You are here: Home / Exposures / Bertram, Satin, Pedersen, Luciani, Sherman, 2007 / Intra- and inter-islet synchronization of metabolically driven insulin secretion

Model Mathematics

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Component: environment

Component: membrane

\frac{d}{d time} (Vm) = \frac{- (Ik + Ica + Ikca + Ikatp)}{cm}

Component: Ik

Ik = gK n (Vm - VK)

Component: n

\frac{d}{d time} (n) = \frac{n_infinity - n}{tau_n} n_infinity = \frac{1.0}{1.0 + ⅇ^{\frac{vn - Vm}{sn}}}

Component: Ica

Ica = gCa m_infinity (Vm - VCa)

Component: m

m_infinity = \frac{1.0}{1.0 + ⅇ^{\frac{v - Vm}{sm}}}

Component: Ikca

Ikca = \frac{gkCa}{1.0 + {(\frac{kd}{c})}^{2.0}} (Vm - VK)

Component: Ikatp

Ikatp = gkATP_katpo (Vm - VK) katpo = \frac{topo}{bottomo} topo = 0.08 (1.0 + \frac{2.0 mgadp}{17.0}) + 0.89 {(\frac{mgadp}{17.0})}^{2.0} bottomo = {(1.0 + \frac{mgadp}{17.0})}^{2.0} (1.0 + \frac{adp3m}{26.0} + \frac{atp4m}{1.0}) mgadp = 0.165 adp adp3m = 0.135 adp atp4m = 0.05 atp

Component: JGPDH

JGPDH = kGPDH \sqrt{| \frac{FBP}{1} |}

Component: G6P

\frac{d}{d time} (G6P) = JGK_ms - JPFK_ms

Component: FBP

\frac{d}{d time} (FBP) = JPFK_ms - (0.5 JGPDH)

Component: F6P

F6P = 0.3 G6P

Component: JPFK

JPFK_ms = kappa JPFK JPFK = \frac{lambda VmaxPFK topa16 + VmaxPFK 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}}{f43 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 f42 1} topa6 = topa5 bottom6 = bottom5 + weight6

weight7 = \frac{FBP {F6P}^{2}}{k2 k3 f23 1} topa7 = topa6 + weight7 bottom7 = bottom6 + weight7

weight8 = \frac{FBP {F6P}^{2} {atp}^{2}}{k2 k3 k4 f23 f42 f43 1^{2}} topa8 = topa7 + weight8 bottom8 = bottom7 + weight8

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

weight10 = \frac{AMP {atp}^{2}}{k1 k4 f41 1} topa10 = topa9 bottom10 = bottom9 + weight10

weight11 = \frac{AMP {F6P}^{2}}{k1 k3 f13 1} topa11 = topa10 + weight11 bottom11 = bottom10 + weight11

weight12 = \frac{AMP {F6P}^{2} {atp}^{2}}{k1 k3 k4 f13 f41 f43 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 f42 f41 1} topa14 = topa13 bottom14 = bottom13 + weight14

weight15 = \frac{AMP FBP {F6P}^{2}}{k1 k2 k3 f23 f13 1} topa15 = topa14 bottom15 = bottom14 + weight15 topb = weight15

weight16 = \frac{AMP FBP {F6P}^{2} {atp}^{2}}{k1 k2 k3 k4 f23 f13 f42 f41 f43 1^{2}} topa16 = topa15 + weight16 bottom16 = bottom15 + weight16

Component: JPDH

JPDH = \frac{p1}{p2 + \frac{NADHm}{NADm}} \frac{Cam}{p3 + Cam} (JGPDH + JGPDHbas)

Component: NADHm

\frac{d}{d time} (NADHm) = gamma (JPDH - JO)

Component: JO

JO = \frac{p4 \frac{NADHm}{p5 + NADHm}}{1.0 + ⅇ^{\frac{delta_psi - p6}{p7}}}

Component: NADm

NADm = NADmtot - NADHm

Component: delta_psi

\frac{d}{d time} (delta_psi) = \frac{JHres - (JHatp + JANT + JHleak + JNaCa + 2.0 Juni)}{Cmito}

Component: JHres

JHres = \frac{p8 \frac{NADHm}{p9 + NADHm}}{1.0 + ⅇ^{\frac{delta_psi - p10}{p11}}}

Component: JF1F0

JF1F0 = \frac{\frac{p16 p13}{p13 + ATPm}}{1.0 + ⅇ^{\frac{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 \frac{\frac{RATm}{RATm + p20}}{ⅇ^{(-0.5) FRT delta_psi}}

Component: RATm

RATm = \frac{ATPm}{ADPm}

Component: Juni

Juni = (p21 delta_psi - p22) c^{2.0}

Component: JNaCa

JNaCa = \frac{p23}{c} Cam ⅇ^{p24 delta_psi}

Component: Cam

\frac{d}{d time} (Cam) = (- fmito) Jmito

Component: Jmito

Jmito = JNaCa - Juni

Component: ADPm

\frac{d}{d time} (ADPm) = gamma (JANT - JF1F0)

Component: ATPm

ATPm = Amtot - ADPm

Component: adp

\frac{d}{d time} (adp) = (- delta) JANT + Jhyd

Component: Jhyd

Jhyd = (khyd c + khydbas) atp

Component: atp

atp = atot - adp

Component: c

\frac{d}{d time} (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

\frac{d}{d time} (Caer) = (- fer) Vc_Ver Jer

Component: model_parameters

delta = \frac{3.9}{53.2}

Source: Derived from workspace Bertram, Satin, Pedersen, Luciani, Sherman, 2007 at changeset 1a78488e2cb0.

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Intra- and inter-islet synchronization of metabolically driven insulin secretion