Table 4.

Experimental and Calculated Kinetic Parameters for the Catalytic Mechanism of Cruzain.^a

Substrate	Cbz-Arg-Arg-AMC			Cbz-Phe-Arg-AMC
Kinetic Parameter	Experimental Value	Calculated Value	Candidate Value	Experimental Value	Calculated Value	Candidate Value
$k_{\text{cat}}/K_{\text{a}}$	$1.9\pm 0.2\mu {\text{M}}^{-1}{\text{s}}^{-1}$	$4\mu {\text{M}}^{-1}{\text{s}}^{-1}$	${}^{\text{D}}{k}_1=1.1$	$27\pm 4\mu {\text{M}}^{-1}{\text{s}}^{-1}$	$25\mu {\text{M}}^{-1}{\text{s}}^{-1}$	${}^{\text{D}}{k}_1=1.1$
$K_{\text{ia}}$	$14\pm 3\mu \text{M}$	$14\mu \text{M}$	${}^{\text{D}}{k}_3\text{ or }{}^{\text{D}}{k}_5=1.4$	$9.8\pm 0.6\mu \text{M}$	$9.8\mu \text{M}$	${}^{\text{D}}{k}_3\text{ or }{}^{\text{D}}{k}_5=1.4$
${}^{\text{D}2\text{O}}\left(k_{\text{cat}}/K_{\text{a}}\right)$	1.15 ± 0.08	1.14	${}^{\text{D}}{k}_7=1.2$	1.4 ± 0.1	1.4	${}^{\text{D}}{k}_7=1.3$
$k_{\text{ac}}$	64.5± 0.2 s−1	65 s−1	${}^{\text{D}}{k}_{11}=1.2$	239 ± 6 s−1	239 s−1	${}^{\text{D}}{k}_{11}=1.6$
${}^{\text{D}2\text{O}}{k}_{\text{ac}}$	1.41 ± 0.01	1.2	${}^{\text{D}}{k}_{13}=1.4$	1.34 ± 0.01	1.2	${}^{\text{D}}{k}_{13}=1.9$
$k_{\text{dac}}$	19.9 ± 0.1 s−1	20 s−1	$a=k_3/k_2=0.14$	35 ± 1 s−1	35 s−1	$a=k_3/k_2=0.5$
${}^{\text{D}2\text{O}}{k}_{\text{dac}}$	1.67± 0.02	1.6	$b=k_5/k_4=2.6$	2.2 ± 0.02	2.3	$b=k_5/k_4=5.0$
$k_{\text{cat}}$	15.2 ± 0.1 s−1	15 s−1	$c=k_6/k_7=0$	30 ± 1 s−1	30 s−1	$c=k_6/k_7=0.0002$
${}^{\text{D}2\text{O}}{k}_{\text{cat}}$	1.61 ± 0.02	1.5	$d=k_5/k_7=0.13$	2.07 ± 0.02	2.08	$d=k_5/k_7=0.18$
$K_{\text{a}}$	$7.0\pm 0.1\mu \text{M}$	4	$e=k_7/k_9=0.8$	$2.3\pm 0.1\mu \text{M}$	1.2	$e=k_7/k_9=0.8$
$\mathit{\text{tKIE}}°$	1.6	1.8	$x=k_{13}/k_{12}=0.18$	2.2	2.1	$x=k_{13}/k_{12}=0.1$
$S_{\text{r}}$	4	4	$y=k_{13}/k_{15}=0.02$	70 ± 50	9	$y=k_{13}/k_{15}=0.015$
			$k_1=50\mu {\text{M}}^{-1}{\text{s}}^{-1}$			$k_1=75\mu {\text{M}}^{-1}{\text{s}}^{-1}$
			$k_2=700{\text{s}}^{-1}$			$k_2=735{\text{s}}^{-1}$
			$k_3=100{\text{s}}^{-1}$			$k_3=400{\text{s}}^{-1}$
			$k_4=300{\text{s}}^{-1}$			$k_4=220{\text{s}}^{-1}$
			$k_5=800{\text{s}}^{-1}$			$k_5=1100{\text{s}}^{-1}$
			$k_6=0{\text{s}}^{-1}$			$k_6=1{\text{s}}^{-1}$
			$k_7=6000{\text{s}}^{-1}$			$k_7=6000{\text{s}}^{-1}$
			$k_9=8000{\text{s}}^{-1}$			$k_9=8000{\text{s}}^{-1}$
			$k_{11}=280{\text{s}}^{-1}$			$k_{11}=300{\text{s}}^{-1}$
			$k_{12}=430{\text{s}}^{-1}$			$k_{12}=700{\text{s}}^{-1}$
			$k_{13}=55{\text{s}}^{-1}$			$k_{13}=135{\text{s}}^{-1}$
			$k_{15}=5000{\text{s}}^{-1}$			$k_{15}=5000{\text{s}}^{-1}$

^aExperimental kinetic parameters are those reported in Tables 2 and 3. Solvent equilibrium isotope effects, $\left({}^{\text{D}}{K}_{\text{eq }}=0.6-0.7\right.$, and $\left.{}^{\text{D}}{K}_{\text{eq11 }}=1.3\right)$, intrinsic isotope effects on each step $\left({}^{\text{D}}{k}_{1–15}\right)$, and microscopic rate constants $\left(k_{1–15}\right)$ were obtained by dynamic simulation of the experimental pre-steady-state kinetic data using Kintek Explorer.⁴⁷ Candidate values obtained from these fittings were then inserted into eqs 14–21 to produce the calculated values in the table. Values for $k_3$ and $k_{13}$ presented here resulted from extrapolation to an infinite concentration of the variable substrates to produce limiting values $k_{\text{cat},}{k}_{\text{ac},}$ and $k_{\text{dac}}$.