An insight into the general relationship between the three dimensional structures of enzymes and their electronic wave functions: Implication for the prediction of functional sites of enzymes

Exploring the electronic structure of knotted proteins: the case of two ornithine transcarbamylase family

CONTEXT

Geometrical knots are rare structural arrangements in proteins in which the polypeptide chain ties itself into a knot, which is very intriguing due to the uncertainty of their impact on the protein properties. Presently, classical molecular dynamics is the most employed technique in the few studies found on this topic, so any information on how the presence of knots affects the reactivity and electronic properties of proteins is even scarcer. Using the electronic structure methods and quantum chemical descriptors analysis, we found that the same amino-acid residues in the knot core have statistically larger values for the unknotted protein, for both hard-hard and soft-soft interaction descriptors. In addition, we present a computationally feasible protocol, where we show it is possible to separate the contribution of the geometrical knot to the reactivity and other electronic structure properties.

METHODS

In order to investigate these systems, we used PRIMoRDiA, a new software developed by our research group, to explore the electronic structure of biological macromolecules. We evaluated several local quantum chemical descriptors to unveil relevant patterns potentially originating from the presence of the geometrical knot in two proteins, belonging to the ornithine transcarbamylase family. We compared several sampled structures from these two enzymes that are highly similar in both tertiary structure and function, but one of them has a knot whereas the other does not. The sampling was carried out through molecular dynamics simulations using ff14SB force field along 50 ns, and the semiempirical convergence was performed with PM7 Hamiltonian.

Thermochemical and Quantum Descriptor Calculations for Gaining Insight into Ricin Toxin A (RTA) Inhibitors

In this work, we performed a study to assess the interactions between the ricin toxin A (RTA) subunit of ricin and some of its inhibitors using modern semiempirical quantum chemistry and ONIOM quantum mechanics/molecular mechanics (QM/MM) methods. Two approaches were followed (calculation of binding enthalpies, ΔH _bind, and reactivity quantum chemical descriptors) and compared with the respective half-maximal inhibitory concentration (IC₅₀) experimental data, to gain insight into RTA inhibitors and verify which quantum chemical method would better describe RTA-ligand interactions. The geometries for all RTA-ligand complexes were obtained after running classical molecular dynamics simulations in aqueous media. We found that single-point energy calculations of ΔH _bind with the PM6-DH+, PM6-D3H4, and PM7 semiempirical methods and ONIOM QM/MM presented a good correlation with the IC₅₀ data. We also observed, however, that the correlation decreased significantly when we calculated ΔH _bind after full-atom geometry optimization with all semiempirical methods. Based on the results from reactivity descriptors calculations for the cases studied, we noted that both types of interactions, molecular overlap and electrostatic interactions, play significant roles in the overall affinity of these ligands for the RTA binding pocket.

GPU algorithms for density matrix methods on MOPAC: linear scaling electronic structure calculations for large molecular systems

Purification of the density matrix methods should be employed when dealing with complex chemical systems containing many atoms. The running times for these methods scale linearly with the number of atoms if we consider the sparsity from the density matrix. Since the efficiency expected from those methods is closely tied to the underlying parallel implementations of the linear algebra operations (e.g., P² = P × P), we proposed a central processing unit (CPU) and graphics processing unit (GPU) parallel matrix-matrix multiplication in SVBR (symmetrical variable block row) format for energy calculations through the SP2 algorithm. This algorithm was inserted in MOPAC's MOZYME method, using the original LMO Fock matrix assembly, and the atomic integral calculation implemented on it. Correctness and performance tests show that the implemented SP2 is accurate and fast, as the GPU is able to achieve speedups up to 40 times for a water cluster system with 42,312 orbitals running in one NVIDIA K40 GPU card compared to the single-threaded version. The GPU-accelerated SP2 algorithm using the MOZYME LMO framework enables the calculations of semiempirical wavefunction with stricter SCF criteria for localized charged molecular systems, as well as the single-point energies of molecules with more than 100.000 LMO orbitals in less than 1 h. Graphical abstract Parallel CPU and GPU purification algorithms for electronic structure calculations were implemented in MOPAC's MOZYME method. Some matrices in these calculations, e.g., electron density P, are compressed, and the developed linear algebra operations deal with non-zero entries only. We employed the NVIDIA/CUDA platform to develop GPU algorithms, and accelerations up to 40 times for larger systems were achieved.

