Protocols Utilizing Constant pH Molecular Dynamics to Compute pH-Dependent Binding Free Energies

Abstract

In protein–ligand binding, the electrostatic environments of the two binding partners may vary significantly in bound and unbound states, which may lead to protonation changes upon binding. In cases where ligand binding results in a net uptake or release of protons, the free energy of binding is pH-dependent. Nevertheless, conventional free energy calculations and molecular docking protocols typically do not rigorously account for changes in protonation that may occur upon ligand binding. To address these shortcomings, we present a simple methodology based on Wyman’s binding polynomial formalism to account for the pH dependence of binding free energies and demonstrate its use on cucurbit[7]uril (CB[7]) host–guest systems. Using constant pH molecular dynamics and a reference binding free energy that is taken either from experiment or from thermodynamic integration computations, the pH-dependent binding free energy is determined. This computational protocol accurately captures the large pKa shifts observed experimentally upon CB[7]:guest association and reproduces experimental binding free energies at different levels of pH. We show that incorrect assignment of fixed protonation states in free energy computations can give errors of >2 kcal/mol in these host–guest systems. Use of the methods presented here avoids such errors, thus suggesting their utility in computing proton-linked binding free energies for protein–ligand complexes.

Computational scheme for pH‐dependent binding free energy calculation with explicit solvent

“…The high sensitivity of the result to the specific choice of partial charges, suggests that, for this method to become truly useful, a serious look at the choice of charge model and associate charge parameters should be warranted. 57 Specific deviations from experimental values seen here are likely due to the use of over-polarized partial charges of the host and the guest. A more accurate charge partial charge assignment scheme may be sufficient to reproduce experimental values, but it is more likely that a more advanced electrostatic model that includes polarization and higher multipole moments may be needed before this method can provide results that are reliably consistent with experiment.…”

“…To assess the effect of partial charges on the pK a calculation, we performed constant-pH simulations with the RESP partial charges 56 that were used in a previous study by Kim et al 57 Through a similar procedure, the constant-pH simulation of the complex with the RESP partial charges were performed with 6 pH values ranging from 1.5 to 7.5 with an interval of 1.0 pH unit. The simulations of the free BZ molecule were performed at pH 5 3.5, 4.5, 5.5, 6.5, and 7.5.…”

“…Generally, a penalty score from ParamChem higher than 50 indicates that an extensive validation and optimization of the partial charges are necessary. 48,49 In the study of Kim et al, 57 they presented a computational scheme to consider the pH effect in binding free energy calculation with the generalized Born (GB) implicit solvent model. 64 Interestingly, the calculated pK a value of the CB [7]:BZ complex using the RESP charge and explicit TIP3P water is 4.14, meaning that the pK a value is shifted in the opposite direction of the experimental result.…”

Computation of pH‐dependent binding free energies

“…and are obtained from the CpHMD simulations while ΔG° ref can be taken either from experiment or from TI computations, where the latter provides a full computational prediction of the pH dependence of binding processes. When applied to binding of small molecules to the cucurbit[7]uril (CB[7]) host, this CpHMD‐based free energy method accurately obtained the pH‐dependent binding free energy profiles (Figure ) . For instance, in Figure , the binding free energy profiles of CB[7] binding to benzimidazole and fuberidazole are shown, computed with the Δ G ° ref obtained from the TI computation, i.e ., Δ G ° TI .…”

“…For instance, in Figure , the binding free energy profiles of CB[7] binding to benzimidazole and fuberidazole are shown, computed with the Δ G ° ref obtained from the TI computation, i.e ., Δ G ° TI . While the CpHMD/TI computation of pH‐dependent binding free energies is prone to greater error than the use of Δ G ° ref from experiment (Δ G ° exp ), the authors found that the errors in assigning incorrect protonation states in free energy computations without correcting for the pH dependence of the binding free energy can give errors in excess of the errors from the typical free energy computations . The method has been further applied to several inhibitor‐bound structures of BACE‐1 in order to capture the pH dependence of protein–ligand systems and highlighted the significance of correctly accounting for the binding‐induced protonation changes in free energy computations …”