Binding Affinities of Factor Xa Inhibitors Estimated by Thermodynamic Integration and MM/GBSA

Genheden, Samuel; Nilsson, Ingrid; Ryde, Ulf

doi:10.1021/ci100458f

Cited by 74 publications

(173 citation statements)

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“…First, the MM free energies were based on 13 rather than three  values. Three  values have been shown to be enough in a previous investigation, giving errors of less than 2 kJ/mol [91]. However, this of course depends on the specific transformations.…”

Section: Fep Results At the Dft-d3 Levelmentioning

confidence: 88%

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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Section: Fep Results At the Dft-d3 Levelmentioning

confidence: 88%

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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Section: Introductionmentioning

confidence: 77%

“…Previously, we have analysed how many unphysical intermediate states and how long simulation are needed to obtain accurate results. 8 We showed that for our test case, rather few intermediate states (3 to 5) were enough and the simulation time should be ~1 ns for the protein-ligand simulations and 2 ns for the free ligand simulations.Apart from improvements in the simulation protocol, the system itself can be changed in a way that reduces the computer requirements. One approach that has been used by some research groups for the calculation of protein-ligand affinities is to simulate only a part of the protein, immersed in a droplet of explicit water molecules.…”

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confidence: 77%

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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“…These systems have been used in previous studies of free energy methods. 15,16,17 MD simulations. The MD simulations of the fXa and ferritin complexes were conducted by the Amber10 software 32 and they were taken from previous studies.…”

Section: δG Bind = G(pl) -G(p) -G(l)mentioning

confidence: 99%

“…These systems have been used in previous studies of free energy methods. 15,16,17 Methods Preparation of proteins and ligands. In this paper, we study eight 3-amidinobenzyl-1H-indole-2-carboxamide inhibitors of fXa, 18 nine inhibitors to ferritin, as well as the two inhibitors amprenavir (APV) and darunavir (DRV) binding to either wild-type (WT) or a double mutant (V82T/I84V, MT) HIV-1 protease (HIV-PR).…”

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confidence: 99%

The Normal-Mode Entropy in the MM/GBSA Method: Effect of System Truncation, Buffer Region, and Dielectric Constant

Genheden

Kühn

Mikulskis

et al. 2012

J. Chem. Inf. Model.

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We have performed a systematic study of the entropy term in the MM/GBSA (molecular mechanics combined with generalised Born and surface-area solvation) approach to calculate ligand-binding affinities. The entropies are calculated by a normal-mode analysis of harmonic frequencies from minimised snapshots of molecular dynamics simulations. For computational reasons, these calculations have normally been performed on truncated systems. We have studied the binding of eight inhibitors of blood clotting factor Xa, nine ligands of ferritin, and two ligands of HIV-1 protease and show that removing protein residues with distances larger than 8-16 Å to the ligand and including a 4 Å shell of fixed protein residues and water molecules, change the absolute entropies by 1-5 kJ/mol on average. However, the change is systematic, so relative entropies for different ligands change by only 0.7-1.6 kJ/mol on average. Consequently, entropies from truncated systems give relative binding affinities that are identical to those obtained for the whole protein within statistical uncertainty (1-2 kJ/mol). We have also tested to use a distance-dependent dielectric constant in the minimisation and frequency calculation (ε = 4r), but it typically gives slightly different entropies and poorer binding affinities. Therefore, we recommend entropies calculated with the smallest truncation radius (8 Å) and ε =1. Such an approach also gives an improved precision for the calculated binding free energies.Keywords: MM/GBSA, entropy, ligand-binding affinities, dielectric constant, factor Xa, ferritin, HIV-1 protease.Introduction MM/GBSA is an approximate method to estimate the absolute binding free energy, ΔG bind , of a ligand L, to a biomacromolecule, e.g. a protein, P, forming a complex PL. It estimates ΔG bind as the difference in free energy between PL, P, and L, viz. ΔG bind = G(PL) -G(P) -G(L). Each of these three free energies are estimated from the following sum 1,2 G = E int + E vdW + E ele + G solv + G np − TS MM ( 1) where the brackets indicate an average over snapshots from a molecular dynamics (MD) simulation. The first three terms on the right-hand side are the molecular mechanics (MM) internal (i.e. bonds, angles, and dihedral), van der Waals, and electrostatic energies, G solv and G np are the polar and nonpolar solvation free energies, and the last term is the absolute temperature multiplied by an entropy estimate. The latter estimate is usually taken as a combination of translational, rotational, and vibrational terms. All the terms are calculated on a system where water molecules from the simulation have been stripped off. Moreover, typically only the complex (PL) is simulated and the free energies of P and L are obtained from the same simulation by simply deleting the coordinates of the other species. 3,4 Thereby, the E int term cancels exactly and the precision is improved by a factor of ~5. 5,6 The most common method to estimate the vibrational entropy in the MM/GBSA method is to use frequencies from a normal-mode analysis (NMA...

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Binding Affinities of Factor Xa Inhibitors Estimated by Thermodynamic Integration and MM/GBSA

Cited by 74 publications

References 55 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

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

The Normal-Mode Entropy in the MM/GBSA Method: Effect of System Truncation, Buffer Region, and Dielectric Constant

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