physical understanding of the processes. The study cases will cover the problems of peptide-receptor recognition and the use of the information obtained for the design of new non-peptidic ligands; the study of the folding mechanism of small proteins and finally the study of the initial stages of peptide self-aggregation.     

Ground-state properties of the retinal molecule: from quantum mechanical to classical mechanical computations of retinal proteins

Retinal proteins are excellent systems for understanding essential physiological processes such as signal transduction and ion pumping. Although the conjugated polyene system of the retinal chromophore is best described with quantum mechanics, simulations of the long-timescale dynamics of a retinal protein in its physiological, flexible, lipid-membrane environment can only be performed at the classical mechanical level. Torsional energy barriers are a critical ingredient of the classical force-field parameters. Here we review briefly current retinal force fields and discuss new quantum mechanical computations to assess how the retinal Schiff base model and the approach used to derive the force-field parameters may influence the torsional potentials.     

NMR spectroscopy of intermetallic compounds: an experimental and theoretical approach to local atomic arrangements in binary gallides

The results of the investigation of MGa(2) with M = Ca, Sr, Ba and of MGa(4) with M = Na, Ca, Sr, Ba by a combined application of NMR spectroscopy and quantum mechanical calculations are comprehensively evaluated. The electric-field gradient (EFG) was identified as the most reliable measure to study intermetallic compounds, since it is accessible with high precision by quantum mechanical calculations and, for nuclear spin I>1/2, by NMR spectroscopy. The EFG values obtained by NMR spectroscopy and quantum mechanical calculations agree very well for both series of investigated compounds. A deconvolution of the calculated EFGs into their contributions reveals its sensitivity to the local environment of the atoms. The EFGs of the investigated di- and tetragallides are dominated by the population of the p(x)-, p(y)-, and p(z)-like states of the Ga atoms. A general combined approach for the investigation of disordered intermetallic compounds by application of diffraction methods, NMR spectroscopy, and quantum mechanical calculations is suggested. This scheme can also be applied to other classes of crystalline disordered inorganic materials.     

New force field for calcium binding sites in annexin-membrane complexes

For accurate classical molecular dynamics (MD) simulations of the calcium mediated bound complexes of annexin and membrane we have developed new force-field parameters correctly describing the interaction of the Ca ion with its environment. We have used quantum chemical calculations to investigate the potential energy surface experienced by the Ca ion within the three different binding sites found in domain 1 of annexin V (ANX V/1). Based on these calculations we were able to quantify the charge polarization of atoms within the binding sites, and to determine the geometry and force constants of harmonic restraints between the Ca ion and its coordinating oxygen atoms. Harmonic restraints were introduced to compensate for the deviations between the quantum mechanical potential energy surface and that of the classical force field. Our analysis has shown that using the refined force field for the Ca binding sites enables long-time MD simulations that conserve the initial structure of ANX V/1 significantly better than MD simulations using the standard force field.     

Quantum entanglement phenomena in photosynthetic light harvesting complexes

We review recent theoretical calculations of quantum entanglement in photosynthetic light harvesting complexes. These works establish, for the first time, a manifestation of this characteristically quantum mechanical phenomenon in biologically functional structures. We begin by summarizing calculations on model biomolecular systems that aim to reveal non-trivial characteristics of quantum entanglement in non-equilibrium biological environments. We then discuss and compare several calculations performed recently of excitonic dynamics in the Fenna-Matthews-Olson light harvesting complex and of the electronic entanglement present in this widely studied pigment-protein structure. We point out the commonalities between the derived results and also identify and explain the differences. We also discuss recent work that examines entanglement in the structurally more intricate light harvesting complex II (LHCII). During this overview, we take the opportunity to clarify several subtle issues relating to entanglement in such biomolecular systems, including the role of entanglement in biological function, the complexity of dynamical modeling that is required to capture the salient features of entanglement in such biomolecular systems, and the relationship between entanglement and other quantum mechanical features that are observed and predicted in light harvesting complexes. Finally, we suggest possible extensions of the current work and also review the options for experimental confirmation of the predicted entanglement phenomena in light harvesting complexes.     

