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A probabilistic model for fitting MWC polynomials in protein-ligand binding.

W E Briggs

    Biophysical Chemistry
    |August 1, 1986
    PubMed
    Summary
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    This study introduces a method for fitting Monod-Wyman-Changeux (MWC) model polynomials to binding polynomials. It uses the property of MWC polynomial zeros lying on a circle for model fitting and goodness-of-fit assessment.

    Area of Science:

    • Biophysics
    • Biochemistry
    • Mathematical Biology

    Background:

    • Binding polynomials, often in Adair form, describe molecular interactions.
    • Fitting these polynomials to models like Monod-Wyman-Changeux (MWC) is crucial for understanding biological systems.
    • A quantitative measure of fit is needed for reliable model analysis.

    Purpose of the Study:

    • To develop a method for fitting Monod-Wyman-Changeux (MWC) model polynomials to Adair form binding polynomials.
    • To establish a quantitative measure for the goodness of fit between the Adair polynomial and the MWC model.
    • Specifically address fitting for Adair polynomials of degree three and four.

    Main Methods:

    • Utilizing the property that zeros of MWC polynomials lie on a circle in the complex plane.

    Related Experiment Videos

  • Determining MWC model parameters by aligning their zero-circle with the Adair polynomial's zero-circle.
  • Employing a probabilistic model to assess the likelihood of zero-circle coincidence and chance occurrences.

    • Main Results:

    • A novel fitting method for MWC polynomials applied to Adair binding polynomials (degree 3-4).
    • Successful parameter determination by matching the geometric property of zero locations.
    • A probabilistic framework for quantifying the goodness of fit and significance of the alignment.

    Conclusions:

    • The proposed method provides a robust approach to fitting MWC models to binding polynomial data.
    • The geometric property of MWC polynomial zeros offers a powerful tool for model parameterization.
    • The probabilistic measure enhances the reliability and interpretability of the fitting results in biophysical contexts.