You are here: Home / Exposures / Lambeth, Kushmerick, 2002 / A computational model for glycogenolysis in skeletal muscle

Model Mathematics

Component based math viewer is available

Component: environment

Component: GLY

\frac{d}{d time} (GLY) = - flux_GP

Component: G1P

\frac{d}{d time} (G1P) = flux_GP - V_PGLM

Component: G6P

\frac{d}{d time} (G6P) = V_PGLM - V_PGI

Component: F6P

\frac{d}{d time} (F6P) = V_PGI - V_PFK

Component: FBP

\frac{d}{d time} (FBP) = V_PFK - V_ALD

Component: DHAP

\frac{d}{d time} (DHAP) = V_ALD + V_TPI

Component: GAP

\frac{d}{d time} (GAP) = V_ALD - (V_TPI + V_GAPDH)

Component: Thirteen_BPG

\frac{d}{d time} (Thirteen_BPG) = V_GAPDH - V_PGK

Component: three_PG

\frac{d}{d time} (three_PG) = V_PGK - V_PGM

Component: two_PG

\frac{d}{d time} (two_PG) = V_PGM - V_ENOL

Component: PEP

\frac{d}{d time} (PEP) = V_ENOL - V_PK

Component: PYR

\frac{d}{d time} (PYR) = V_PK - V_LDH

Component: LAC

\frac{d}{d time} (LAC) = V_LDH - output output = 0.2 LAC

Component: Pi

\frac{d}{d time} (Pi) = V_ATPase - (flux_GP + V_GAPDH)

Component: ADP

\frac{d}{d time} (ADP) = V_PFK + 2.0 V_ADK + V_CK + V_ATPase + (- (V_PGK + V_PK))

Component: ATP

\frac{d}{d time} (ATP) = V_PGK + V_PK + (- (V_PFK + V_ADK + V_CK + V_ATPase))

Component: AMP

\frac{d}{d time} (AMP) = - V_ADK

Component: PCr

\frac{d}{d time} (PCr) = V_CK

Component: Cr

\frac{d}{d time} (Cr) = - V_CK

Component: NADH

\frac{d}{d time} (NADH) = V_GAPDH - V_LDH

Component: NAD

\frac{d}{d time} (NAD) = V_LDH - V_GAPDH

Component: flux_GP

flux_GP = frac_a V_GPa + frac_b V_GPb

Component: V_GPa

V_GPa = \frac{V_max_f \frac{GLY Pi}{Ki_GLY_f K_Pi} - (V_max_r \frac{GLY G1P}{Ki_GLY_b Ki_G1P})}{1.0 + \frac{GLY}{Ki_GLY_f} + \frac{Pi}{Ki_Pi} + \frac{GLY}{Ki_GLY_b} + \frac{G1P}{Ki_G1P} + \frac{GLY Pi}{K_GLY_f Ki_Pi} + \frac{GLY G1P}{K_GLY_b Ki_G1P}} V_max_r = \frac{V_max_f K_GLY_b Ki_G1P}{Ki_GLY_f K_Pi Keq_GP}

Component: V_GPb

V_GPb = \frac{V_max_f \frac{GLY Pi}{Ki_GLY_f K_Pi} - (V_max_r \frac{GLY G1P}{Ki_GLY_b Ki_G1P})}{1.0 + \frac{GLY}{Ki_GLY_f} + \frac{Pi}{Ki_Pi} + \frac{GLY}{Ki_GLY_b} + \frac{G1P}{Ki_G1P} + \frac{GLY Pi}{K_GLY_f Ki_Pi} + \frac{GLY G1P}{K_GLY_b Ki_G1P}} \frac{\frac{{AMP}^{nH}}{K_AMP}}{1.0 + \frac{{AMP}^{nH}}{K_AMP}} V_max_r = \frac{V_max_f Ki_GLY_b K_G1P}{K_GLY_f Ki_Pi Keq_GP}

