Ion channels and the diversity of spontaneous firing in anterior pituitary corticotrophs: a dynamical analysis. (English) Zbl 1533.92015
Summary: Pituitary cells release hormones based on firing patterns, mediated by multiple ionic currents. Analyzing a single channel’s effect on firing is insufficient. We used a four-dimensional Hodgkin-Huxley-type corticotroph model to analyze its dynamics from a geometric perspective. We conducted a two-parameter bifurcation analysis of the system and found that activation levels of BK, NS, Kir, Ca, and LCa channels are crucial in generating and transitioning between different firing patterns. Chaotic firing can arise during the transition between firing patterns. We have employed the Poincaré map method and sequence reconstructions to construct return maps to characterize chaos-firing. The membrane potential time series is affected by fluctuations in intracellular calcium \(([\mathrm{Ca}^{2+}]_i)\). We studied the variable \(c\) using fast-slow analysis techniques and phase portraits to explore its relationship with phase portraits. The study revealed that the system exhibits bistability, which is dependent on the initial values of \(c\) or \(V\). The findings indicate that firing activities can arise from either a supercritical or subcritical Hopf bifurcation. Analyses show the interaction between the membrane potential and \([\mathrm{Ca}^{2+}]_i\) at various BK channel activation levels.
MSC:
| 92B20 | Neural networks for/in biological studies, artificial life and related topics |
| 92C37 | Cell biology |
| 34C23 | Bifurcation theory for ordinary differential equations |
| 37N25 | Dynamical systems in biology |
Keywords:
geometric methods; bifurcation analysis; fast-slow analysis techniques; phase portraits; chaosSoftware:
MathematicaReferences:
| [1] | Lu, B.; Liu, S.; Liu, X.; Jiang, X.; Wang, X., Bifurcation and spike adding transition in chay-keizer model, Int J Bifurcation Chaos, 26, 05, Article 1650090 pp., (2016) · Zbl 1343.34119 |
| [2] | Wang, J.; Lu, B.; Liu, S.; Jiang, X., Bursting types and bifurcation analysis in the pre-Bötzinger complex respiratory rhythm neuron, Int J Bifurcation Chaos, 27, 01, Article 1750010 pp., (2017) · Zbl 1358.34057 |
| [3] | Zhan, F.; Liu, S.; Zhang, X.; Wang, J.; Lu, B., Mixed-mode oscillations and bifurcation analysis in a pituitary model, Nonlinear Dynam, 94, 807-826, (2018) |
| [4] | Van Goor, F.; Zivadinovic, D.; Stojilkovic, S. S., Differential expression of ionic channels in rat anterior pituitary cells, Mol Endocrinol, 15, 7, 1222-1236, (2001) |
| [5] | Stojilkovic, S. S.; Tabak, J.; Richard, B., Ion channels and signaling in the pituitary gland, Endocrine Rev, 31, 6, 845-915, (2010) |
| [6] | Stojilkovic, S. S., Molecular mechanisms of pituitary endocrine cell calcium handling, Cell Calcium, 51, 3-4, 212-221, (2012) |
| [7] | Macgregor, D. J.; Leng, G., Ion channels and electrical activity in pituitary cells: a modeling perspective, Computational neuroendocrinology, 80-110, (2016), John Wiley and Sons, Ltd |
| [8] | Duncan, P. J.; Tabak, J.; Ruth, P.; Bertram, R.; Shipston, M. J., Glucocorticoids inhibit CRH/AVP-evoked bursting activity of male murine anterior pituitary corticotrophs, Endocrinology, 157, 8, 3108-3121, (2016) |
| [9] | Fletcher, P. A.; Sherman, A.; Stojilkovic, S. S., Common and diverse elements of ion channels and receptors underlying electrical activity in endocrine pituitary cells, Molecul Cellular Endocrinol, 463, 5, 23-36, (2018) |
| [10] | Duncan, P. J.; Fazli, M.; Romanò, N.; Le Tissier, P.; Bertram, R.; Shipston, M. J., Chronic stress facilitates bursting electrical activity in pituitary corticotrophs, J Physiol, 600, 2, 313-332, (2022) |
| [11] | Fletcher, P. A.; Zemkova, H.; Stojilkovic, S. S.; Sherman, A., Modeling the diversity of spontaneous and agonist-induced electrical activity in anterior pituitary corticotrophs, J Neurophysiol, 117, 6, 2298-2311, (2017) |
| [12] | Tsaneva-Atanasova, K.; Sherman, A.; van Goor, F.; Stojilkovic, S. S., Mechanism of spontaneous and receptor-controlled electrical activity in pituitary somatotrophs: experiments and theory, J Neurophysiol, 98, 1, 131-144, (2007) |
| [13] | Churilov, A. N.; Milton, J. G., Modeling pulsativity in the hypothalamic-pituitary-adrenal hormonal axis, Sci Rep, 12, 1, 8480, (2022) |
| [14] | Tabak, J.; Tomaiuolo, M.; Gonzalez-Iglesias, A. E.; Milescu, L. S.; Bertram, R., Fast-activating voltage- and calcium-dependent potassium (BK) conductance promotes bursting in pituitary cells: a dynamic clamp study, J Neurosci, 31, 46, 16855-16863, (2011) |
