You are here: Home / Exposures / Chay, Lee, Fan, 1995 / Appearance of Phase-locked Wenchbach-like Rhythms, Devil's Staircase and Universality in Intracellular Calcium Spikes in Non-excitable Cell Models

Model Mathematics

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Component: environment

Component: G_alpha_GTP

\frac{d}{d time} (G_alpha_GTP) = kg G_alpha_GDP - (4.0 kp {G_alpha_GTP}^{4.0} PLC + hg G_alpha_GTP) kp = kp_\frac{{DAG}^{2.0}}{{KD}^{2.0} + {DAG}^{2.0}}

Component: DAG

\frac{d}{d time} (DAG) = (kd PLC_active - (hd DAG)) + ld kd = kd_\frac{{DAG}^{2.0}}{{KD}^{2.0} + {DAG}^{2.0}}

Component: Ca_i

\frac{d}{d time} (Ca_i) = (rho_kc \frac{{IP3}^{3.0}}{{Ks}^{3.0} + {IP3}^{3.0}} - (rho_hc Ca_i)) + rho_lc IP3 = DAG

Component: PLC_active

\frac{d}{d time} (PLC_active) = kp {G_alpha_GTP}^{4.0} PLC - (hp PLC_active) hp = hp_\frac{{DAG}^{2.0}}{{KD}^{2.0} + {DAG}^{2.0}}

Component: PLC

PLC = PLC_total - PLC_active

Component: G_alpha_GDP

\frac{d}{d time} (G_alpha_GDP) = G_total - (G_alpha_GTP + 4.0 PLC_active)

Source: Derived from workspace Chay, Lee, Fan, 1995 at changeset 4df2a542a083.

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Appearance of Phase-locked Wenchbach-like Rhythms, Devil's Staircase and Universality in Intracellular Calcium Spikes in Non-excitable Cell Models