Model Mathematics

kp_act = \{\begin{matrix} 5.5 if time > 0.1 \land time < 0.2 \\ 5.5 if time > 4.1 \land time < 4.2 \\ 1.6e-5 otherwise \end{matrix}

\frac{d}{d time} (CNG_o) = kp_act (CNG_tot - CNG_o - CNG_i) - (km_CNG_0 CNG_o) - (kp_CNG_i CNG_o CaM4) CNG_o_normalized = \frac{CNG_o}{CNG_tot}

\frac{d}{d time} (Ca) = \frac{CNG_o}{sigma} i_Ca - (\frac{\frac{k_Ca}{sigma} Ca}{Ca + K_Ca}) - (4 (kp_CaM4 {Ca}^{2} (CaM_tot - CaM4 - (\frac{CNG_i}{sigma})) - (km_CaM4 CaM4))) Ca_normalized = Ca 10000

\frac{d}{d time} (CaM4) = (kp_CaM4 {Ca}^{2} (CaM_tot - CaM4 - (\frac{CNG_i}{sigma})) - (km_CaM4 CaM4) - (\frac{kp_CNG_i}{sigma} CaM4 (CNG_tot - CNG_o))) + \frac{km_CNG_i}{sigma} CNG_i CaM4_normalized = \frac{CaM4}{CaM_tot}

\frac{d}{d time} (CNG_i) = (- km_CNG_i) CNG_i + kp_CNG_i CaM4 (CNG_tot - CNG_i) CNG_i_normalized = \frac{CNG_i}{CNG_tot}

CNG_c = CNG_tot - CNG_o - CNG_i

CaM = CaM_tot - CaM4 - (\frac{1}{sigma} CNG_i)