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

Abstract

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 ...

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

“…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].…”

Can MM/GBSA calculations be sped up by system truncation?

“…The ligands are shown in Figure . The preparation of the proteins and the ligands has been described before . Functional ferritin is a multimer of almost 100 protein chains, but following earlier investigations, it was modelled as a dimer (the ligand binds at the interface between two subunits) .…”

“…However, some groups still use truncated systems, in particular for LIE calculations . Recently, we showed that relative binding free energies calculated by FEP did not change by more than 1.4 kJ/mol if the size of the simulated system was reduced from 46 to 15 Å (from 38,844 to 1480 atoms) …”

“…As test cases, we use the binding of nine phenol derivatives to a ferritin dimer, 17 ligands to p38α MAP kinase (p38), and 10 ligands to blood‐clotting factor Xa (fXa) . These systems have been used in several previous computational studies of binding affinities …”

In Silico Exploration for New Antimalarials: Arylsulfonyloxy Acetimidamides as Prospective Agents

“…For these systems free energy simulations 48 would have provided more reliable estimates of protein−ligand binding affinities and energetics of conformational changes. However, we could not implement them as they are computationally expensive and beyond our reach.…”