Two-state model

(according to Fersht, Alan. Chapter 17 Section A2 in Structure and Mechanism in Protein Science: A Guide to Enzyme Catalysis and Protein Folding. New York: W.H. Freeman, 1999. p. 514-16)

To determine ΔG of the unfolding reaction, which is commonly used as a measure for conformational stability, one usually assumes a two state model described by the following reaction:

Native (N) ↔ Unfolded (U)

The reaction constant for the unfolding reaction is therefore

and the free energy of this reaction at a given denaturant concentration is calculated as

Since usually the value of ΔG at 0 M denaturant (i.e. in buffer) is of interest, the obtained values for ΔG in the transition region are extrapolated by the fit to return the desired value ΔG_b.

Making the assumption that only native and unfolded state are significantly populated during the reaction, i.e. the fractions of U and N add up to 1, we can describe the fraction of unfolded molecules by the following equation:

It is generally assumed that ΔG varies linearly with the denaturant concentration. If we introduce a proportionality constant m (J/mol M), representing the slope of the denaturation curve in the transition region, we can extrapolate towards 0 M denaturant and determine ΔG in buffer, which is the value of interest. Therefore, ΔG at a given denaturant concentration c can be described by the linear equation:

Combining the two equations above and including terms for sloping baselines, we can describe the fluorescence signal as a function of the denaturant concentration using the following equation:

Where F denotes the fluorescence signal and the terms  and  the sloping baselines of native and unfolded state respectively. The parameter c50 denotes the transition midpoint, i.e. the denaturant concentration where half of the molecules are unfolded, and is derived from m and ΔG_b in the following way:

The image below illustrates the parameters used for the fitting routine superimposed on a typical two-state unfolding curve.

Three-state model

 (according to Lazar, Kristi L., Thomas W. Patapoff, and Vikas K. Sharma. "Cold Denaturation of Monoclonal Antibodies." MAbs 2.1 (2010): 42-52.)

The three-state model assumes that the unfolding reaction proceeds through an intermediate state I:

Native (N) ↔ Intermediate (I) ↔ Unfolded (U)

The two reactions have individual free energies and occur at distinct transition points, therefore the software returns two values for ΔG and two values for c50. The following formula is used for approximation of the data: