Modelling the Hypothalamic-Pituitary-Adrenal (HPA) Axis As a Complex Oscillating Reaction System

Modelling the Hypothalamic-Pituitary-Adrenal (HPA) axis as a complex oscillating reaction system

Ljiljana Kolar-Anić1,2

1Faculty of Physical Chemistry, University of Belgrade, Studentski trg 12-16, 11000 Belgrade, Serbia

2Institute of Chemistry, Technology and Metallurgy, University of Belgrade, Department of Catalysis and Chemical Engineering, Njegoševa 12, 11000 Belgrade, Serbia

To analyze dynamic states in a reaction system, the system’s evolution in time is described using a set of differential equations. These equations can be obtained either by postulating a stoichiometric model or by a more general mathematical approach, using differential equations with nonlinear terms to mimic the temporal behaviour of the investigated system. Even though it is not possible to assign a mechanism with complete certainty to any real chemical reaction, the stoichiometric approach to modelling is advantageous because it is consistent with known biochemical data, model predictions can be more directly compared with real experiments and the model can be more easily expanded to account for additional species that modulate the main process.

To demonstrate the validity of the stoichiometric approach for describing complex biological systems, we shall consider a low-dimensional model of the Hypothalamic-Pituitary-Adrenal (HPA) axis, which is a highly dynamical structure that integrates and controls the functions of the nervous and endocrines systems under normal physiological conditions and stress[1-5]. We also show that the model can be easily expanded to account for additional reactions and additional species, such as cholesterol, which is the only precursor of steroid hormones and modulates the HPA axis dynamics. [6]

References

[1] Jelić S, Čupić Ž, Kolar-Anić Lj. Mathematical modeling of the hypothalamic-pituitary-adrenal system activity. Math Biosci. 2005,197:173-187.

[2] Jelić S, Čupić Ž, Kolar-Anić Lj, Vukojević V. Predictive Modelling of the Hypothalamic-Pituitary-Adrenal (HPA) function. Dynamic Systems Theory Approach by Stoichiometric Network Analysis and Quenching Small Amplitude Oscillations. Int J Nonlin Sci Num, 2009, 10:1451-1472.

[3] Marković V. M, Čupić Ž, Vukojević V, Kolar-Anić Lj. Predictive modeling of the hypothalamic-pituitary-adrenal (HPA) axis response to acute and chronic stress. Endocr J. 2011,58:889-904.

[4] Marković VM, Čupić Ž, Ivanović A, Kolar-Anić Lj. The stability of the extended model of hypothalamic-pituitary-adrenal (HPA) axis examined by stoichiometric network analysis (SNA). Russ. J. Phys. Chem. A, 2011 85:2327-2335.

[5] Čupić Ž, Marković V, Ivanović A, Kolar-Anić Lj. Modeling of the Complex Nonlinear Processes: Determination of the Instability Region by the Stoichiometric Network Analysis, In: Christopher R. Brennan, Ed. Mathematical Modelling, Nova Science Publishers Inc., New York, 2011, pp. 111-178, ISBN: 978-1-61209-651-3.

[6] Marković, V.M, Čupić, Ž, Maćešić, S, Stanojević, A, Vukojević, V, Kolar-Anić, Lj,Modelling cholesterol effects on the dynamics of thehypothalamic–pituitary–adrenal (HPA) axis, Mathematical Medicine and Biology (2014), doi:10.1093/imammb/dqu020.