Communication: Quantum polarized fluctuating charge model: a practical method to include ligand polarizability in biomolecular simulations

We present a simple and practical method to include ligand electronic polarization in molecular dynamics (MD) simulation of biomolecular systems. The method involves periodically spawning quantum mechanical (QM) electrostatic potential (ESP) calculations on an extra set of computer processors using molecular coordinate snapshots from a running parallel MD simulation. The QM ESPs are evaluated for the small-molecule ligand in the presence of the electric field induced by the protein, solvent, and ion charges within the MD snapshot. Partial charges on ligand atom centers are fit through the multi-conformer restrained electrostatic potential (RESP) fit method on several successive ESPs. The RESP method was selected since it produces charges consistent with the AMBER/GAFF force-field used in the simulations. The updated charges are introduced back into the running simulation when the next snapshot is saved. The result is a simulation whose ligand partial charges continuously respond in real-time to the short-term mean electrostatic field of the evolving environment without incurring additional wall-clock time. We show that (1) by incorporating the cost of polarization back into the potential energy of the MD simulation, the algorithm conserves energy when run in the microcanonical ensemble and (2) the mean solvation free energies for 15 neutral amino acid side chains calculated with the quantum polarized fluctuating charge method and thermodynamic integration agree better with experiment relative to the Amber fixed charge force-field.     

A multicentered approach to integrated QM/QM calculations. Applications to multiply hydrogen bonded systems

A multicentered integrated QM/QM technique has been developed. By separating high-level calculations in distinct regions of molecules, the multicentered approach supplants a single large high-level calculation with several smaller calculations. Due to the steep polynomial scaling of traditional ab initio quantum chemical methods, this separation significantly enhances the computational efficiency of QM/QM methods. The straightforward implementation of this multicentered approach is illustrated with several large poly-alcohols that form hydrogen bonds with water. The largest alcohol-water complex contains 81 atoms. For properly selected model systems, this multicentered approach introduces essentially no error in the dissociation energies of these complexes relative to conventional QM/QM schemes. This multicentered technique should be easily extended to other, more general integrated methods (QM/MM, ONIOM, etc).     

Ab Initio Calculation of Rate Constants for Molecule–Surface Reactions with Chemical Accuracy

The ab initio prediction of reaction rate constants for systems with hundreds of atoms with an accuracy that is comparable to experiment is a challenge for computational quantum chemistry. We present a divide‐and‐conquer strategy that departs from the potential energy surfaces obtained by standard density functional theory with inclusion of dispersion. The energies of the reactant and transition structures are refined by wavefunction‐type calculations for the reaction site. Thermal effects and entropies are calculated from vibrational partition functions, and the anharmonic frequencies are calculated separately for each vibrational mode. This method is applied to a key reaction of an industrially relevant catalytic process, the methylation of small alkenes over zeolites. The calculated reaction rate constants (free energies), pre‐exponential factors (entropies), and enthalpy barriers show that our computational strategy yields results that agree with experiment within chemical accuracy limits (less than one order of magnitude).     

Integrated computational strategies for UV/vis spectra of large molecules in solution

In recent years, the margin of interaction between computational chemistry and most branches of experimental chemistry has increased at a fast pace. The experimental characterization of new systems relies on computational methods for the rationalization of structural, energetic, electronic and dynamical features. In particular, novel computational approaches allow accurate estimates of molecular parameters from spectroscopic optical observables, giving rise to synergic interactions between experimentalists and theoretically-oriented chemists. Our main objective in this tutorial review is to delineate the degree of advancement of possible integrated computational approaches to the interpretation of optical spectroscopies, with an accent on large molecules in solvated environments, based on the combination of advanced quantum mechanical treatments and stochastic modelling of relaxation processes.     

Quantum chemical methods for the investigation of photoinitiated processes in biological systems: theory and applications.