Theoretical characterization of the shikimate 5-dehydrogenase reaction from Mycobacterium tuberculosis by hybrid QC/MM simulations and quantum chemical descriptors

In this study, we have investigated the enzyme shikimate 5-dehydrogenase from the causative agent of tuberculosis, Mycobacterium tuberculosis. We have employed a mixture of computational techniques, including molecular dynamics, hybrid quantum chemical/molecular mechanical potentials, relaxed surface scans, quantum chemical descriptors and free-energy simulations, to elucidate the enzyme's reaction pathway. Overall, we find a two-step mechanism, with a single transition state, that proceeds by an energetically uphill hydride transfer, followed by an energetically downhill proton transfer. Our mechanism and calculated free energy barrier for the reaction, 64.9 kJ mol^- 1, are in good agreement with those predicted from experiment. An analysis of quantum chemical descriptors along the reaction pathway indicated a possibly important, yet currently unreported, role of the active site threonine residue, Thr65.

Elucidating Enzymatic Catalysis Using Fast Quantum Chemical Descriptors

In general, computational simulations of enzymatic catalysis processes are thermodynamic and structural surveys to complement experimental studies, requiring high level computational methods to match accurate energy values. In the present work, we propose the usage of reactivity descriptors, theoretical quantities calculated from the electronic structure, to characterize enzymatic catalysis outlining its reaction profile using low-level computational methods, such as semiempirical Hamiltonians. We simulate three enzymatic reactions paths, one containing two reaction coordinates and without prior computational study performed, and calculate the reactivity descriptors for all obtained structures. We observed that the active site local hardness does not change substantially, even more so for the amino-acid residues that are said to stabilize the reaction structures. This corroborates with the theory that activation energy lowering is caused by the electrostatic environment of the active sites. Also, for the quantities describing the atom electrophilicity and nucleophilicity, we observed abrupt changes along the reaction coordinates, which also shows the enzyme participation as a reactant in the catalyzed reaction. We expect that such electronic structure analysis allows the expedient proposition and/or prediction of new mechanisms, providing chemical characterization of the enzyme active sites, thus hastening the process of transforming the resolved protein three-dimensional structures in catalytic information.

Docking of Covalent Ligands: Challenges and Approaches

Covalent ligands have recently regained considerable attention in drug discovery. The rational design of such ligands, however, is still faced with particular challenges, mostly related to the fact that covalent bond formation is a quantum mechanical phenomenon which cannot adequately be handled by the force fields or empirical approaches typically used for noncovalent protein-ligand interactions. Although the necessity for quantum chemical approaches is clear, they cannot yet routinely be applied on large data sets of ligands or for a broader exploration of binding modes in docking calculations. On the other hand, technical solutions for performing docking calculations with covalent ligands are available, but their scope is normally quite limited. Scoring functions typically neglect the contribution from covalent bond formation completely. In this situation, the question arises how to approach covalent ligands and which methods to choose for their docking and design.

Charge-patching method for the calculation of electronic structure of polypeptides

Based on the CPM method, the charge densities of polypeptides can be generated and their electronic structure can be further calculated.

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.

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.

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.

The Utility of the HSAB Principle via the Fukui Function in Biological Systems

The hard/soft acid-base principle has long been known to be an excellent predictor of chemical reactivity. The Fukui function, a reactivity descriptor from conceptual density functional theory, has been shown to be related to the local softness of a system. The usefulness of the Fukui function is explored and demonstrated herein for three common biological problems: ligand docking, active site detection, and protein folding. In each type of study, a scoring function is developed based on the local HSAB principle using atomic Fukui indices. Even with necessary approximations for its use in large systems, the Fukui function remains a useful descriptor for predicting chemical reactivity and understanding chemical systems.