Ranking Reversible Covalent Drugs: From Free Energy Perturbation to Fragment Docking

Abstract

Reversible covalent inhibitors have drawn increasing attention in drug design, as they are likely more potent than noncovalent inhibitors and less toxic than covalent inhibitors. Despite those advantages, the computational prediction of reversible covalent binding presents a formidable challenge because the binding process consists of multiple steps and quantum mechanics (QM) level calculation is needed to estimate the covalent binding free energy. It has been shown that the dissociation rates and the equilibrium dissociation constants vary significantly even with similar warheads, due to noncovalent interactions. We have previously used a simplistic two-state model for predicting the relative binding selectivity of reversible covalent inhibitors ( J. Am. Chem. Soc. 2017, 139 , 17945 ). Here we go beyond binding selectivity and demonstrate that it is possible to use free energy perturbation (FEP) molecular dynamics (MD) to calculate the overall reversible covalent binding using a specially designed thermodynamic cycle. We show that FEP can predict the varying binding free energies of the analogs sharing a common warhead. More importantly, our results revealed that the chemical modification away from warhead alters the binding affinity at both noncovalent and covalent binding states, and the computational prediction can be improved by considering the binding free energy of both states. Furthermore, we explored the possibility of using a more rapid computational method, site-identification by ligand competitive saturation (SILCS), to rank the same set of reversible covalent inhibitors. We found that the fragment docking to a set of precomputed fragment maps produces a reasonable ranking. In conclusion, two independent approaches provided consistent results that the covalent binding state is suitable for the initial ranking of the reversible covalent drug candidates. For lead-optimization, the FEP approach designed here can provide more rigorous and detailed information regarding how much the covalent and noncovalent binding states are contributing to the overall binding affinity, thus offering a new avenue for fine-tuning the noncovalent interactions for optimizing reversible covalent drugs.

Figure 1. A simplified free energy profile of two-state binding for a reversible covalent binder.

Equation 1 shows the relation between the association constant, 1/Kd, and the total binding free energy ∆Gtot, the binding free energy of the covalent state ∆Gdc and noncovalent state ∆Gdm. Each binding state and the corresponding free energy term are illustrated on the free energy profile.

Figure 2. The thermodynamic cycle of reversible covalent binding.

The cycle illustrates the steps to calculate the ligand binding free energy at noncovalent state $\mathrm{\Delta }{\text{G}}_{\text{dm}}^{\text{L}}$ and covalent state $\mathrm{\Delta }{\text{G}}_{\text{dc}}^{\text{L}}$ using five free energy terms in the figure colored in megenta or blue. The relative free energy terms between a ligand and the reference compound are in blue, which include free energy of transforming R to R’ in solvent $\mathrm{\Delta }{\text{G}}_{\text{solv}}$, in noncovalent state $\mathrm{\Delta }{\text{G}}_{\text{noncov}}$, and in covalent state $\mathrm{\Delta }{\text{G}}_{\mathrm{cov}}$. The absolute binding free energy terms (magenta) are only calculated for a reference compound at noncovalent state, which includes the free energy of decoupling whole reference compound from its environment in solvent $\mathrm{\Delta }{\text{G}}_{\text{solv}}^{\text{ref}}$ and at noncovalent binding state $\mathrm{\Delta }{\text{G}}_{\text{noncov}}^{\text{ref}}$. The same color code is used in Eq. 2, 4, and 5.

Figure 3

(A) The reversible covalent binding scheme of α-ketoamide catalyzed by calpain-1. (B) Binding pose of the reference ligand in calpain-1 catalytic site is shown in noncovalent (left) and covalent state (right). Protein backbone is shown in white. The reference compound is shown in licorice and catalytic Cys115 and His272 are shown in CPK mode in atom color code: cyan carbon, blue nitrogen, red oxygen, and yellow sulfur. All hydrogen atoms are omitted for clarity.

Figure 4

(A) The functional groups of nine ligands are shown in black, and the one for the reference ligand is shown in magenta. The scaffold structure is shown in Figure 3. (B, C, D) Correlation between experimental and calculated noncovalent state binding free energies, covalent state binding free energies, and total binding free energies. All free energy data are in kcal/mol unit. Experimental data were obtained using ΔG(exp) = RT ln(Ki), in which Ki is the inhibitory constants for each compound in human calpain-1 from ref. R is gas constant, and T is room temperature at 300 Kelvin. For each plot, R², Pearson R, and Spearman ρ are reported. The error bars represent the standard deviation reported in Table 1.

Figure 5

SILCS FragMaps and the calpain-1 crystal structure. Apolar (green), H-bond donor (blue) and acceptor (red), negatively charged (yellow) and positively charged (cyan) SILCS FragMaps are shown. All the FragMaps are set to a cutoff of −1.2 kcal/mol. Residue Cys115 of the calpain-1 is shown in CPK mode. All hydrogen atoms are omitted for clarity.

Figure 6

(A) Correlations between experimental relative binding free energy and calculated lowest ΔLGFE values. All free energy data are in kcal/mol unit. Experimental data were obtained same as described before. (B) Correlations between experimental relative binding free energy and calculated average ΔLGFE values based on five independent runs. The error bar of average ΔLGFE was calculated using the minimum LGFE from five independent runs. For each plot, R², Pearson R, and Spearman ρ. The compound5 is excluded in both plots as an outlier.