A new mathematical approach for qualitative modeling of the insulin-TOR-MAPK network

Abstract

In this paper we develop a novel mathematical model of the insulin-TOR-MAPK signaling network that controls growth. Most data on the properties of the insulin and MAPK signaling networks are static and the responses to experimental interventions, such as knockouts, overexpression, and hormonal input are typically reported as scaled quantities. The modeling paradigm we develop here uses scaled variables and is ideally suited to simulate systems in which much of the available data are scaled. Our mathematical representation of signaling networks provides a way to reconcile theory and experiments, thus leading to a better understanding of the properties and function of these signaling networks. We test the performance of the model against a broad diversity of experimental data. The model correctly reproduces experimental insulin dose-response relationships. We study the interaction between insulin and MAPK signaling in the control of protein synthesis, and the interactions between amino acids, insulin and TOR signaling. We study the effects of variation in FOXO expression on protein synthesis and glucose transport capacity, and show that a FOXO knockout can partially rescue protein synthesis capacity of an insulin receptor (INR) knockout. We conclude that the modeling paradigm we develop provides a simple tool to investigate the qualitative properties of signaling networks.

Keywords: FOXO; MAPK; TOR; growth; insulin; mathematical model; sigmoid.

Figure 1

Insulin and MAPK signaling network. The acronyms for the components of the network and the rationale for the connectivity are explained in the text.

Figure 2

Time-dependent sigmoids (effect of parameters a and b). Parameter a controls when the response attains saturation. Parameter b controls the saturation point of the response.

Figure 3

Graphs of the value of b in Equation (2) as a function parameter c. Parameter c controls the steepness of the sigmoid; the smaller c is, the steeper the sigmoid.

Figure 4

MAPK cascade simulation shows that the signal becomes more switchlike as it travels down the MAPK cascade, as shown in Huang and Ferrell (1996).

Figure 5

MAPK cascade with negative feedback from MAPK to MAPKKK. The negative feedback makes the response less switchlike.

Figure 6

Insulin dose response curves of various components of the insulin and MAPK signaling pathways replicating (Stagsted et al., ; Sedaghat et al., ; Danielsson et al., 2005). The GLUT4 transporters are the most sensitive to insulin signaling, and achieve their maximum response at relatively low levels of insulin stimulation (0.4).

Figure 7

(A) Protein synthesis as a function of MAPK and insulin. MAPK and insulin act synergistically, and the maximum protein synthesis occurs when both pathways are activated. Nevertheless, at low levels of MAPK signaling, insulin is still able to stimulate protein synthesis. (B) Same figure but with TOR knockout. The effect of the TOR knockout on protein synthesis is only noticeable when there is weak MAPK signaling (right corner of the figure); when TOR is knocked out and MAPK signaling is low, insulin alone cannot stimulate protein synthesis.

Figure 8

Effect of PTEN over expression and knock-down on the sensitivity of insulin stimulated protein synthesis (A) and GLUT4 activation (B). PTEN overexpression reduces the maximum level of protein synthesis, and completely abrogates the response of GLUT4 to insulin stimulation. PTEN underexpression does not have as dramatic an effect, but does increase the sensitivity of protein synthesis in response to insulin especially at high insulin levels. In contrast, the stimulatory effect of PTEN underexpression on GLUT 4 sensitivity is mainly observed at low insulin levels.

Figure 9

Effect of overexpression and knockout of FOXO on insulin-stimulated protein synthesis. FOXO knockout increases protein synthesis especially at low levels of insulin stimulation. On the other hand, FOXO overexpression primarily affects protein synthesis when insulin signaling is high. These two observations can be explained by the fact that FOXO inhibits TOR and this inhibition is inhibited by PKB when insulin is high. At low insulin levels, FOXO should inhibit TOR and protein synthesis, and hence the knockout relieves this inhibition. At high insulin levels, FOXO should be inhibited by PKB and therefore not have an inhibitory effect on protein synthesis, but FOXO overexpression prevents PKB from entirely relieving the constitutive inhibition of protein synthesis by FOXO.

Figure 10

FOXO knockout rescues the growth defects of INR mutants. In an INR deficient mutant, protein synthesis is severely depressed and regulated primarily by MAPK (activation of MAPK is set at 0.1 in this experiment). FOXO knockout alone has no effect on protein synthesis, but can partially rescue protein synthesis in an INR knockout. Protein synthesis values are scaled to those of a “wild type.” Input into the MAPK pathway is 0.1.

Figure 11

Effects of oxygen on protein synthesis (growth), mediated by the insulin and TOR signaling pathways are most strongly observed at high insulin signaling levels (>0.7). This suggests that in poor nutritional conditions, hypoxia or hyperoxia are unlikely to have strong effects on growth and size; only in good nutritional conditions will oxygen show an effect. Hypoxia decreases the rate of insulin-stimulated protein synthesis. Hyperoxia causes protein synthesis to reach its saturating rate at a slightly lower level of insulin signaling, so it has a slight stimulatory effect for insulin between 0.7 and 0.8. At levels of insulin signaling >0.8, hyperoxia provides no additional stimulation of growth because growth rate has attained its maximum.