With the advent of modern computers and advances in the development of efficient quantum chemical computer codes, the meaningful computation of large molecular systems at a quantum mechanical level became feasible. Recent experimental effort to understand photoinitiated processes in biological systems, for instance photosynthesis or vision, at a molecular level also triggered theoretical investigations in this field. In this Minireview, standard quantum chemical methods are presented that are applicable and recently used for the calculation of excited states of photoinitiated processes in biological molecular systems. These methods comprise configuration interaction singles, the complete active space self-consistent field method, and time-dependent density functional theory and its variants. Semiempirical approaches are also covered. Their basic theoretical concepts and mathematical equations are briefly outlined, and their properties and limitations are discussed. Recent successful applications of the methods to photoinitiated processes in biological systems are described and theoretical tools for the analysis of excited states are presented.     

对含重元素体系的接合二分量-标量相对论密度泛函计算方法

在相对论密度泛函ZORA方法的基础上,提出一种用于含重元素体系的接合二分量-标量相对论密度泛函计算方法.对于只含少数几个重元素的较大体系,仅对其中旋轨耦合作用强的重元素作二分量相对论计算,而对体系的其余部分则作标量相对论计算,通过对动能矩阵元的近似处理实现两种计算的接合.对一系列含6p区重元素分子进行计算的结果表明,当非重元素是第三周期以前的元素时,此方法与二分量ZO-RA方法的计算结果吻合得很好.当非重元素为第四周期元素时,计算结果有一定偏差,表明在后一种情况下旋轨耦合作用已比较显著,但误差仍在目前近似密度泛函计算的精度范围内.此方法可以有效地节省计算量,而且避免了Dyall方法的缺点.     

On the use of symmetry in the ab initio quantum mechanical simulation of nanotubes and related materials

Nanotubes can be characterized by a very high point symmetry, comparable or even larger than the one of the most symmetric crystalline systems (cubic, 48 point symmetry operators). For example, N = 2n rototranslation symmetry operators connect the atoms of the (n,0) nanotubes. This symmetry is fully exploited in the CRYSTAL code. As a result, ab initio quantum mechanical large basis set calculations of carbon nanotubes containing more than 150 atoms in the unit cell become very cheap, because the irreducible part of the unit cell reduces to two atoms only. The nanotube symmetry is exploited at three levels in the present implementation. First, for the automatic generation of the nanotube structure (and then of the input file for the SCF calculation) starting from a two‐dimensional structure (in the specific case, graphene). Second, the nanotube symmetry is used for the calculation of the mono‐ and bi‐electronic integrals that enter into the Fock (Kohn‐Sham) matrix definition. Only the irreducible wedge of the Fock matrix is computed, with a saving factor close to N. Finally, the symmetry is exploited for the diagonalization, where each irreducible representation is separately treated. When M atomic orbitals per carbon atom are used, the diagonalization computing time is close to Nt, where t is the time required for the diagonalization of each 2M × 2M matrix. The efficiency and accuracy of the computational scheme is documented. © 2009 Wiley Periodicals, Inc. J Comput Chem, 2010     

Introducing ONETEP: linear-scaling density functional simulations on parallel computers

We present ONETEP (order-N electronic total energy package), a density functional program for parallel computers whose computational cost scales linearly with the number of atoms and the number of processors. ONETEP is based on our reformulation of the plane wave pseudopotential method which exploits the electronic localization that is inherent in systems with a nonvanishing band gap. We summarize the theoretical developments that enable the direct optimization of strictly localized quantities expressed in terms of a delocalized plane wave basis. These same localized quantities lead us to a physical way of dividing the computational effort among many processors to allow calculations to be performed efficiently on parallel supercomputers. We show with examples that ONETEP achieves excellent speedups with increasing numbers of processors and confirm that the time taken by ONETEP as a function of increasing number of atoms for a given number of processors is indeed linear. What distinguishes our approach is that the localization is achieved in a controlled and mathematically consistent manner so that ONETEP obtains the same accuracy as conventional cubic-scaling plane wave approaches and offers fast and stable convergence. We expect that calculations with ONETEP have the potential to provide quantitative theoretical predictions for problems involving thousands of atoms such as those often encountered in nanoscience and biophysics.     

