Quenching Small-Amplitude Limit Cycle Oscillations for Predictive Modeling of Complex Molecular Mechanisms Underlying Chemical and Biochemical Oscillatory Reactions. Insights into the Effects of Ethanol on the Hypothalamic-Pituitary-Adrenal (HPA) Axis Dynamics

Vladana Vukojević

Department of Clinical Neuroscience (CNS), Center for Molecular Medicine (CMM), Karolinska Institute, Stockholm, Sweden

WG Virtual Seminars, Oct 17^th 2024

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http://www.arlotto.com/newsletter/filmshot.png; https://ki.se/en/about/karolinska-institutet-in-brief

Karolinska Institutet, medical university with a mission �to significantly contribute to the improvement of human health through research, education and information

Research goals

Our research aims to deepen our understanding of normal physiology and diseases mechanisms. We focus on making scientific breakthroughs and turning them into practical, innovative solutions that healthcare can adopt to improve quality of life for everyone.

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Educational goals

Our educational programs aim to offer the best learning opportunities, strengthen connections with research and prepare students for their future professional roles, equipping them with knowledge and skills to work, lead, and innovate across disciplines.

Functional Fluorescence Microscopy Imaging (fFMI)

Dynamic self-regulation of the neuroendocrine system

We study cellular and molecular mechanisms underlying alcohol use disorder (AUD), focusing on the opioid system role in its development and management. To this aim, we use and further develop quantitative time-resolved analytical methods with single-molecule sensitivity and integrative approaches from dynamical systems theory.

Early biomarker of amyloid diseases

Experimental alcohol and drug dependence

research group

OUTLINE

Quenching small-amplitude limit cycle oscillations for predictive modeling of complex molecular mechanisms underlying chemical and biochemical oscillatory reactions

• Oscillatory reactions in a Continuously-fed well Stirred Tank Reactor (CSTR)
• Supercritical Hopf bifurcation
• Quenching small-amplitude limit cycle oscillations
• Reconstruction of small-amplitude limit cycle oscillations from quenching experiments

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Insights into the effects of ethanol on the hypothalamic-pituitary-adrenal (HPA) axis dynamics

• Circadian and ultradian rhythmicity of hormones constituting the HPA axis
• The HPA axis and stress
• Ethanol effect on HPA axis dynamics
• HPA axis in the Lateral Hypothalamic Kindling (LHK) model of acute mania

Confocal

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Quenching small-amplitude limit cycle oscillations�

Hynne F, Sørensen PG. �Quenching of Chemical Oscillations�J. Phys. Chem. 1987 91:6573-6575.

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Hynne F, Sørensen PG, Nielsen K. �Quenching of chemical oscillations – General theory. �J. Chem. Phys. 1990 92:1747-1757.

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Vukojević V, Sørensen PG, Hynne F. �Quenching Analysis of the Briggs-Rauscher Reaction. �J. Phys. Chem. 1993 97:4091-4100.

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Vukojević V, Sørensen PG, Hynne F. �Predictive value of a model of the Briggs-Rauscher reaction fitted to quenching experiments.

J. Phys. Chem. 1996 100:17175-17185.

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The Briggs-Rauscher (BR) oscillatory reaction

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The BR oscillatory reaction in the CSTR and the supercritical Hopf bifurcation

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CSTR schematic: http://www.hydrochemistry.eu/exmpls/cstr.htmlhttps://youtu.be/_gyzhvMLImg

Vukojević V, Sørensen PG, Hynne F. Quenching Analysis of the Briggs-Rauscher Reaction. J. Phys. Chem. 1993 97: 4091-4100.

j₀ increased

j₀ decreased

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Concentration phase space, limit cycle oscillations near a supercritical Hopf bifurcation and quenching of small-amplitude limit cycle oscillations

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Vukojević V, Sørensen PG, Hynne F. Quenching Analysis of the Briggs-Rauscher Reaction. J. Phys. Chem. 1993 97: 4091-4100.

Arthur T. Winfree, The Geometry of Biological Time, 2001, Springer-Verlag, New York.

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Quenching yields two values, the quenching concentration (q_i) and phase angle (ϕ_i) that are uniquely defined for each reaction species

Vukojević V, Sørensen PG, Hynne F. Quenching Analysis of the Briggs-Rauscher Reaction. J. Phys. Chem. 1993 97: 4091-4100.

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Quenching small-amplitude limit cycle oscillations by removal of a single species is equivalent to quenching by addition of a stoichiometrically equivalent amount at an opposite phase angle

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Vukojević V, Sørensen PG, Hynne F. Quenching Analysis of the Briggs-Rauscher Reaction. J. Phys. Chem. 1993 97: 4091-4100.

