Model Mathematics

\frac{d}{d t} (g_i) = 1 q_Ao = g_o V_o q_Ai = g_i V_i q_tot = \frac{GC V_E 1}{1000} v_max_free = \frac{v_oi_max V_E}{k_m_1_free} k_m_1_free = k_oi_math V_i K_Ai k_m_2_free = \frac{v_io_max V_E}{v_max_free} lambda = \frac{kappa_r2}{kappa_r1} v_max = \frac{q_tot kappa_r2 K_3}{\frac{K_3}{K_1} + \frac{K_3}{K_4}} k_m_1 = \frac{\frac{K_3}{K_1} + \frac{K_3}{K_4}}{\frac{K_3}{K_2} + \frac{lambda K_3}{K_4}} k_m_2 = \frac{\frac{K_3}{K_1} + \frac{K_3}{K_4}}{1 + \frac{lambda K_3}{K_1}} k_m_3 = \frac{\frac{K_3}{K_1} + \frac{K_3}{K_4}}{lambda (1 + \frac{K_3}{K_2})} v = \frac{v_max (K_Ao q_Ao - (K_Ai q_Ai))}{1 + \frac{K_Ao q_Ao}{k_m_1} + \frac{K_Ai q_Ai}{k_m_2} + \frac{K_Ao q_Ao K_Ai q_Ai}{k_m_3}} v_free = \frac{v_max_free (K_Ao q_Ao - (K_Ai q_Ai))}{1 + \frac{K_Ao q_Ao}{k_m_1_free} + \frac{K_Ai q_Ai}{k_m_2_free} + \frac{K_Ao q_Ao K_Ai q_Ai}{k_m_3_free}}

q_init_Ao = g_o V_o q_init_Ai = g_i V_i