Linear parameter estimation of rational biokinetic functions.

Area of Science:

• Biokinetics
• Enzyme kinetics
• Environmental engineering

Background:

• Nonlinear least-squares (NLS) methods are common for biokinetic parameter estimation but risk local minima.
• Linearization techniques like Lineweaver-Burk distort errors and introduce 'errors-in-variables' problems.
• Ordinary least squares (OLS) on linearized models ensures a global minimum but yields biased estimates when variables have errors.

Purpose of the Study:

• To propose a novel bias compensated total least squares (CTLS) method for rational biokinetic function parameter estimation.
• To demonstrate the advantages of CTLS over traditional NLS and OLS methods.
• To address the bias and local minimum issues inherent in existing estimation techniques.

Main Methods:

• Development and application of a bias compensated total least squares (CTLS) method.
• Utilizing a general linear reparameterization procedure for biokinetic models.
• Comparison of CTLS with OLS and NLS using simulation examples and real-world data.

Main Results:

• CTLS provides a direct method for parameter estimation, ensuring a global minimum.
• CTLS effectively compensates for bias in regression variables, unlike OLS.
• Simulations and real data analysis show CTLS outperforms NLS and OLS for Michaelis-Menten and enzyme kinetics with substrate inhibition.

Conclusions:

• CTLS is a powerful and accurate alternative for estimating parameters in rational biokinetic models.
• The method effectively handles errors-in-variables and bias issues.
• CTLS demonstrates significant advantages for Michaelis-Menten kinetics, enzyme kinetics with substrate inhibition, and activated sludge experiments.