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
`$K_(app)$` :

`$K_(app) = ([MK_1]+[MK_2])/(MKU)$` ............(i)

`$MK_1 \rightleftharpoons^(k1) \ MK_2 \rightleftharpoons^(k2) MKU$`

`$K_1 = ([MK_2])/([MK_1]) \ \text{ and} \ K_2 = ([MKU])/([MK_2])$`

`$K_(app) = ([MK_1]+[MK_2])/(MKU)$`

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

`$K_(app)= (([MK_1])/([MK_2])+1)/(([MKU])/([MK_2]))$` ................(ii)

`$K_(app) = ((1)/(K_1)+1)/(K_2)$`

`$=(K_1+1)/(K_1 K_2)$`

Therefore the required expression is :

`$K_(app)= (K_1+1)/(K_1 K_2)$`