TABLE 1.

Reactions and Rate equations included in the model

All the enzymatic steps follow a Michaelis-Menten mechanism. The parameters of the Michaelis-Menten equations are V_mi and K_mi where subscript i represents the reaction r_i with i = 0 to 5. The reactions catalysed by α-secretase, r₁ and r₅, have a slightly more complicated rate equations (v_r1,α and v_r5,α) since there are two competing substrates, C99 and APP, that individually give Michaelis-Menten kinetics when studied separately (40, 41). The same applies for the rate equations depending on γ-secretase, v_r3,γ and v_r4,γ, where C99 and C83 are substrates competing for this enzyme. v_r,j represents the rate of reaction r_i catalyze by secretase j, with j = α, β or γ and i = 1 to 5. v_r0 is the rate of reaction r₀.

Reaction	Secretase	Reaction rate
r0 (→ APP)		vr0 = constant
r1 (APP → C83)	α	$v_{{\text{r}}_{1,\alpha }}=\frac{V_{m1}\text{APP}/K_{m1}}{1+\text{APP}/K_{m1}+\text{C}99/K_{m5}}$
r2 (APP → C99)	β	$v_{{\text{r}}_{2,\beta }}=\frac{V_{m2}\text{APP}/K_{m2}}{1+\text{APP}/K_{m2}}$
r3 (C83 → p3)	γ	$v_{{\text{r}}_{3,\gamma }}=\frac{V_{m3}\text{C}83/K_{m3}}{1+\text{C}83/K_{m3}+\text{C}99/K_{m4}}$
r4 (C99 → Aβ)	γ	$v_{{\text{r}}_{4,\gamma }}=\frac{V_{m4}\text{C}99/K_{m4}}{1+\text{C}83/K_{m3}+\text{C}99/K_{m4}}$
r5 (C99 → C83)	α	$v_{{\text{r}}_{5,\alpha }}=\frac{V_{m5}\text{C}99/K_{m5}}{1+\text{APP}/K_{m1}+\text{C}99/K_{m5}}$