Model Mathematics

t_ave = \frac{mRNA_halflife}{\ln 2}

\frac{d}{d time} (M_lacl) = \frac{K_m}{efficiency t_ave} (\frac{alpha {K_m}^{n}}{{K_m}^{n} + {P_cl}^{n}} + alpha_0) - (\frac{M_lacl}{t_ave})

\frac{d}{d time} (M_tetR) = \frac{K_m}{efficiency t_ave} (\frac{alpha {K_m}^{n}}{{K_m}^{n} + {P_lacl}^{n}} + alpha_0) - (\frac{M_tetR}{t_ave})

\frac{d}{d time} (M_cl) = \frac{K_m}{efficiency t_ave} (\frac{alpha {K_m}^{n}}{{K_m}^{n} + {P_tetR}^{n}} + alpha_0) - (\frac{M_cl}{t_ave})

\frac{d}{d time} (P_lacl) = beta (\frac{M_lacl efficiency}{t_ave} - (\frac{P_lacl}{t_ave}))

\frac{d}{d time} (P_tetR) = beta (\frac{M_tetR efficiency}{t_ave} - (\frac{P_tetR}{t_ave}))

\frac{d}{d time} (P_cl) = beta (\frac{M_cl efficiency}{t_ave} - (\frac{P_cl}{t_ave}))