An upgraded model of the Hypothalamic-Pituitary-Adrenal (HPA) axis has been developed that 
advances our previously proposed low-dimensional HPA model by including the effects of arginine 
vasopressin (AVP) that is a key modulator of HPA axis function. The upgraded model allows us to 
emulate AVP effects on HPA axis dynamics individually and in synergy with the corticotropin-releasing hormone (CRH). In this work, we examine how coupling of the circadian function through 
summarised reaction steps describing CRH and AVP biosynthesis in the same neuronal cell group of the hypothalamic paraventricular nucleus (PVN) affects HPA axis dynamics. Results of numerical simulations show that coupling of the circadian function through both, CRH and AVP summarised biosynthesis reaction steps simultaneously, emulates best the HPA axis dynamics, in line with literature findings

Ivanović-Šašić, Ana

Kolar-Anić, Ljiljana

Stanojević, Ana

Stojiljković, Aleksandra

Čupić, Željko

Central Repository of the Institute of Chemistry, Technology and Metallurgy (CER)

       PHYSICAL CHEMISTRY 2021  15th International Conference on Fundamental and Applied Aspects of Physical Chemistry    Proceedings Volume I    The Conference is dedicated to the   30th Anniversary of the founding of the Society of Physical Chemists of Serbia  and  100th Anniversary of Bray-Liebhafsky reaction        September 20-24, 2021 Belgrade, Serbia  II  Title: Physical Chemistry 2021 (Proceedings) ISBN 978-86-82475-40-8 Volume I: ISBN 978-86-82475-38-5 Editors: Željko Čupić and Slobodan Anić Published by: Society of Physical Chemists of Serbia, Studentski Trg 12-16, 11158, Belgrade, Serbia Publisher: Society of Physical Chemists of Serbia For Publisher: S. Anić, President of Society of Physical Chemists of Serbia Printed by: ʺJovanʺ, <Printing and Publishing Company, 200 Copies Number of pages: 6+344, Format A4, printing finished in December 2021  Text and Layout: ʺJovanʺ   Neither this book nor any part may be reproduced or transmitted in any form or by any means, including photocopying, or by any information storage and retrieval system, without permission in writing from the publisher.            200 - Copy printing                                III           CONTENT    Volume I  Organizer IV Comittes V Plenary Lecture 1 Chemical Thermodynamics 41 Spectroscopy, Molecular Structure, Physical Chemistry of Plasma 55 Kinetics, Catalysis  107 Nonlinear Dynamics, Oscillatory Reactions, Chaos 197 Electrochemistry  273 Biophysical Chemistry, EPR investigations of  Bio-systems 305      IV        PHYSICAL CHEMISTRY 2021  15th International Conference on  Fundamental and Applied Aspects of Physical Chemistry     Organized by  The Society of Physical Chemists of Serbia  in co-operation with  Institute of Catalysis Bulgarian Academy of Sciences  and  Boreskov Institute of Catalysis Siberian Branch of   Russian Academy of Sciences  and  University of Belgrade, Serbia:  Faculty of Physical Chemistry Institute of Chemistry, Technology and Metallurgy Vinča Institute of Nuclear Sciences Faculty of Pharmacy  and  Institute of General and Physical Chemistry, Belgrade, Serbia        V  International Organizing Committee   Chairman:   S. Anić (Serbia) Vice-chairman: M. Gabrovska (Bulgaria)                                A. A. Vedyagin (Russia)       S. N. Blagojević (Serbia)  Members: N. Cvjetićanin (Serbia), S. M. Blagojević (Serbia), M. Daković (Serbia), J. Dimitrić Marković (Serbia), T. Grozdić (Serbia), Lj. Ignjatović (Serbia), D. Jovanović (Serbia), M. Kuzmanović (Serbia), D. Marković (Serbia), B. Milosavljević (USA), M. Mojović (Serbia), N. Pejić (Serbia), M. Petković (Serbia), A. Popović-Bjelić (Serbia), B. Simonović (Serbia), M.Stanković (Serbia), B. Šljukić (Serbia), G. Tasić (Serbia), S. Veličković (Serbia), N. Vukelić (Serbia)  International Scientific Committee  Chairman:   Ž. Čupić (Serbia) Vice-chairman: V. Bukhtiyarov (Russia) S. Todorova (Bulgaria) B. Adnađević (Serbia)  Members: S. Anić (Serbia), A. Antić-Jovanović (Serbia), A. Azizoğlu (Turky), R. Cervellati (Italy), G. Ćirić-Marjanović (Serbia), V. Dondur (Serbia), I. I. Grinvald (Russia), R. Jerala (Slovenia), M. Jeremić (Serbia), G. N. Kaluđerović (Germany), E. Kiš (Serbia), A.V. Knyazev (Russia), Lj. Kolar-Anić (Serbia), U. Kortz (Germany), T. Kowalska (Poljska), A. Lemarchand (France), G. Lente (Hungary), Z. Marković (Serbia), S. Mentus (Serbia), K. Novaković (UK), N. Ostrovski (Serbia), V. Parmon (Russia), Z. Petkova Cherkezova-Zheleva (Bulgary), M. Plavšić (Serbia), J. Savović (Serbia), G. Schmitz (Belgium), I. Schreiber (Czech), L. Schreiberova (Czech), D. Stanisavljev (Serbia), N. Stepanov (Russia), M. Stojanović (USA), E. Szabó (Slovakia), Zs. Szakacs (Romania), Z. Šaponjić (Serbia), Á. Tóth (Hungary), M. Trtica (Serbia), V. Vasić (Serbia), D. Veselinović (Serbia), V. Vukojević (Sweden)  Local Executive Committee  Chairman:   S. N. Blagojević Vice-chairman: A. Ivanović-Šašić       N. Jović-Jovičić       A. Stanojević   Members:  M. Ajduković, I. N. Bubanja, A. Dobrota, J. Dostanić, D. Dimić, S. Jovanović, Z. Jovanović, D. Lončarević, M. Kragović, J. Krstić, B. Marković, S. Maćešić, J. Maksimović, S. Marinović, D. Milenković, T. Mudrinić, M. Pagnacco, N. Potkonjak, B. Stanković, I. Stefanović, G. Stevanović, A. Stoiljković, M. Vasić        VI        SPONSORS  Ministry of Education, Science and Technological Development of the Republic Serbia  Institute of General and Physical Chemistry, Belgrade Belgrade Analysis d.o.o.  PHYSICAL CHEMISTRY 2021        D-12-P  246  CIRCADIAN RHYTHM FUNCTION COUPLING TO THE UPGRADED HYPOTHALAMIC-PITUITARY-ADRENAL (HPA) AXIS WITH INCORPORATED ARGININE VASOPRESSIN   A. S. Stojiljković 1, A. Stanojević 2, A. Ivanović-Šašić 3, Ž. Čupić 3 and Lj. Kolar-Anić 2,3  1 Institute of General and Physical Chemistry, University of Belgrade, Studentski trg 12/V, P.O. Box 45, Belgrade, Serbia (alek.stoj@gmail.com) 2 Faculty of Physical Chemistry, University of Belgrade, Studentski trg 12-16, 11000 Belgrade, Serbia 3 Institute of Chemistry, Technology and Metallurgy, University of Belgrade, Njegoševa 12, 11000 Belgrade, Serbia.  ABSTRACT An upgraded model of the Hypothalamic-Pituitary-Adrenal (HPA) axis has been developed that advances our previously proposed low-dimensional HPA model by including the effects of arginine vasopressin (AVP) that is a key modulator of HPA axis function. The upgraded model allows us to emulate AVP effects on HPA axis dynamics individually and in synergy with the corticotropin-releasing hormone (CRH). In this work, we examine how coupling of the circadian function through summarised reaction steps describing CRH and AVP biosynthesis in the same neuronal cell group of the hypothalamic paraventricular nucleus (PVN) affects HPA axis dynamics. Results of numerical simulations show that coupling of the circadian function through both, CRH and AVP summarised biosynthesis reaction steps simultaneously, emulates best the HPA axis dynamics, in line with literature findings.   INTRODUCTION The hypothalamic-pituitary-adrenal (HPA) axis represents a complex neuroendocrine system that couples the functions of hypothalamus, pituitary and adrenal glands to preserve the organism’s homeostasis under physiologically normal and various stressful conditions. For that purpose, a proper oscillatory dynamics of HPA axis comprising hormones, with ultradian oscillations (period of 20 minutes to 2 hours) superimposed on circadian oscillations (period of about 24 hours), is an essential precondition [1].  The aim of this study is to examine the coupling conditions between ultradian and circadian rhythms of the hormones of the upgraded HPA axis model with incorporated arginine vasopressin (AVP), using modelling of reaction mechanism and numerical simulations. For that purpose, a low-dimensional model with five dynamic variables is employed as the initial model [2]. The upgraded low-dimensional model is now consisted of six dynamic variables: the corticotropin-releasing hormone (CRH), arginine vasopressin (AVP), adrenocorticotropic hormone (ACTH), cortisol (CORT), aldosterone (ALDO) and cholesterol (CHOL), as the only precursor of all steroid hormones.  MODEL AND METHODS The pre-existing low-dimensional HPA model [2] has been extended to describe arginine vasopressin (AVP) effects on adrenocorticotropic hormone (ACTH) release (Table 1).   