Explicit derivation of the standard fitting technique for two-state protein transitions using differential scanning calorimetry data

This paper has three main objectives. First, we aim to derive from first principles a linear heat capacity model for proteins exhibiting two-state conformational transition dynamics, which includes, as a special case, the constant heat capacity model frequently referenced in the literature. Second, we present a protocol for inferring the Gibbs free energy of protein folding by fitting the linear heat capacity model to differential scanning calorimetry data. Third, we demonstrate this protocol using Mathematica software, applying it to real datasets and comparing the linear and constant heat capacity models. While most of our derivations are well established in the literature, we provide a step-by-step bridge from mathematical modeling to application, addressing a practical gap in existing resources that benefits researchers.