Evaluation of the paraoxonase-1 kinetic parameters of the lactonase activity by nonlinear fit of progress curves

Figures & data

Figure 1. Fit of kinetic progress curve data for each sample. Symbols represent absorbance readings at the given reaction time. Only one progress curve per sample and only half of the data points per progress curve are shown, for clarity. Smooth lines represent least-square model curves generated by fit of the theoretical equation Equation (2)(2) $${\left[P\right]}_t={\left[S\right]}_0-K_{\mathrm{m}}\cdot \left(1.45869\cdot \hspace{0.17em}\text{ln}\hspace{0.17em}\left(1.2\cdot \frac{x}{\hspace{0.17em}\text{ln}\hspace{0.17em}\left(2.4\cdot \frac{x}{\hspace{0.17em}\text{ln}\hspace{0.17em}\left(1+2.4\cdot x\right)}\right)}\right)-0.45869\cdot \hspace{0.17em}\text{ln}\hspace{0.17em}\left(2\cdot \frac{x}{\hspace{0.17em}\text{ln}\hspace{0.17em}\left(1+2\cdot x\right)}\right)\right)$$(2) with the parameter values obtained by modified model (GraphPad, Lambert W) shown in Table 1.

Table 1. Parameters aquired by progress–curve fitting. Comparison of fitted values obtained using the numerical integration approach (DynaFit, see Ref. [9]), the exact algebraic model Equation (1)(1) $${\left[P\right]}_t={\left[S\right]}_0-K_{\mathrm{m}}\cdot W_0\left\{\frac{{\left[S\right]}_0}{K_{\mathrm{m}}}\cdot \hspace{0.17em}\text{exp}\hspace{0.17em}\left(\frac{{\left[S\right]}_0-V_{\max }\cdot t}{K_{\mathrm{m}}}\right)\right\}$$(1) with the Lambert W(x) function (DynaFit, see Ref. [9]), and the approximation of W(x) of the modified model Equation (2)(2) $${\left[P\right]}_t={\left[S\right]}_0-K_{\mathrm{m}}\cdot \left(1.45869\cdot \hspace{0.17em}\text{ln}\hspace{0.17em}\left(1.2\cdot \frac{x}{\hspace{0.17em}\text{ln}\hspace{0.17em}\left(2.4\cdot \frac{x}{\hspace{0.17em}\text{ln}\hspace{0.17em}\left(1+2.4\cdot x\right)}\right)}\right)-0.45869\cdot \hspace{0.17em}\text{ln}\hspace{0.17em}\left(2\cdot \frac{x}{\hspace{0.17em}\text{ln}\hspace{0.17em}\left(1+2\cdot x\right)}\right)\right)$$(2) (GraphPad, Lambert W, see Ref. [11]). The measurements for each sample were carried in duplicate or triplicate. Data are means ± SD.

	DynaFit numerical integration	DynaFit Lambert W	GraphPad Lambert W		DynaFit numerical integration	DynaFit Lambert W	GraphPad Lambert W
	Sample 1				Sample 2
[S]0 (μM)	101.0 ± 0.1	101.0 ± 0.1	100.9 ± 0.1	[S]0 (μM)	100.6 ± 0.1	100.6 ± 0.1	100.6 ± 0.1
Km (μM)	11.3 ± 0.5	11.3 ± 0.5	11.0 ± 0.5	Km (μM)	11.8 ± 0.6	11.8 ± 0.6	11.5 ± 0.5
Vmax (μM/min)	250.2 ± 2.1	222.3 ± 8.6	248.8 ± 1.8	Vmax (μM/min)	241.3 ± 2.3	204.5 ± 8.6	239.9 ± 2.1
	Sample 3				Sample 4
[S]0 (μM)	98.3 ± 0.2	98.3 ± 0.2	98.3 ± 0.1	[S]0 (μM)	99.9 ± 0.1	99.9 ± 0.1	99.9 ± 0.1
Km (μM)	8.6 ± 0.5	8.6 ± 0.5	8.4 ± 0.4	Km (μM)	9.5 ± 0.3	9.5 ± 0.3	9.2 ± 0.1
Vmax (μM/min)	129.2 ± 1.1	150.5 ± 7.4	128.6 ± 1.0	Vmax (μM/min)	204.3 ± 1.1	214.7 ± 6.1	202.9 ± 0.3
	Sample 5				Sample 6
[S]0 (μM)	99.2 ± 0.2	97.6 ± 0.1	99.2 ± 0.2	[S]0 (μM)	101.9 ± 0.3	101.1 ± 0.2	101.9 ± 0.2
Km (μM)	13.8 ± 1.2	11.4 ± 0.6	13.5 ± 1.1	Km (μM)	10.7 ± 0.9	9.6 ± 0.6	10.4 ± 0.8
Vmax (μM/min)	304.2 ± 5.7	252 ± 10	302.6 ± 5.2	Vmax (μM/min)	176.5 ± 2.4	179.5 ± 9.7	175.5 ± 2.1

Figure 2. Paraoxonase-1 lactone substrate dihydrocoumarine (left) and its competitive inhibitor 2-hydroxyquinoline (right).

Reytor Gonzales ML, Cornell-Kennon S, Shaefer E, Kuzmič P. An algebraic model to determine substrate kinetic parameters by global nonlinear fit of progress curves. Anal Biochem 2017;518:16.

 PubMed Web of Science ®Google Scholar

Goličnik M. On the Lambert W function and its utility in biochemical kinetics. Biochem Eng J 2012;406:94.

 Google Scholar