Model-based hypothesis testing of key mechanisms in initial phase of insulin signaling

Abstract

Type 2 diabetes is characterized by insulin resistance of target organs, which is due to impaired insulin signal transduction. The skeleton of signaling mediators that provide for normal insulin action has been established. However, the detailed kinetics, and their mechanistic generation, remain incompletely understood. We measured time-courses in primary human adipocytes for the short-term phosphorylation dynamics of the insulin receptor (IR) and the IR substrate-1 in response to a step increase in insulin concentration. Both proteins exhibited a rapid transient overshoot in tyrosine phosphorylation, reaching maximum within 1 min, followed by an intermediate steady-state level after approximately 10 min. We used model-based hypothesis testing to evaluate three mechanistic explanations for this behavior: (A) phosphorylation and dephosphorylation of IR at the plasma membrane only; (B) the additional possibility for IR endocytosis; (C) the alternative additional possibility of feedback signals to IR from downstream intermediates. We concluded that (A) is not a satisfactory explanation; that (B) may serve as an explanation only if both internalization, dephosphorylation, and subsequent recycling are permitted; and that (C) is acceptable. These mechanistic insights cannot be obtained by mere inspection of the datasets, and they are rejections and thus stronger and more final conclusions than ordinary model predictions.

Figure 1. The experimental data and three representative model simulations.

(A) shows experimental data for IR and their estimated standard deviations (vertical lines), and the agreement of a model without an overshoot (ℳ_m,a, dashed line), and of a model with internalization and dephosphorylation but without recycling (ℳ_i,c, solid line). (B) shows the same experimental data together with an acceptable model (ℳ_i,a), and (C) shows the agreement between ℳ_f and the IRS1 experimental data. Note that the experimental data has been normalised such that time-point zero has no standard deviation.

Figure 2. All models with only states at the membrane that can be rejected directly by lack of agreement, i.e., by a χ ² test or by direct inspection of the properties of the transfer function.

All these figures correspond to unique model structures, or sets of differential equations, as is explained in Text S1.

Figure 3. Models with a reasonable overshoot.

The top left model structure only has states at the membrane, and that means that the last state before IR, (IR⋅ins)⋅PTP, will have a steady state value of at least 25% of the total receptor concentration. This is unrealistic and ℳ_m,PTP is therefore rejected. ℳ_i,a, ℳ_i,b, and ℳ_f, on the other hand, are accepted. All these figures correspond to unique model structures, or sets of differential equations, as is explained in Text S1.

Figure 4. Some key simulations with the model structures ℳ_i,a (or ℳ_m,PTP).

(A) Simulations of IR⋅P⋅ins (solid line) and IR_i⋅P⋅ins (dashed). (B) IR (solid) and IR_i⋅ins (dashed).