Table 1. Kinetic Parameters of Inhibition of Cathepsins by 3-Cyano-3-aza-β-amino Acid Derivatives 22–25 and Balicatib.

^aIC₅₀ values were obtained from duplicate measurements in the presence of five different inhibitor concentrations. IC₅₀ values were determined by nonlinear regression using equation v_s = v₀/(1 + [I]/IC₅₀), were v_s is the steady-state rate, v₀ is the rate in the absence of the inhibitor, and [I] is the inhibitor concentration. K_i values were calculated from IC₅₀ values by applying the equation K_i = IC₅₀/(1 + [S]/K_m), where [S] is the substrate concentration.

^bThe cathepsin K assay was performed with the fluorogenic substrate Z-Leu-Arg-AMC at a final concentration of 40 μM (13.3 × K_m). The reaction was followed over 60 min.¹³

^cThe cathepsin S assay was performed with the fluorogenic substrate Z-Phe-Arg-AMC at a final concentration of 40 μM (0.74 × K_m). The reaction was followed over 60 min.³⁸

^dThe cathepsin B assay was performed with the chromogenic substrate Z-Arg-Arg-pNA at a final concentration of 500 μM (0.45 × K_m). The reaction was followed over 30 min.¹³

^eThe cathepsin L assay was performed with the chromogenic substrate Z-Phe-Arg-pNA at a final concentration of 100 μM (5.88 × K_m). The reaction was followed over 30 min.¹³

^fProgress curves were analyzed by nonlinear regression using the slow-binding equation [P] = v_st + (v_i – v_s)(1 – exp(−k_obst))/(k_obs + d) to give v_s, v_i, and k_obs, where [P] is the product concentration, v_i is the initial rate, k_obs is the observed first-order rate constant, and d is the offset. To obtain IC₅₀ values, v_s values from reactions in the presence of the inhibitor and v₀ values obtained by linear regression of the progress curves in the absence of the inhibitor were used. The second-order rate constants k_on were obtained by linear regression according to equation k_obs = k_on[I]/(1 + [S]/K_m) + k_off, where k_off is the first-order rate constant of dissociation.

^gProgress curves were analyzed by linear regression after steady-state was reached (5–30 min).

^hThe reaction was followed over 20 min, and progress curves were analyzed by linear regression. For literature IC₅₀ values and corresponding assay conditions, see refs (39) and (40).