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Quenching small-amplitude limit cycle oscillations by removal of a single species – the H⁺ / OH^- paradox in BR

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The quenching concentrations of H⁺ and OH^- differ by a factor of 26 and the phase angles difference is ≈ 8O°!

Vukojević V, Sørensen PG, Hynne F. Quenching Analysis of the Briggs-Rauscher Reaction. J. Phys. Chem. 1993 97: 4091-4100.

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Quenching small-amplitude limit �cycle oscillations by dilution

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Vukojević V, Sørensen PG, Hynne F. Quenching Analysis of the Briggs-Rauscher Reaction. J. Phys. Chem. 1993 97: 4091-4100.

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Existing mathematical models of the BR reaction

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Vukojević et al. Predictive value of a model of the Briggs-Rauscher reaction fitted to quenching experiments. J. Phys. Chem. 1996 100:17175-17185.

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Mathematical model of the BR reaction developed

based on quenching experiments

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Vukojević et al. Predictive value of a model of the Briggs-Rauscher reaction fitted to quenching experiments. J. Phys. Chem. 1996 100:17175-17185.

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Mathematical model of the BR reaction developed

based on quenching experiments

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Vukojević et al. Predictive value of a model of the Briggs-Rauscher reaction fitted to quenching experiments. J. Phys. Chem. 1996 100:17175-17185.

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Predictive value of the mathematical model of the BR reaction developed based on quenching experiments

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Vukojević et al. Predictive value of a model of the Briggs-Rauscher reaction fitted to quenching experiments. J. Phys. Chem. 1996 100:17175-17185.

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Predictive value of the mathematical model of the BR reaction developed based on quenching experiments

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Vukojević et al. Predictive value of a model of the Briggs-Rauscher reaction fitted to quenching experiments. J. Phys. Chem. 1996 100:17175-17185.

De Kepper, P. Ph.D. Thesis, Bordeaux, France, 1978.

Bistability

Complex oscillations

Bursting

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Mathematical formalism behind quenching experiments

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Hynne F, Sørensen PG. Quenching of Chemical Oscillations. J. Phys. Chem. 1987 91:6573-6575.

Hynne F, Sørensen PG, Nielsen K. Quenching of chemical oscillations – General theory. J. Chem. Phys. 1990 92: 1747-1757.

Vukojević et al. Predictive value of a model of the Briggs-Rauscher reaction fitted to quenching experiments. J. Phys. Chem. 1996 100:17175-17185.

Confocal

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The Hypothalamic-Pituitary-Adrenal (HPA) axis�

Čupić Ž, Stanojević A, Marković VM, Kolar-Anić L, Terenius L, Vukojević V. �The HPA axis and ethanol: a synthesis of mathematical modelling and experimental observations. �Addict. Biol. 2017 22(6):1486-1500. doi: 10.1111/adb.12409

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Abulseoud OA, Ho MC, Choi D-S, Stanojević A, Čupić Ž, Kolar-Anić Lj, Vukojević V. �Corticosterone oscillations during mania induction in the lateral hypothalamic kindled rat experimental observations and mathematical modelling. �PLoS One 2017, 12(5):e0177551. doi: 10.1371/journal.pone.0177551

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Stanojević A, Marković VM, Čupić Ž, Kolar-Anić Lj, Vukojević V. �Advances in mathematical modelling of the hypothalamic–pituitary–adrenal (HPA) axis dynamics and the neuroendocrine response to stress. �Current Opinion in Chemical Engineering 2018, 21:84–95. doi:10.1016/j.coche.2018.04.003

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Neuroendocrine transformations underlying the HPA axis

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• The HPA axis integrates and synchronizes the nervous and the endocrine systems function at the organism level by linking the activity of the hypothalamus, pituitary and adrenal glands through the action of steroid and peptide hormones on their corresponding receptors.

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• Main representatives of steroid HPA axis hormones in humans are cortisol (CORT) and aldosterone (ALDO), and the most relevant peptide hormones are the corticotropin-releasing hormone (CRH) and the adrenocorticotropic hormone (ACTH).

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• The HPA axis is a complex and highly dynamic neuroendocrine system of vital importance for maintaining homeostasis of metabolic functions under normal physiological conditions and stress.

• The HPA axis controls a wide range of physiological, behavioral and cognitive functions and plays a decisive role in the regulation of response to stress, emotional and social behaviors like attachment, temperament and mood.

