Harmonic oscillator model of the insulin and IGF1 receptors' allosteric binding and activation

Vladislav V Kiselyov¹, Soetkin Versteyhe¹, Lisbeth Gauguin¹ & Pierre De Meyts¹

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Synopsis

Insulin and insulin-like growth factor 1 (IGF1) have similar structures and exert their action by activating two closely related receptor tyrosine kinases—insulin receptor (IR) and IGF1 type I receptor (IGF1R), which have virtually identical signalling pathways (De Meyts and Whittaker, 2002). Despite this similarity, the two hormones produce markedly different responses: mostly metabolic for insulin and mitogenic for IGF1 (Kim and Accili, 2002). So far, there is poor understanding of how these hormones produce such markedly different biological effects using basically the same machinery (Kim and Accili, 2002). In recent years, it has become clear that a systems biology approach is required to understand the combinatorial nature of signalling specificity (Kholodenko, 2007). However, the two receptors' mechanism of ligand binding and activation displays complex allosteric properties (i.e. negative cooperativity and ligand dependence of the receptor dissociation rate), which no mathematical model has been able to account for. Therefore, development of a reliable mathematical model describing the two receptors' binding kinetics and activation is a critical first step in a systems biology approach to understand the function of these receptors.

Both IR and IGF1R exist in the membrane as pre-formed covalent dimers of two identical moieties. Their extracellular domains comprise two leucine-rich (L₁ and L₂) modules separated by a cystein-rich domain, followed by three fibronectin type III (Fn_1–3) modules (see Figure 1A) (McKern et al, 2006). The bivalent insulin molecule can bind to a site consisting of residues located in L₁ and a 12 amino-acid peptide from the insert in Fn₂, which combine to form 'site 1', and also to a site consisting of residues located in L2, Fn₁ and Fn₂ ('site 2') (De Meyts and Whittaker, 2002). A crystal structure of the extracellular (unliganded) IR dimer (McKern et al, 2006) in the inactive conformation displays a symmetrical antiparallel arrangement of the receptor's binding sites for insulin (as previously suggested by De Meyts (1994)) (see Figure 1A–C). Binding of insulin to both sites simultaneously is thought to produce a conformational change in IR, which is necessary for its activation. The crystal structure is consistent with an assumption (as previously suggested by De Meyts, 1994) that this conformational change is produced by a tilt of the receptor subunits, leading to a movement of sites 1 and 2 towards each other and to a corresponding movement of the other sites away from each other (Figure 1D and E).

Figure 1

Insulin receptor structure. In all of the panels, the individual monomers of the insulin receptor dimer are coloured in green and blue, respectively, and location of the binding sites is shown approximately, as the residues involved in binding to insulin are not known precisely. (A) Crystal structure of the ecto-domain of the insulin receptor dimer (PDB code: 2DTG). Labelling of the modules is shown only for the blue-coloured monomer. (B) Half of the insulin receptor dimer is shown. The placement of insulin in the binding cavity is shown approximately. (C) A view of the insulin receptor dimer (shown in (A)) as seen from the 'top'. (D) Simplified representation of the insulin receptor dimer, in which the insulin-binding subunits are represented as rigid bodies. (E) Crosslinked (tilted) conformations of the rigid-body representation of the insulin receptor dimer. Insulin is depicted as a black dot.

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Mathematical modelling of the insulin binding to the inactive conformation of IR requires four parameters: association rate constants for sites 1 and 2 (designated a₁ and a₂, respectively) and dissociation rate constants for sites 1 and 2 (designated d₁ and d₂, respectively). However, the precise mechanism of the IR activation required for mathematical modelling is not known. On the basis of the available structural data, we developed a physically plausible model of the IR activation, which builds on a thermodynamically and structurally justified assumption that the IR conformational change (required for activation) can be described by harmonic oscillations of the receptor subunits. Analysis of the behaviour of an ensemble of the IR 'harmonic oscillators' in thermal equilibrium with the surrounding allows to model the receptor activation in a simple way (Figure 4A) and substantially reduces the combinatorial complexity. Binding of insulin to IR in the context of the model leads to a network of interactions shown in a simplified way in Figure 4B.

Figure 4

Reaction scheme for the insulin receptor binding. (A) Scheme of the crosslinking reaction. (B) Simplified scheme of the insulin receptor kinetic network. S1 and S2 stand for sites 1 and 2, respectively. Insulin is depicted as a black dot.

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Fitting of the model to the experimental data results in accurate reproduction of all the kinetic properties of IR and IGF1R and in robust estimation of the parameters, thus providing insight into the differences in kinetics between the two receptors. Recently, it has become clear that kinetics of the receptor activation contribute to, and sometimes play an essential role in, determining signalling specificity by means of kinetic proofreading (McKeithan, 1995), which states that the activated receptor must complete a cascade of reversible modifications before a cellular response can occur. If the receptor becomes inactive before the full set of modifications is complete, the receptor reverts to its basal unmodified state. The presented model predicts that upon ligand binding IR and IGF1R exist in the ligand-bound state for a long time: on average for 2 and 6 h, respectively. However, in the ligand-bound state the two receptors shuttle between the inactive and active states, and the average lifetimes in the activated states are approximately 76 s for IR and 135 s for IGF1R. This difference in the average lifetimes is expected to favour activation of the Ras–MAP kinase pathway (involved in cell growth control) by IGF1, as this pathway seems to require that the activated state is maintained for 3–5 min (Krüger et al, 2007), thus providing a possible explanation for the fact that IGF1 is more mitogenic than insulin.

Thus, our model represents an essential first step in building a systems biology analysis of the insulin/IGF-I signalling networks to explain the combinatorial nature of their biological specificity. Furthermore, the model can potentially contribute to analysis of signalling specificity of other receptors as well, as it may be adaptable for a large number of dimeric or dimerizing receptor tyrosine kinases, cytokine receptors and G-protein-coupled receptors where a ligand crosslinking occurs.

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