Jimmy Heimdal

Do quantum mechanical energies calculated for small models of protein-active sites converge?

A common approach for the computational modeling of enzyme reactions is to study a rather small model of the active site (20-200 atoms) with quantum mechanical (QM) methods, modeling the rest of the surroundings by a featureless continuum with a dielectric constant of approximately 4. In this paper, we discuss how the residues included in the QM model should be selected and how many residues need to be included before reaction energies converge. As a test case, we use a proton-transfer reaction between a first-sphere cysteine ligand and a second-sphere histidine group in the active site of [Ni,Fe] hydrogenase. We show that it is not a good approach to add groups according to their distance to the active site. A better approach is to add groups according to their contributions to the QM/MM energy difference. However, the energies can still vary by up to 50 kJ/mol for QM systems of sizes up to 230 atoms. In fact, the QM-only approach is based on the hope that a large number of sizable contributions will cancel. Interactions with neutral groups are, in general, short-ranged, with net energy contributions of less than 4 kJ/mol at distances above 5 A from the active site. Interactions with charged groups are much more long-ranged, and interactions with buried charges 20 A from the active site can still contribute by 5 kJ/mol to the reaction energy. Thus, to accurately model the influence of the surroundings on enzyme reaction energies, a detailed and unbiased atomistic account of the surroundings needs to be included.

Convergence of QM/MM free-energy perturbations based on molecular-mechanics or semiempirical simulations

Lately, there has been great interest in performing free-energy perturbation (FEP) at the combined quantum mechanics and molecular mechanics (QM/MM) level, e.g. for enzyme reactions. Such calculations require extensive sampling of phase space, which typically is prohibitive with density-functional theory or ab initio methods. Therefore, such calculations have mostly been performed with semiempirical QM (SQM) methods, or by using a thermodynamic cycle involving sampling at the MM level and perturbations between the MM and QM/MM levels of theory. However, the latter perturbations typically have convergence problems, unless the QM system is kept fixed during the simulations, because the MM and QM/MM descriptions of the internal degrees of freedom inside the QM system are too dissimilar. We have studied whether the convergence of the MM → QM/MM perturbation can be improved by using a thoroughly parameterised force field or by using SQM/MM methods. As a test case we use the first half-reaction of haloalkane dehalogenase and the QM calculations are performed with the PBE, B3LYP, and TPSSH density-functional methods. We show that the convergence can be improved with a tailored force field, but only locally around the parameterised state. Simulations based on SQM/MM methods using the MNDO, AM1, PM3, RM1, PDDG-MNDO, and PDDG-PM3 Hamiltonians have slightly better convergence properties, but very long simulations are still needed (~10 ns) and convergence is obtained only if electrostatic interactions between the QM system and the surroundings are ignored. This casts some doubts on the common practice to base QM/MM FEPs on semiempirical simulations without any reweighting of the trajectories.

QM/MM-PBSA method to estimate free energies for reactions in proteins

We have developed a method to estimate free energies of reactions in proteins, called QM/MM-PBSA. It estimates the internal energy of the reactive site by quantum mechanical (QM) calculations, whereas bonded, electrostatic, and van der Waals interactions with the surrounding protein are calculated at the molecular mechanics (MM) level. The electrostatic part of the solvation energy of the reactant and the product is estimated by solving the Poisson-Boltzmann (PB) equation, and the nonpolar part of the solvation energy is estimated from the change in solvent-accessible surface area (SA). Finally, the change in entropy is estimated from the vibrational frequencies. We test this method for five proton-transfer reactions in the active sites of [Ni,Fe] hydrogenase and copper nitrite reductase. We show that QM/MM-PBSA reproduces the results of a strict QM/MM free-energy perturbation method with a mean absolute deviation (MAD) of 8-10 kJ/mol if snapshots from molecular dynamics simulations are used and 4-14 kJ/mol if a single QM/MM structure is used. This is appreciably better than the original QM/MM results or if the QM energies are supplemented with a point-charge model, a self-consistent reaction field, or a PB model of the protein and the solvent, which give MADs of 22-36 kJ/mol for the same test set.

