Model Mathematics

\frac{d}{d time} (c) = \frac{L0}{\frac{kr}{kf}} r + 2.0 \frac{ku}{kr} c2 - (c + 2.0 \frac{R0}{\frac{kr}{kc}} c^{2.0})

\frac{d}{d time} (c2) = \frac{R0}{\frac{kr}{kc}} c^{2.0} + \frac{kc_minus}{kr} c_star - (\frac{ku}{kr} c + \frac{kc_plus}{kr} c2)

\frac{d}{d time} (c_star) = \frac{kc_plus}{kr} c2 + \frac{kr_1}{kr} \frac{A1_T}{R0} c_star_a1 + \frac{kr_12}{kr} \frac{A2_T}{R0} e0_star - (\frac{kc_minus}{kr} c_star + \frac{kf_1 A1_T}{kr} c_star a1 + \frac{kf_12 A1_T}{kr} c_star a1a2)

\frac{d}{d time} (c_star_a1) = \frac{kf_1 R0}{kr} c_star a1 + \frac{kr_2}{kr} \frac{A2_T}{A1_T} e0_star + \frac{kcat_x}{kr} \frac{E4_T}{A1_T} e0_star_e4_star - (\frac{kr_1}{kr} c_star_a1 + \frac{kf_2 A2_T}{kr} c_star_a1 a2)

\frac{d}{d time} (e0_star) = \frac{kf_2 A1_T}{kr} c_star_a1 a2 + \frac{kf_12 A1_T}{kr} c_star a1a2 + \frac{k1_minus + kcat_1}{kr} \frac{E1_T}{A2_T} e1_e0_star + \frac{kx_minus}{kr} \frac{E4_T}{A2_T} e0_star_e4_star - (\frac{kr_2}{kr} e0_star + \frac{kr_12}{kr} e0_star + \frac{k1_plus E1_T}{kr} e0_star e1 + \frac{kx_plus E4_T}{kr} e0_star e4_star)

\frac{d}{d time} (a1a2) = \frac{kr_12}{kr} \frac{A2_T}{A1_T} e0_star + \frac{kc_12 A2_T}{kr} a1 a2 - (\frac{kd_12}{kr} a1a2 + \frac{kf_12 R0}{kr} c_star a1a2)

r = 1.0 - (c + 2.0 (c2 + c_star + \frac{A1_T}{R0} c_star_a1 + \frac{A2_T}{R0} e0_star + \frac{E4_T}{R0} e0_star_e4_star + \frac{E1_T}{R0} e1_e0_star))

a1 = 1.0 - (c_star_a1 + a1a2 + \frac{A2_T}{A1_T} e0_star + \frac{E4_T}{A1_T} e0_star_e4_star + \frac{E1_T}{A1_T} e1_e0_star)

a2 = 1.0 - (\frac{A1_T}{A2_T} a1a2 + e0_star + \frac{E4_T}{A2_T} e0_star_e4_star + \frac{E1_T}{A2_T} e1_e0_star + a2_minus)

\frac{d}{d time} (a2_minus) = \frac{kcat_x}{kr} \frac{E4_T}{A2_T} e0_star_e4_star

\frac{d}{d time} (e1_star_p1) = \frac{kP1_plus E1_T}{kr} e1_star p1 - ((\frac{kP1_minus}{kr} + \frac{kcat_P1}{kr}) e1_star_p1)

\frac{d}{d time} (e2_star_p2) = \frac{kP2_plus E2_T}{kr} e2_star p2 - ((\frac{kP2_minus}{kr} + \frac{kcat_P2}{kr}) e2_star_p2)

\frac{d}{d time} (e3_star_p3) = \frac{kP3_plus E3_T}{kr} e3_star p3 - ((\frac{kP3_minus}{kr} + \frac{kcat_P3}{kr}) e3_star_p3)

\frac{d}{d time} (e4_star_p4) = \frac{kP4_plus E4_T}{kr} e4_star p4 - ((\frac{kP4_minus}{kr} + \frac{kcat_P4}{kr}) e4_star_p4)

\frac{d}{d time} (e5_star_p5) = \frac{kP5_plus E5_T}{kr} e5_star p5 - ((\frac{kP5_minus}{kr} + \frac{kcat_P5}{kr}) e5_star_p5)

\frac{d}{d time} (e1_e0_star) = \frac{k1_plus A2_T}{kr} e1 e0_star - ((\frac{k1_minus}{kr} + \frac{kcat_1}{kr}) e1_e0_star)

\frac{d}{d time} (e2_e1_star) = \frac{k2_plus E1_T}{kr} e2 e1_star - ((\frac{k2_minus}{kr} + \frac{kcat_2}{kr}) e2_e1_star)

\frac{d}{d time} (e3_e2_star) = \frac{k3_plus E2_T}{kr} e3 e2_star - ((\frac{k3_minus}{kr} + \frac{kcat_3}{kr}) e3_e2_star)

