Research article Special Issues

Monoamine neurotransmitters and mood swings: a dynamical systems approach


  • Received: 23 November 2021 Revised: 17 January 2022 Accepted: 09 February 2022 Published: 15 February 2022
  • Serotonin, dopamine and norepinephrine are monoamine neurotransmitters that modulate our mood state. Hence, imbalances in the levels of these neurotransmitters have been linked to the incidence of several psychiatric disorders. Here, a mathematical model written in terms of ordinary differential equations is proposed to represent the interaction of these three neurotransmitters. It is analytically and numerically shown that this model can experience a Hopf bifurcation. Thus, by varying a parameter value, the neurotransmitter levels can change from a steady state to an oscillatory behavior, which may be at least a partial explanation of the mood swings observed in depressed people.

    Citation: R. Loula, L. H. A. Monteiro. Monoamine neurotransmitters and mood swings: a dynamical systems approach[J]. Mathematical Biosciences and Engineering, 2022, 19(4): 4075-4083. doi: 10.3934/mbe.2022187

    Related Papers:

  • Serotonin, dopamine and norepinephrine are monoamine neurotransmitters that modulate our mood state. Hence, imbalances in the levels of these neurotransmitters have been linked to the incidence of several psychiatric disorders. Here, a mathematical model written in terms of ordinary differential equations is proposed to represent the interaction of these three neurotransmitters. It is analytically and numerically shown that this model can experience a Hopf bifurcation. Thus, by varying a parameter value, the neurotransmitter levels can change from a steady state to an oscillatory behavior, which may be at least a partial explanation of the mood swings observed in depressed people.