Reorganization Energy for Internal Electron Transfer in Multicopper Oxidases

We have calculated the reorganization energy for the intramolecular electron transfer between the reduced type 1 copper site and the peroxy intermediate of the trinuclear cluster in the multicopper oxidase CueO. The calculations are performed at the combined quantum mechanics and molecular mechanics (QM/MM) level, based on molecular dynamics simulations with tailored potentials for the two copper sites. We obtain a reorganization energy of 91-133 kJ/mol, depending on the theoretical treatment. The two Cu sites contribute by 12 and 22 kJ/mol to this energy, whereas the solvent contribution is 34 kJ/mol. The rest comes from the protein, involving small contributions from many residues. We have also estimated the energy difference between the two electron-transfer states and show that the reduction of the peroxy intermediate is exergonic by 43-87 kJ/mol, depending on the theoretical method. Both the solvent and the protein contribute to this energy difference, especially charged residues close to the two Cu sites. We compare these estimates with energies obtained from QM/MM optimizations and QM calculations in a vacuum and discuss differences between the results obtained at various levels of theory.

Proton Transfer at Metal Sites in Proteins Studied by Quantum Mechanical Free-Energy Perturbations.

Catalytic metal sites in enzymes frequently have second-sphere carboxylate groups that neutralize the charge of the site and share protons with first-sphere ligands. This gives rise to an ambiguity concerning the position of this proton, which has turned out to be hard to settle with experimental, as well as theoretical, methods. We study three such proton-transfer reactions in two proteins and show that, in [Ni,Fe] hydrogenase, the bridging Cys-546 ligand is deprotonated by His-79, whereas in oxidized copper nitrite reductase, the His-100 ligand is neutral and the copper-bound water molecule is deprotonated by Asp-98. We show that these reactions strongly depend on the electrostatic interactions with the surrounding protein and solvent, because there is a large change in the dipole moment of the active site (2-6 D). Neither vacuum quantum mechanical (QM) calculations with large models, a continuum solvent, or a Poisson-Boltzmann treatment of the surroundings, nor combined QM and molecular mechanics (QM/MM) optimizations give reliable estimates of the proton-transfer energies (mean absolute deviations of over 20 kJ/mol). Instead, QM/MM free-energy perturbations are needed to obtain reliable estimates of the reaction energies. These calculations also indicate what interactions and residues are important for the energy, showing how the quantum system may be systematically enlarged. With such a procedure, results with an uncertainty of ∼10 kJ/mol can be obtained, provided that a proper QM method is used.

Reduction potentials and acidity constants of Mn superoxide dismutase calculated by QM/MM free-energy methods.

We used two theoretical methods to estimate reduction potentials and acidity constants in Mn superoxide dismutase (MnSOD), namely combined quantum mechanical and molecular mechanics (QM/MM) thermodynamic cycle perturbation (QTCP) and the QM/MM-PBSA approach. In the latter, QM/MM energies are combined with continuum solvation energies calculated by solving the Poisson-Boltzmann equation (PB) or by the generalised Born approach (GB) and non-polar solvation energies calculated from the solvent-exposed surface area. We show that using the QTCP method, we can obtain accurate and precise estimates of the proton-coupled reduction potential for MnSOD, 0.30±0.01 V, which compares favourably with experimental estimates of 0.26-0.40 V. However, the calculated potentials depend strongly on the DFT functional used: The B3LYP functional gives 0.6 V more positive potentials than the PBE functional. The QM/MM-PBSA approach leads to somewhat too high reduction potentials for the coupled reaction and the results depend on the solvation model used. For reactions involving a change in the net charge of the metal site, the corresponding results differ by up to 1.3 V or 24 pK(a) units, rendering the QM/MM-PBSA method useless to determine absolute potentials. However, it may still be useful to estimate relative shifts, although the QTCP method is expected to be more accurate.

