Kinetic substrate quantification by fitting the enzyme reaction curve to the integrated Michaelis–Menten equation

Abstract

The reliability of kinetic substrate quantification by nonlinear fitting of the enzyme reaction curve to the integrated Michaelis–Menten equation was investigated by both simulation and preliminary experimentation. For simulation, product absorptivity ε was 3.00 mmol⁻¹ L cm⁻¹ and K_m was 0.10 mmol L⁻¹, and uniform absorbance error σ was randomly inserted into the error-free reaction curve of product absorbance A_i versus reaction time t_i calculated according to the integrated Michaelis–Menten equation $\ln \left[ {Am/\left( {Am - Ai} \right)} \right] + Ai/\left( {\varepsilon \times Km} \right) = \left( {Vm/Km} \right) \times ti$. The experimental reaction curve of arylesterase acting on phenyl acetate was monitored by phenol absorbance at 270 nm. Maximal product absorbance A_m was predicted by nonlinear fitting of the reaction curve to Eq. (1) with K_m as constant. There were unique A_m for best fitting of both the simulated and experimental reaction curves. Neither the error in reaction origin nor the variation of enzyme activity changed the background-corrected value of A_m. But the range of data under analysis, the background absorbance, and absorbance error σ had an effect. By simulation, A_m from 0.150 to 3.600 was predicted with reliability and linear response to substrate concentration when there was 80% consumption of substrate at σ of 0.001. Restriction of absorbance to 0.700 enabled A_m up to 1.800 to be predicted at σ of 0.001. Detection limit reached A_m of 0.090 at σ of 0.001. By experimentation, the reproducibility was 4.6% at substrate concentration twice the K_m, and A_m linearly responded to phenyl acetate with consistent absorptivity for phenol, and upper limit about twice the maximum of experimental absorbance. These results supported the reliability of this new kinetic method for enzymatic analysis with enhanced upper limit and precision.