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

$\frac{V_{maxf} \frac{Glycogen_{n+1} \times Pi}{K_{iGlyf} \times K_{Pi}} -\frac{V_{maxf} \times K_{Glyb} \times K_{iGlc1P}}{K_{iGlyf} \times K_{Pi} \times Keq} \times \frac{Glycogen_n \times Glc1P}{K_{Glyb} \times K_{iGlc1P}} }{1 + \frac{Glycogen_{n+1}}{K_{iGlyf}} + \frac{Pi}{K_{iPi}} + \frac{Glycogen_n}{K_{iGlyb}} + \frac{Glc1P}{K_{iGlc1P}} \frac{Glycogen_{n+1} \times Pi}{K_{Glyf} \times K_{iPi}} + \frac{Glycogen_n \times Glc1P}{K_{Glyb} \times K_{iGlc1P}} }$

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	Value	Units	Organism	Remarks
$V_{maxf}$	50	$\text{mM min}^{-1}$	Rabbit
$K_{iGlyf}$	15	mM
$K_{Pi}$	4	mM
$K_{Glyb}$	0.15	mM
$K_{iGlc1P}$	10.1	mM
$K_{iPi}$	4.6	mM
$K_{iGlyb}$	4.4	mM
$K_{Glyf}$	1.7	mM
$Keq$	0.42	mM

Parameters with uncertainty

Parameter	Value	Units	Organism	Remarks
$n$	2	Dimensionless	Recombinant, human muscle
$V_{max}$	$31.446 \pm 0.917$	$\text{mM min}^{-1}$
$K_{r,Pi}$	$2.08 \pm 0.044$	mM
$K_{u,Pi}$	$4.32 \pm 0.177$	mM
$K_{t,Pi}$	$41.53 \pm 547.57$	mM
$K_{r, Glc1P}$	$0.67 \pm 0.083$	mM
$K_{u, Glc1P}$	$82.02 \pm 53.35$	mM
$K_{t, Glc1P}$	$27.92 \pm 9.31$	mM
$K_{r, AMP}$	$0.00336 \pm 0.00395$	mM
$K_{t, AMP}$	$0.53 \pm 0.283$	mM
$K_{t, ATP}$	$3.9 \pm 22.627$	mM
$K_{r, Glc6P}$	$7.42 \pm 2.73$	mM
$K_{u, Glc6P}$	$0.56 \pm 0.12$	mM
$K_{t, Glc6P}$	$0.27 \pm 0.0485$	mM
$L_{u}$	$5.93 \pm 0.40$	Dimensionless
$L_{t}$	$34741 \pm 72931$	Dimensionless

The parameter for the alternative equation are

Parameter	Value	Units	Organism	Remarks
$V_{maxf}$	$31.446 \pm 0.917$	$\text{mM min}^{-1}$	Rabbit
$K_{iGlyf}$	15	mM
$K_{Pi}$	$4 \pm 0.8$	mM
$K_{Glyb}$	$0.15 \pm 0.03$	mM
$K_{iGlc1P}$	$10.1 \pm 2.5$	mM
$K_{iPi}$	$4.6 \pm 2.0$	mM
$K_{iGlyb}$	4.4	mM
$K_{Glyf}$	$1.7 \pm 0.4$	mM
$Keq$	$0.36 \pm 0.08$	mM			Two $Keq$ values of 0.30, 0.42 are reported in . Mean and Std. Dev. from these two values are taken.