    加载中


    [1] G. Hasler, Pathophysiology of depression: do we have any solid evidence of interest to clinicians?, World Psychiatry, 9 (2010), 155–161. https://doi.org/10.1002/j.2051-5545.2010.tb00298.x doi: 10.1002/j.2051-5545.2010.tb00298.x
    [2] M. Hamon, P. Blier, Monoamine neurocircuitry in depression and strategies for new treatments, Prog. Neuro-Psychopharmacol. Biol. Psychiatry, 45 (2013), 54–63. https://doi.org/10.1016/j.pnpbp.2013.04.009 doi: 10.1016/j.pnpbp.2013.04.009
    [3] Y. Liu, J. P. Zhao, W. B. Guo, Emotional roles of mono-aminergic neurotransmitters in major depressive disorder and anxiety disorders, Front. Psychol., 9 (2018), 2201. https://doi.org/10.3389/fpsyg.2018.02201 doi: 10.3389/fpsyg.2018.02201
    [4] L. Perez-Caballero, S. Torres-Sanchez, C. Romero-López-Alberca1, F. González-Saiz, J. A. Mico, E. Berrocoso, Monoaminergic system and depression, Cell Tissue Res., 377 (2019), 107–113. https://doi.org/10.1007/s00441-018-2978-8 doi: 10.1007/s00441-018-2978-8
    [5] X. J. Shao, G. Zhu, Associations among monoamine neurotransmitter pathways, personality traits, and major depressive disorder, Front. Psychiatry, 11 (2020), 381. https://doi.org/10.3389/fpsyt.2020.00381 doi: 10.3389/fpsyt.2020.00381
    [6] F. Benedetti, B. Barbini, C. Colombo, E. Campori, E. Smeraldi, Infradian mood fluctuations during a major depressive episode, J. Affect. Disord., 41 (1996), 81–87. https://doi.org/10.1016/S0165-0327(96)00071-7 doi: 10.1016/S0165-0327(96)00071-7
    [7] R. C. Bowen, Y. Wang, L. Balbuena, A. Houmphan, M. Baetz, The relationship between mood instability and depression: implications for studying and treating depression, Med. Hypotheses, 81 (2013), 459–462. https://doi.org/0.1016/j.mehy.2013.06.010 doi: 10.1016/j.mehy.2013.06.010
    [8] R. Bowen, E. Peters, S. Marwaha, M. Baetz, L. Balbuena, Moods in clinical depression are more unstable than severe normal sadness, Front. Psychiatry, 8 (2017), 56. https://doi.org/10.3389/fpsyt.2017.00056 doi: 10.3389/fpsyt.2017.00056
    [9] D. Savić, S. Jelić, A mathematical model of the hypothalamo-pituitary-adrenocortical system and its stability analysis, Chaos, Solitons Fractals, 26 (2005), 427–436. https://doi.org/10.1016/j.chaos.2005.01.013 doi: 10.1016/j.chaos.2005.01.013
    [10] E. O. Bangsgaard, J. T. Ottesen, Patient specific modeling of the HPA axis related to clinical diagnosis of depression, Math. Biosci., 287 (2017), 24–35. https://doi.org/10.1016/j.mbs.2016.10.007 doi: 10.1016/j.mbs.2016.10.007
    [11] A. Menke, Is the HPA axis as target for depression outdated, or is there a new hope?, Front. Psychiatry, 10 (2019), 101. https://doi.org/10.3389/fpsyt.2019.00101 doi: 10.3389/fpsyt.2019.00101
    [12] J. A. Best, H. F. Nijhout, R. C. Reed, Homeostatic mechanisms in dopamine synthesis and release: a mathematical model, Theor. Biol. Med. Model., 6 (2009), 21. https://doi.org/10.1186/1742-4682-6-21 doi: 10.1186/1742-4682-6-21
    [13] J. A. Best, H. F. Nijhout, R. C. Reed, Serotonin synthesis, release and reuptake in terminals: a mathematical model, Theor. Biol. Med. Model., 7 (2010), 34. https://doi.org/10.1186/1742-4682-7-34 doi: 10.1186/1742-4682-7-34
    [14] E. Brown, J. Moehlis, P. Holmes, E. Clayton, J. Rajkowski, G. Aston-Jones, The influence of spike rate and stimulus duration on noradrenergic neurons, J. Comput. Neurosci., 17 (2004), 13–29. https://doi.org/10.1023/B:JCNS.0000023867.25863.a4 doi: 10.1023/B:JCNS.0000023867.25863.a4
    [15] World Health Organization (WHO), Depression and other Common Mental Disorders: Global Health Estimates, Geneva, WHO, 2017.
    [16] T. C. Wu, X. Q. Jia, H. F. Shi, J. Q. Niu, X. H. Yin, J. L. Xie, et al., Prevalence of mental health problems during the COVID-19 pandemic: a systematic review and meta-analysis, J. Affect. Disord., 281 (2021), 91–98. https://doi.org/10.1016/j.jad.2020.11.117 doi: 10.1016/j.jad.2020.11.117
    [17] M. D. Nemesure, M. V. Heinz, R. Huang, N. C. Jacobson, Predictive modeling of depression and anxiety using electronic health records and a novel machine learning approach with artificial intelligence, Sci. Rep., 11 (2021), 1980. https://doi.org/10.1038/s41598-021-81368-4 doi: 10.1038/s41598-021-81368-4
    [18] S. A. Akar, S. Kara, S. Agambayev, V. Bilgiç, Nonlinear analysis of EEGs of patients with major depression during different emotional states, Comput. Biol. Med., 67 (2015), 49–60. https://doi.org/10.1016/j.compbiomed.2015.09.019 doi: 10.1016/j.compbiomed.2015.09.019
    [19] R. Loula, L. H. A. Monteiro, A game theory-based model for predicting depression due to frustration in competitive environments, Comput. Math. Method. Med., 2020 (2020), 3573267. https://doi.org/10.1155/2020/3573267 doi: 10.1155/2020/3573267
