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Model Mathematics

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Component: environment

Component: Ca_i

\frac{d}{d time} (Ca_i) = J1 - J2 J1 = c1 (v1 P_open + v2) (Ca_ER - Ca_i) J2 = \frac{v3 {Ca_i}^{2.0}}{{Ca_i}^{2.0} + {k3}^{2.0}}

Component: Ca_ER

Ca_ER = \frac{c0 - Ca_i}{c1}

Component: IP3

\frac{d}{d time} (IP3) = v4 \frac{Ca_i + (1.0 - alpha) k4}{Ca_i + k4} - (Ir IP3)

Component: receptor_dissociation_constants

d1 = K_d1 - IP3_cold

d2 = \frac{b2}{a2}

d3 = (K_d2 - IP3_cold) (1 + d2) - (d1 d2)

d4 = \frac{d1 d2}{d3}

d5 = \frac{b5}{a5}

Component: probability_of_an_open_IP3_receptor_channel

P_open = {(\frac{Ca_i IP3 d2}{(Ca_i IP3 + IP3 d2 + d1 d2 + Ca_i d3) (Ca_i + d5)})}^{3.0}

Component: x_000

\frac{d}{d time} (x_000) = - V1 - V3

Component: x_001

\frac{d}{d time} (x_001) = V1 - V4

Component: x_010

\frac{d}{d time} (x_010) = V3 - V2

Component: x_011

x_011 = 1.0 - (x_000 + x_001 + x_010)

Component: fluxes

V1 = a4 (Ca_i x_000 - (d4 x_001)) V2 = a4 (Ca_i x_010 - (d4 x_011)) V3 = a5 (Ca_i x_000 - (d5 x_010)) V4 = a5 (Ca_i x_001 - (d5 x_011))

Component: constants

b1 = d1 a1 b3 = d3 a3 b4 = d4 a4

Source: Derived from workspace Deyoung, Keizer, 1992 at changeset 5221e51ca22f.

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A single-pool inositol 1,4,5-triphosphate-receptor-based model for agonist-stimulated oscillations in Ca 2+ concentration