Design and Quantitative Structure−Activity Relationship of 3-Amidinobenzyl-1<i>H</i>-indole-2-carboxamides as Potent, Nonchiral, and Selective Inhibitors of Blood Coagulation Factor Xa

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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“…The experimental affinities are shown in kJ/mol. 18,19,49 Figure 2. Illustration of the truncation approaches.…”

Section: Discussionmentioning

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.

189

148

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“…Table 1. Relative binding free energies (in kJ/mol) for the eight pairs of fXa inhibitors in Figure 1, calculated in a spherical water droplet including the full protein-ligand complex and compared to experimental data (Exp), 23 as well as to previous calculation in a periodic octahedral box (PBC). 8 Mean absolute deviation compared to calculations using 11 λ values.…”

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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“…77,78 We performed a 5 ns simulation of ligand-free trypsin to investigate the binding-site hydration and found on average seven water molecules in the site. This is similar to what was observed in the TI calculations ( Table 5).…”

Section: -Aminobenzimidazole Binding To Trypsinmentioning

confidence: 99%

Accurate Predictions of Nonpolar Solvation Free Energies Require Explicit Consideration of Binding-Site Hydration

Genheden

Mikulskis

et al. 2011

J. Am. Chem. Soc.

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Continuum-solvation methods are frequently used to increase the efficiency of computational methods to estimate free energies. In this paper, we have evaluated how well such methods estimate the non-polar solvation free-energy change when a ligand binds to a protein. Three different continuum methods at various levels of approximation were considered, viz. the polarised continuum model (PCM), a method based on cavity and dispersion terms (CD), and a method based on a linear relation to the solvent-accessible surface area (SASA). Formally rigorous double-decoupling thermodynamic integration was used as a benchmark for the continuum methods. We have studied four protein-ligand complexes with binding sites of varying solvent exposure, namely the binding of phenol to ferritin, a biotin analogue to avidin, 2-aminobenzimidazole to trypsin, and a substituted galactoside to galectin-3. For ferritin and avidin, which have relatively hidden binding sites, rather accurate non-polar solvation free energies could be obtained with the continuum methods if the binding site is prohibited to be filled by continuum water in the unbound state, even though experiments show that the ligand replaces several water molecules upon binding. For the more solvent exposed binding sites of trypsin and galectin-3, no accurate continuum estimates could be obtained, even if the binding site was allowed or prohibited to be filled by continuum water. This shows that continuum methods fail to give accurate free energies on a wide range of systems with varying solvent exposure, because they lack a microscopic picture of bindingsite hydration as well as information about the entropy of water molecules that are in the binding site before the ligand binds. Consequently, binding-affinity estimates based upon continuum solvation methods will give absolute binding energies that may differ by up to 200 kJ/mol depending on the method used. Moreover, even relative energies between ligands with the same scaffold may differ by up to 75 kJ/mol. We have tried to improve the continuumsolvation methods by adding information about the solvent exposure of the binding site or of the hydration of the binding site and the results are promising at least for this small set of complexes.2

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Design and Quantitative Structure−Activity Relationship of 3-Amidinobenzyl-1H-indole-2-carboxamides as Potent, Nonchiral, and Selective Inhibitors of Blood Coagulation Factor Xa

Cited by 86 publications

References 70 publications

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

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

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

Accurate Predictions of Nonpolar Solvation Free Energies Require Explicit Consideration of Binding-Site Hydration

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