János Hugo Bruno "Hans" Selye "The Stress of Life"

Jelić et al. Int. J. Nonlin. Sci. Num. 2009 10:1451-1472

Marković et al. Endocr. J. 2011 58:889-904

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HPA axis dynamics has two characteristic periods

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Walker et al. Proc. Biol. Sci. 2010 277:1627-33

Charloux et al. Am. J. Physiol. 1999 276(1 Pt 1):E43-9.

The anatomical origin of the circadian oscillations is in the suprachiasmatic nucleus (SCN).

The anatomical origin of ultradian oscillations is not known.

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HPA axis dynamics is altered in different diseases

and by different external/internal stimuli

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Van Cauter E. Physiology and Pathology of Circadian Rhythms. in Recent Advances in Endocrinology and Metabolism, Edwards CW and Lincoln DW (Eds), Edinburgh, Churchill Livingstone 1989 3:109-134; Charloux et al. Am. J. Physiol. 1999 276(1 Pt 1):E43-9.

Weikel et al. Ghrelin promotes slow-wave sleep in humans. Am. J. Physiol. Endocrinol. Metab. 2003;284(2):E407-15.

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Neurochemical transformations underlying the

HPA axis

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Marković et al. Math. Med. Biol., 2016 33 1-28 pii: dqu020.

Čupić et al. Chaos 2016 26(3):033111. doi: 10.1063/1.4944040

Čupić et al. Addict. Biol. 2016 doi: 10.1111/adb.12409.

Abulseoud OA et al. PLoS One 2017 12(5): e0177551.

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Stoichiometric network model of the HPA axis in humans

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Marković et al. Math. Med. Biol., 2016 33 1-28 pii: dqu020.

Čupić et al. Chaos 2016 26(3):033111. doi: 10.1063/1.4944040

Čupić et al. Addict. Biol. 2016 doi: 10.1111/adb.12409.

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Stoichiometric network analysis (SNA). Instability conditions for the proposed network of stoichiometric relations

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Clarke B. Stability of complex reaction networks. In: Prigogine I. Rice S, editors. Advances in chemical physics. 1980, New York: Wiley, pp. 1–216.

Clarke B. Stoichiometric network analysis. Cell Biophys 1988 12: 237-253.

Kolar-Anić et al. Improvement of the stoichiometric network analysis for determination of instability conditions of complex nonlinear reaction systems. Chemical Engineering Science 2010 65: 3718-3728.

Jelić et al. Int. J. Nonlin. Sci. Num. 2009 10:1451-1472 .

Marković et al. Math. Med. Biol., 2016 33 1-28 pii: dqu020.

Čupić et al. Chaos 2016 26(3):033111. doi: 10.1063/1.4944040

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Coupling the system of ODEs describing temporal changes in the concentration of HPA axis hormones in the peripheral blood circulation with an external forcing function that describes the circadian rhythm

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Marković VM, Čupić Ž, Maćešić S, Stanojević A, Vukojević V, Kolar-Anić Lj. Modelling cholesterol effects on the dynamics of the hypothalamic-pituitary-adrenal (HPA) axis. Math. Med. Biol., 2016 33 1-28 pii: dqu020. Čupić Ž, Marković VM, Maćešić S, Stanojević A, Damjanović S, Vukojević V, Kolar-Anić Lj. Dynamic transitions in a model of the hypothalamic-pituitary-adrenal (HPA) axis. Chaos 2016 26(3):033111.

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Numerical simulations of HPA axis dynamics in humans and rodents

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Walker et al. J. Neuroendocrinology 2010, 22:1226–1238.

Abulseoud OA et al. PLoS One 2017 12(5): e0177551.

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Predictive value of the model for humans and rodents

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Čupić et al. Addict. Biol. 2016 doi: 10.1111/adb.12409.

Abulseoud OA et al. PLoS One 2017 12(5): e0177551.

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The models mimic the “inverted U response” of HPA axis activity to glucocorticoids

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Čupić et al. Addict. Biol. 2016 doi: 10.1111/adb.12409.

Abulseoud OA et al. PLoS One 2017 12(5): e0177551.

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Modeling acute ethanol effects on the HPA axis dynamics

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Čupić et al. Addict. Biol. 2016 doi: 10.1111/adb.12409.

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HPA axis recovery time depends on the intensity of the acute ethanol challenge

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Čupić et al. Addict. Biol. 2016 doi: 10.1111/adb.12409.

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Complex ethanol effects on HPA axis dynamics.

The same acute dose of ethanol applied at different time points does not elicit the same HPA axis response

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Čupić et al. Addict. Biol. 2016 doi: 10.1111/adb.12409.

