Modelling of the thyroid hormone synthesis as a part of nonlinear reaction mechanism with feedback

Abstract

The synthesis of thyroid hormones in the hypothalamic-pituitary-thyroid (HPT) axis was studied. For this purpose, a reaction model for HPT axis with stoichiometric relations between the main reaction species was postulated. Using the law of mass action, this model has been transformed into a set of nonlinear ordinary differential equations. This new model has been examined by stoichiometric network analysis (SNA) with the aim to see if it possesses the ability to reproduce oscillatory ultradian dynamics founded on the internal feedback mechanism. In particular, a feedback regulation of TSH production based on the interplay between TRH, TSH, somatostatin and thyroid hormones was proposed. Besides, the ten times larger amount of produced T4 with respect to T3 in the thyroid gland was successfully simulated. The properties of SNA in combination with experimental results, were used to determine the unknown parameters (19 rate constants of particular reaction steps) necessary for numerical investigations. The steady-state concentrations of 15 reactive species were tuned to be consistent with the experimental data. The predictive potential of the proposed model was illustrated on numerical simulations of somatostatin influence on TSH dynamics investigated experimentally by Weeke et al. in 1975. In addition, all programs for SNA analysis were adapted for this kind of a large model. The procedure of calculating rate constants from steady-state reaction rates and very limited available experimental data was developed. For this purpose, a unique numerical method was developed to fine-tune model parameters while preserving the fixed rate ratios and using the magnitude of the experimentally known oscillation period as the only target value. The postulated model was numerically validated by perturbation simulations with somatostatin infusion and the results were compared with experiments available in literature. Finally, as far as we know, this reaction model with 15 variables is the most dimensional one that have been analysed mathematically to obtain instability region and oscillatory dynamic states. Among the existing models of thyroid homeostasis this theory represents a new class that may improve our understanding of basic physiological processes and helps to develop new therapeutic approaches. Additionally, it may pave the way to improved diagnostic methods for pituitary and thyroid disorders.