Table 2.

A summary of formulas for the apparent linearity in the denaturation free energy curves (m^app) and the corresponding preferential binding parameter differences (ΔΓ₂₃) for different models of protein denaturation. See text for an explanation of the symbols. We have used the fact that m₃ = ρ₃/φ₁ for the Local-bulk model (140) and ${(\partial {\rho }_3∕\partial {\rho }_1)}_{P,T}=-{\stackrel{‒}{V}}_1∕{\stackrel{‒}{V}}_3$ for the Exchange 2 model. N₃₃’ is the derivative of N₃₃ with respect to cosolvent concentration

Model	mapp	ΔΓ23
m-value	m	$\frac{m{\rho }_3}{a_{33}}$
Transfer	$\frac{a_{33}}{{\rho }_3}{\sum }_i{n}_i{\alpha }_i{\Gamma }_{i3}$	${\sum }_i{n}_i{\alpha }_i{\Gamma }_{i3}$
Binding site	$\frac{\Delta n{K}_b}{1+K_b{\rho }_3}$	$\frac{\Delta n{K}_b{\rho }_3}{1+K_b{\rho }_3}\frac{1}{a_{33}}$
Exchange 1	$\frac{\Delta n(K_e^{’}-1)a_{33}}{{\rho }_1+{\rho }_3+{\rho }_3(K_e^{’}-1)}$	$\frac{\Delta n{\rho }_3(K_e^{’}-1)}{{\rho }_1+{\rho }_3+{\rho }_3(K_e^{’}-1)}$
Exchange 2	$\frac{m_e}{{\rho }_1{\varphi }_1}$	$\frac{m_e{\rho }_3}{{\rho }_1{\varphi }_1{a}_{33}}$
Local-bulk	$\frac{(K_P-1)b_1^{\mathrm{O}}\Delta ASA{a}_{33}}{m_1{\varphi }_1(1+K_P{S}_3{m}_3∕m_1)}$	$\frac{{\rho }_3(K_P-1)b_1^{\mathrm{O}}\Delta ASA}{m_1{\varphi }_1(1+K_P{S}_3{m}_3∕m_1)}$
LCPE	$A[1+B(N_{33}+{\rho }_3{N}_{33}^{’})]$	$\frac{{\rho }_{3}A[1+B(N_{33}+{\rho }_3{N}_{33}^{’})]}{a_{33}}$