Combined quantum and molecular mechanics calculations on metalloproteins

The combination of quantum mechanics and molecular mechanics (QM/MM) methods is one of the most promising approaches to study the structure, function and properties of proteins. The number of QM/MM applications on metalloproteins is steadily increasing, especially studies with density functional methods on redox-active metal centres. Recent developments include new parameterised methods to treat covalent bonds between the quantum and classical systems, methods to obtain free energy from QM/MM results, and the combination of quantum chemistry and protein crystallography.     

Polyprotein cleavage mechanism of SARS CoV Mpro and chemical modification of the octapeptide

The cleavage mechanism of severe acute respiratory syndrome (SARS) coronavirus main proteinase (M(pro) or 3CL(pro)) for the octapeptide AVLQSGFR is studied using molecular mechanics (MM) and quantum mechanics (QM). The catalytic dyad His-41 and Cys-145 in the active pocket between domain I and II seem to polarize the pi-electron density of the peptide bond between Gln and Ser in the octapeptide, leading to an increase of positive charge on C(CO) of Gln and negative charge on N(NH) of Ser. The possibility of enhancing the chemical bond between Gln and Ser based on the "distorted key" theory [Anal. Biochem. 233 (1996) 1] is examined. The scissile peptide bond between Gln and Ser is found to be solidified through "hybrid peptide bond" by changing the carbonyl group CO of Gln to CH(2) or CF(2). This leads to a break of the pi-bond system for the peptide bond, making the octapeptide (AVLQSGFR) a "distorted key" and a potential starting system for the design of anti SARS drugs.     

Chromophore Structure of Cyanobacterial Phytochrome Cph1 in the Pr State: Reconciling Structural and Spectroscopic Data by QM/MM Calculations

A quantum mechanics (QM)/molecular mechanics (MM) hybrid method was applied to the Pr state of the cyanobacterial phytochrome Cph1 to calculate the Raman spectra of the bound PCB cofactor. Two QM/MM models were derived from the atomic coordinates of the crystal structure. The models differed in the protonation site of His²⁶⁰ in the chromophore-binding pocket such that either the δ-nitrogen (M-HSD) or the ɛ-nitrogen (M-HSE) carried a hydrogen. The optimized structures of the two models display small differences specifically in the orientation of His²⁶⁰ with respect to the PCB cofactor and the hydrogen bond network at the cofactor-binding site. For both models, the calculated Raman spectra of the cofactor reveal a good overall agreement with the experimental resonance Raman (RR) spectra obtained from Cph1 in the crystalline state and in solution, including Cph1 adducts with isotopically labeled PCB. However, a distinctly better reproduction of important details in the experimental spectra is provided by the M-HSD model, which therefore may represent an improved structure of the cofactor site. Thus, QM/MM calculations of chromoproteins may allow for refining crystal structure models in the chromophore-binding pocket guided by the comparison with experimental RR spectra. Analysis of the calculated and experimental spectra also allowed us to identify and assign the modes that sensitively respond to chromophore-protein interactions. The most pronounced effect was noted for the stretching mode of the methine bridge A-B adjacent to the covalent attachment site of PCB. Due a distinct narrowing of the A-B methine bridge bond angle, this mode undergoes a large frequency upshift as compared with the spectrum obtained by QM calculations for the chromophore in vacuo. This protein-induced distortion of the PCB geometry is the main origin of a previous erroneous interpretation of the RR spectra based on QM calculations of the isolated cofactor.Abbreviations: Agp1, phytochrome from Agrobacterium tumefaciens; α-CPC, α-subunit of C-phycocyanin; BV, biliverdin IXα; B3LYP, three-parameter exchange functional according to Becke, Lee, Yang, and Parr; DFT, density functional theory; DrBphP, phytochrome from Deinococcus radiodurans; GAF, domain found in cGMP-specific phosphodiesterases; MM, molecular mechanics; MD, molecular dynamics; N-H ip, N-H in-plane bending; PCB, phycocyanobilin; PED, potential energy distribution; phyA, plant phytochrome; Pr, Pfr, red- and far-red absorbing parent states of phytochrome; PΦB, phytochromobilin; QM, quantum mechanics; RMSD, root mean-square deviation; RR, resonance Raman     

Modeling reaction routes from rhodopsin to bathorhodopsin

The quantum mechanical–molecular mechanical (QM/MM) theory was applied to calculate accurate structural parameters, vibrational and optical spectra of bathorhodopsin (BATHO), one of the primary photoproducts of the functional cycle of the visual pigment rhodopsin (RHO), and to characterize reaction routes from RHO to BATHO. The recently resolved crystal structure of BATHO (PDBID: 2G87) served as an initial source of coordinates of heavy atoms. Protein structures in the ground electronic state and vibrational frequencies were determined by using the density functional theory in the PBE0/cc‐pVDZ approximation for the QM part and the AMBER force field parameters in the MM part. Calculated and assigned vibrational spectra of both model protein systems, BATHO and RHO, cover three main regions referring to the hydrogen‐out‐of‐plan (HOOP) motion, the C?C ethylenic stretches, and the C? C single‐bond stretches. The S₀–S₁ electronic excitation energies of the QM part, including the chromophore group in the field of the protein matrix, were estimated by using the advanced quantum chemistry methods. The computed structural parameters as well as the spectral bands match perfectly the experimental findings. A structure of the transition state on the S₀ potential energy surface for the ground electronic state rearrangement from RHO to BATHO was located proving a possible route of the thermal protein activation to the primary photoproduct. Proteins 2010. © 2009 Wiley‐Liss, Inc.     

The 'push' effect of the thiolate ligand in cytochrome P450: a theoretical gauging

The 'push' effect of the thiolate ligand in cytochrome P450 is investigated using density functional calculations. Theory supports Dawson's postulate that the 'push' effect is crucial for the heterolytic O-O bond cleavage of ferric-peroxide, as well as for controlling the Fe(III)/Fe(II) redox process and gating the catalytic cycle. Two energetic factors that contribute to the 'push' effect are revealed. The dominant one is the field factor (DeltaE(field)=54-103 kcal/mol) that accounts for the classical electrostatic repulsion with the negative charge of thiolate. The smaller factor is a quantum mechanical effect (DeltaE(QM)(sigma)=39 kcal/mol, DeltaE(QM)(pi)=4 kcal/mol), which is associated with the sigma- and pi-donor capabilities of thiolate. The effects of ligand replacement, changes in hydrogen bonding and dielectric screening are discussed in term of these quantities. In an environment with a dielectric constant of 5.7, the total 'push' effect is reduced to 29-33 kcal/mol. Manifestations of the 'push' effect on other properties of thiolate enzymes are discussed.     

A classical and ab initio study of the interaction of the myosin triphosphate binding domain with ATP.

We used classical molecular mechanics (MM) simulations and quantum mechanical (QM) structural relaxations to examine the active site of myosin when bound to ATP. Two conformations of myosin have been determined by x-ray crystallography. In one, there is no direct interaction between switch 2 and the nucleotide (open state). In the other (closed state), the universally conserved switch 2 glycine forms a hydrogen bond with a gamma-phosphate oxygen. MM simulations indicate that the two states are thermodynamically stable and allow us to investigate the extent to which the P-loop, switch 1, and switch 2 are involved in hydrolysis. We find that the open structure has a higher affinity for ATP than the closed structure, and that ATP is distorted toward a transition state by interactions with the protein. We also examine how the structure of the binding site changes with either MgATP or CaATP as the nucleotide in myosin in the open conformer. Our analyses suggest that higher CaATPase rates occur because the leaving phosphate (P(i)) group is more weakly bound and dissociation occurs faster. Finally, we validate the use of a particular formulation of a QM methodology (Car-Parrinello) to further refine the structures of the active site.     

Harder,better, faster,stronger: Large-scale QM and QM/MM for predictive modeling in enzymes and proteins

Computational prediction of enzyme mechanism and protein function requires accurate physics-based models and suitable sampling. We discuss recent advances in large-scale quantum mechanical (QM) modeling of biochemical systems that have reduced the cost of high-accuracy models. Tradeoffs between sampling and accuracy have motivated modeling with molecular mechanics (MM) in a multiscale QM/MM or iterative approach. Limitations to both conventional density-functional theory and classical MM force fields remain for describing noncovalent interactions in comparison to experiment or wavefunction theory. Because predictions of enzyme action (i.e. electrostatics), free energy barriers, and mechanisms are sensitive to the protocol and embedding method in QM/MM, convergence tests and systematic methods for quantifying QM-level interactions are a needed, active area of development.     

