Abstract
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.
Highlights
Physical activity and insulin control the energy metabolism in mammalian cells
We focus on transition invariants (TIs) and their interpretation to understand the functional modules of the insulin receptor (IR) life cycle
Both Petri net (PN) models, the P/T model and the timed PNs (TPNs) model, are based on the reaction system proposed by Sedaghat et al [34]
Summary
Physical activity and insulin control the energy metabolism in mammalian cells. In response to elevated blood glucose levels, pancreatic beta cells located in the islets of Langerhans secrete insulin. The models either completely neglect the synthesis and degradation of the IR or apply a reaction rate constant of k = 1.67 × 10−18 min−1 [34,35,41,42,51] for the degradation process This assumes an astronomic time scale of 1.1 × 1012 years, leading to a theoretical steady-state value of 100 M IR concentration for a cell [37]. We chose the network topology, shown, in accordance with the reaction system of Sedaghat et al [34], who proposed a mathematical model of the metabolic insulin signaling pathways They abstain from describing allosteric properties of the insulin binding mechanism. The results of the PN approach demonstrate that, even without knowing the kinetic parameters, the experimental findings of insulin-induced long-term down-regulation of the cellular IR level can be confirmed [53,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91]
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