Explicit analytic equations for multimolecular thermal melting curves

• Exact mathematical solutions to plot or analyze thermal melting curves are presented.
• The derivation of explicit equations for molecularities n = 1 to n = 4 is given.
• Explicit equations for molecularities n > 3 are new to the field.
• A software tool is provided to support fast plots and data export for any molecularity.
• The equations facilitate curve fit based analysis of thermal melting curves.

The analysis of thermal melting curves requires the knowledge of equations for the temperature dependence of the relative fraction of folded and unfolded components. To implement these equations as standard tools for curve fitting, they should be as explicit as possible. From the van't Hoff formalism it is known that the equilibrium constant and hence the folded fraction is a function of the absolute temperature, the van't Hoff transition enthalpy, and the melting temperature. The work presented here is devoted to the mathematically self-contained derivation and the listing of explicit equations for the folded fraction as a function of the thermodynamic parameters in the case of arbitrary molecularities. Part of the results are known, others are new. It is in particular shown for the first time that the folded fraction is the composition of a universal function which depends solely on the molecularity and a dimensionless function which is governed by the concrete thermodynamic regime but is independent of the molecularity. The results will prove useful for extracting the thermodynamic parameters from experimental data on the basis of regression analysis. As supporting information, open-source Matlab scripts for the computer implementation of the equations are provided.

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