\frac{d}{d time} (e4_e3_star) = \frac{k4_plus E3_T}{kr} e4 e3_star - ((\frac{k4_minus}{kr} + \frac{kcat_4}{kr}) e4_e3_star)

\frac{d}{d time} (e5_e4_star) = \frac{k5_plus E4_T}{kr} e5 e4_star - ((\frac{k5_minus}{kr} + \frac{kcat_5}{kr}) e5_e4_star)

\frac{d}{d time} (e2_star_e4_star) = \frac{kz_plus E2_T}{kr} e4_star e2_star - ((\frac{kz_minus}{kr} + \frac{kcat_z}{kr}) e2_star_e4_star)

\frac{d}{d time} (e0_star_e4_star) = \frac{kx_plus A2_T}{kr} e4_star e0_star - ((\frac{kx_minus}{kr} + \frac{kcat_x}{kr}) e0_star_e4_star)

\frac{d}{d time} (e2_minus) = \frac{kcat_z}{kr} \frac{E4_T}{E2_T} e2_star_e4_star

\frac{d}{d time} (e1_star) = \frac{kcat_1}{kr} e1_e0_star + \frac{k2_minus + kcat_2}{kr} \frac{E2_T}{E1_T} e2_e1_star + \frac{kP1_minus}{kr} \frac{P1_T}{E1_T} e1_star_p1 - (\frac{k2_plus E2_T}{kr} e1_star e2 + \frac{kP1_plus P1_T}{kr} e1_star p1)

\frac{d}{d time} (e3_star) = \frac{kcat_3}{kr} e3_e2_star + \frac{k4_minus + kcat_4}{kr} \frac{E4_T}{E3_T} e4_e3_star + \frac{kP3_minus}{kr} \frac{P3_T}{E3_T} e3_star_p3 - (\frac{k4_plus E4_T}{kr} e3_star e4 + \frac{kP3_plus P3_T}{kr} e3_star p3)

\frac{d}{d time} (e5_star) = \frac{kcat_5}{kr} e5_e4_star + \frac{kP5_minus}{kr} \frac{P5_T}{E5_T} e5_star_p5 - (\frac{kP5_plus P5_T}{kr} e5_star p5)

\frac{d}{d time} (e2_star) = \frac{kcat_2}{kr} e2_e1_star + \frac{k3_minus + kcat_3}{kr} \frac{E3_T}{E2_T} e3_e2_star + \frac{kP2_minus}{kr} \frac{P2_T}{E2_T} e2_star_p2 + \frac{kz_minus}{kr} \frac{E4_T}{E2_T} e2_star_e4_star - (\frac{k3_plus E3_T}{kr} e2_star e3 + \frac{kP2_plus P2_T}{kr} e2_star p2 + \frac{kz_plus E4_T}{kr} e2_star e4_star)

\frac{d}{d time} (e4_star) = \frac{kcat_4}{kr} e4_e3_star + \frac{k5_minus + kcat_5}{kr} \frac{E5_T}{E4_T} e5_e4_star + \frac{kP4_minus}{kr} \frac{P4_T}{E4_T} e4_star_p4 + (\frac{kx_minus}{kr} + \frac{kcat_x}{kr}) e0_star_e4_star + (\frac{kz_minus}{kr} + \frac{kcat_z}{kr}) e2_star_e4_star - (\frac{k5_plus E5_T}{kr} e4_star e5 + \frac{kP4_plus P4_T}{kr} e4_star p4 + \frac{kx_plus A2_T}{kr} e0_star e4_star + \frac{kz_plus E2_T}{kr} e2_star e4_star)

p1 = 1.0 - e1_star_p1

p2 = 1.0 - e2_star_p2

p3 = 1.0 - e3_star_p3

p4 = 1.0 - e4_star_p4

p5 = 1.0 - e5_star_p5

e1 = 1.0 - (e1_e0_star + e1_star + \frac{E2_T}{E1_T} e2_e1_star + \frac{P1_T}{E1_T} e1_star_p1)

e3 = 1.0 - (e3_e2_star + e3_star + \frac{E4_T}{E3_T} e4_e3_star + \frac{P3_T}{E3_T} e3_star_p3)

e5 = 1.0 - (e5_e4_star + e5_star + \frac{P5_T}{E5_T} e5_star_p5)

e2 = 1.0 - (e3_e2_star + e3_star + \frac{E3_T}{E2_T} e3_e2_star + \frac{E4_T}{E2_T} e2_star_e4_star + \frac{P2_T}{E2_T} e2_star_p2)

e4 = 1.0 - (e4_e3_star + e4_star + \frac{E5_T}{E4_T} e5_e4_star + \frac{P4_T}{E4_T} e4_star_p4 + e0_star_e4_star + e2_star_e4_star)

L0 = \frac{kr}{kf} kr_1 = kf_1 (1E-7) kr_2 = kf_2 (1E-7) kr_12 = kf_12 (1E-7) kd_12 = kc_12 (1E-7)