Component: V_PGLM

V_PGLM = \frac{V_max_f \frac{G1P}{K_G1P} - (V_max_r \frac{G6P}{K_G6P})}{1.0 + \frac{G1P}{K_G1P} + \frac{G6P}{K_G6P}} V_max_r = \frac{V_max_f K_G6P}{K_G1P Keq_PGLM}

Component: V_PGI

V_PGI = \frac{V_max_f \frac{G6P}{K_G6P} - (V_max_r \frac{F6P}{K_F6P})}{1.0 + \frac{G6P}{K_G6P} + \frac{F6P}{K_F6P}} V_max_f = \frac{V_max_r K_G6P Keq_PGI}{K_F6P}

Component: V_PFK

V_PFK = \frac{V_max_f \frac{ATP F6P}{K_ATP K_F6P} - (V_max_r \frac{ADP FBP}{K_ADP K_FBP})}{delta} \frac{1.0 + alpha L {(\frac{delta_}{delta})}^{3.0}}{1.0 + L {(\frac{delta_}{delta})}^{4.0}} delta = (1.0 + \frac{F6P}{K_F6P}) (1.0 + \frac{ATP}{K_ATP}) + \frac{ADP}{K_ADP} + \frac{FBP}{K_FBP} (1.0 + \frac{ADP}{K_ADP}) delta_= (1.0 + \frac{F6P}{K_F6P_}) (1.0 + \frac{ATP}{K_ATP_}) + \frac{ADP}{K_ADP_} + \frac{FBP}{K_FBP_} (1.0 + \frac{ADP}{K_ADP_}) alpha = \frac{K_F6P K_ATP}{K_F6P_K_ATP_} L = Lo {(\frac{1.0 + \frac{ATP}{Ki_ATP}}{1.0 + d \frac{ATP}{Ki_ATP}} \frac{1.0 + var_e \frac{AMP}{Ka_AMP}}{1.0 + \frac{AMP}{Ka_AMP}})}^{4.0} V_max_r = \frac{V_max_f K_ADP K_FBP}{K_ATP K_F6P}

Component: V_ALD

V_ALD = \frac{V_max_f \frac{FBP}{K_FBP} - (V_max_r \frac{DHAP GAP}{K_DHAP K_GAP})}{1.0 + \frac{FBP}{K_FBP} + \frac{DHAP}{K_DHAP} + \frac{GAP}{K_GAP}} V_max_r = \frac{V_max_f K_DHAP K_GAP}{K_FBP Keq_ALD}

Component: V_TPI

V_TPI = \frac{V_max_f \frac{GAP}{K_GAP} - (V_max_r \frac{DHAP}{K_DHAP})}{1.0 + \frac{DHAP}{K_DHAP} + \frac{GAP}{K_GAP}} V_max_r = \frac{V_max_f K_DHAP}{K_GAP Keq_TPI}

Component: V_GAPDH

V_GAPDH = \frac{V_max_f \frac{GAP NAD Pi}{K_GAP K_NAD K_Pi} - (V_max_r \frac{Thirteen_BPG NADH}{K_Thirteen_BPG K_NADH})}{D_GAPDH} D_GAPDH = 1.0 + \frac{GAP}{K_GAP} + \frac{NAD}{K_NAD} + \frac{Pi}{K_Pi} + \frac{GAP NAD}{K_GAP K_NAD} + \frac{GAP NAD Pi}{K_GAP K_NAD K_Pi} + \frac{Thirteen_BPG}{K_Thirteen_BPG} + \frac{NADH}{K_NADH} + \frac{Thirteen_BPG NADH}{K_Thirteen_BPG K_NADH} V_max_r = \frac{V_max_f 1 K_Thirteen_BPG K_NADH}{K_GAP K_NAD K_Pi Keq_GAPDH}