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The same dose of ethanol applied during daytime or at night does not elicit the same HPA axis response

Čupić et al. Addict. Biol. 2016 doi: 10.1111/adb.12409.

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Blunted HPA axis response to repeated ethanol challenge

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Čupić et al. Addict. Biol. 2016 doi: 10.1111/adb.12409.

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HPA axis allostasis, allostatic load and “inversion” of circadian rhythmicity in chronic alcohol use

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Čupić et al. Addict. Biol. 2016 doi: 10.1111/adb.12409.

Koob GF. Alcoholism: allostasis and beyond. Alcohol Clin Exp Res. 2003 27(2):232-243.

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HPA axis dynamics in a rat model of mania induced by lateral hypothalamic kindling (LHK)

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Abulseoud OA et al. PLoS One 2017 12(5): e0177551.

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Electrical stimulation of the hypothalamus induces a frequency dependent CRH output

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Abulseoud OA et al. PLoS One 2017 12(5): e0177551.

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HPA axis dynamics in an acute mania-like state induced by lateral hypothalamic kindling

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Abulseoud OA et al. PLoS One 2017 12(5): e0177551.

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HPA axis dynamics in states induced by prolonged LHK and LHK of different intensity

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Abulseoud OA et al. PLoS One 2017 12(5): e0177551.

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Concluding remarks

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• Quenching of small limit cycle oscillations is an experimentally simple to apply and very powerful method to provide unbiased quantitative information about complex chemical/biochemical systems.
• The quenching concentration and the quenching phase angle are uniquely defined when the system is in the vicinity of a supercritical Hopf bifurcation, and their values are closely related to the underlying kinetic mechanism.
• Quenching parameters can be easily calculated and used for assessing mathematical models of a chemical/biochemical system.

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• Mathematical modeling suggests that the HPA axis operates under conditions that are close to a supercritical Hopf bifurcation.
• Quenching of ultradian oscillations reveals why the same ethanol challenge does not always elicit the same response.
• Proximity to a supercritical Hopf bifurcation may provide insights into how the experimentally observed blunted HPA axis response occurs.
• Mathematical modeling shows that HPA axis circadian rhythmicity can be changed, even though the functioning of the circadian clock system is conserved and not affected by ethanol.
• Mathematical modeling gives a quantitative explanation for the concepts of allostasis and allostatic load.
• Chronopharmacotherpy – mathematical modeling and numerical simulations reveal the synergistic effects that can be achieved when pharmacotherapy is synchronized with patient physiology.

1. Stanojević A, Marković VM, Čupić Ž, Kolar-Anić Lj, Vukojević V.

Advances in mathematical modelling of the hypothalamic–pituitary–adrenal (HPA) axis dynamics and the neuroendocrine response to stress.

Current Opinion in Chemical Engineering 2018 21: 84–95.

2. Stanojević A, Marković VM, Maćešić S, Kolar-Anić Lj, Vukojević V.

Kinetic modelling of testosterone-related differences in the hypothalamic–pituitary–adrenal axis response to stress

Reac. Kinet. Mech. Cat. 2018 123: 17. https://doi.org/10.1007/s11144-017-1315-7.

3. Abulseoud OA, Ho MC, Choi D-S, Stanojević A, Čupić Ž, Kolar-Anić Lj. Vukojević V. �Corticosterone oscillations during mania induction in the lateral hypothalamic kindled rat – experimental observations and mathematical modeling. �PLoS One 2017 12(5): e0177551.

4. Čupić Ž, Stanojević A, Marković VM, Kolar-Anić Lj, Terenius L, Vukojević V. �The HPA axis and ethanol: a synthesis of mathematical modelling and experimental observations. �Addict. Biol. 2016 doi: 10.1111/adb.12409.

5. Čupić Ž, Marković VM, Maćešić S, Stanojević A, Damjanović S, Vukojević V, Kolar-Anić Lj. �Dynamic transitions in a model of the hypothalamic-pituitary-adrenal (HPA) axis. �Chaos 2016 26(3): 033111. doi: 10.1063/1.4944040.

6. Marković VM, Čupić Ž, Maćešić S, Stanojević A, Vukojević V, Kolar-Anić Lj. �Modelling cholesterol effects on the dynamics of the hypothalamic-pituitary-adrenal (HPA) axis. �Math. Med. Biol., 2016 33 1-28 pii: dqu020.

7. Marković VM, 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.

8. 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.

Confocal

https://ki.se/en/cns/vladana-vukojevics-research-group

Acknowledgements

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Confocal

THANK YOU!