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

Kaukonen, Maria; Söderhjelm, Pär; Heimdal, Jimmy; Ryde, Ulf

doi:10.1021/ct700347h

Cited by 41 publications

(119 citation statements)

References 94 publications

(263 reference statements)

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“…We use the same test system as in our previous studies [16,17,22,26,30], viz. a simple proton-transfer reaction in [Ni,Fe] hydrogenase that has been shown to be sensitive to the surroundings.…”

Section: Resultsmentioning

confidence: 99%

“…the QM system D13), both if the calculations are performed in a vacuum or in the COSMO continuum solvent [16]. Likewise, the reaction energy converges if groups are instead added according to their importance in a QM/MM free-energy study [26] after the addition of about ~20 groups (i.e. the QM system E20).…”

Section: Resultsmentioning

confidence: 99%

“…The calculations were started from our previous QM/MM structure of [Ni,Fe] hydrogenase [16,26,30]. It is based on the 1.81-Å crystal structure of the Ser499Ala mutant from Desulfovibrio fructosovorans [31].…”

Section: The Proteinmentioning

confidence: 99%

See 2 more Smart Citations

Effect of Geometry Optimizations on QM-Cluster and QM/MM Studies of Reaction Energies in Proteins

Sumner

Söderhjelm

Ryde

2013

J. Chem. Theory Comput.

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118

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We have examined the effect of geometry optimisation on energies calculated with the quantum-mechanical (QM) cluster, the combined QM and molecular-mechanics (QM/MM), the big-QM approaches (very large single-point QM calculations taken from QM/MMoptimised structures, including all atoms within 4.5 Å of the minimal active site, all buried charged groups in the protein, and truncations moved at least three residues away from the active site). We study a simple proton-transfer reaction between His-79 and Cys-546 in the active site of [Ni,Fe] hydrogenase and optimise QM systems of 50 different sizes (56-362 atoms). Geometries optimised with QM/MM are stable and reliable, whereas QM-cluster optimisations give larger changes in the structures and sometimes lead to large distortions in the active site if some hydrogen-bond partners to the metal ligands are omitted. Keeping 2-3 atoms for each truncated residue (rather than one) fixed in the optimisation improves the results, but does not solve all problems for the QM-cluster optimisations. QM-cluster energies in vacuum and a continuum solvent are insensitive to the geometry optimisations with a mean absolute change upon the optimisations of only 4-7 kJ/mol. This shows that geometry optimisations do not improve the convergence of QM-cluster calculations -there is still a ~60 kJ/mol difference between calculations in which groups have been added to the QM system according to their distance to the active site or based on QM/MM free-energy components. QM/MM energies do not show such a difference, but they converge rather slowly with respect to the size of the QM system, although the convergence is improved by moving away truncations from the active site. The big-QM energies are stable over the 50 different optimised structures, 57±1 kJ/mol, although some smaller trends can be discerned. This shows that both QM-cluster geometries and energies should be interpreted with caution. Instead, we recommend QM/MM for geometry optimisations and energies calculated by the big-QM approach.Key Words: Quantum mechanical cluster calculations, QM/MM, geometry optimisation, density-functional theory, [Ni,Fe] hydrogenase. 2 IntroductionDuring the latest two decades, quantum mechanical (QM) calculations have been established as an important and powerful complement to experiments for the study of biochemical reactions [1,2,3,4,5,6,7,8]. In particular, it has been shown that QM calculations can give structures of active sites with an accuracy that is better than what is obtained in lowand medium-resolution crystal structures [9], and they can provide structures of transition states of putative enzyme reactions, which are hard to study experimentally. The calculations also give energies of the transition states and intermediates, which can be used to compare different putative reaction mechanisms.Two approaches are used for such calculations. In the QM cluster approach, the most important residues of the active site (typically 50-200 atoms) are cut out of the enzyme [1,2,3,4]. The geom...

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Section: Resultsmentioning

confidence: 99%

Section: Resultsmentioning

confidence: 99%

See 1 more Smart Citation

Effect of Geometry Optimizations on QM-Cluster and QM/MM Studies of Reaction Energies in Proteins

Sumner

Söderhjelm

Ryde

2013

J. Chem. Theory Comput.

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118

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“…On the other hand, the results are in good agreement with previous studies showing that only residues within 12-16 Å of the active site of an enzyme need to be considered when studying chemical reactions. 45,46 Third, we have investigated how many intermediate states have to be included in the BAR calculations. We showed that only a single intermediate state (λ = 0.5) needs to be simulated, if average and maximum deviations of 0.5 and 1.4 kJ/mol are acceptable.…”

Section: Discussionmentioning

confidence: 99%

Improving the Efficiency of Protein–Ligand Binding Free-Energy Calculations by System Truncation

Genheden

Ryde

2012

J. Chem. Theory Comput.

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We have studied whether the efficiency of alchemical free-energy calculations with the Bennett acceptance ratio method of protein-ligand binding energies can be improved by simulating only a part of the protein. To this end, we solvated the full protein in a spherical droplet with a radius of 46 Å, surrounded by vacuum. Then, we systematically reduced the size of the droplet and at the same time ignored protein residues that were outside the droplet. Radii of 40 to 15 Å were tested. Ten inhibitors of the blood clotting factor Xa were studied and the results were compared to an earlier study in which the protein was solvated in a periodic box, showing complete agreement between the two set of calculations within statistical uncertainty. We then show that the simulated system can be truncated down to 15 Å, without changing the calculated affinities by more than 0.5 kJ/mol on average (maximum difference 1.4 kJ/mol). Moreover, we show that reducing the number of intermediate states in the calculations from eleven to three gave deviations that on average were only 0.5 kJ/mol (maximum 1.4 kJ/mol). Together this shows that truncation is an appropriate way to improve efficiency of free-energy calculations for small mutations that preserve the net charge of the ligand. In fact, each calculation of a relative binding affinity requires only 6 simulations, each of which takes ~15 CPU hours of computation on a single processor.Keywords: free-energy perturbation, Bennett acceptance ratio, ligand-binding affinities, periodic boundary conditions, system truncation, long-range electrostatics.2 Introduction Accurate estimation of protein-ligand binding affinities is a major challenge in computational chemistry. Although formally correct relative free energies can be obtained by alchemical free-energy techniques such a free energy perturbation (FEP) and thermodynamic integration (TI), they have found little use outside academia. 1,2 The main reason for this is that such methods are computationally demanding, because they require simulations of unphysical intermediate states involving extensive sampling of the phase space. 3 More approximate methods to estimate binding affinities exists, which do not require simulations of intermediate states. 4 They are usually referred to as end-points methods because they sample only the complex, and possibly the free protein and the free ligand. 5 A popular method in this class is MM/GBSA (molecular mechanics with generalised Born and surface-area solvation). 6,7 Although it only requires a simulation of the complex, we have shown that it can actually be computationally more expensive than TI because it is intrinsically imprecise and requires averaging over many independent simulations to reach a precision comparable to that of FEP or TI. 8 In addition, the accuracy of some of the terms in MM/GBSA have been questioned and the method often fails to give a useful accuracy of the predicted affinities. 9,10,11 Another popular end-point method is the linear interaction energy (LIE). 12 We ...

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“…Typical structures are shown in Figure S1. Our previous studies of both ligand binding and enzyme reaction energies have shown that neutral groups (protein residues or water molecules) outside a distance of 4.5-6.0 Å from the ligand or active site have only a very small influence (<1 kJ/mol) on the binding or reaction energy [64,65,66,67].…”

Section: Dft-d Fep Calculationsmentioning

confidence: 99%

Free-energy perturbation and quantum mechanical study of SAMPL4 octa-acid host–guest binding energies

Mikulskis

Cioloboc

Andrejić

et al. 2014

J Comput Aided Mol Des

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220

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Free-energy perturbation and quantum mechanical study of SAMPL4 octa-acid hostguest binding energies. Link to publication Citation for published version (APA): Mikulskis, P., Cioloboc, D., Andrejić, M., Khare, S., Brorsson, J., Genheden, S., ... Ryde, U. (2014). Free-energy perturbation and quantum mechanical study of SAMPL4 octa-acid host-guest binding energies. Journal of Computer-Aided Molecular Design, 28(4), 375-400. DOI: 10.1007/s10822-014-9739-x General rights Copyright and moral rights for the publications made accessible in the public portal are retained by the authors and/or other copyright owners and it is a condition of accessing publications that users recognise and abide by the legal requirements associated with these rights.• Users may download and print one copy of any publication from the public portal for the purpose of private study or research.• You may not further distribute the material or use it for any profit-making activity or commercial gain • You may freely distribute the URL identifying the publication in the public portal AbstractWe have estimated free energies for the binding of nine cyclic carboxylate guest molecules to the octa-acid host in the SAMPL4 blind-test challenge with four different approaches. First, we used standard free-energy perturbation calculations of relative binding affinities, performed at the molecular-mechanics (MM) level with TIP3P waters, the GAFF force field, and two different sets of charges for the host and the guest, obtained either with the restrained electrostatic potential or AM1-BCC methods. Both charge sets give good and nearly identical results, with a mean absolute deviation (MAD) of 4 kJ/mol and a correlation coefficient (R 2 ) of 0.8 compared to experimental results. Second, we tried to improve these predictions with 28 800 density-functional theory (DFT) calculations for selected snapshots and the non-Boltzmann Bennett acceptance-ratio method, but this led to much worse results, probably because of a too large difference between the MM and DFT potential-energy functions. Third, we tried to calculate absolute affinities using minimised DFT structures. This gave intermediate-quality results with MADs of 5-9 kJ/mol and R 2 = 0.6-0.8, depending on how the structures were obtained. Finally, we tried to improve these results using local coupled-cluster calculations with single and double excitations, and non-iterative perturbative treatment of triple excitations (LCCSD(T0)), employing the polarisable multipole interactions with supermolecular pairs approach. Unfortunately, this only degraded the predictions, probably because a mismatch between the solvation energies obtained at the DFT and LCCSD(T0) levels.Key Words: binding affinities, host-guest, free-energies perturbation, density-functional calculations, CCSD(T), polarisable multipole interactions. 2 IntroductionOne of the largest challenges of computational chemistry is to predict the binding affinity of a small ligand to a larger receptor molecule, e.g. a drug candidate to its receptor prot...

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

Cited by 41 publications

References 94 publications

Effect of Geometry Optimizations on QM-Cluster and QM/MM Studies of Reaction Energies in Proteins

Effect of Geometry Optimizations on QM-Cluster and QM/MM Studies of Reaction Energies in Proteins

Improving the Efficiency of Protein–Ligand Binding Free-Energy Calculations by System Truncation

Free-energy perturbation and quantum mechanical study of SAMPL4 octa-acid host–guest binding energies

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