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Model Mathematics

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Component: environment

Component: F6P

\frac{d}{d time} (F6P) = V_hk - (V_pfk - V_pfk2)

Component: F26P

\frac{d}{d time} (F26P) = V_pfk2

Component: GAP

\frac{d}{d time} (GAP) = 2.0 V_pfk - V_pk

Component: PYR

\frac{d}{d time} (PYR) = V_pk - (V_op + V_ldh)

Component: LAC

\frac{d}{d time} (LAC) = 2.25 V_ldh + V_lac

Component: ATP

\frac{d}{d time} (ATP) = (2.0 V_pk + 15.0 V_op + V_ck - (V_hk + V_pfk + V_pfk2 + V_ATPase)) {(1 - dAMP_dATP)}^{-1}

Component: PCr

\frac{d}{d time} (PCr) = - V_ck

Component: V_hk

V_hk = Vmax_hk \frac{ATP}{ATP + Km_ATP_hk} {(1 + {(\frac{F6P}{KI_F6P})}^{4})}^{-1}

Component: V_pfk

V_pfk = Vmax_pfk \frac{F6P}{F6P + Km_F6P_pfk} \frac{ATP}{ATP + Km_ATP_pfk} \frac{F26P}{F26P + Km_F26P_pfk} ATP_inh AMP_act

Component: V_pfk2

V_pfk2 = Vmaxf_pfk2 \frac{ATP}{ATP + Km_ATP_pfk2} \frac{F6P}{F6P + Km_F6P_pfk2} AMP_pfk2 - (Vmaxr_pfk2 \frac{F26P}{F26P + Km_F26P_pfk2})

Component: V_pk

V_pk = Vmax_pk \frac{GAP}{GAP + Km_GAP_pk} \frac{ADP}{ADP + Km_ADP_pk} ATP_inh

Component: V_op

V_op = Vmax_op \frac{PYR}{PYR + Km_PYR_op} \frac{ADP}{ADP + Km_ADP_op} \frac{1}{1 + 0.1 \frac{ATP}{ADP}}

Component: V_ldh

V_ldh = kf_ldh PYR - (kr_ldh LAC)

Component: V_ck

V_ck = kf_ck PCr ADP - (kr_ck Cr ATP)

Component: Cr

Cr = PCrtot - PCr

Component: V_ATPase

V_ATPase = Vmax_ATPase \frac{ATP}{ATP + Km_ATP} (1 + v_stim)

Component: V_lac

V_lac = Vlac_0 (1 + v_stim K_LAC) - (K_LAC_eff LAC)

Component: ADP

ADP = \frac{ATP}{2} ((- Q_adk) + \sqrt{u})

u = {Q_adk}^{2} + 4 Q_adk (\frac{ANP}{ATP} - 1)

Component: dAMP_dATP

dAMP_dATP = (- 1) + \frac{Q_adk}{2} + (- (0.5 \sqrt{u})) + Q_adk \frac{ANP}{ATP \sqrt{u}}

Component: AMP

AMP = ANP - (ATP + ADP)

Component: ATP_inh

ATP_inh = {(\frac{1 + nATP \frac{ATP}{KI_ATP}}{1 + \frac{ATP}{KI_ATP}})}^{4}

Component: AMP_act

AMP_act = {(\frac{1 + \frac{AMP}{Ka_AMP}}{1 + nAMP \frac{AMP}{Ka_AMP}})}^{4}

Component: v_stim

v_stim = stim (v1_n + v2_n \frac{time - to}{t_n_stim} ⅇ^{- ((time - to) \frac{unitpulseSB}{t_n_stim})}) unitpulseSB

unitpulseSB = \{\begin{matrix} 1 if time \geq to \land time ≦ to + tend \\ 0 otherwise \end{matrix}

Component: model_parameters

Component: AMP_pfk2

AMP_pfk2 = \frac{{(\frac{AMP}{Kamp_pfk2})}^{nh_amp}}{1 + {(\frac{AMP}{Kamp_pfk2})}^{nh_amp}}

Source: Derived from workspace Cloutier Wellstead 2009 at changeset ac493499b199.

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