Is there a weak H‐bond → LBHB transition on tetrahedral complex formation in serine proteases?

The transformation of a weak hydrogen bond in the free enzyme into a low-barrier hydrogen bond (LBHB) in the tetrahedral intermediate has been suggested as an important factor facilitating catalysis in serine proteases. In this work, we examine the structure of the H-bond in the Asp102-His57 diad of serine proteases in the free enzyme and in a covalent tetrahedral complex (TC) with a trifluoromethylketone inhibitor. We apply ab initio quantum mechanical calculations to models consisting of a large molecular fragment of the enzyme active site, and the combined effect of the rest of the protein body and the solvation by surrounding bulk water was simulated by a self-consistent reaction field method in our novel QM/SCRF(VS) approach. Potential profiles of adiabatic proton transfer in the Asp102-His57 diad in these model systems were calculated. We conclude that the hydrogen bond in both the free enzyme and in the enzyme-inhibitor TC is a strong ionic asymmetric one-well hydrogen bond, in contrast to a previous suggestion that it is a weak H-bond in the former and a double-well LBHB in the latter.     

Protein Structure Validation and Refinement Using Amide Proton Chemical Shifts Derived from Quantum Mechanics

We present the ProCS method for the rapid and accurate prediction of protein backbone amide proton chemical shifts - sensitive probes of the geometry of key hydrogen bonds that determine protein structure. ProCS is parameterized against quantum mechanical (QM) calculations and reproduces high level QM results obtained for a small protein with an RMSD of 0.25 ppm (r = 0.94). ProCS is interfaced with the PHAISTOS protein simulation program and is used to infer statistical protein ensembles that reflect experimentally measured amide proton chemical shift values. Such chemical shift-based structural refinements, starting from high-resolution X-ray structures of Protein G, ubiquitin, and SMN Tudor Domain, result in average chemical shifts, hydrogen bond geometries, and trans-hydrogen bond (^h3 J_NC'') spin-spin coupling constants that are in excellent agreement with experiment. We show that the structural sensitivity of the QM-based amide proton chemical shift predictions is needed to obtain this agreement. The ProCS method thus offers a powerful new tool for refining the structures of hydrogen bonding networks to high accuracy with many potential applications such as protein flexibility in ligand binding.     

Conformational Dynamics and Cooperativity Drive the Specificity of a Protein-Ligand Interaction

Molecular recognition is critical for the fidelity of signal transduction in biology. Conversely, the disruption of protein-protein interactions can lead to disease. Thus, comprehension of the molecular determinants of specificity is essential for understanding normal biological signaling processes and for the development of precise therapeutics. Although high-resolution structures have provided atomic details of molecular interactions, much less is known about the influence of cooperativity and conformational dynamics. Here, we used the Tiam2 PSD-95/Dlg/ZO-1 (PDZ) domain and a quadruple mutant (QM), engineered by swapping the identity of four residues important for specificity in the Tiam1 PDZ into the Tiam2 PDZ domain, as a model system to investigate the role of cooperativity and dynamics in PDZ ligand specificity. Surprisingly, equilibrium binding experiments found that the ligand specificity of the Tiam2 QM was switched to that of the Tiam1 PDZ. NMR-based studies indicated that Tiam2 QM PDZ, but not other mutants, had extensive microsecond to millisecond motions distributed throughout the entire domain suggesting structural cooperativity between the mutated residues. Thermodynamic analyses revealed energetic cooperativity between residues in distinct specificity subpockets that was dependent upon the identity of the ligand, indicating a context-dependent binding mechanism. Finally, isothermal titration calorimetry experiments showed distinct entropic signatures along the mutational trajectory from the Tiam2 wild-type to the QM PDZ domain. Collectively, our studies provide unique insights into how structure, conformational dynamics, and thermodynamics combine to modulate ligand-binding specificity and have implications for the evolution, regulation, and design of protein-ligand interactions.     

