Modeling the effects of insulin and amino acids on the phosphorylation of mTOR, Akt, and 4EBP1 in mammary cells

The objective of this work was to develop a mathematical representation of the effects of insulin and essential amino acid (EAA) on phosphorylation of protein kinase B (Akt), mammalian target of rapamycin (mTOR) and eukaryotic initiation factor 4E binding protein 1 (4EBP1), the latter being critical for initiation of protein synthesis. The model included six protein pools (Q) representing phosphorylated (P) and unphosphorylated (U) forms of Akt, mTOR, and 4EBP1. Mass action equations were used to represent kinase (F-U,F-P(X)) and phosphatase (F-P,F-U(X)) reactions. The F-U,F-P(X) for Akt and mTOR were regulated by extracellular insulin (C-Ins) and EAA (C-EAA) concentrations, respectively. Exponents were used to adjust the sensitivity of the fluxes to the regulators. Changes in pool size with respect to time were calculated as the difference between F-U,F-P(X) and F-P,F-U(X). The Q(U(X)) were determined by numerical integration of the differentials starting from specified initial pool sizes. The Q(P(X)) were calculated by subtracting Q(U(X)) from the fixed total protein mass (Q(T(X))). The model was fitted to observed phosphorylation data obtained from a bovine mammary epithelial cell line treated with four C-Ins (0, 5, 10, and 100 ng/ml) and four C-EAA (0, 0.35, 1.00, and 3.5 mM) arranged in a 4x4 factorial design. Model optimization and sensitivity analyses were carried out in ACSLXtreme. The data were adequate to describe the model parameters as standard deviations of model parameters were <20% of the parameter estimates. Sensitivity exponent estimates were greater than 1 indicating EAA and insulin signal loss associated with transmission down the cascade was partially mitigated. Phosphorylation of Akt was highly sensitive to insulin compared to mTOR and 4EBP1. Phosphorylation of mTOR and 4EBP1 responded similarly to insulin and EAA. The model was able to predict Q(P(X)) with root mean square prediction errors less than 10% of the observed means. There appeared to be a slight negative slope bias for Q(P(Akt)), indicating the model tended to overpredict Q(P(Akt)) as predicted Q(P(Akt)) increased.