Glycogen phosphorylase

Glycogen phosphorylase (GP) is a dimeric enzyme that catalyses the reaction in which the terminal glucose residue from a glycogen chain is phosphorylated and cleaved from the chain, releasing it as Glc1P.

Chemical equation

$Glycogen_{n+1} + Pi \rightleftharpoons Glycogen_{n} + Glc1P$

Rate equation

MWC model was used to formualte the rate law.

$\frac{V_{max} \times n \times \frac{[Pi]}{K_{r,Pi}} \left( 1 + \frac{[Pi]}{K_{r,Pi}} + \frac{[Glc1P]}{K_{r,Glc1P}} \right)^{n-1} }{\left( 1 + \frac{[Pi]}{K_{r,Pi}} + \frac{[Glc1P]}{K_{r,Glc1P}} \right)^n + L_u \left( 1 + \frac{[Pi]}{K_{u,Pi}} + \frac{[Glc1P]}{K_{u,Glc1P}} \right)^n \left( \frac{1 + \frac{[Glc6P]}{K_{u,Glc6P}}}{1 + \frac{[AMP]}{K_{r,AMP}} + \frac{[Glc6P]}{K_{r,Glc6P}}} \right)^n } + \frac{V_{max} \times n \times \frac{[Pi]}{K_{r,Pi}} \left( 1 + \frac{[Pi]}{K_{r,Pi}} + \frac{[Glc1P]}{K_{r,Glc1P}} \right)^{n-1} }{\left( 1 + \frac{[Pi]}{K_{r,Pi}} + \frac{[Glc1P]}{K_{r,Glc1P}} \right)^n + L_t \left( 1 + \frac{[Pi]}{K_{t,Pi}} + \frac{[Glc1P]}{K_{t,Glc1P}} \right)^n \left( \frac{1 + \frac{[AMP]}{K_{t,AMP}} \frac{[Glc6P]}{K_{t,Glc6P}}}{1 + \frac{[AMP]}{K_{r,AMP}} + \frac{[Glc6P]}{K_{r,Glc6P}}} \right)^n \left( 1 + \frac{[ATP]}{K_{t,ATP}} \right)^n }$

An alternative rate equation without considering the allosteric regulation is given as

Failed to parse (Cannot store math image on filesystem.): \frac{\frac{V_{max}}{Ka \times Kb} \left( A \times B - \frac{P \times Q}{Keq} \right) }{ 1 + \frac{A}{Ka} + \frac{Q}{Kq} + \frac{B}{Kb} + \frac{A \times B}{Ka \times Kb} + \frac{B \times Q}{Kb \times Kq} + + \frac{P}{Kp} + \frac{A \times P}{Ka \times Kp} + \frac{P \times Q}{Kp \times Kq} + \frac{I_1}{Ki_1} + \frac{I_2}{Ki_2} + \frac{I_3}{Ki_3} }

Parameter values

Parameter	Value	Units	Organism	Remarks
$n$	2	Dimensionless	Recombinant, human muscle
$V_{max}$	50	$\text{mM min}^{-1}$
$K_{r,Pi}$	2.08	mM
$K_{u,Pi}$	4.32	mM
$K_{t,Pi}$	41.53	mM
$K_{r, Glc1P}$	0.67	mM
$K_{u, Glc1P}$	82.02	mM
$K_{t, Glc1P}$	27.92	mM
$K_{r, AMP}$	$3.36 \times 10^{-3}$	mM
$K_{t, AMP}$	0.53	mM
$K_{t, ATP}$	3.9	mM
$K_{r, Glc6P}$	7.42	mM
$K_{u, Glc6P}$	0.56	mM
$K_{t, Glc6P}$	0.27	mM
$L_{u}$	5.93	Dimensionless
$L_{t}$	34741	Dimensionless

The parameter for the alternative equation are

Parameter values

Parameter	Value	Units	Organism	Remarks
$V_{max}$	50	$\text{mM min}^{-1}$	Rabbit
Failed to parse (Cannot store math image on filesystem.): Ka	4	mM
Failed to parse (Cannot store math image on filesystem.): Kb	1.7	mM
Failed to parse (Cannot store math image on filesystem.): Kp	2.7	mM
Failed to parse (Cannot store math image on filesystem.): Kq	0.15	mM
Failed to parse (Cannot store math image on filesystem.): Ki_1	2	mM
Failed to parse (Cannot store math image on filesystem.): Ki_2	4.7	mM
Failed to parse (Cannot store math image on filesystem.): Ki_3	10.1	mM
$Keq$	0.42	mM