    [20] R. Loula, L. H. A. Monteiro, An individual-based model for predicting the prevalence of depression, Ecol. Complex., 38 (2019), 168–172. https://doi.org/10.1016/j.ecocom.2019.03.003 doi: 10.1016/j.ecocom.2019.03.003
    [21] S. F. Lu, X. Shi, M. Li, J. A. Jiao, L. Feng, G. Wang, Semi-supervised random forest regression model based on co-training and grouping with information entropy for evaluation of depression symptoms severity, Math. Biosci. Eng., 18 (2021), 4586–4602. https://doi.org/10.3934/mbe.2021233 doi: 10.3934/mbe.2021233
    [22] B. Bachmann, L. Pëske, K. Kalev, K. Aarma, A. Lehtmets, P. Ööpik, et al., Methods for classifying depression in single channel EEG using linear and nonlinear signal analysis, Comput. Methods Programs Biomed., 155 (2018), 11–17. https://doi.org/10.1016/j.cmpb.2017.11.023 doi: 10.1016/j.cmpb.2017.11.023
    [23] Z. H. Xu, J. Du, A mental health informatics study on the mediating effect of the regulatory emotional self-efficacy, Math. Biosci. Eng., 18 (2021), 2775–2788. https://doi.org/10.3934/mbe.2021141 doi: 10.3934/mbe.2021141
    [24] J. Guckenheimer, P. Holmes, Nonlinear Oscillations, Dynamical Systems, and Bifurcations of Vector Fields, New York, Springer, 2002.
    [25] Y. A. Kuznetsov, Elements of Applied Bifurcation Theory, New York, Springer-Verlag, 2004.
    [26] L. H. A. Monteiro, M. A. Bussab, J. G. C. Berlinck, Analytical results on a Wilson-Cowan neuronal network modified model, J. Theor. Biol., 219 (2002), 83–91. https://doi.org/10.1006/yjtbi.3111 doi: 10.1006/yjtbi.3111
    [27] H. Ryu, S. A. Campbell, Stability, bifurcation and phase-locking of time-delayed excitatory-inhibitory neural networks, Math. Biosci. Eng., 17 (2020), 7931–7957. https://doi.org/10.3934/mbe.2020403 doi: 10.3934/mbe.2020403
    [28] B. P. Guiard, M. El Mansari, Z. Merali, P. Blier, Functional interactions between dopamine, serotonin and norepinephrine neurons: an in-vivo electrophysiological study in rats with monoaminergic lesions, Int. J. Neuropsychopharmacol., 11 (2008), 625–639. https://doi.org/10.1017/S1461145707008383 doi: 10.1017/S1461145707008383
    [29] P. Blier, Crosstalk between the norepinephrine and serotonin systems and its role in the antidepressant response, J. Psychiatry Neurosci., 26 (2001), S3–S10.
    [30] L. K. Nisenbaum, M. J. Zigmond, A. F. Sved, E. D. Abercrombie, Prior exposure to chronic stress results in enhanced synthesis and release of hippocampal norepinephrine in response to a novel stressor, J. Neurosci., 11 (1991), 1478–1484. https://doi.org/10.1523/JNEUROSCI.11-05-01478.1991 doi: 10.1523/JNEUROSCI.11-05-01478.1991
    [31] K. Ogata, Modern Control Engineering, New York, Prentice-Hall, 2001.
    [32] S. Bhatt, T. Devadoss, S. N. Manjula, J. Rajangam, 5-HT3 receptor antagonism: a potential therapeutic approach for the treatment of depression and other disorders, Curr. Neuropharmacol., 19 (2021), 1545–1559. https://doi.org/10.2174/1570159X18666201015155816 doi: 10.2174/1570159X18666201015155816
    [33] L. S. Almocera, J. Zhujun, P. W. Sy, Hopf bifurcation and analysis of equilibrium for a third-order differential equation in a model of competition, Acta Math. Appl. Sin., 17 (2001), 68–80. https://doi.org/10.1007/BF02669686 doi: 10.1007/BF02669686
    [34] L. H. A. Monteiro, A. C. Lisboa, M. Eisencraft, Route to chaos in a third-order phase-locked loop network, Signal Process., 89 (2009), 1678–1682. https://doi.org/10.1016/j.sigpro.2009.03.006 doi: 10.1016/j.sigpro.2009.03.006
    [35] C. C. Chernecky, B. J. Berger, Laboratory Tests and Diagnostic Procedures, St. Louis, Elsevier, 2013.
    [36] R. Bowen, M. Clark, M. Baetz, Mood swings in patients with anxiety disorders compared with normal controls, J. Affect. Disord., 78 (2004), 185–192. https://doi.org/10.1016/S0165-0327(02)00304-X doi: 10.1016/S0165-0327(02)00304-X
    [37] W. Mansell, A. P. Morrison, G. Reid, I. Lowens, S. Tai, The interpretation of, and responses to, changes in internal states: an integrative cognitive model of mood swings and bipolar disorders, Behav. Cognit. Psychther., 35 (2007), 515–539. https://doi.org/10.1017/S1352465807003827 doi: 10.1017/S1352465807003827
  • Reader Comments
  • © 2022 the Author(s), licensee AIMS Press. This is an open access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0)
通讯作者: 陈斌, bchen63@163.com
  • 1. 

    沈阳化工大学材料科学与工程学院 沈阳 110142

  1. 本站搜索
  2. 百度学术搜索
  3. 万方数据库搜索
  4. CNKI搜索

Metrics

Article views(3642) PDF downloads(269) Cited by(7)

Article outline

Figures and Tables

Figures(3)

Other Articles By Authors

/

DownLoad:  Full-Size Img  PowerPoint
Return
Return

Catalog