Hypothesis A assumes that the overshoot of receptor phosphorylation is generated by autophosphorylation and dephosphorylation at the plasma membrane only. For a model to be acceptable, the authors require the ability to produce an overshoot and a maximal value of at least 150 % of the steady state value. In addition, at least 35 % of the receptors should remain unphosphorylated.

One model that satisfies all conditions is sufficient to prevent the rejection of a hypothesis. A very simple model that satisfies all requirements consists of three states: IR_0, IR_p and IR_g. IR_0 is the unphosphorylated receptor that can be phosphorylated to IR_p. IR_p is dephosphorylated to IR_g which is an unphosphorylated intermediate state filling the gap between the original unphosphorylated receptor and the phosphorylated receptor.
The occurring reactions

IR_0->IR_p
IR_p->IR_g
IR_g->IR_0

correspond to the reaction rates

r0=p1*IR_0
r1=p2*IR_p
r2=p3*IR_g

and define the differential equations

(d/dt)IR_0=-r0+r2
(d/dt)IR_p=r0-r1
(d/dt)IR_g=r1-r2.

Choosing p1=0.3, p2=0.8, and p3=0.1 as parameter values and IR_0=1, IR_p=0 and IR_g=0 as initial conditions, the simulation results match the experimental data set quite well. In particular, the requirements above are fulfilled. This holds for a wide range of parameter values.

The state IR_g contributes a significant fraction to the total receptor in the steady state of this proposed model. Therefore, the main question is that of whether it is biologically acceptable that the state IR_g shows a high steady state concentration.

The authors consider qualitatively similar models, in particular the model M_m,PTP. A hallmark of all these models is the presence of intermediate unphosphorylated states in the reaction chain connecting the phosphorylated and the unphosphorylated receptor.

Such models can satisfy all requirements necessary for accepting hypothesis A. In this case, at least 25 % of all receptors in the steady state have to be in an intermediate unphosphorylated state as it is IR_g in our model and the state (IR*Ins)*PTP in the model M_m,PTP.

The authors assume that all these intermediate unphosphorylated states are complexes of the unphosphorylated receptor and a phosphatase which they characterize as unphysiologic. Therefore the authors reject a whole class of models and finally hypothesis A.

This argumentation bases on two major assumptions:

1) All intermediate receptor states in the reaction chain connecting the phosphorylated and the unphosphorylated receptor are complexes of the unphosphorylated receptor and a phosphatase.

2) It is unphysiologic that 25 % of all receptors in the steady state are in such an intermediate state.

However, assumption 1) is much too restrictive. There are many other possible interpretations for the state IR_g which can be interpreted as a generalized equivalent to the state (IR*Ins)*PTP in the model M_m,PTP. Two of these possible interpretations are a special conformation of the receptor and a complex of the receptor with a structural protein. All these possibilities could be characterized by a relatively high steady state concentration.

Using an unspecified intermediate state as IR_g is legitimate as the authors make wide use of other intermediate states without defining their nature. In the model structure M_m,c they even allow for an unlimited amount of intermediate states in a reaction chain connecting the unphosphorylated receptor and the phosphorylated receptor.

In addition, the authors cite a reference showing that more than 90 % of the original pool of receptors remains unphosphorylated [14]. Therefore, the presence of an unphosphorylated intermediate receptor state (such as IR_g) with a high steady state concentration is a realistic possibility.

Assumption 2) is only of interest if assumption 1) holds, which is not the case. In addition, assumption 2) is not supported by references and is therefore not strong enough to reject a model structure or a hypothesis.

Altogether, a model was presented that satisfies all requirements of hypothesis A. The rejection of hypothesis A is therefore not justified.