Linear Discriminant Analysis for the <i>in Silico</i> Discovery of Mechanism-Based Reversible Covalent Inhibitors of a Serine Protease: Application of Hydration Thermodynamics Analysis and Semi-empirical Molecular Orbital Calculation

Abstract

We recently reported that the Gibbs free energy of hydrolytic water molecules (ΔG) in acyl-trypsin intermediates calculated by hydration thermodynamics analysis could be a useful metric for estimating the catalytic rate constants (k) of mechanism-based reversible covalent inhibitors. For thorough evaluation, the proposed method was tested with an increased number of covalent ligands that have no corresponding crystal structures. After modeling acyl-trypsin intermediate structures using flexible molecular superposition, ΔG values were calculated according to the proposed method. The orbital energies of antibonding π* molecular orbitals (MOs) of carbonyl C=O in covalently modified catalytic serine (E) were also calculated by semi-empirical MO calculations. Then, linear discriminant analysis (LDA) was performed to build a model that can discriminate covalent inhibitor candidates from substrate-like ligands using ΔG and E. The model was built using a training set (10 compounds) and then validated by a test set (4 compounds). As a result, the training set and test set ligands were perfectly discriminated by the model. Hydrolysis was slower when (1) the hydrolytic water molecule has lower ΔG; (2) the covalent ligand presents higher E (higher reaction barrier). Results also showed that the entropic term of hydrolytic water molecule (-TΔS) could be used for estimating k and for covalent inhibitor optimization; when the rotational freedom of the hydrolytic water molecule is limited, the chance for favorable interaction with the electrophilic acyl group would also be limited. The method proposed in this study would be useful for screening and optimizing the mechanism-based reversible covalent inhibitors.

Reversible Covalent Inhibition─Desired Covalent Adduct Formation by Mass Action

“…Despite using training set and test set compounds that would more appropriately be described as competitive substrates, the model still provides useful information demonstrating that (intuitively) both the lower Gibbs free energy of water and the increased activation energy for bond-cleavage lead to a slower reverse reaction of the covalent adduct. In their work, the entropic component of the Gibbs free energy equation (-TΔ S ) correlates well with k cat , suggesting that their model utilizing the Gibbs free energy of water and the activation energy of covalent–adduct bond cleavage may be effective parameters by which to discriminate covalent inhibitors . Efforts by Chatterjee et al have been to probe free energy perturbations using quantum mechanics/molecular mechanics (QM/MM) calculations to predict binding affinities and binding kinetics for warheads and their target enzymes.…”

“…In their work, the entropic component of the Gibbs free energy equation (-TΔ S ) correlates well with k cat , suggesting that their model utilizing the Gibbs free energy of water and the activation energy of covalent–adduct bond cleavage may be effective parameters by which to discriminate covalent inhibitors. 19 Efforts by Chatterjee et al have been to probe free energy perturbations using quantum mechanics/molecular mechanics (QM/MM) calculations to predict binding affinities and binding kinetics for warheads and their target enzymes. They found that using this approach, when covalent binding was 5.5 kcal/mol stronger than noncovalent binding, selectivity could be predicted by the relative free binding energy of the covalent state.…”