PHYSICAL CHEMISTRY 2021        D-12-P  247   All reaction steps presented in Table 1 describe end-results of a series of complex biochemical processes. In more detail, series of processes of the biosynthesis of AVP in the parvicellular part of the hypothalamic paraventricular nucleus (PVN), and in the magnocellular neurosecretory system of the hypothalamus, resulting in corresponding inflows of AVP into the pituitary portal system are described by reaction steps (R1) and (R2), respectively. Reaction step (R3) describes summarised series of complex biochemical processes resulting in ACTH secretion stimulated by AVP originating from both of these neuronal populations. Series of complex biochemical reactions leading to ACTH production and release due to a strong synergistic effect of CRH and AVP on ACTH secretion by the pituitary gland, are summarised by reaction step (R4) [3]. Reaction step (R5) describes summarised series of complex biochemical processes leading to the elimination of AVP. Numerical simulations were conducted using the Matlab software package and the ode15s solver routine based on the Gear algorithm for integration of stiff differential equations. In all simulations, the absolute and relative tolerance errors were 3·10-20 and 1·10-14, respectively. The initial concentrations, expressed in mol dm−3 and designated as M, were: [CHOL]0 = 3,4·10-4 M, [CRH]0 = 1·10-12 M, [AVP]0 = 1·10-12 M, [ACTH]0 = 8·10-8 M, [CORT]0 = 4·10-8 M and [ALDO]0 = 1,5·10-9 M. If not otherwise stated, the rate constants were: k1 = 1,83 · 10−8 mol dm−3 min−1, k2 = 1,537 · 10−9 mol dm−3 min−1, k3 = 7,79 · 10-3 min−1, k4 = 1,098 · 109 mol−1 dm3 min−1 and k5 = 1,386 · 10−1 min−1. The circadian rhythm function D=d1 − 0,079145093 · d2 + {0,064 · sin(2πt/1440) + 0,12 · abs[sin(πt/1440)]} · d2 is used to couple to the upgraded model through the reaction steps describing biosynthesis of CRH and AVP in the same neuron cell groups of the hypothalamic PVN.   RESULTS Couplings of the circadian function D to the upgraded HPA model through reaction steps related to the inflows of CRH and AVP into the system from the same neuron cell group and sharing the same rate constant = 1,830 · 10−8 mol dm−3 min−1, have been examined in silico for inflow reaction steps both individually and simultaneously (Figure 1.). These results were further compared with those obtained from the initial HPA model, where CRH is the only species that influence ACTH secretion. The same value for rate constant is used. Namely, when function D is coupled to the upgraded model through CRH and AVP inflow reaction steps simultaneously (Figure 1, case (3)), results show decrease of the amplitude of [CORT] ultradian oscillations compared to those obtained by the coupling of function D through CRH inflow reaction step solely (Figure 1, case (1)). On the other hand, function D coupling through solely AVP inflow reaction step (R1), produces very low amplitude of ultradian oscillations (AUD), that are uniformly superimposed on circadian [CORT] oscillations of also low circadian amplitudes (ACD) (Figure 1, case (2)). By comparing the results obtained by coupling the function D through CRH inflow to the initial minimal HPA model that does not include AVP (Fig. 1, (0)) and the upgraded model with AVP using the same rate constant value for CRH inflow (Fig. 1, (1)), it can be noticed that cortisol AUD is higher in the upgraded HPA model, Table 1. Summarised reaction steps associated with arginine vasopressin (AVP) that are incorporated in the upgraded low-dimensional model of the HPA axis 1k AVP⎯⎯→  (R1) 2k AVP⎯⎯→  (R2) 3kAVP ACTH  ⎯⎯→  (R3) 4kCRH + AVP ACTH⎯⎯→  (R4) 5k 3AVP P⎯⎯→  (R5) PHYSICAL CHEMISTRY 2021        D-12-P  248  which is in better agreement with experimentally measured values reported in the literature. Taken together, AUD increases between the examined cases in the following manner: A(2)UD < A(0)UD < A(3)UD < A (1)UD. There are numerous studies on humans indicating several-fold increased [CORT] due to CRH and AVP acting synergistically on corticotrope cells that could fall into the domain of AUD [4-6].     