©Freund Publishing House Ltd., International Journal of Nonlinear Sciences & Numerical Simulation 10(11-12): 1451-1472, 2009 Ljiljana Kolar-Anić, E-mail: lkolar@ffh.bg.ac.rs Predictive Modeling of the Hypothalamic-Pituitary-Adrenal (HPA) Function. Dynamic Systems Theory Approach by Stoichiometric Network Analysis and Quenching Small Amplitude Oscillations Smiljana Jelić,1 Željko Čupić,2 Ljiljana Kolar-Anić,3,#,* Vladana Vukojević4,#,* 1 Department of Theoretical Physics and Physics of Condensed Matter 020/2, Vinča Institute of Nuclear Sciences, University of Belgrade, P. O. Box 522, 11001 Belgrade, Serbia 2 Institute of Chemistry, Technology and Metallurgy, University of Belgrade, Department of Catalysis and Chemical Engineering, Njegoševa 12, 11000 Belgrade, Serbia 3 Faculty of Physical Chemistry, University of Belgrade, Studentski trg 12-16, P. O. Box 137, 11001 Belgrade, Serbia 4 Department of Clinical Neuroscience, Karolinska Institutet, CMM L8:01, 17176 Stockholm, Sweden Abstract 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. Keywords: Hypothalamic-Pituitary-Adrenal (HPA) System; Ultradian Cortisol Pulsation; Stress; Modeling biochemical networks; Stoichiometric Network Analysis (SNA); Quenching Small Amplitude Oscillations; Nonlinear Dynamics; Systems Biology. Introduction To resolve the complexity of biological systems at the molecular level analytical and integrative approaches are required. In analytical approaches the following questions are typically being asked. Which molecules and processes contribute to a specific biological system? How do biological molecules interact with their particular targets? How are components of one pathway/process separated from the related ones? Are structural variations at the single-molecule level relevant for conveying different information? What are the feedback mechanisms through which favourable and unfavourable adaptive trans- formations occur in biological systems? These questions are addressed by experimental approaches using molecular biology and physicochemical methods of analysis.