# Model Mathematics

### Component: membrane

$ddtime Vm =- Ik + Ica + Ikca + Ikatp cm$

### Component: Ik

$Ik = gK ⁢ n ⁢ Vm - VK$

### Component: n

$ddtime n = n_infinity - n tau_n n_infinity = 1.0 1.0 +ⅇ vn - Vm sn$

### Component: Ica

$Ica = gCa ⁢ m_infinity ⁢ Vm - VCa$

### Component: m

$m_infinity = 1.0 1.0 +ⅇ v - Vm sm$

### Component: Ikca

$Ikca = gkCa 1.0 + kd c 2.0 ⁢ Vm - VK$

### Component: Ikatp

$Ikatp = gkATP_ ⁢ katpo ⁢ Vm - VK katpo =topobottomo topo = 0.08 ⁢ 1.0 + 2.0 ⁢ mgadp 17.0 + 0.89 ⁢ mgadp 17.0 2.0 bottomo = 1.0 + mgadp 17.0 2.0 ⁢ 1.0 + adp3m 26.0 + atp4m 1.0 mgadp = 0.165 ⁢ adp adp3m = 0.135 ⁢ adp atp4m = 0.05 ⁢ atp$

### Component: JGPDH

$JGPDH = kGPDH ⁢| FBP 1|$

### Component: G6P

$ddtime G6P = JGK_ms - JPFK_ms$

### Component: FBP

$ddtime FBP = JPFK_ms - 0.5 ⁢ JGPDH$

### Component: F6P

$F6P = 0.3 ⁢ G6P$

### Component: JPFK

$JPFK_ms = kappa ⁢ JPFK JPFK =lambda⁢VmaxPFK⁢topa16+VmaxPFK⁢topbbottom16$$weight2=atp2k4⁢1topa2=topa1bottom2=bottom1+weight2$$weight3=F6P2k3⁢1topa3=topa2+weight3bottom3=bottom2+weight3$$weight4=F6P⁢atp2f43⁢k3⁢k4⁢12topa4=topa3+weight4bottom4=bottom3+weight4$$weight5=FBPk2topa5=topa4bottom5=bottom4+weight5$$weight6=FBP⁢atp2k2⁢k4⁢f42⁢1topa6=topa5bottom6=bottom5+weight6$$weight7=FBP⁢F6P2k2⁢k3⁢f23⁢1topa7=topa6+weight7bottom7=bottom6+weight7$$weight8=FBP⁢F6P2⁢atp2k2⁢k3⁢k4⁢f23⁢f42⁢f43⁢12topa8=topa7+weight8bottom8=bottom7+weight8$$weight9=AMPk1topa9=topa8bottom9=bottom8+weight9$$weight10=AMP⁢atp2k1⁢k4⁢f41⁢1topa10=topa9bottom10=bottom9+weight10$$weight11=AMP⁢F6P2k1⁢k3⁢f13⁢1topa11=topa10+weight11bottom11=bottom10+weight11$$weight12=AMP⁢F6P2⁢atp2k1⁢k3⁢k4⁢f13⁢f41⁢f43⁢12topa12=topa11+weight12bottom12=bottom11+weight12$$weight13=AMP⁢FBPk1⁢k2topa13=topa12bottom13=bottom12+weight13$$weight14=AMP⁢FBP⁢atp2k1⁢k2⁢k4⁢f42⁢f41⁢1topa14=topa13bottom14=bottom13+weight14$$weight15=AMP⁢FBP⁢F6P2k1⁢k2⁢k3⁢f23⁢f13⁢1topa15=topa14bottom15=bottom14+weight15topb=weight15$$weight16=AMP⁢FBP⁢F6P2⁢atp2k1⁢k2⁢k3⁢k4⁢f23⁢f13⁢f42⁢f41⁢f43⁢12topa16=topa15+weight16bottom16=bottom15+weight16$

### Component: JPDH

$JPDH = p1 p2 + NADHm NADm ⁢ Cam p3 + Cam ⁢ JGPDH + JGPDHbas$

$ddtime NADHm = gamma ⁢ JPDH - JO$

### Component: JO

$JO = p4 ⁢ NADHm p5 + NADHm 1.0 +ⅇ delta_psi - p6 p7$

$NADm = NADmtot - NADHm$

### Component: delta_psi

$ddtime delta_psi = JHres - JHatp + JANT + JHleak + JNaCa + 2.0 ⁢ Juni Cmito$

### Component: JHres

$JHres = p8 ⁢ NADHm p9 + NADHm 1.0 +ⅇ delta_psi - p10 p11$

### Component: JF1F0

$JF1F0 = p16 ⁢ p13 p13 + ATPm 1.0 +ⅇ p14 - delta_psi p15$

### Component: JHatp

$JHatp = 3.0 ⁢ JF1F0$

### Component: JGK

$JGK_ms = kappa ⁢ JGK$

### Component: JHleak

$JHleak = p17 ⁢ delta_psi + p18$

### Component: JANT

$JANT = p19 ⁢ RATm RATm + p20 ⅇ -0.5 ⁢ FRT ⁢ delta_psi$

### Component: RATm

$RATm = ATPm ADPm$

### Component: Juni

$Juni = p21 ⁢ delta_psi - p22 ⁢ c 2.0$

### Component: JNaCa

$JNaCa = p23 c ⁢ Cam ⁢ⅇ p24 ⁢ delta_psi$

### Component: Cam

$ddtime Cam =- fmito ⁢ Jmito$

### Component: Jmito

$Jmito = JNaCa - Juni$

$ddtime ADPm = gamma ⁢ JANT - JF1F0$

### Component: ATPm

$ATPm = Amtot - ADPm$

$ddtime adp =- delta ⁢ JANT + Jhyd$

### Component: Jhyd

$Jhyd = khyd ⁢ c + khydbas ⁢ atp$

### Component: atp

$atp = atot - adp$

### Component: c

$ddtime c = fcyt ⁢ Jmem + Jer + delta ⁢ Jmito$

### Component: Jmem

$Jmem =- alpha ⁢ Ica + kPMCA ⁢ c - Cbas$

### Component: Jleak

$Jleak = pleak ⁢ Caer - c$

### Component: JSERCA

$JSERCA = kSERCA ⁢ c$

### Component: Jer

$Jer = Jleak - JSERCA$

### Component: Caer

$ddtime Caer =- fer ⁢ Vc_Ver ⁢ Jer$

### Component: model_parameters

$delta = 3.9 53.2$
Source
Derived from workspace Bertram, Satin, Pedersen, Luciani, Sherman, 2007 at changeset 1a78488e2cb0.
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