Model Mathematics

\frac{d}{d t} (q_A) = (- v_R_34) + v_R_78 \frac{d}{d t} (q_M) = (- v_R_12) + v_R_78 \frac{d}{d t} (q_Mp) = v_R_12 - v_R_34 \frac{d}{d t} (q_AM) = v_R_56 - v_R_78 \frac{d}{d t} (q_AMp) = v_R_34 - v_R_56 \frac{d}{d t} (q_Pi) = (- v_R_12) + v_R_56 \frac{d}{d t} (q_Ca_i) = n_Cai_SM (- v_R_12 - v_R_56) \frac{d}{d t} (q_cGMP) = v_R_12 + v_R_56 + v_R_1b_cGMP - v_R_2a_cGMP - v_R_2b_cGMP - (2 v_R_4_sGC) \frac{d}{d t} (q_GTP) = - v_R_1a_cGMP \frac{d}{d t} (q_E5c) = (- v_R_1a_cGMP) + v_R_1b_cGMP + v_R_2_sGC + v_R_3_sGC - v_R_4_sGC \frac{d}{d t} (q_PDE) = (- v_R_2a_cGMP) + v_R_2b_cGMP \frac{d}{d t} (q_GTP_E5c) = v_R_1a_cGMP - v_R_1b_cGMP \frac{d}{d t} (q_cGMP_PDE) = v_R_2a_cGMP - v_R_2b_cGMP \frac{d}{d t} (q_GMP) = v_R_2b_cGMP \frac{d}{d t} (q_Eb) = (- v_R_1_sGC) + v_R_4_sGC \frac{d}{d t} (q_NO) = ((- v_R_1_sGC) + v_R_4_sGC - v_R_DNO_sGC) + v_NO_generation \frac{d}{d t} (q_E6c) = v_R_1_sGC - v_R_2_sGC - v_R_3_sGC \frac{d}{d t} (q_NO_product) = v_R_DNO_sGC

stress = \frac{q_AM + q_AMp}{1}

\frac{d}{d time} (q_A) = (- v_R_34) + v_R_78 \frac{d}{d time} (q_M) = (- v_R_12) + v_R_78 \frac{d}{d time} (q_Mp) = v_R_12 - v_R_34 \frac{d}{d time} (q_AM) = v_R_56 - v_R_78 \frac{d}{d time} (q_AMp) = v_R_34 - v_R_56 \frac{d}{d time} (q_Pi) = (- v_R_12) + v_R_56 \frac{d}{d time} (q_Ca_i) = n_Cai_SM (- v_R_12 - v_R_56) \frac{d}{d time} (q_cGMP) = v_R_12 + v_R_56

stress = \frac{q_AM + q_AMp}{1}

mu_A = R T \ln (K_A q_A) mu_M = R T \ln (K_M q_M) mu_Mp = R T \ln (K_Mp q_Mp) mu_AM = R T \ln (K_AM q_AM) mu_AMp = R T \ln (K_AMp q_AMp) mu_Pi = R T \ln (K_Pi q_Pi) mu_Ca_i = R T \ln (K_Ca_i q_Ca_i) mu_cGMP = R T \ln (K_cGMP q_cGMP) v_R_12 = kappa_R_12 (ⅇ^{\frac{mu_M + mu_Pi + n_Cai_SM mu_Ca_i}{R T}} - (ⅇ^{\frac{mu_Mp + mu_cGMP}{R T}})) v_R_34 = kappa_R_34 (ⅇ^{\frac{mu_A + mu_Mp}{R T}} - (ⅇ^{\frac{mu_AMp}{R T}})) v_R_56 = kappa_R_56 (ⅇ^{\frac{mu_AMp + n_Cai_SM mu_Ca_i}{R T}} - (ⅇ^{\frac{mu_AM + mu_Pi + mu_cGMP}{R T}})) v_R_78 = kappa_R_78 (ⅇ^{\frac{mu_AM}{R T}} - (ⅇ^{\frac{mu_A + mu_M}{R T}}))

