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Model Mathematics

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Component: environment

Component: Gi

\frac{d}{d time} (Gi) = Jglut - Jgk

Component: Ge

\frac{d}{d time} (Ge) = \frac{G_infinity - Ge}{tau_G} G_infinity = Gmin + \frac{Gmax - Gmin}{1 + ⅇ^{\frac{I - I_}{SG}}}

Component: G6P

\frac{d}{d time} (G6P) = kappa (Jgk - JPFK)

Component: FBP

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

Component: F6P

F6P = 0.3 G6P

Component: Jglut

Jglut = \frac{Vglut (Ge - Gi) Kglut}{(Kglut + Ge) (Kglut + Gi)}

Component: Jgk

Jgk = \frac{Vgk {Gi}^{ngk}}{{Kgk}^{ngk} + {Gi}^{ngk}}

Component: JGPDH

JGPDH = 0.2 \sqrt{\frac{FBP}{1}}

Component: JPFK

JPFK = \frac{Vmax ((1 - lambda) w1110 + lambda (w0010 + w1010 + w0011 + w1110 + w0111 + w1011 + w0110 + w1111))}{w0000 + w1000 + w0100 + w0010 + w0001 + w1100 + w1010 + w1001 + w0101 + w0011 + w0110 + w1110 + w0111 + w1011 + w1101 + w1111}

Component: w

w0000 = 1 w1000 = {(\frac{AMP}{K1})}^{1} w0100 = {(\frac{FBP}{K2})}^{1} w0010 = {(\frac{{F6P}^{2}}{K3})}^{1} w0001 = {(\frac{{ATP}^{2}}{K4})}^{1} w1100 = {(\frac{AMP}{K1})}^{1} {(\frac{FBP}{K2})}^{1} w1010 = \frac{1}{{f13}^{1 1}} {(\frac{AMP}{K1})}^{1} {(\frac{{F6P}^{2}}{K3})}^{1} w1001 = \frac{1}{{f41}^{1 1}} {(\frac{AMP}{K1})}^{1} {(\frac{{ATP}^{2}}{K4})}^{1} w0101 = \frac{1}{{f42}^{1 1}} {(\frac{FBP}{K2})}^{1} {(\frac{{ATP}^{2}}{K4})}^{1} w0011 = \frac{1}{{f43}^{1 1}} {(\frac{{F6P}^{2}}{K3})}^{1} {(\frac{{ATP}^{2}}{K4})}^{1} w0110 = \frac{1}{{f23}^{1 1}} {(\frac{FBP}{K2})}^{1} {(\frac{{F6P}^{2}}{K3})}^{1} w1110 = \frac{1}{{f13}^{1 1} {f23}^{1 1}} {(\frac{AMP}{K1})}^{1} {(\frac{FBP}{K2})}^{1} {(\frac{{F6P}^{2}}{K3})}^{1} w0111 = \frac{1}{{f23}^{1 1} {f42}^{1 1} {f43}^{1 1}} {(\frac{FBP}{K2})}^{1} {(\frac{{F6P}^{2}}{K3})}^{1} {(\frac{{ATP}^{2}}{K4})}^{1} w1011 = \frac{1}{{f13}^{1 1} {f41}^{1 1} {f43}^{1 1}} {(\frac{AMP}{K1})}^{1} {(\frac{{F6P}^{2}}{K3})}^{1} {(\frac{{ATP}^{2}}{K4})}^{1} w1101 = \frac{1}{{f41}^{1 1} {f42}^{1 1}} {(\frac{AMP}{K1})}^{1} {(\frac{FBP}{K2})}^{1} {(\frac{{ATP}^{2}}{K4})}^{1} w1111 = \frac{1}{{f13}^{1 1} {f23}^{1 1} {f41}^{1 1} {f42}^{1 1} {f43}^{1 1}} {(\frac{AMP}{K1})}^{1} {(\frac{FBP}{K2})}^{1} {(\frac{{F6P}^{2}}{K3})}^{1} {(\frac{{ATP}^{2}}{K4})}^{1}

Component: ATP

ATP = Atot - (ADP + AMP)

Component: AMP

AMP = \frac{{ADP}^{2}}{ATP}

Component: ADP

\frac{d}{d time} (ADP) = \frac{1}{tau_a} (ATP - (ADP ⅇ^{(r + gamma) (1 - (\frac{Ca}{r1}))}))

Component: gamma

gamma = \frac{v_gamma JGPDH}{k_gamma + JGPDH}

Component: membrane

\frac{d}{d time} (v) = \frac{- (I_K + I_Ca + I_K_Ca + I_K_ATP)}{cm}

Component: I_K

I_K = gK_n (v - vK)

Component: n

\frac{d}{d time} (n) = \frac{n_infinity - n}{tau_n} tau_n = \frac{1}{0.035 \cosh (\frac{v + 16}{22.4})} n_infinity = \frac{1}{1 + ⅇ^{\frac{- (v + 16)}{5.6}}}

Component: I_Ca

I_Ca = gCa_m_infinity (v - vCa)

Component: m

m_infinity = \frac{1}{1 + ⅇ^{\frac{- (v + 20)}{12}}}

Component: I_K_Ca

I_K_Ca = gkCa (v - vK) gkCa = \frac{gkCa_{Ca}^{2}}{{KD}^{2} + {Ca}^{2}}

Component: I_K_ATP

I_K_ATP = gkATP (v - vK) gkATP = gkATP_o_infinity o_infinity = \frac{0.08 (1 + \frac{2 MgADP}{17}) + 0.89 {(\frac{MgADP}{17})}^{2}}{{(1 + \frac{MgADP}{17})}^{2} (1 + \frac{ADP3_}{26} + \frac{ATP4_}{1})} MgADP = 0.165 ADP ADP3_= 0.135 ADP ATP4_= 0.005 ATP

Component: Ca

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

Component: Caer

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

Component: Jmem

Jmem = - (alpha I_Ca + kPMCA Ca)

Component: Jer

Jer = Jleak - JSERCA

Component: JSERCA

JSERCA = kSERCA Ca

Component: Jleak

Jleak = pleak (Caer - Ca)

Component: I

\frac{d}{d time} (I) = \frac{I_infinity - I}{tau_I} I_infinity = \{\begin{matrix} I_slope (Ca - Canull) if Ca \geq Canull \\ 0 if Ca < Canull \end{matrix}

Component: model_parameters

Source: Derived from workspace Pedersen, Bertram, Sherman, 2005 at changeset 3a769cef2496.; This exposure was expired. A more up-to-date exposure is available, or view related resources.

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