The role of axial ligands for the structure and function of chlorophylls

We have studied the effect of axial ligation of chlorophyll and bacteriochlorophyll using density functional calculations. Eleven different axial ligands have been considered, including models of histidine, aspartate/glutamate, asparagine/glutamine, serine, tyrosine, methionine, water, the protein backbone, and phosphate. The native chlorophylls, as well as their cation and anion radical states and models of the reaction centres P680 and P700, have been studied and we have compared the geometries, binding energies, reduction potentials, and absorption spectra. Our results clearly show that the chlorophylls strongly prefer to be five-coordinate, in accordance with available crystal structures. The axial ligands decrease the reduction potentials, so they cannot explain the high potential of P680. They also redshift the Q band, but not enough to explain the occurrence of red chlorophylls. However, there is some relation between the axial ligands and their location in the various photosynthetic proteins. In particular, the intrinsic reduction potential of the second molecule in the electron transfer path is always lower than that of the third one, a feature that may prevent back-transfer of the electron.

The effect of hydrogen bonding on torsional dynamics: A combined far-infrared jet and matrix isolation study of methanol dimer

The effect of strong intermolecular hydrogen bonding on torsional degrees of freedom is investigated by far-infrared absorption spectroscopy for different methanol dimer isotopologues isolated in supersonic jet expansions or embedded in inert neon matrices at low temperatures. For the vacuum-isolated and Ne-embedded methanol dimer, the hydrogen bond OH librational mode of the donor subunit is finally observed at ~560 cm(-1), blue-shifted by more than 300 cm(-1) relative to the OH torsional fundamental of the free methanol monomer. The OH torsional mode of the acceptor embedded in neon is observed at ~286 cm(-1). The experimental findings are held against harmonic predictions from local coupled-cluster methods with single and double excitations and a perturbative treatment of triple excitations [LCCSD(T)] and anharmonic. VPT2 corrections at canonical MP2 and density functional theory (DFT) levels in order to quantify the contribution of vibrational anharmonicity for this important class of intermolecular hydrogen bond vibrational motion.

Interpreting melanin-based coloration through deep time: a critical review.

Colour, derived primarily from melanin and/or carotenoid pigments, is integral to many aspects of behaviour in living vertebrates, including social signalling, sexual display and crypsis. Thus, identifying biochromes in extinct animals can shed light on the acquisition and evolution of these biological traits. Both eumelanin and melanin-containing cellular organelles (melanosomes) are preserved in fossils, but recognizing traces of ancient melanin-based coloration is fraught with interpretative ambiguity, especially when observations are based on morphological evidence alone. Assigning microbodies (or, more often reported, their ‘mouldic impressions’) as melanosome traces without adequately excluding a bacterial origin is also problematic because microbes are pervasive and intimately involved in organismal degradation. Additionally, some forms synthesize melanin. In this review, we survey both vertebrate and microbial melanization, and explore the conflicts influencing assessment of microbodies preserved in association with ancient animal soft tissues. We discuss the types of data used to interpret fossil melanosomes and evaluate whether these are sufficient for definitive diagnosis. Finally, we outline an integrated morphological and geochemical approach for detecting endogenous pigment remains and associated microstructures in multimillion-year-old fossils.

Protonation of the Proximal Histidine Ligand in Heme Peroxidases

The heme peroxidases have a histidine group as the axial ligand of iron. This ligand forms a hydrogen bond to an aspartate carboxylate group by the other nitrogen atom in the side chain. The aspartate is not present in the globins and it has been suggested that it gives an imidazolate character to the histidine ligand. Quantum chemical calculations have indicated that the properties of the heme site strongly depend on the position of the proton in this hydrogen bond. Therefore, we have studied the location of this proton in all intermediates in the reaction mechanism, using a set of different quantum mechanical and combined experimental and computational methods. Quantum refinements of a crystal structure of the resting FeIII state in yeast cytochrome c peroxidase show that the geometric differences of the two states are so small that it cannot be unambiguously decided where the proton is in the crystal structure. Vacuum calculations indicate that the position of the proton is sensitive to the surroundings and to the side chains of the porphyrin ring. Combined quantum and molecular mechanics (QM/MM) calculations indicate that the proton prefers to reside on the His ligand in all states in the reaction mechanism of the peroxidases. QM/MM free energy perturbations confirm these results, but reduce the energy difference between the two states to 12-44 kJ/mol.