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Model Mathematics

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Component: environment

Component: geometry

Cc = \frac{1}{Vc 6.022e2}

Cp = \frac{1}{Vc Rpc}

Cpc = \frac{Cc}{Cp}

Component: Galpha_interface

J_gain_Gd = plcJ5 + plcJ6 - (gpcrJ2 + gpcrJ3)

J_gain_Gt = gpcrJ6 - (plcJ2 + plcJ3)

Component: calcium_interface

J_gain_Ca = Cpc (-1) (plcJ1 + plcJ4)

Component: IP3_interface

J_gain_IP3 = Cpc (pip2J1 + pip2J2) - IP3degJ

Component: ligand

L = \{\begin{matrix} \frac{Ls}{1.0 + ⅇ^{(-80.0) (t - ts - 0.05)}} if t < ts + 0.15 \land t \geq ts \\ Ls if t \geq ts + 0.15 \\ 0 otherwise \end{matrix}

Component: GPCR_Cycle

kr1 = kf1 Kd1

J1 = kf1 R L - (kr1 Rl)

kr2 = kf2 Kd2

J2 = kf2 R Gd - (kr2 Rg)

\frac{d}{d t} (R) = (-1.0) J1 - J2

J3 = kf3 Rl Gd - (kr3 Rlg)

\frac{d}{d t} (Rl) = J1 + J6 - J3

kr4 = kf4 Kd4

J4 = kf4 L Rg - (kr4 Rlg)

\frac{d}{d t} (Rg) = J2 - J4

J5 = kf5 Rlg

\frac{d}{d t} (Rlgp) = J5

J6 = kf6 Rlg

\frac{d}{d t} (Rlg) = (J3 - J5) + (J4 - J6)

Component: Galpha

\frac{d}{d t} (Gd) = J1 + J_gain_Gd

\frac{d}{d t} (Gt) = J_gain_Gt - J1

J1 = kf1 Gt

Component: calcium

\frac{d}{d t} (Ca) = J_gain_Ca

Component: PLC_Cycle

J2 = kf2 P Gt - (kr2 Pg)

J1 = kf1 P Ca - (kr1 Pc)

J3 = kf3 Pc Gt - (kr3 Pcg)

kr4 = kf4 Kd4

J4 = kf4 Pg Ca - (kr4 Pcg)

J5 = kf5 Pcg

J6 = kf6 Pg

\frac{d}{d t} (P) = J6 - (J2 + J1)

\frac{d}{d t} (Pg) = J2 - (J4 + J6)

\frac{d}{d t} (Pc) = J1 + J5 - J3

\frac{d}{d t} (Pcg) = J3 + J4 - J5

Component: PIP2

J1 = \frac{kf1 Eb PIP2}{\frac{Km1}{Cpc} + PIP2}

J2 = \frac{kf2 Es PIP2}{\frac{Km2}{Cpc} + PIP2}

Component: IP3

\frac{d}{d t} (IP3) = J_gain_IP3

Component: IP3_degradation

J1 = kf1 IP3

Source: Derived from workspace Cooling, Hunter, Crampin, Cellml, 2008 at changeset b685dbf53979.

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Cooling, Hunter, Crampin, 2008