Component: V_PGK

V_PGK = \frac{V_max_f \frac{Thirteen_BPG ADP}{K_Thirteen_BPG K_ADP} - (V_max_r \frac{three_PG ATP}{K_three_PG K_ATP})}{1.0 + \frac{Thirteen_BPG}{K_Thirteen_BPG} + \frac{ADP}{K_ADP} + \frac{Thirteen_BPG ADP}{K_Thirteen_BPG K_ADP} + \frac{three_PG}{K_three_PG} + \frac{ATP}{K_ATP} + \frac{three_PG ATP}{K_three_PG K_ATP}} V_max_f = \frac{V_max_r K_Thirteen_BPG K_ADP Keq_PGK}{K_three_PG K_ATP}

Component: V_PGM

V_PGM = \frac{V_max_f \frac{three_PG}{K_three_PG} - (V_max_r \frac{two_PG}{K_two_PG})}{1.0 + \frac{three_PG}{K_three_PG} + \frac{two_PG}{K_two_PG}} V_max_r = \frac{V_max_f K_two_PG}{K_three_PG Keq_PGM}

Component: V_ENOL

V_ENOL = \frac{V_max_f \frac{two_PG}{K_two_PG} - (V_max_r \frac{PEP}{K_PEP})}{1.0 + \frac{two_PG}{K_two_PG} + \frac{PEP}{K_PEP}} V_max_r = \frac{V_max_f K_PEP}{K_two_PG Keq_ENOL}

Component: V_PK

V_PK = \frac{V_max_f \frac{PEP ADP}{K_PEP K_ADP} - (V_max_r \frac{PYR ATP}{K_PYR K_ATP})}{1.0 + \frac{PEP}{K_PEP} + \frac{ADP}{K_ADP} + \frac{PEP ADP}{K_PEP K_ADP} + \frac{PYR}{K_PYR} + \frac{ATP}{K_ATP} + \frac{PYR ATP}{K_PYR K_ATP}} V_max_r = \frac{V_max_f K_ATP K_PYR}{K_PEP K_ADP Keq_PK}

Component: V_LDH

V_LDH = \frac{V_max_f \frac{PYR NADH}{K_PYR K_NADH} - (V_max_r \frac{LAC NAD}{K_LAC K_NAD})}{1.0 + \frac{PYR}{K_PYR} + \frac{NADH}{K_NADH} + \frac{PYR NADH}{K_PYR K_NADH} + \frac{LAC}{K_LAC} + \frac{NAD}{K_NAD} + \frac{LAC NAD}{K_LAC K_NAD}} V_max_r = \frac{V_max_f K_LAC K_NAD}{K_PYR K_NADH Keq_LDH}

Component: V_CK

V_CK = \frac{V_max_f \frac{ATP Cr}{Ki_ATP K_Cr} - (V_max_r \frac{ADP PCr}{Ki_ADP K_PCr})}{1.0 + \frac{ADP}{Ki_ADP} + \frac{PCr}{Ki_PCr} + \frac{ADP PCr}{Ki_ADP K_PCr} + \frac{ATP}{Ki_ATP} + \frac{ATP Cr}{Ki_ATP K_Cr}} V_max_f = \frac{V_max_r Ki_ATP K_Cr Keq_CK}{Ki_ADP K_PCr}

Component: V_ADK

V_ADK = \frac{V_max_f \frac{ATP AMP}{K_ATP K_AMP} - (V_max_r \frac{{ADP}^{2.0}}{{K_ADP}^{2.0}})}{1.0 + \frac{ATP}{K_ATP} + \frac{AMP}{K_AMP} + \frac{ATP AMP}{K_ATP K_AMP} + \frac{2.0 ADP}{K_ADP} + \frac{{ADP}^{2.0}}{{K_ADP}^{2.0}}} V_max_r = \frac{V_max_f {K_ADP}^{2.0}}{K_ATP K_AMP Keq_ADK}

Component: V_ATPase

Source: Derived from workspace Lambeth, Kushmerick, 2002 at changeset 0cfa157d09ca.

Collaboration: To begin collaborating on this work, please use your git client and issue this command:

Downloads

Views Available

Tools

License: This work is licensed under a Creative Commons Attribution 3.0 Unported License.

A computational model for glycogenolysis in skeletal muscle