3.4. SARS-CoV-2 Mpro Inhibition Assay

The in vitro inhibition potency of the compounds against M^pro was assessed through the estimation of the inhibition constant, K_i, and the half-maximal inhibitory concentration, IC₅₀, from experimental inhibition curves. Inhibition curves were obtained by measuring the enzyme activity (at fixed 0.2 μM enzyme concentration and fixed 20 μM substrate concentration) as a function of compound concentration (serial 2-fold dilution from 125 µM to 0 μM), maintaining the percentage of DMSO (2.5%) constant. The enzymatic activity was quantitated as the initial slope of the substrate fluorescence emission time evolution curve, and was plotted as a function of compound concentration. The ratio between the activity (slope) in the presence and absence of the compound provides the residual percentage of activity at a given compound concentration. Nonlinear regression analysis employing a simple inhibition model (considering inhibitor depletion due to enzyme binding) allowed us to estimate the apparent inhibition constant, K_i^app, for each compound according to Equation (1):

where [EI] is the concentration of the enzyme–inhibitor complex, [E]_T and [I]_T are the total concentrations of the enzyme and the inhibitor, K_i^app is the apparent inhibition constant for the inhibitors (quercetin and derivatives), [I] is the concentration of the free inhibitor, and v is the initial slope of the enzymatic activity trace at a given (free) inhibitor concentration [I] (or total inhibitor concentration [I]_T). No approximation for the free inhibitor concentration (e.g., assuming to be equal to the total inhibitor concentration) was made, thus having general validity for any total enzyme and inhibitor concentration and any value of the inhibition constant (even for tight-binding inhibitors). In addition, if the inhibitor acts through a purely competitive mechanism, the previous equation can be substituted by Equation (2):

where K_i is the intrinsic (i.e., substrate concentration-independent) inhibition constant, K_m is the Michaelis–Menten constant for the enzyme–substrate interaction, and [S] is the substrate concentration. Because K_m and [S] are known, the intrinsic inhibition constant can be determined. Furthermore, approximating the free compound concentration by the total compound concentration and neglecting ligand depletion, the K_i^app in Equation (2) is equivalent to the IC₅₀, as reported in Table 3. However, it should be emphasized that the IC₅₀ is an assay-dependent inhibition potency index (among other parameters, it depends on the enzyme and substrate concentrations, as well as on the K_m); thus, the intrinsic inhibition constant is a better inhibition potency index. Uncertainties have been reported as 95% profile likelihood asymmetric confidence intervals, as especially recommended for equilibrium constants (i.e., binding association/dissociation constants and inhibition constants) [32].