Model Mathematics

t_ave = \frac{mRNA_halflife}{\ln 2} kd_prot = \frac{\ln 2}{prot_halflife} kd_mRNA = \frac{\ln 2}{mRNA_halflife} k_tl = efficiency kd_mRNA a_tr = (tps_active - tps_repr) 60 a0_tr = tps_repr 60 alpha = \frac{a_tr efficiency}{kd_prot K_m} alpha_0 = \frac{a0_tr efficiency}{kd_prot K_m} beta = \frac{kd_prot}{kd_mRNA}

\frac{d}{d time} (M_lacl) = a0_tr + \frac{a_tr {K_m}^{n}}{{K_m}^{n} + {P_cl}^{n}} - (kd_mRNA M_lacl)

\frac{d}{d time} (M_tetR) = \frac{a_tr {K_m}^{n}}{{K_m}^{n} + {P_lacl}^{n}} + a0_tr - (kd_mRNA M_tetR)

\frac{d}{d time} (M_cl) = \frac{a_tr {K_m}^{n}}{{K_m}^{n} + {P_tetR}^{n}} + a0_tr - (kd_mRNA M_cl)

\frac{d}{d time} (P_lacl) = k_tl M_lacl - (kd_prot P_lacl)

\frac{d}{d time} (P_tetR) = k_tl M_tetR - (kd_prot P_tetR)

\frac{d}{d time} (P_cl) = k_tl M_cl - (kd_prot P_cl)