On the mechanical properties of poly(ethylene terephthalate). Force-field parametrization and conformational analysis for the prediction of the crystal moduli

A force-field suitable for the calculation of the mechanical properties of poly(ethylene terephthalate) and their relation with the molecular structure of the polymer has been developed. The force-field parameters were derived from quantum mechanical AM1 calculations and tested against thermodynamic and vibrational spectroscopy data available for a set of closely related small molecules. The crystal moduli of the two solid phases known for poly(ethylene terephthalate) were estimated by means of this new force-field considering both the isolated chain and the chain within the unit cell. Results were qualitatively consistent with reported x-ray data showing that the triclinic crystal form is stiffer than the mesomorphic phase provided that sample heterogeneities were taken into account. Although overestimated moduli resulted for both cases, divergences with experimental values were found to be slighter than those obtained by other theoretical methods. © 1996 John Wiley & Sons, Inc.     

Quantum chemistry simulation on quantum computers: theories and experiments

It has been claimed that quantum computers can mimic quantum systems efficiently in the polynomial scale. Traditionally, those simulations are carried out numerically on classical computers, which are inevitably confronted with the exponential growth of required resources, with the increasing size of quantum systems. Quantum computers avoid this problem, and thus provide a possible solution for large quantum systems. In this paper, we first discuss the ideas of quantum simulation, the background of quantum simulators, their categories, and the development in both theories and experiments. We then present a brief introduction to quantum chemistry evaluated via classical computers followed by typical procedures of quantum simulation towards quantum chemistry. Reviewed are not only theoretical proposals but also proof-of-principle experimental implementations, via a small quantum computer, which include the evaluation of the static molecular eigenenergy and the simulation of chemical reaction dynamics. Although the experimental development is still behind the theory, we give prospects and suggestions for future experiments. We anticipate that in the near future quantum simulation will become a powerful tool for quantum chemistry over classical computations.     

Reaction path potential for complex systems derived from combined ab initio quantum mechanical and molecular mechanical calculations

Combined ab initio quantum mechanical and molecular mechanical calculations have been widely used for modeling chemical reactions in complex systems such as enzymes, with most applications being based on the determination of a minimum energy path connecting the reactant through the transition state to the product in the enzyme environment. However, statistical mechanics sampling and reaction dynamics calculations with a combined ab initio quantum mechanical (QM) and molecular mechanical (MM) potential are still not feasible because of the computational costs associated mainly with the ab initio quantum mechanical calculations for the QM subsystem. To address this issue, a reaction path potential energy surface is developed here for statistical mechanics and dynamics simulation of chemical reactions in enzymes and other complex systems. The reaction path potential follows the ideas from the reaction path Hamiltonian of Miller, Handy and Adams for gas phase chemical reactions but is designed specifically for large systems that are described with combined ab initio quantum mechanical and molecular mechanical methods. The reaction path potential is an analytical energy expression of the combined quantum mechanical and molecular mechanical potential energy along the minimum energy path. An expansion around the minimum energy path is made in both the nuclear and the electronic degrees of freedom for the QM subsystem internal energy, while the energy of the subsystem described with MM remains unchanged from that in the combined quantum mechanical and molecular mechanical expression and the electrostatic interaction between the QM and MM subsystems is described as the interaction of the MM charges with the QM charges. The QM charges are polarizable in response to the changes in both the MM and the QM degrees of freedom through a new response kernel developed in the present work. The input data for constructing the reaction path potential are energies, vibrational frequencies, and electron density response properties of the QM subsystem along the minimum energy path, all of which can be obtained from the combined quantum mechanical and molecular mechanical calculations. Once constructed, it costs much less for its evaluation. Thus, the reaction path potential provides a potential energy surface for rigorous statistical mechanics and reaction dynamics calculations of complex systems. As an example, the method is applied to the statistical mechanical calculations for the potential of mean force of the chemical reaction in triosephosphate isomerase.