Circadian function D coupling through the CRH inflow reaction step only will result in [AVP] minimum appearing around 8 o’clock in the morning (8 h) and [AVP] maximum around midnight (24 h). This is in contrast with [AVP] extreme values appearance when the function D is coupled through CRH and AVP inflow reaction steps simultaneously (data not shown). Since [AVP] reaches   Figure 1. Temporal evolution of cortisol concentration ([CORT]) emulated using the minimal or the upgraded model of HPA axis dynamics with the circadian function being coupled through CRH and/or AVP inflow. Daily changes in blood cortisol concentration emulated using: (0) the minimal HPA axis model without AVP, when the rate constant of CRH inflow is 1,830 · 10−8 M; (1) the upgraded HPA axis model with AVP, when the rate constant of CRH inflow is 1,830 · 10−8 M and AVP inflow is disregarded; (2) the upgraded HPA axis model with AVP, when the rate constant of AVP inflow is 1,830 · 10−8 M and CRH inflow is disregarded; (3) the upgraded HPA axis model with AVP, when the rate constant of CRH and AVP inflow are both 1,830 · 10−8 M. Of note, when function D is coupled to the model simultaneously through these inflow reaction steps (3) or only through CRH inflow reaction step, (1) parameters of the circadian function D were: d1 = 0,840978 and d2 = 0,957. On the other hand, when function D is coupled through AVP inflow reaction step (R1) solely (2), corresponding parameters were: d1 = 1,1331072 and d2 = 0,957. In the initial HPA model, (0) with CRH as the only species that influence ACTH secretion, d1 = 0,88524 and d2 = 0,957 were parameters of function D coupling only through CRH inflow reaction step. Time is given in hours (h) and cortisol concentration in mol dm-3.    (1) (2) (3) (0) PHYSICAL CHEMISTRY 2021        D-12-P  249  its minimum in the early evening, around 18-20 o’clock, and a maximum around 2-6 o’clock in the morning [7], the best agreement with experimental results could be achieved when the daily function D is coupled to the model through both, CRH and AVP inflows simultaneously. Additionally, it has been pinpointed in the literature that both parvocellular CRH and AVP participate in the generation of a circadian ACTH and CORT rhythm [8]. In line with these experimental findings, results obtained using the upgraded model favour coupling of the circadian function through CRH and AVP inflow reaction steps simultaneously.  CONCLUSION The pre-existing low-dimensional mathematical model of HPA axis dynamics is extended to include AVP. This enhances the comprehensiveness and physiological plausibility of the model, while preserving its tractability to mathematical analysis and simulation. A step forward is made by finding the appropriate conditions for coupling between ultradian and circadian rhythms of the HPA axis hormones. However, the proposed model still needs further improvements and refinements for examination of AVP and CRH effects and synergistic influence on the HPA axis dynamics.  Acknowledgement  This study was supported by Ministry of Education, Science and Technological Development of the Republic of Serbia (Contracts no. 451-03-9/2021-14/200146, 451-03-9/2021-14/200026 and 451-03-9/2021-14/ 200051).   REFERENCES [1] C. Tsigos and G. P. Chrousos, Journal of Psychosomatic Research (2002) 53, 865-871. [2] V. M. Marković, Ž. Čupić, S. Maćešić, A. Stanojević, V. Vukojević and Lj. Kolar-Anić, Mathematical Medicine and Biology (2016) 33 (1), 1–28.  [3] F. A. Antoni, Frontiers in Neuroendocrinology (1993) 14 (2), 76-122.  [4] R. A. Salata, D. B. Jarrett, J. G. Verbalis, A. G. Robinson, The Journal of Clinical Investigation (1988) 81(3), 766-774. [5] C. R. DeBold, W. R. Sheldon, G. S. DeCherney, R. V. Jackson, A. N. Alexander, W. Vale, J. Rivier, and D. N. Orth, The Journal of Clinical Investigation (1984) 73(2), 533-538. [6] J.H. Liu, K. Muse, P. Contreras, D. Gibbs, W. Vale, J. Rivier, S. S. C. Yen, The Journal of Clinical Endocrinology & Metabolism (1983) 57 (5), 1087-1089.  [7] ML Forsling, H Montgomery, D Halpin, RJ Windle, DF Treacher, Experimental Physiology (1998) 83 (3), 409-418. [8] George P. Chrousos, Endocrinology (1998) 139 (2), 437–40.     

Circadian rhythm function coupling to the upgraded hypothalamic-pituitary-adrenal (hpa) axis with incorporated arginine vasopressin

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Circadian rhythm function coupling to the upgraded hypothalamic-pituitary-adrenal (hpa) axis with incorporated arginine vasopressin

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