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. 2009:5:243.
doi: 10.1038/msb.2008.78. Epub 2009 Feb 17.

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

Vladislav V Kiselyov  1 , Soetkin Versteyhe, Lisbeth Gauguin, Pierre De Meyts
Affiliations

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

Vladislav V Kiselyov et al. Mol Syst Biol. 2009.

Abstract

The insulin and insulin-like growth factor 1 receptors activate overlapping signalling pathways that are critical for growth, metabolism, survival and longevity. Their mechanism of ligand binding and activation displays complex allosteric properties, which no mathematical model has been able to account for. Modelling these receptors' binding and activation in terms of interactions between the molecular components is problematical due to many unknown biochemical and structural details. Moreover, substantial combinatorial complexity originating from multivalent ligand binding further complicates the problem. On the basis of the available structural and biochemical information, we develop a physically plausible model of the receptor binding and activation, which is based on the concept of a harmonic oscillator. Modelling a network of interactions among all possible receptor intermediaries arising in the context of the model (35, for the insulin receptor) accurately reproduces for the first time all the kinetic properties of the receptor, and provides unique and robust estimates of the kinetic parameters. The harmonic oscillator model may be adaptable for many other dimeric/dimerizing receptor tyrosine kinases, cytokine receptors and G-protein-coupled receptors where ligand crosslinking occurs.

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Conflict of interest statement

The authors declare that they have no conflict of interest.

Figures

Figure 1
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.
Figure 2
Figure 2
Inactive (A) and crosslinked (B, C) insulin receptor intermediaries used in the model. S1 and S2 stand for sites 1 and 2, respectively. Insulin is depicted as a black dot.
Figure 3
Figure 3
Harmonic oscillator model of the insulin receptor activation mechanism. (A) Plot of the Maxwell–Boltzmann distribution for a one-dimensional harmonic oscillator and reaction scheme for the spontaneous receptor activation. The 5% fraction of the activated receptor molecules (with energy of oscillations ranging from the activation energy to ‘infinity') is indicated by the hatched region. (B) Reaction scheme for the insulin receptor activation. The forces acting to restore the inactive/symmetrical conformation of the receptor subunits are represented by elastic springs, which can be compressed and stretched during movement of the receptor subunits. E stands for energy of oscillations, Eactivation—activation energy, F—random force vector acting on the receptor subunits, υ—vector showing direction of movement of the crosslinking subunits. S1 and S2 stand for sites 1 and 2, respectively. Insulin is depicted as a black dot.
Figure 4
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.
Figure 5
Figure 5
Fitting of the model to the experimental data for the insulin/IGF1 binding. (A, B) Competition experiments for the insulin and IGF1 binding, respectively (shown also as Scatchard plots in the insets). (C, D) Percentages of hot insulin and IGF1, respectively, remaining after dissociation for 20 and 60 min in the presence of various concentrations of the respective cold ligand. (E, F) Simulation of the ligand dependence of the receptor dissociation for insulin and IGF1, respectively, using the estimated parameter values.
Figure 6
Figure 6
Scheme of the insulin receptor binding at physiological insulin concentrations.
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