ABSTRACT
In this appendix, we start from the steady-state equations of the PI3K-AKT-TOR pathway:
−a1[AKT][E1] + d1[AKT: E1] + k2[pAKT : E2] = 0, (B.1) a1[AKT][E1] − (d1 + k1) [AKT: E1] = 0, (B.2)
−a2[pAKT][E2] + d2[pAKT: E2] + k1[AKT : E1] = 0, (B.3) a2[pAKT][E2] − (d2 + k2) [pAKT: E2] = 0, (B.4) I + ( − [pIRS]) [pAKT] − δ[pIRS] = 0, (B.5)
[AKT] + [pAKT] = Amax, (B.6) [E1] + [AKT: E1] = E1T , (B.7)
[E2] + [pAKT: E2] = E2T , (B.8) β[pIRS] = E1T , (B.9)
to derive the master equation of AKT activation:
G (I, A, p) = 0, (B.10) where G (I, A, p) abbreviates a long expression:
G = θ A3 + (
(K1 + K2) φ − (K1 + 1) θ + βγ I − 1 )
A2
+ (
K1 + 1 + (K2 − 1) βγ I − K2φ )
A − K2βγ I (B.11)
and where
p = (φ, θ, β, γ, K1, K2), γ = k1
δk2 E2T ,
φ = βγ Amax, θ = (βγ − /δ) Amax,
K1 = Km1Amax = d1 + k1 a1 Amax
,
K2 = Km2Amax = d2 + k2 a2 Amax
.