Model Mathematics

\frac{d}{d time} (V) = \frac{- (IK + ICa + IKCa + IKATP)}{Cm}

IK = gK n (V - VK)

IKCa = \frac{gKCa}{1 + {(\frac{kd}{c})}^{2}} (V - VK)

ICa = gCa minf (V - VCa)

minf = \frac{1}{1 + ⅇ^{\frac{- (20 + V)}{12}}}

ninf = \frac{1}{1 + ⅇ^{\frac{- (16 + V)}{5}}}

\frac{d}{d time} (n) = \frac{ninf - n}{taun}

\frac{d}{d time} (c) = fcyt (Jmem + Jer)

\frac{d}{d time} (cer) = (- fer) sigmaV Jer

Jserca = Kserca c

Jleak = pleak (cer - c)

Jer = \frac{epser (Jleak - Jserca)}{lambdaer}

Jmem = - (alpha ICa + kpmca c)

f6p = 0.3 g6p

rgpdh = 0.2 \sqrt{\frac{fbp}{1}}

\frac{d}{d time} (fbp) = lambda (\frac{pfk}{1} - (0.5 rgpdh))

\frac{d}{d time} (g6p) = lambda (Rgk 1 - (\frac{pfk}{1}))

pfk = 1 \frac{pfkbas cat topa16 + cat topb}{bottom16}

weight2 = \frac{{atp}^{2}}{k4 1} topa2 = topa1 bottom2 = bottom1 + weight2

weight3 = \frac{{f6p}^{2}}{k3 1} topa3 = topa2 + weight3 bottom3 = bottom2 + weight3

weight4 = \frac{{(f6p atp)}^{2}}{fatp k3 k4 1^{2}} topa4 = topa3 + weight4 bottom4 = bottom3 + weight4

weight5 = \frac{fbp}{k2} topa5 = topa4 bottom5 = bottom4 + weight5

weight6 = \frac{fbp {atp}^{2}}{k2 k4 fbt 1} topa6 = topa5 bottom6 = bottom5 + weight6

weight7 = \frac{fbp {f6p}^{2}}{k2 k3 ffbp 1} topa7 = topa6 + weight7 bottom7 = bottom6 + weight7

weight8 = \frac{fbp {f6p}^{2} {atp}^{2}}{k2 k3 k4 ffbp fbt fatp 1^{2}} topa8 = topa7 + weight8 bottom8 = bottom7 + weight8

weight9 = \frac{amp}{k1} topa9 = topa8 bottom9 = bottom8 + weight9

weight10 = \frac{amp {atp}^{2}}{k1 k4 fmt 1} topa10 = topa9 bottom10 = bottom9 + weight10

weight11 = \frac{amp {f6p}^{2}}{k1 k3 famp 1} topa11 = topa10 + weight11 bottom11 = bottom10 + weight11

weight12 = \frac{amp {f6p}^{2} {atp}^{2}}{k1 k3 k4 famp fmt fatp 1^{2}} topa12 = topa11 + weight12 bottom12 = bottom11 + weight12

weight13 = \frac{amp fbp}{k1 k2} topa13 = topa12 bottom13 = bottom12 + weight13

weight14 = \frac{amp fbp {atp}^{2}}{k1 k2 k4 fbt fmt 1} topa14 = topa13 bottom14 = bottom13 + weight14

weight15 = \frac{amp fbp {f6p}^{2}}{k1 k2 k3 ffbp famp 1} topa15 = topa14 bottom15 = bottom14 + weight15 topb = weight15

weight16 = \frac{amp fbp {f6p}^{2} {atp}^{2}}{k1 k2 k3 k4 ffbp famp fbt fmt fatp 1^{2}} topa16 = topa15 + weight16 bottom16 = bottom15 + weight16

mgadp = 0.165 adp

adp3m = 0.135 adp

atp4m = 0.05 atp

topo = 0.08 (1 + \frac{2 mgadp}{kdd 1}) + 0.89 {(\frac{mgadp}{kdd 1})}^{2}

bottomo = {(1 + \frac{mgadp}{kdd 1})}^{2} (1 + \frac{adp3m}{ktd 1} + \frac{atp4m}{ktt 1})

katpo = \frac{topo}{bottomo}

IKATP = gkatpbar katpo (V - VK)

\frac{d}{d time} (adp) = \frac{atp - (adp ⅇ^{fback (1 - (\frac{c}{r1}))})}{taua 1}

fback = r + y

y = vg \frac{rgpdh}{kg + rgpdh}

atp = 0.5 ((atot - adp) + rad 1)

amp = \frac{adp adp}{atp}

ratio = \frac{atp}{adp}

rad = \frac{\sqrt{{(adp - atot)}^{2} - (4 {adp}^{2})}}{1}