An evaluation of the cross-linking model for the interaction of insulin with its receptor

Quasi-Steady-State Analysis based on Structural Modules and Timed Petri Net Predict System's Dynamics: The Life Cycle of the Insulin Receptor

The insulin-dependent activation and recycling of the insulin receptor play an essential role in the regulation of the energy metabolism, leading to a special interest for pharmaceutical applications. Thus, the recycling of the insulin receptor has been intensively investigated, experimentally as well as theoretically. We developed a time-resolved, discrete model to describe stochastic dynamics and study the approximation of non-linear dynamics in the context of timed Petri nets. Additionally, using a graph-theoretical approach, we analyzed the structure of the regulatory system and demonstrated the close interrelation of structural network properties with the kinetic behavior. The transition invariants decomposed the model into overlapping subnetworks of various sizes, which represent basic functional modules. Moreover, we computed the quasi-steady states of these subnetworks and demonstrated that they are fundamental to understand the dynamic behavior of the system. The Petri net approach confirms the experimental results of insulin-stimulated degradation of the insulin receptor, which represents a common feature of insulin-resistant, hyperinsulinaemic states.

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

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.

Signaling through receptors and scaffolds: independent interactions reduce combinatorial complexity

After activation, many receptors and their adaptor proteins act as scaffolds displaying numerous docking sites and engaging multiple targets. The consequent assemblage of a variety of protein complexes results in a combinatorial increase in the number of feasible molecular species presenting different states of a receptor-scaffold signaling module. Tens of thousands of such microstates emerge even for the initial signal propagation events, greatly impeding a quantitative analysis of networks. Here, we demonstrate that the assumption of independence of molecular events occurring at distinct sites enables us to approximate a mechanistic picture of all possible microstates by a macrodescription of states of separate domains, i.e., macrostates that correspond to experimentally verifiable variables. This analysis dissects a highly branched network into interacting pathways originated by protein complexes assembled on different sites of receptors and scaffolds. We specify when the temporal dynamics of any given microstate can be expressed using the product of the relative concentrations of individual sites. The methods presented here are equally applicable to deterministic and stochastic calculations of the temporal dynamics. Our domain-oriented approach drastically reduces the number of states, processes, and kinetic parameters to be considered for quantification of complex signaling networks that propagate distinct physiological responses.