Absolute binding free energy calculations: on the accuracy of computational scoring of protein-ligand interactions

Abstract

Calculating the absolute binding free energies is a challenging task. Reliable estimates of binding free energies should provide a guide for rational drug design. It should also provide us with deeper understanding of the correlation between protein structure and its function. Further applications may include identifying novel molecular scaffolds and optimizing lead compounds in computer-aided drug design. Available options to evaluate the absolute binding free energies range from the rigorous but expensive free energy perturbation to the microscopic linear response approximation (LRA/beta version) and related approaches including the linear interaction energy (LIE) to the more approximated and considerably faster scaled protein dipoles Langevin dipoles (PDLD/S-LRA version) as well as the less rigorous molecular mechanics Poisson-Boltzmann/surface area (MM/PBSA) and generalized born/surface area (MM/GBSA) to the less accurate scoring functions. There is a need for an assessment of the performance of different approaches in terms of computer time and reliability. We present a comparative study of the LRA/beta, the LIE, the PDLD/S-LRA/beta, and the more widely used MM/PBSA and assess their abilities to estimate the absolute binding energies. The LRA and LIE methods perform reasonably well but require specialized parameterization for the nonelectrostatic term. The PDLD/S-LRA/beta performs effectively without the need of reparameterization. Our assessment of the MM/PBSA is less optimistic. This approach appears to provide erroneous estimates of the absolute binding energies because of its incorrect entropies and the problematic treatment of electrostatic energies. Overall, the PDLD/S-LRA/beta appears to offer an appealing option for the final stages of massive screening approaches.

Figure 1

The thermodynamics cycle that describes the binding of a ligand to a protein. ℓ and ℓ′ represents the charged and uncharged forms of the ligand, respectively, while ℓ″ represents the ligand being reduced to “nothing”. For more details on this cycle, see ref.

Figure 2

Illustrating the construction of the explicit SCAAS simulation system on the crystal structure (PDB ID:1K1L) of bovine trypsin (flat ribbon) in complex with the cocrystallized inhibitor (stick) is solvated in water molecules (ball and stick) representing the model system used in the study. In PDLD/S-LRA/β, Region I is the ‘inhibitor’ or the group whose electrostatic energy is of interest, region II includes all protein residues within 18Å cutoff radius from the center of region I. Region III includes explicit water molecules in and around regions I and II and is completed by a 2Å surface which is subjected to polarization and radial constraints. This is surrounded by bulk solvent (region IV) with a high dielectric constant (ε =80). The electrostatic effects of regions I, II and III are treated explicitly while those of region IV are treated by a macroscopic continuum formulation.

Figure 3

Structural formulae for the ligands used in this study. All structural formulae were drawn using ChemDraw Ultra 11.0.

Figure 4

Correlating the calculated and the experimentally observed absolute binding free energies obtained by the PDLD/S-LRA/β, the LRA/β and the LIE methods using default values i.e. same β (graphs a, c and d) and fitted values i.e. variable β (graphs b, d, and e). Note that in PDLD/S-LRA/β approach, we used ε _p = 20 for the charged ligands.

Figure 5

The observed binding mode for compound 18 (TBO) and its analogs, 19-22 (the structures of which were obtained by docking studies) within the active site of HIV-1 RT. Different structures have been color coded: 18 blue; 19 purple; 20 lavender; 21 cyan; and 22 orange. Hydrogen atoms are not shown for clarity purposes.

Figure 6

(a) A comparison of the experimental absolute binding free energies for compounds 16-22 to those obtained by MM/PBSA and the corresponding values calculated by PDLD/S-LRA/β approach (also see Table 3). (b) Illustrating the fact that the MM/PBSA appears to provide reasonable results for some molecules only because of the major overestimate of the entropic effect by comparing the absolute binding free energy calculated by MM/PBSA reported in the literature, to the absolute binding free energies calculated by replacing the MM/PBSA entropy with the entropy calculated by the RR method for compounds (16-22). The experimentally determined absolute binding free energies are also provided.