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Model Mathematics

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Component: environment

Component: volume_i

volume_i = volume_i0

Component: volume_er

volume_er = \frac{volume_i}{gamma}

Component: volumeCa_i

\frac{d}{d time} (volumeCa_i) = (Jipt + Jryr + Jer - Jserca) + (Jin - Jpm)

Component: Ca_i

Ca_i = \frac{volumeCa_i}{volume_i}

Component: volumeCa_er

\frac{d}{d time} (volumeCa_er) = - (Jipt + Jryr + Jer - Jserca)

Component: Ca_er

Ca_er = \frac{volumeCa_er}{volume_er}

Component: volume_iIP3

\frac{d}{d time} (volume_iIP3) = (J_ip3P - J_ip3D) volume_i

Component: IP3

IP3 = \frac{volume_iIP3}{volume_i}

Component: PIP2

\frac{d}{d time} (PIP2) = J_ip3R IPX - (\frac{J_ip3P}{PIP2_Total})

Component: IPX

IPX = 1 - (\frac{IP3}{PIP2_Total}) - PIP2

Component: J_ip3R

J_ip3R = J_ip3R0

Component: receptor

V_mech = \{\begin{matrix} V_mech0 if time > 10 \land time < 25 \land MechanicalStimulation > 0 \\ 0 otherwise \end{matrix} V_IP3 = \frac{C_1 ATP_e}{C_2 + ATP_e} + \frac{C_3 {ATP_e}^{2}}{{C_4}^{2} + {ATP_e}^{2}} \frac{d}{d time} (ATP_e) = \frac{(- V_ATP) ATP_e}{K_ATP + ATP_e}

Component: J_ip3P

J_ip3P = V_IP3 PIP2

Component: J_ip3D

F_Ca = \frac{Ca_i}{K_rc + Ca_i} J_ip3D = \frac{(Beta_1 + Beta_2 {F_Ca}^{2}) IP3}{K_IP3 + IP3}

Component: Jipt

Pipt = O^{4} Jipt = Jipt0 volume_i0 Pipt (Ca_er - Ca_i)

Component: Jryr

W_inf = \frac{1 + {(\frac{Ka}{Ca_i})}^{4} + {(\frac{Ca_i}{Kb})}^{3}}{1 + \frac{1}{Kc} + {(\frac{Ca_i}{Kb})}^{3} + {(\frac{Ka}{Ca_i})}^{4}} Pryr = \frac{W_inf (1 + {(\frac{Ka}{Ca_i})}^{4} + {(\frac{Ca_i}{Kb})}^{3})}{1 + \frac{1}{Kc} + {(\frac{Ca_i}{Kb})}^{3} + {(\frac{Ka}{Ca_i})}^{4}} Jryr = Jryr0 volume_i0 (Ca_er - Ca_i)

Component: Jer

Jer = Jer0 volume_i0 (Ca_er - Ca_i)

Component: Jserca

Jserca = \frac{\frac{volume_i0 Vserca {Ca_i}^{2}}{{Kserca}^{2} + {Ca_i}^{2}} 1}{Ca_er}

Component: Jin

V_Ca = \frac{R T}{z_Ca F} \ln (\frac{Ca_ext}{Ca_i}) Iin_1 = volume_i0 P_pm_1 (V_Ca - Vm) Iin_2 = volume_i0 P_pm_2 V_mech (V_Ca - Vm) Jin_1 = \frac{Iin_1}{z_Ca F} Jin_2 = \frac{Iin_2}{z_Ca F} Jin = Jin_1 + Jin_2

Component: Jpm

Jpm = \frac{Vpm volume_i0 {Ca_i}^{2}}{{Kpm}^{2} + {Ca_i}^{2}}

Component: O

\frac{d}{d time} (O) = k1 IP3 S - (k1_O + k2 O) S = 1 - (O + I1 + I2)

Component: I1

\frac{d}{d time} (I1) = k2 O - ((k3 + k4) I1)

Component: I2

\frac{d}{d time} (I2) = k4 I1 - (k5 I2)

Component: constants

k1 = \frac{alpha_1 {Ca_i}^{3}}{{beta_1}^{3} + {Ca_i}^{3}} k4 = \frac{alpha_4 IP3}{beta_4 + IP3}

Source: Derived from workspace Warren, Tawhai, Crampin, 2009 at changeset 7a277ddc5b1a.

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Mathematical modelling of calcium wave propagation in mammalian airway epithelium: evidence for regenerative ATP release