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Explicit analytic equations for multimolecular thermal melting curves.

Albrecht Böttcher1, Danny Kowerko2, Roland K O Sigel2

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This study derives explicit equations for folded fraction in thermal melting curve analysis. These equations simplify extracting thermodynamic parameters from experimental data using regression analysis.

Keywords:
Curve fittingMultimolecular reactionSoftwareThermal melting curveThermodynamic parameterVan't Hoff analysis

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Area of Science:

  • Biophysics
  • Chemical Thermodynamics
  • Biochemical Analysis

Background:

  • Accurate analysis of thermal melting curves is crucial for understanding biomolecular stability.
  • Existing models often lack explicit equations for temperature-dependent folded fractions.
  • The van't Hoff formalism relates equilibrium constants to thermodynamic parameters.

Purpose of the Study:

  • To derive and list explicit equations for the folded fraction as a function of thermodynamic parameters.
  • To provide mathematically self-contained derivations for arbitrary molecularities.
  • To facilitate the use of these equations in standard curve-fitting tools.

Main Methods:

  • Mathematical derivation based on the van't Hoff formalism.
  • Analysis of temperature dependence of folded and unfolded components.
  • Development of explicit equations for arbitrary molecularities.

Main Results:

  • Explicit equations for folded fraction as a function of temperature, enthalpy, and melting temperature.
  • Demonstration that the folded fraction comprises a universal molecularity-dependent function and a dimensionless thermodynamic regime-dependent function.
  • Provision of new and known results for thermodynamic parameter extraction.

Conclusions:

  • The derived explicit equations simplify the extraction of thermodynamic parameters from thermal melting curve data.
  • The findings offer a more robust framework for regression analysis of experimental data.
  • Open-source Matlab scripts are provided for practical implementation.