The reaction mechanism of paraoxon hydrolysis by phosphotriesterase from combined QM/MM simulations

Molecular dynamics simulations employing combined quantum mechanical and molecular mechanical (QM/MM) potentials have been carried out to investigate the reaction mechanism of the hydrolysis of paraoxon by phosphotriesterase (PTE). We used a dual-level QM/MM approach that synthesizes accurate results from high-level electronic structure calculations with computational efficiency of semiempirical QM/MM potentials for free energy simulations. In particular, the intrinsic (gas-phase) energies of the active site in the QM region are determined by using density functional theory (B3LYP) and second-order M?ller-Plesset perturbation theory (MP2) and the molecular dynamics free energy simulations are performed by using the mixed AM1:CHARMM potential. The simulation results suggest a revised mechanism for the phosphotriester hydrolysis mechanism by PTE. The reaction free energy profile is mirrored by structural motions of the binuclear metal center in the active site. The two zinc ions occupy a compact conformation with an average zinc-zinc distance of 3.5 +/- 0.1 A in the Michaelis complex, whereas it is elongated to 5.3 +/- 0.3 A at the transition state and product state. The substrate is loosely bound to the more exposed zinc ion (Znbeta2+) at an average distance of 3.8 A +/- 0.3 A. The P=O bond of the substrate paraoxon is activated by adopting a tight coordination to the Znbeta2+, releasing the coordinate to the bridging hydroxide ion and increasing its nucleophilicity. It was also found that a water molecule enters into the binding pocket of the loosely bound binuclear center, originally occupied by the nucleophilic hydroxide ion. We suggest that the proton of this water molecule is taken up by His254 at low pH or released to the solvent at high pH, resulting in a hydroxide ion that pulls the Znbeta2+ ion closer to form the compact configuration and restores the resting state of the enzyme.     

The new physician as unwitting quantum mechanic: is adapting Dirac's inference system best practice for personalized medicine, genomics, and proteomics?

What is the Best Practice for automated inference in Medical Decision Support for personalized medicine? A known system already exists as Dirac's inference system from quantum mechanics (QM) using bra-kets and bras where A and B are states, events, or measurements representing, say, clinical and biomedical rules. Dirac's system should theoretically be the universal best practice for all inference, though QM is notorious as sometimes leading to bizarre conclusions that appear not to be applicable to the macroscopic world of everyday world human experience and medical practice. It is here argued that this apparent difficulty vanishes if QM is assigned one new multiplication function @, which conserves conditionality appropriately, making QM applicable to classical inference including a quantitative form of the predicate calculus. An alternative interpretation with the same consequences is if every i = radical-1 in Dirac's QM is replaced by h, an entity distinct from 1 and i and arguably a hidden root of 1 such that h2 = 1. With that exception, this paper is thus primarily a review of the application of Dirac's system, by application of linear algebra in the complex domain to help manipulate information about associations and ontology in complicated data. Any combined bra-ket can be shown to be composed only of the sum of QM-like bra and ket weights c(), times an exponential function of Fano's mutual information measure I(A; B) about the association between A and B, that is, an association rule from data mining. With the weights and Fano measure re-expressed as expectations on finite data using Riemann's Incomplete (i.e., Generalized) Zeta Functions, actual counts of observations for real world sparse data can be readily utilized. Finally, the paper compares identical character, distinguishability of states events or measurements, correlation, mutual information, and orthogonal character, important issues in data mining and biomedical analytics, as in QM.     

Possible configuration of dimers of Gua-Cyt bases. Computation by molecular mechanic models and density functional theory

The energies of interactions between guanine and cytosine in various mutual positions were calculated by the methods of molecular mechanics with refined atom-atom potential functions and the quantum mechanics theory of density functional. Both methods indicate three types of mutual positions of bases in local energy minima. These types correspond to (1) nearly coplanar base positions with intermolecular hydrogen bond formation (base pairing); (2) arrangements of two bases in nearly parallel planes one above another (base stacking); and (3) nearly perpendicular positions of base planes. According to the calculations, the global energy minimum corresponds to the Watson-Crick base pair with three hydrogen bonds. A specific feature of the pair is a transition from many positions of type (2) to positions of type (1) without any energy barrier. This feature is revealed by both methods. Another special feature of this pair is a deviation, for most of mutual base positions, of the amine group atoms from the ring plane, the deviation being more pronounced for Gua. These features are important for understanding the conformational behavior of DNA fragments and the RNA structure.