# Model Mathematics

### Component: c

$dd time c = L0 kr kf ⁢ r + 2.0 ⁢ ku kr ⁢ c2 - c + 2.0 ⁢ R0 kr kc ⁢ c 2.0$

### Component: c2

$dd time c2 = R0 kr kc ⁢ c 2.0 + kc_minus kr ⁢ c_star - ku kr ⁢ c + kc_plus kr ⁢ c2$

### Component: c_star

$dd time c_star = kc_plus kr ⁢ c2 + kr_1 kr ⁢ A1_T R0 ⁢ c_star_a1 + kr_12 kr ⁢ A2_T R0 ⁢ e0_star - kc_minus kr ⁢ c_star + kf_1 ⁢ A1_T kr ⁢ c_star ⁢ a1 + kf_12 ⁢ A1_T kr ⁢ c_star ⁢ a1a2$

### Component: c_star_a1

$dd time c_star_a1 = kf_1 ⁢ R0 kr ⁢ c_star ⁢ a1 + kr_2 kr ⁢ A2_T A1_T ⁢ e0_star + kcat_x kr ⁢ E4_T A1_T ⁢ e0_star_e4_star - kr_1 kr ⁢ c_star_a1 + kf_2 ⁢ A2_T kr ⁢ c_star_a1 ⁢ a2$

### Component: e0_star

$dd time e0_star = kf_2 ⁢ A1_T kr ⁢ c_star_a1 ⁢ a2 + kf_12 ⁢ A1_T kr ⁢ c_star ⁢ a1a2 + k1_minus + kcat_1 kr ⁢ E1_T A2_T ⁢ e1_e0_star + kx_minus kr ⁢ E4_T A2_T ⁢ e0_star_e4_star - kr_2 kr ⁢ e0_star + kr_12 kr ⁢ e0_star + k1_plus ⁢ E1_T kr ⁢ e0_star ⁢ e1 + kx_plus ⁢ E4_T kr ⁢ e0_star ⁢ e4_star$

### Component: a1a2

$dd time a1a2 = kr_12 kr ⁢ A2_T A1_T ⁢ e0_star + kc_12 ⁢ A2_T kr ⁢ a1 ⁢ a2 - kd_12 kr ⁢ a1a2 + kf_12 ⁢ R0 kr ⁢ c_star ⁢ a1a2$

### Component: r

$r = 1.0 - c + 2.0 ⁢ c2 + c_star + A1_T R0 ⁢ c_star_a1 + A2_T R0 ⁢ e0_star + E4_T R0 ⁢ e0_star_e4_star + E1_T R0 ⁢ e1_e0_star$

### Component: a1

$a1 = 1.0 - c_star_a1 + a1a2 + A2_T A1_T ⁢ e0_star + E4_T A1_T ⁢ e0_star_e4_star + E1_T A1_T ⁢ e1_e0_star$

### Component: a2

$a2 = 1.0 - A1_T A2_T ⁢ a1a2 + e0_star + E4_T A2_T ⁢ e0_star_e4_star + E1_T A2_T ⁢ e1_e0_star + a2_minus$

### Component: a2_minus

$dd time a2_minus = kcat_x kr ⁢ E4_T A2_T ⁢ e0_star_e4_star$

### Component: e1_star_p1

$dd time e1_star_p1 = kP1_plus ⁢ E1_T kr ⁢ e1_star ⁢ p1 - kP1_minus kr + kcat_P1 kr ⁢ e1_star_p1$

### Component: e2_star_p2

$dd time e2_star_p2 = kP2_plus ⁢ E2_T kr ⁢ e2_star ⁢ p2 - kP2_minus kr + kcat_P2 kr ⁢ e2_star_p2$

### Component: e3_star_p3

$dd time e3_star_p3 = kP3_plus ⁢ E3_T kr ⁢ e3_star ⁢ p3 - kP3_minus kr + kcat_P3 kr ⁢ e3_star_p3$

### Component: e4_star_p4

$dd time e4_star_p4 = kP4_plus ⁢ E4_T kr ⁢ e4_star ⁢ p4 - kP4_minus kr + kcat_P4 kr ⁢ e4_star_p4$

### Component: e5_star_p5

$dd time e5_star_p5 = kP5_plus ⁢ E5_T kr ⁢ e5_star ⁢ p5 - kP5_minus kr + kcat_P5 kr ⁢ e5_star_p5$

### Component: e1_e0_star

$dd time e1_e0_star = k1_plus ⁢ A2_T kr ⁢ e1 ⁢ e0_star - k1_minus kr + kcat_1 kr ⁢ e1_e0_star$

### Component: e2_e1_star

$dd time e2_e1_star = k2_plus ⁢ E1_T kr ⁢ e2 ⁢ e1_star - k2_minus kr + kcat_2 kr ⁢ e2_e1_star$

### Component: e3_e2_star

$dd time e3_e2_star = k3_plus ⁢ E2_T kr ⁢ e3 ⁢ e2_star - k3_minus kr + kcat_3 kr ⁢ e3_e2_star$

### Component: e4_e3_star

$dd time e4_e3_star = k4_plus ⁢ E3_T kr ⁢ e4 ⁢ e3_star - k4_minus kr + kcat_4 kr ⁢ e4_e3_star$

