Model Mathematics

\frac{d}{d time} (h1) = phi3_c1 (1 - h1) - (\frac{phi1_c1 phi2_c1 h1 p}{phi1_c1 p + phi_1_c1})

\frac{d}{d time} (h2) = phi3_c2 (1 - h2) - (\frac{phi1_c2 phi2_c2 h2 p}{phi1_c2 p + phi_1_c2})

phi1_c1 = \frac{r2 c1}{R1 + c1} phi_1_c1 = \frac{k1}{R3 + c1} phi2_c1 = \frac{k2 + r4 c1}{R3 + c1} phi3_c1 = \frac{k3}{R5 + c1} phi1_c2 = \frac{r2 c2}{R1 + c2} phi_1_c2 = \frac{k1}{R3 + c2} phi2_c2 = \frac{k2 + r4 c2}{R3 + c2} phi3_c2 = \frac{k3}{R5 + c2}

j_pump_c1 = \frac{Vp {c1}^{2}}{{Kp}^{2} + {c1}^{2}}

j_pump_c2 = \frac{Vp {c2}^{2}}{{Kp}^{2} + {c2}^{2}}

j_receptor_c1 = kf {(\frac{p h1 phi1_c1}{phi1_c1 p + phi_1_c1})}^{4}

j_receptor_c2 = kf {(\frac{p h2 phi1_c2}{phi1_c2 p + phi_1_c2})}^{4}

j_diffusion = D (c2 - c1)

\frac{d}{d time} (c1) = (j_receptor_c1 - j_pump_c1) + j_leak + j_diffusion

\frac{d}{d time} (c2) = (j_receptor_c2 - j_pump_c2) + j_leak + j_diffusion