Model Mathematics

k_f_1 = kappa_1 K_1 K_6 k_r_1 = kappa_1 K_3 k_f_2 = kappa_2 K_4 k_r_2 = kappa_2 K_2 K_5 k_f_3 = kappa_3 K_3 k_r_3 = kappa_3 K_4 k_f_4 = kappa_4 K_5 k_r_4 = kappa_4 K_6 \frac{d}{d t} (q_1) = - v_1 \frac{d}{d t} (q_2) = v_2 - (1000 q_2) \frac{d}{d t} (q_3) = v_1 - v_3 \frac{d}{d t} (q_4) = v_3 - v_2 \frac{d}{d t} (q_5) = v_2 - v_4 q_6 = q_tot - q_3 - q_4 - q_5 v_1 = k_f_1 q_1 q_6 - (k_r_1 q_3) v_2 = k_f_2 q_4 - (k_r_2 q_2 q_5) v_3 = k_f_3 q_3 - (k_r_3 q_4) v_4 = k_f_4 q_5 - (k_r_4 q_6)

v_SF = \frac{q_tot kappa_3 kappa_4 K_m K_s (q_1 - q_2)}{2 kappa_4 + (kappa_3 + kappa_4) K_s (q_1 + q_2) + 2 kappa_3 K_s K_s q_1 q_2} k_m = \frac{2}{K_s (1 + \frac{kappa_3}{kappa_4})} v_max = \frac{q_tot kappa_3 K_m}{1 + \frac{kappa_3}{kappa_4}}

v_MM = \frac{v_max q_1}{k_m + q_1}