Novel differential elimination method for determining kinetic coefficients under substrate self-inhibition

Area of Science:

• Biochemical Engineering
• Enzyme Kinetics
• Mathematical Modeling

Background:

• Substrate self-inhibition is a common phenomenon in biological systems.
• Accurate estimation of kinetic coefficients is crucial for understanding and modeling these systems.
• Traditional methods like nonlinear least square regression (NLSR) can be computationally intensive and sensitive to initial parameter estimates.

Purpose of the Study:

• To develop a novel differential elimination method (DEM) for determining kinetic coefficients in substrate self-inhibition models.
• To enable linearization of kinetic equations for parameter estimation without relying on NLSR.
• To compare the performance of DEM with NLSR under various data conditions.

Main Methods:

• Finite differentiation of kinetic equations to eliminate specific inhibition (K(I)) or saturation (K(S)) coefficients.
• Linearization of the modified equations for direct estimation of kinetic parameters (q, K(S), K(I)).
• Evaluation of DEM accuracy and robustness using simulated data with varying error levels and substrate concentration intervals (geometric vs. arithmetic).

Main Results:

• DEM accurately estimates kinetic parameters when data are error-free and collected at geometric intervals.
• DEM performs comparably to NLSR with minor data errors at geometric intervals.
• DEM shows limitations in estimating maximum substrate utilization rate (q(max)) but provides invariant estimates for S(max).
• Both DEM and NLSR perform poorly with arithmetic data intervals and errors, highlighting the importance of data acquisition strategy.

Conclusions:

• DEM provides a viable, computationally simpler alternative to NLSR for estimating kinetic coefficients in substrate self-inhibition.
• The method's performance is highly dependent on the substrate concentration sampling strategy; geometric intervals are preferred.
• DEM can serve as a valuable tool for assessing experimental data quality by comparing parameter estimates derived from different DEM options or NLSR.