Fig 2: Development of the mTORC1 pathway model combined with the AA- and Ins-sensing pathways.(A) Schematic representation of reactions involved in the spatiotemporal regulation of the mTORC1 pathway. A mathematical model of the AKT-TSC1/2-Rheb axis consisting of 25 equations was defined based on available mathematical models. A mathematical model of the AA-sensing (Ragulator/LAMTOR-Rag) axis was defined based on a standard reaction network system with nine equations. Reactions depicting mTORC1 activation on the lysosomal surface, mediated by the active forms of RagGTP and RhebGTP, were defined using six equations. k (solid-line arrow) and l (dotted line arrow) represent the rate constants, whereas Φ represents the degradation of the insulin receptor (IR). (B) Comparison of the phosphorylation levels of mTOR at S2481, S6K at T389, AKT at T308, and TSC2 at T1462 between simulation and experimental values under AA(+) Ins(+) stimulation. The solid black lines indicate the values obtained from the simulation, whereas the blue dots indicate the values measured during the experiment. Error bars indicate the SEM (n = 3).

Fig 3: Compartment model of the mTORC1 pathway reproduces the temporal changes of P-AKT, P-TSC, and P-S6K better than the crosstalk model.(A) Schematic representation of reactions involved in the spatiotemporal regulation of the mTORC1 pathway. A compartment model of the mTORC1 pathway was described based on the without-crosstalk model (Fig 2A) with the following modifications. Parameters k25, k27, and k28 were defined as the transport (import) rates for TSC, GATOR1, and mTORC1 from the cytoplasm to the lysosomes, whereas l25, l27, and l28 were defined as their export rates from the lysosomes to the cytoplasm. Parameter l26 was also defined as the dephosphorylation rate of TSC2 on the lysosomal surfaces. (B, C, D) Simulation of phospho-AKT at T308 and S473 (B), phospho-TSC2 at T1462 (C), and phospho-S6K at T389 (D) in the compartment model. The dots indicate the experimental values. AU, arbitrary units. (E) Correlations between the simulation and actual values of P-AKT(T308) (left), P-TSC2 (T1462) (middle), and P-S6K(T389) (right) were evaluated by the correlation indexes (CI) based on the residual sum of squares (RSS). A smaller CI (RSS) indicates a higher fitting rate of the model to the actual data.

Fig 4: Ins-induced phosphorylation of TSC2 at T1462 is substantially inhibited under AA-free conditions.Phosphorylation levels of AKT at T308 and TSC2 at T1462 monitored in p18Rev and p18-KO MEFs subjected to AA deprivation and subsequent Ins treatment, alone or in combination with AA. Cells were cultured in minimal medium without AA for 1 h and then incubated with medium containing Ins (10 μg/ml) alone or in combination with AA for the indicated time. Cell lysates were analyzed by Western blotting using the indicated antibodies. Note that trial-1 bands of P-TSC2 (P-T1462) and P-AKT (P-T308) are the same ones in Fig 6E.Source data are available for this figure.

Fig 5: Ragulator (p18)-Rag cooperates with Rheb to regulate Ins-induced TSC2 phosphorylation in an intracellular AA-dependent manner.(A) Expression levels of p18, Rheb, and β-actin were monitored in MEF (control), p18Rev, p18-KO, p18/Rheb-double KO (dKO), and p18/Rheb-dKO cells re-expressing Flag-Rheb and human p18, alone or in combination as indicated. β-Actin was used as a loading control. (B) Phosphorylation levels of AKT at T308 and S473, TSC2 at T1462, S6K at T389, and S6 at S235 and S236 monitored when p18/Rheb-dKO cells and Rheb and/or p18 re-expressing p18/Rheb-dKO cells were exposed to AA deprivation for 1 h and subsequently treated with AA or Ins, alone or in combination, for 20 min. Cell lysates were analyzed by Western blotting using the indicated antibodies.Source data are available for this figure.