### Component: e5_e4_star

$dd time e5_e4_star = k5_plus ⁢ E4_T kr ⁢ e5 ⁢ e4_star - k5_minus kr + kcat_5 kr ⁢ e5_e4_star$

### Component: e2_star_e4_star

$dd time e2_star_e4_star = kz_plus ⁢ E2_T kr ⁢ e4_star ⁢ e2_star - kz_minus kr + kcat_z kr ⁢ e2_star_e4_star$

### Component: e0_star_e4_star

$dd time e0_star_e4_star = kx_plus ⁢ A2_T kr ⁢ e4_star ⁢ e0_star - kx_minus kr + kcat_x kr ⁢ e0_star_e4_star$

### Component: e2_minus

$dd time e2_minus = kcat_z kr ⁢ E4_T E2_T ⁢ e2_star_e4_star$

### Component: e1_star

$dd time e1_star = kcat_1 kr ⁢ e1_e0_star + k2_minus + kcat_2 kr ⁢ E2_T E1_T ⁢ e2_e1_star + kP1_minus kr ⁢ P1_T E1_T ⁢ e1_star_p1 - k2_plus ⁢ E2_T kr ⁢ e1_star ⁢ e2 + kP1_plus ⁢ P1_T kr ⁢ e1_star ⁢ p1$

### Component: e3_star

$dd time e3_star = kcat_3 kr ⁢ e3_e2_star + k4_minus + kcat_4 kr ⁢ E4_T E3_T ⁢ e4_e3_star + kP3_minus kr ⁢ P3_T E3_T ⁢ e3_star_p3 - k4_plus ⁢ E4_T kr ⁢ e3_star ⁢ e4 + kP3_plus ⁢ P3_T kr ⁢ e3_star ⁢ p3$

### Component: e5_star

$dd time e5_star = kcat_5 kr ⁢ e5_e4_star + kP5_minus kr ⁢ P5_T E5_T ⁢ e5_star_p5 - kP5_plus ⁢ P5_T kr ⁢ e5_star ⁢ p5$

### Component: e2_star

$dd time e2_star = kcat_2 kr ⁢ e2_e1_star + k3_minus + kcat_3 kr ⁢ E3_T E2_T ⁢ e3_e2_star + kP2_minus kr ⁢ P2_T E2_T ⁢ e2_star_p2 + kz_minus kr ⁢ E4_T E2_T ⁢ e2_star_e4_star - k3_plus ⁢ E3_T kr ⁢ e2_star ⁢ e3 + kP2_plus ⁢ P2_T kr ⁢ e2_star ⁢ p2 + kz_plus ⁢ E4_T kr ⁢ e2_star ⁢ e4_star$

### Component: e4_star

$dd time e4_star = kcat_4 kr ⁢ e4_e3_star + k5_minus + kcat_5 kr ⁢ E5_T E4_T ⁢ e5_e4_star + kP4_minus kr ⁢ P4_T E4_T ⁢ e4_star_p4 + kx_minus kr + kcat_x kr ⁢ e0_star_e4_star + kz_minus kr + kcat_z kr ⁢ e2_star_e4_star - k5_plus ⁢ E5_T kr ⁢ e4_star ⁢ e5 + kP4_plus ⁢ P4_T kr ⁢ e4_star ⁢ p4 + kx_plus ⁢ A2_T kr ⁢ e0_star ⁢ e4_star + kz_plus ⁢ E2_T kr ⁢ e2_star ⁢ e4_star$

### Component: p1

$p1 = 1.0 - e1_star_p1$

### Component: p2

$p2 = 1.0 - e2_star_p2$

### Component: p3

$p3 = 1.0 - e3_star_p3$

### Component: p4

$p4 = 1.0 - e4_star_p4$

### Component: p5

$p5 = 1.0 - e5_star_p5$

### Component: e1

$e1 = 1.0 - e1_e0_star + e1_star + E2_T E1_T ⁢ e2_e1_star + P1_T E1_T ⁢ e1_star_p1$

### Component: e3

$e3 = 1.0 - e3_e2_star + e3_star + E4_T E3_T ⁢ e4_e3_star + P3_T E3_T ⁢ e3_star_p3$

### Component: e5

$e5 = 1.0 - e5_e4_star + e5_star + P5_T E5_T ⁢ e5_star_p5$

### Component: e2

$e2 = 1.0 - e3_e2_star + e3_star + E3_T E2_T ⁢ e3_e2_star + E4_T E2_T ⁢ e2_star_e4_star + P2_T E2_T ⁢ e2_star_p2$

### Component: e4

$e4 = 1.0 - e4_e3_star + e4_star + E5_T E4_T ⁢ e5_e4_star + P4_T E4_T ⁢ e4_star_p4 + e0_star_e4_star + e2_star_e4_star$

### Component: model_parameters

$L0 = kr kf kr_1 = kf_1 ⁢ 1E-7 kr_2 = kf_2 ⁢ 1E-7 kr_12 = kf_12 ⁢ 1E-7 kd_12 = kc_12 ⁢ 1E-7$
Source
Derived from workspace Asthagiri, Lauffenburger, 2001 at changeset eaae38522e8b.
Collaboration
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