Question

Derive the expression for the apparent equilibrium constant (Kapp) for the folding of MKU in terms of K1 and K2, where Kapp

Answer 1

The question is incomplete. The complete question is :

In the native state, myokinase exists in two distinct conformations (MK1 and MK2).  It unfolds to the unfolded state (MKU) only from MK2.

K1 K2

MK1 ⇄ MK2 ⇄ MKU

Derive the expression for the apparent equilibrium constant (Kapp) for the folding of MKU in terms of K1 and K2, where Kapp = ( [MK1] + MK2] ) / [MKU].

Solution :

Derive the expression for the apparent equilibrium constant $K_{app}$ :

$K_{app} = \frac{[MK_1]+[MK_2]}{MKU}$  ............(i)

$MK_1 \rightleftharpoons^{k1} \ MK_2 \rightleftharpoons^{k2} MKU$

$K_1 = \frac{[MK_2]}{[MK_1]} \ \text{ and} \ K_2 = \frac{[MKU]}{[MK_2]}$

$K_{app} = \frac{[MK_1]+[MK_2]}{MKU}$  

Divide by $MK_2$ in both numerator and the denominator.

$K_{app}= \frac{\frac{[MK_1]}{[MK_2]}+1}{\frac{[MKU]}{[MK_2]}}$  ................(ii)

$K_{app} = \frac{\frac{1}{K_1}+1}{K_2}$

        $=\frac{K_1+1}{K_1 K_2}$

Therefore the required expression is :

$K_{app}= \frac{K_1+1}{K_1 K_2}$