Table 1.4.

Equilibrium-folding models for homodimeric proteins

Mechanism	2-state model $N_{2} \overset{K_{eq}}{\leftrightarrow} 2 U$	3-state model (monomeric intermediate) $N_{2} \overset{K_{2}}{\leftrightarrow} 2 I \overset{K_{2}}{\leftrightarrow} 2 U$
Equilibrium constants and total protein concentration	$\frac{K = \frac{{[U]}^{2}}{[N_{2}]}}{P_{T} = 2 [N_{2}] + [U]}$	$\frac{K_{1} = \frac{{[I]}^{2}}{[N_{2}]}; K_{2} = \frac{[U]}{[I]}}{P_{T} = 2 [N_{2}] + [I] + [U]}$
Definition of molar fraction f_N₂ =	1 - f_U	1 - f_I - f_U
Definition of molar fraction f_I₂ =	—	—
Definition of molar fraction f_I =	—	$\frac{- (K_{1} + K_{1} K_{2}) + \sqrt{{(K_{1} + K_{1} K_{2})}^{2} + 8 K_{1} P_{T}}}{4 P_{T}}$
Definition of molar fraction f_U =	$\frac{- K + \sqrt{K^{2} + 8 K P_{T}}}{4 P_{T}}$	K₂f_I
Fitting equation	Y = Y_N₂f_N₂ + Y_Uf_U	Y = Y_N₂f_N₂ + Y_If_I + Y_Uf_U

Mechanism	3-state model (dimeric intermediate) $N_{2} \overset{K_{1}}{\leftrightarrow} I_{2} \overset{K_{2}}{\leftrightarrow} 2 U$	4-state model $N_{2} \overset{K_{1}}{\leftrightarrow} I_{2} \overset{K_{2}}{\leftrightarrow} 2 I \overset{K_{3}}{\leftrightarrow} 2 U$
Equilibrium constants and total protein concentration	$\frac{K_{1} = \frac{[I_{2}]}{[N_{2}]}; K_{2} = \frac{{[U]}^{2}}{[I_{2}]}}{P_{T} = 2 [N_{2}] + 2 [I_{2}] + [U]}$	$\frac{K_{1} = \frac{[I_{2}]}{[N_{2}]}; K_{2} = \frac{{[I]}^{2}}{[I_{2}]}; K_{3} = \frac{[U]}{[I]}}{P_{T} = 2 [N_{2}] + 2 [I_{2}] + [I] + [U]}$
Definition of molar fraction f_N₂ =	1 - f_I₂ - f_U	1 - f_I₂ - f_I - f_U
Definition of molar fraction f_I₂ =	$\frac{2 f_{U}^{2} P_{T}}{K_{2}}$	$\frac{2 f_{I}^{2} P_{T}}{K_{2}}$
Definition of molar fraction f_I =	—	$\frac{f_{U}}{K_{3}}$
Definition of molar fraction _{f_U} =	$\frac{- K_{1} K_{2} + \sqrt{{(K_{1} K_{2})}^{2} + 8 P_{T} (K_{1} K_{2} + K_{1}^{2} K_{2})}}{4 P_{T} (1 + K_{1})}$	$\frac{(- K_{1} K_{2} K_{3} (1 + K_{3})) + \sqrt{K_{1}^{2} K_{2}^{2} K_{3}^{2} {(1 + K_{3})}^{2} + 8 P_{T} (1 + K_{1}) (K_{1} K_{2} K_{3}^{2})}}{4 P_{T} (1 + K_{1})}$
Fitting equation	Y = Y_N₂f_N₂ + Y_I₂f_I₂ + Y_Uf_U	Y = Y_N₂f_N₂ + Y_I₂f_I₂ + Y_If_I + Y_Uf_U

Notes: Abbreviations used are the same as described for Table 1.3, with the representing addition of the N₂ native homodimer and I₂ representing the homodimeric intermediate. f_N₁ and f_I₂ are the mole fraction of the homodimer and of the dimeric intermediate, respectively, and Y_N₂ and Y_I₂ are the amplitudes of the spectroscopic signal for the specified species.