Model Mathematics

L_iso = \{\begin{matrix} 1 if time > 120 \land time ≦ 720 \\ 1 otherwise \end{matrix}

L_ach = \{\begin{matrix} 0 if time > 240 \land time ≦ 540 \\ 0 otherwise \end{matrix}

R = R_Total - LR - LRG - RG LR = \frac{L_iso R}{K_L} LRG = \frac{L_iso R G}{\frac{K_H K_C}{K_L}} RG = \frac{R G}{K_C}

R = R_Total - LR - LRG - RG LR = \frac{L_ach R}{K_L} LRG = \frac{L_ach R G}{\frac{K_H K_C}{K_L}} RG = \frac{R G}{K_C}

\frac{d}{d time} (Gs_alpha_GTP) = RG k_act2 + LRG k_act1 - (Gs_alpha_GTP k_hydr) \frac{d}{d time} (Gs_beta_gamma) = RG k_act2 + LRG k_act1 - (Gs_alpha_GDP Gs_beta_gamma k_reas) \frac{d}{d time} (Gs_alpha_GDP) = Gs_alpha_GTP k_hydr - (Gs_alpha_GDP Gs_beta_gamma k_reas) Gs_alpha_beta_gamma = Gs_Total - Gs_alpha_GTP - Gs_alpha_GDP

\frac{d}{d time} (Gi_alpha_GTP) = RG k_act2 + LRG k_act1 - (Gi_alpha_GTP k_hydr) \frac{d}{d time} (Gi_beta_gamma) = RG k_act2 + LRG k_act1 - (Gi_alpha_GDP Gi_beta_gamma k_reas) \frac{d}{d time} (Gi_alpha_GDP) = Gi_alpha_GTP k_hydr - (Gi_alpha_GDP Gi_beta_gamma k_reas) Gi_alpha_beta_gamma = Gi_Total - Gi_alpha_GTP - Gi_alpha_GDP

R = R_Total - LR - LRG - RG LR = \frac{L_iso R}{K_L} LRG = \frac{L_iso R G}{\frac{K_H K_C}{K_L}} RG = \frac{R G}{K_C}

R = R_Total - LR - LRG - RG LR = \frac{L_ach R}{K_L} LRG = \frac{L_ach R G}{\frac{K_H K_C}{K_L}} RG = \frac{R G}{K_C}

\frac{d}{d time} (Gs_alpha_GTP) = RG k_act2 + LRG k_act1 - (Gs_alpha_GTP k_hydr) \frac{d}{d time} (Gs_beta_gamma) = RG k_act2 + LRG k_act1 - (Gs_alpha_GDP Gs_beta_gamma k_reas) \frac{d}{d time} (Gs_alpha_GDP) = Gs_alpha_GTP k_hydr - (Gs_alpha_GDP Gs_beta_gamma k_reas) Gs_alpha_beta_gamma = Gs_Total - Gs_alpha_GTP - Gs_alpha_GDP

\frac{d}{d time} (Gi_alpha_GTP) = RG k_act2 + LRG k_act1 - (Gi_alpha_GTP k_hydr) \frac{d}{d time} (Gi_beta_gamma) = RG k_act2 + LRG k_act1 - (Gi_alpha_GDP Gi_beta_gamma k_reas) \frac{d}{d time} (Gi_alpha_GDP) = Gi_alpha_GTP k_hydr - (Gi_alpha_GDP Gi_beta_gamma k_reas) Gi_alpha_beta_gamma = Gi_Total - Gi_alpha_GTP - Gi_alpha_GDP

k_AC56 = \frac{(0.7 + \frac{3.8234 {(\frac{Gs_alpha_GTP}{1})}^{0.9787}}{0.1986 + {(\frac{Gs_alpha_GTP}{1})}^{0.9787}}) (1 + \frac{\frac{1}{1.4432} (- 1.0061) {(\frac{Gi_alpha_GTP}{1})}^{0.8356}}{0.1918 + {(\frac{Gi_alpha_GTP}{1})}^{0.8356}}) MW_AC56}{60} 0.001 dcAMP_AC_56_dt = \frac{k_AC56 AC_56 AF56 ATP}{Km_ATP + ATP}

k_AC47_ecav = \frac{(0.063 + \frac{2.01 {(Gs_alpha_GTP 1000)}^{1.0043}}{31.544 + {(Gs_alpha_GTP 1000)}^{1.0043}}) (1 + \frac{\frac{1}{3.01} 49.1 {(Gi_beta_gamma 1000)}^{0.8921}}{25.44 + {(Gi_beta_gamma 1000)}^{0.8921}}) MW_AC47}{60} 0.001 dcAMP_AC_47_ecav_dt = \frac{k_AC47_ecav AC_47_ecav AF47 ATP}{Km_ATP + ATP}

dcAMP_AC_47_cyt_dt = \frac{k_AC47_cyt AC_47_cyt AF47 ATP}{Km_ATP + ATP}

dcAMP_cav_PDE2_dt = \frac{k_PDE2 PDE2 cAMP_cav}{Km_PDE2 + cAMP_cav} dcAMP_cav_PDE3_dt = \frac{k_PDE3 PDE3 cAMP_cav}{Km_PDE3 + cAMP_cav} dcAMP_cav_PDE4_dt = \frac{k_PDE4 PDE4 cAMP_cav}{Km_PDE4 + cAMP_cav}

dcAMP_ecav_PDE2_dt = \frac{k_PDE2 PDE2 cAMP_ecav}{Km_PDE2 + cAMP_ecav} dcAMP_ecav_PDE4_dt = \frac{k_PDE4 PDE4 cAMP_ecav}{Km_PDE4 + cAMP_ecav}

dcAMP_cyt_PDE2_dt = \frac{k_PDE2 PDE2 cAMP_cyt}{Km_PDE2 + cAMP_cyt} dcAMP_cyt_PDE3_dt = \frac{k_PDE3 PDE3 cAMP_cyt}{Km_PDE3 + cAMP_cyt} dcAMP_cyt_PDE4_dt = \frac{k_PDE4 PDE4 cAMP_cyt}{Km_PDE4 + cAMP_cyt}

V_cav = 0.01 V_cell V_ecav = 0.02 V_cell V_cyt = 0.5 V_cell \frac{d}{d time} (cAMP_cav) = dcAMP_AC_56_dt - (dcAMP_cav_PDE2_dt + dcAMP_cav_PDE3_dt + dcAMP_cav_PDE4_dt) - (\frac{J_cav_ecav (cAMP_cav - cAMP_ecav)}{V_cav}) - (\frac{J_cav_cyt (cAMP_cav - cAMP_cyt)}{V_cav}) \frac{d}{d time} (cAMP_ecav) = (dcAMP_AC_47_ecav_dt - (dcAMP_ecav_PDE2_dt + dcAMP_ecav_PDE4_dt)) + \frac{J_cav_ecav (cAMP_cav - cAMP_ecav)}{V_ecav} - (\frac{J_ecav_cyt (cAMP_ecav - cAMP_cyt)}{V_ecav}) \frac{d}{d time} (cAMP_cyt) = (dcAMP_AC_47_cyt_dt - (dcAMP_cyt_PDE2_dt + dcAMP_cyt_PDE3_dt + dcAMP_cyt_PDE4_dt)) + \frac{J_cav_cyt (cAMP_cav - cAMP_cyt)}{V_cyt} + \frac{J_ecav_cyt (cAMP_ecav - cAMP_cyt)}{V_cyt}