Two-state analysis of GdmHCl denaturation

A two-state hypothesis was used to fit the denaturation curve of GdmHCl. The folding free energy of AR-LBD WT and mutant proteins without GdmHCl is estimated by a linear extrapolation:

where [θ_i] is the ellipticity at the ith gdmHCl concentration, [θ_F] is the ellipticity of the protein completely folded, [θ_U] is the ellipticity of the protein in 5 M GdmHCl. It is assumed that the protein in 5 M GdmHCl has been fully unfolded.

where K_i is the folding constant of the monomer protein at the ith GdmHCl concentration, which can be calculated by the folding fraction α_i. The free energy of protein folding can be estimated by the following equation:

where R is the gas constant, T is the absolute temperature, and K_F is the folding constant of monomer protein, which can be calculated by the function K_F = [F]/[U], where [F] and [U] represent respectively folded and unfolded fractions.

The free energy of protein folding is a linear function of GdmHCl concentration, where ΔG_i is the free energy of protein at the ith GdmHCl concentration, and ΔG₀ is the free energy of protein folding without GdmHCl.