A Simple QM/MM Approach for Capturing Polarization Effects in Protein−Ligand Binding Free Energy Calculations

Beierlein, Frank R.; Michel, Julien; Essex, Jonathan W.

doi:10.1021/jp109054j

Cited by 103 publications

(164 citation statements)

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“…7), which would give a QTCP-like approach. Similar corrections have been used in similar contexts before [68][69][70][71][72][73][74]. Unfortunately, such an approach becomes unstable if the differences between the MM and QM potentials are too large, leading to corrections that depend only in a few of the DFT calculations [90].…”

Section: Fep Results At the Dft-d3 Levelmentioning

confidence: 99%

“…We use two types of approaches to get around this problem and still retain the rigorousness. The first type is an endpoint approach, previously applied in reference-potential methods such as QM/FEP, QTCP (QM/MM thermodynamic cycle perturbation), and paradynamics [68,69,70,71,72,73,74]. Here, a thermodynamic cycle is used to obtain…”

Section: Dft-d Fep Calculationsmentioning

confidence: 99%

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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

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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Section: Fep Results At the Dft-d3 Levelmentioning

confidence: 99%

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

220

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“…Beierlein et al 15 use the difference between the Coulombic contribution to the interaction energy and Fox et al 23 use the full quantum interaction energy where they perform Density Functional Theory (DFT) calculations on the whole ligand-solvent system using the ONETEP linear-scaling DFT program. 24 Interaction energies are defined by:…”

Section: Figure 1: Extended Thermodynamic Cycle For Computing Free Enmentioning

confidence: 99%

A “Stepping Stone” Approach for Obtaining Quantum Free Energies of Hydration

et al. 2015

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We present a method which uses DFT (quantum, QM) calculations to improve free energies of binding computed with classical force fields (classical, MM). To overcome the incomplete overlap of configurational spaces between MM and QM, we use a hybrid Monte Carlo approach to generate quickly correct ensembles of structures of intermediate states between the MM and a QM/MM description, hence taking into account a great fraction of the electronic polarisation of the quantum system, while being able to use thermodynamic integration to compute the free energy of transition between the MM and QM/MM. Then we perform a final transition from QM/MM to full QM using a one step free energy perturbation approach. By using QM/MM as a stepping stone towards the full QM description we find very small convergence errors (< 1 kJ/mol) in the transition to full QM.We apply this method to compute hydration free energies and we obtain consistent improvements over the MM values for all molecules we used in this study. This approach requires large-scale DFT calculations as the full QM systems involved the ligands and all waters in their simulation cells, so the linear-scaling DFT code ONETEP was used for these calculations.

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“…For small ligands, this results in about 400 water molecules described by DFT while for the ASP-SER and LYS-SER complexes this results in about 700 DFT water molecules. In light of this observation, results obtained with previous QM/MM approaches 11,45,50 which treat only the solute by QM and the solvent by MM would need to be re-examined as for example calculations of free energies and other properties using these approaches may be dominated by the variation (noise) that the interaction energies have when zero or a very small number of quantum waters are included. We expect that one of the first applications of our embedding approach will be in schemes for the calculation of free energies of binding of biomolecular assemblies with full inclusion of charge transfer and polarisation effects via large-scale DFT calculations.…”

Section: Discussionmentioning

confidence: 99%

“…Particularly useful in this context is the ability to accurately calculate interaction energies as these can be used to obtain Gibbs free energies of binding which are essential in drug design. A variety of methods are available for this such as the recent approach by Beierlein et al 45 who have demonstrated via a series of careful tests how the free energies obtained via a classical force field can be converted to free energies that would be obtained if a quantum description was used for the ligand and classical force field for the surrounding atoms. The mutation from the classical to the quantum state happens via a one-step free energy perturbation formula (the Zwanzig equation), as follows:…”

Section: A Interaction Energiesmentioning

confidence: 99%

Electrostatic embedding in large-scale first principles quantum mechanical calculations on biomolecules

Fox

Pittock

Fox

et al. 2011

The Journal of Chemical Physics

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Biomolecular simulations with atomistic detail are often required to describe interactions with chemical accuracy for applications such as the calculation of free energies of binding or chemical reactions in enzymes. Force fields are typically used for this task but these rely on extensive parameterisation which in cases can lead to limited accuracy and transferability, for example for ligands with unusual functional groups. These limitations can be overcome with first principles calculations with methods such as density functional theory (DFT) but at a much higher computational cost. The use of electrostatic embedding can significantly reduce this cost by representing a portion of the simulated system in terms of highly localised charge distributions. These classical charge distributions are electrostatically coupled with the quantum system and represent the effect of the environment in which the quantum system is embedded. In this paper we describe and evaluate such an embedding scheme in which the polarisation of the electronic density by the embedding charges occurs self-consistently during the calculation of the density. We have implemented this scheme in a linear-scaling DFT program as our aim is to treat with DFT entire biomolecules (such as proteins) and large portions of the solvent. We test this approach in the calculation of interaction energies of ligands with biomolecules and solvent and investigate under what conditions these can be obtained with the same level of accuracy as when the entire system is described by DFT, for a variety of neutral and charged species.

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A Simple QM/MM Approach for Capturing Polarization Effects in Protein−Ligand Binding Free Energy Calculations

Cited by 103 publications

References 95 publications

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

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

A “Stepping Stone” Approach for Obtaining Quantum Free Energies of Hydration

Electrostatic embedding in large-scale first principles quantum mechanical calculations on biomolecules

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