\frac{d}{d time} (q_GTP) = - v_R_1a_cGMP \frac{d}{d time} (q_E5c) = (- v_R_1a_cGMP) + v_R_1b_cGMP \frac{d}{d time} (q_cGMP) = v_R_1b_cGMP - v_R_2a_cGMP - v_R_2b_cGMP \frac{d}{d time} (q_PDE) = (- v_R_2a_cGMP) + v_R_2b_cGMP \frac{d}{d time} (q_GTP_E5c) = v_R_1a_cGMP - v_R_1b_cGMP \frac{d}{d time} (q_cGMP_PDE) = v_R_2a_cGMP - v_R_2b_cGMP \frac{d}{d time} (q_GMP) = v_R_2b_cGMP

mu_GTP = R T \ln (K_GTP q_GTP) mu_E5c = R T \ln (K_E5c q_E5c) mu_cGMP = R T \ln (K_cGMP q_cGMP) mu_PDE = R T \ln (K_PDE q_PDE) mu_GTP_E5c = R T \ln (K_GTP_E5c q_GTP_E5c) mu_cGMP_PDE = R T \ln (K_cGMP_PDE q_cGMP_PDE) mu_GMP = R T \ln (K_GMP q_GMP) v_R_1a_cGMP = kappa_R_1a_cGMP (ⅇ^{\frac{mu_GTP + mu_E5c}{R T}} - (ⅇ^{\frac{mu_GTP_E5c}{R T}})) v_R_1b_cGMP = kappa_R_1b_cGMP (ⅇ^{\frac{mu_GTP_E5c}{R T}} - (ⅇ^{\frac{mu_cGMP + mu_E5c}{R T}})) v_R_2a_cGMP = kappa_R_2a_cGMP (ⅇ^{\frac{mu_cGMP + mu_PDE}{R T}} - (ⅇ^{\frac{mu_cGMP_PDE}{R T}})) v_R_2b_cGMP = kappa_R_2b_cGMP (ⅇ^{\frac{mu_cGMP_PDE + mu_cGMP}{R T}} - (ⅇ^{\frac{mu_GMP + mu_PDE}{R T}}))

\frac{d}{d time} (q_Eb) = (- v_R_1_sGC) + v_R_4_sGC \frac{d}{d time} (q_NO) = ((- v_R_1_sGC) + v_R_4_sGC - v_R_DNO_sGC) + v_NO_generation \frac{d}{d time} (q_E6c) = v_R_1_sGC - v_R_2_sGC - v_R_3_sGC \frac{d}{d time} (q_E5c) = v_R_2_sGC + v_R_3_sGC - v_R_4_sGC \frac{d}{d time} (q_cGMP) = (- 2) v_R_4_sGC \frac{d}{d time} (q_NO_product) = v_R_DNO_sGC

mu_Eb = R T \ln (K_Eb q_Eb) mu_NO = R T \ln (K_NO q_NO) mu_E6c = R T \ln (K_E6c q_E6c) mu_E5c = R T \ln (K_E5c q_E5c) mu_cGMP = R T \ln (K_cGMP q_cGMP) mu_NO_product = R T \ln (K_NO_product q_NO_product) v_R_1_sGC = kappa_R_1_sGC (ⅇ^{\frac{mu_Eb + mu_NO}{R T}} - (ⅇ^{\frac{mu_E6c}{R T}})) v_R_2_sGC = kappa_R_2_sGC (ⅇ^{\frac{mu_E6c}{R T}} - (ⅇ^{\frac{mu_E5c}{R T}})) v_R_3_sGC = kappa_R_3_sGC (ⅇ^{\frac{mu_E6c + mu_NO}{R T}} - (ⅇ^{\frac{mu_E5c + mu_NO}{R T}})) v_R_4_sGC = kappa_R_4_sGC (ⅇ^{\frac{mu_E5c + mu_cGMP 2}{R T}} - (ⅇ^{\frac{mu_Eb + mu_NO}{R T}})) v_R_DNO_sGC = kappa_R_DNO_sGC (ⅇ^{\frac{mu_NO}{R T}} - (ⅇ^{\frac{mu_NO_product}{R T}}))