# Model Mathematics

### Component: Gi

$ddtimeGi=Jglut-Jgk$

### Component: Ge

$Ge=glubasa1+gluamp⁢1-glustep⁢cos⁡time⁢2⁢π60000⁢gluper+GeStepGeStep=glustep⁢gluampiftime-steptime1000.0>1.0time-steptime1000.0⁢glustep⁢gluampiftime-steptime1000.0>0.0∧time-steptime1000.0<1.00.0iftime-steptime1000.0<0.0$

### Component: G6P

$ddtimeG6P=kappa⁢Jgk-JPFK$

### Component: FBP

$ddtimeFBP=kappa⁢JPFK-0.5⁢JGPDH$

### Component: F6P

$F6P=0.3⁢G6P$

### Component: Jglut

$Jglut=Vglut⁢Ge-Gi⁢KglutKglut+Ge⁢Kglut+Gi$

### Component: Jgk

$Jgk=Vgk⁢GingkKgkngk+Gingk$

### Component: JGPDH

$JGPDH=0.2⁢FBP1$

### Component: JPFK

$JPFK=pfkbas⁢cat⁢topa16+cat⁢topbbottom16$

### Component: w

$weight1=1topa1=0bottom1=1weight9=AMPK1topa9=topa8bottom9=bottom8+weight9weight5=FBPK2topa5=topa4bottom5=bottom4+weight5weight3=F6P21⁢K3topa3=topa2+weight3bottom3=bottom2+weight3weight2=ATP21⁢K4topa2=topa1bottom2=bottom1+weight2weight13=AMP⁢FBPK1⁢K2topa13=topa12bottom13=bottom12+weight13weight11=AMP⁢F6P21⁢K1⁢K3⁢famptopa11=topa10+weight11bottom11=bottom10+weight11weight10=AMP⁢ATP21⁢K1⁢K4⁢fmttopa10=topa9bottom10=bottom9+weight10weight6=FBP⁢ATP21⁢K2⁢K4⁢fbttopa6=topa5bottom6=bottom5+weight6weight4=F6P⁢ATP21⁢fatp⁢K3⁢K4topa4=topa3+weight4bottom4=bottom3+weight4weight7=FBP⁢F6P21⁢K2⁢K3⁢ffbptopa7=topa6+weight7bottom7=bottom6+weight7weight15=AMP⁢FBP⁢F6P21⁢K1⁢K2⁢K3⁢ffbp⁢famptopa15=topa14topb=weight15bottom15=bottom14+weight15weight8=FBP⁢F6P2⁢ATP21⁢K2⁢K3⁢K4⁢ffbp⁢fbt⁢fatptopa8=topa7+weight8bottom8=bottom7+weight8weight12=AMP⁢F6P2⁢ATP21⁢K1⁢K3⁢K4⁢famp⁢fmt⁢fatptopa12=topa11+weight12bottom12=bottom11+weight12weight14=AMP⁢FBP⁢ATP21⁢K1⁢K2⁢K4⁢fbt⁢fmttopa14=topa13bottom14=bottom13+weight14weight16=AMP⁢FBP⁢F6P2⁢ATP21⁢K1⁢K2⁢K3⁢K4⁢ffbp⁢famp⁢fbt⁢fmt⁢fatptopa16=topa15+weight16bottom16=bottom15+weight16$

### Component: ATP

$ATP=0.5⁢Atot+rad-ADPrad=ADP-Atot2-4⁢ADP2$

### Component: AMP

$AMP=ADP2ATP$

$ddtimeADP=autoadp⁢+ATP-ADP⁢ⅇfback⁢1-Car1tau_a+1⁢1-autoadp⁢adpknot-ADPy=ky⁢JGPDHkg+JGPDHfback=r+y$

### Component: membrane

$ddtimev=-I_K+I_Ca+I_K_Ca+I_K_ATPcm$

### Component: I_K

$I_K=gK⁢n⁢v-vK$

### Component: n

$ddtimen=n_infinity-ntau_ntau_n=10.035⁢cosh⁡v--1622.4n_infinity=0.5⁢1+tanh⁡v--1611.2$

### Component: I_Ca

$I_Ca=gCa⁢m_infinity⁢v-vCa$

### Component: m

$m_infinity=0.5⁢1+tanh⁡v--2024$

### Component: I_K_Ca

$I_K_Ca=gkCa1+KDCanh⁢v-vK$

### Component: I_K_ATP

$I_K_ATP=gkATP_bar⁢katpo⁢v-vKkatpo=20.0⁢topobottomotopo=0.08⁢1+2⁢MgADP17+0.89⁢MgADP172bottomo=1+MgADP172⁢1+ADP326+ATP41MgADP=0.165⁢ADPADP3=0.135⁢ADPATP4=0.05⁢ATP$

### Component: Ca

$ddtimeCa=fcyt⁢Jmem+Jer$

### Component: Caer

$ddtimeCaer=-fer⁢sigmav⁢Jer$

### Component: Jmem

$Jmem=-alpha⁢1⁢I_Ca+kPMCA⁢Ca$

### Component: Jer

$Jer=Jleak-JSERCA$

### Component: JSERCA

$JSERCA=kSERCA⁢Ca$

### Component: Jleak

$Jleak=pleak⁢Caer-Ca$

### Component: I

$ddtimeI=I_infinity-Itau_II_infinity=I_max⁢Cadeltakidelta+Cadelta$

### Component: model_parameters

Source
Derived from workspace Pedersen, Bertram, Sherman, 2005 at changeset 54a5b1477c85.
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