Some pitfalls in curve-fitting and how to avoid them: a case in point

Area of Science:

• Biophysical Chemistry
• Chemical Kinetics
• Computational Modeling

Background:

• Complex nonlinear models with multiple exponential terms, especially those with closely-spaced time constants, present significant challenges in curve-fitting analysis.
• Ensuring the uniqueness and statistical validity of model parameters is critical for accurate interpretation of experimental data.

Purpose of the Study:

• To emphasize the necessity of rigorous validation when employing curve-fitting for complex nonlinear models.
• To advocate for the inclusion of statistical tests for error and parameter independence, alongside detailed procedural descriptions.

Main Methods:

• Exploration and discussion of solution uniqueness in nonlinear curve-fitting.
• Application of statistical tests to assess parameter error and independence.
• Detailed documentation of curve-fitting procedures.
• Case study: Analysis of electron transfer kinetics from cytochrome oxidase to O2 using SVD-based least squares.

Main Results:

• Demonstration of potential ambiguities and lack of uniqueness in curve-fitting solutions for complex models.
• Highlighting the importance of statistical validation to confirm parameter reliability.
• Illustrating how specific fitting procedures can impact the interpretation of kinetic data.

Conclusions:

• Curve-fitting complex nonlinear models demands a high burden of proof, including uniqueness and statistical validation of parameters.
• Recommended procedures enhance the reliability and interpretability of kinetic analyses, particularly in biophysical and chemical studies.
• The principles discussed are broadly applicable to diverse curve-fitting applications in scientific modeling.