Predictive modeling of the hypothalamic-pituitary-adrenal (HPA) function. dynamic systems theory approach by stoichiometric network analysis and quenching small amplitude oscillations

Two methods for dynamic systems analysis, Stoichiometric Network Analysis (SNA) and Quenching of Small Amplitude Oscillations (QA), are used to study the behaviour of a vital biological system. Both methods use geometric approaches for the study of complex reaction systems. In SNA, methods based on convex polytopes geometry are applied for stability analysis and optimization of reaction networks. QA relies on a geometric representation of the concentration phase space, introduces the concept of manifolds and the singular perturbation theory to study the dynamics of complex processes. The analyzed system, the Hypothalamic-Pituitary-Adrenal (HPA) axis, as a major constituent of the neuroendocrine system has a critical role in integrating biological responses in basal conditions and during stress. Self-regulation in the HPA system was modeled through a positive and negative feedback effect of Cortisol. A systematically reduced low-dimensional model of HPA activity in humans was fine-tuned by SNA, until quantitative agreement with experimental findings was achieved. By QA, we revealed an important dynamic regulatory mechanism that is a natural consequence of the intrinsic rhythmicity of the considered system