| [15] | Duncan, P. J.; Şengül, S.; Tabak, J.; Ruth, P.; Bertram, R.; Shipston, M. J., Large conductance \(C a^{2 +}\)-activated \(K{}^+\) (BK) channels promote secretagogue-induced transition from spiking to bursting in murine anterior pituitary corticotrophs, J Physiol, 593, 5, 1197-1211, (2015) |
| [16] | Shipston, M. J., Glucocorticoid action in the anterior pituitary gland: insights from corticotroph physiology, Curr Opin Endocr Metab Res, 25, Article 100358 pp., (2022) |
| [17] | Bauer, C.; Schäfer, R.; Schiemann, D.; Reid, G.; Hanganu, I.; Schwarz, J., A functional role of the erg-like inward-rectifying k+ current in prolactin secretion from rat lactotrophs, Molecul Cell Endocrinol, 148, 1-2, 37-45, (1999) |
| [18] | Lecchi, M.; Redaelli, E.; Rosati, B.; Gurrola, G.; Florio, T.; Crociani, O., Isolation of a long-lasting eag-related gene-type k+ current in MMQ lactotrophs and its accommodating role during slow firing and prolactin release, J Neurosci, 22, 9, 3414-3425, (2002) |
| [19] | Andric, S. A.; Zivadinovic, D.; Gonzalez-Iglesias, A. E.; Lachowicz, A.; Tomic, M.; Stojilkovic, S. S., Endothelin-induced, long lasting, and Ca2+ influx-independent blockade of intrinsic secretion in pituitary cells by gz subunits, J Biol Chem, 280, 29, 26896-26903, (2005) |
| [20] | Fakler, B.; Adelman, J. P., Control of KCa channels by calcium nano/microdomains, Neuron, 59, 6, 873-881, (2008) |
| [21] | Hou, S.; Heinemann, S. H.; Hoshi, T., Modulation of BKCa channel gating by endogenous signaling molecules, Physiology, 24, 1, 26-35, (2009) |
| [22] | Catterall, W. A.; Goldin, A. L.; Waxman, S. G., International union of pharmacology. XLVII. Nomenclature and structure-function relationships of voltage-gated sodium channels, Pharmacol Rev, 57, 4, 397-409, (2005) |
| [23] | Stern, J. V.; Osinga, H. M.; Lebeau, A.; Sherman, A., Resetting behavior in a model of bursting in secretory pituitary cells: Distinguishing plateaus from pseudo-plateaus, Bull Math Biol, 70, 1, 68-88, (2008) · Zbl 1281.92021 |
| [24] | Vo, T.; Bertram, R.; Tabak, J.; Wechselberger, M., Mixed mode oscillations as a mechanism for pseudo-plateau bursting, J Comput Neuroence, 28, 3, 443-458, (2010) · Zbl 1246.34053 |
| [25] | Teka, W.; Tabak, J.; Vo, T.; Wechselberger, M.; Bertram, R., The dynamics underlying pseudo-plateau bursting in a pituitary cell model, J Math Neurosci, 1, 12, 1-12, (2011) · Zbl 1259.37063 |
| [26] | Teka, W.; Tsaneva-Atanasova, K.; Bertram, R.; Tabak, J., From plateau to pseudo-plateau bursting: Making the transition, Bull Math Biol, 73, 6, 1292, (2011) · Zbl 1215.92012 |
| [27] | Duncan, P. J.; Joël, T.; Peter, R.; Richard, B.; Shipston, M. J., Glucocorticoids inhibit CRH/AVP-evoked bursting activity of male murine anterior pituitary corticotrophs, Endocrinology, 157, 8, 3108-3121, (2016) |
| [28] | Fazli, M.; Vo, T.; Bertram, R., Fast-slow analysis of a stochastic mechanism for electrical bursting, Chaos, 31, 10, (2021) · Zbl 07867387 |
| [29] | Brøns, M.; Krupa, M.; Wechselberger, M., Mixed mode oscillations due to the generalized canard phenomenon, Fields Inst Commun, 49, 1, 39-63, (2006) · Zbl 1228.34063 |
| [30] | Brøns, M.; Kaper, T. J.; Rotstein, H. G., Introduction to focus issue: Mixed mode oscillations: Experiment, computation, and analysis, Chaos, 18, 1, 1-4, (2008) |
| [31] | Osinga, H. M.; Tsaneva-Atanasova, K. T., Dynamics of plateau bursting depending on the location of its equilibrium, J Neuroendocrinol, 22, 12, 1301-1314, (2010) |
| [32] | Nowacki, J.; Mazlan, S.; Osinga, H. M.; Tsaneva-Atanasova, K., The role of large-conductance calcium-activated K+ (BK) channels in shaping bursting oscillations of a somatotroph cell model, Physica D, 239, 9, 485-493, (2010) · Zbl 1186.92014 |
| [33] | Vo, T.; Tabak, J.; Bertram, R.; Wechselberger, M., A geometric understanding of how fast activating potassium channels promote bursting in pituitary cells, J Comput Neurosci, 36, 259-278, (2014) · Zbl 1382.92098 |
| [34] | Xu, Q.; Tan, X.; Zhu, D.; Bao, H.; Hu, Y.; Bao, B., Bifurcations to bursting and spiking in the chay neuron and their validation in a digital circuit, Chaos Solitons Fractals, 141, Article 110353 pp., (2020) |
| [35] | Erhardt, A. H.; Solem, S., On complex dynamics in a purkinje and a ventricular cardiac cell model, Commun Nonlinear Sci Numer Simul, 93, Article 105511 pp., (2021) · Zbl 1454.37089 |
| [36] | LeBeau, A. P.; Robson, A.; McKinnon, A. E.; Sneyd, J., Analysis of a reduced model of cortiocotroph action potentials, J Theoret Biol, 192, 3, 319-339, (1998) |
| [37] | Duan, L.; Lu, Q.; Wang, Q., Two-parameter bifurcation analysis of firing activities in the chay neuronal model, Neurocomputing, 72, 1-3, 341-351, (2008) |
| [38] | García, I.; Llibre, J.; Maza, S., On the periodic orbit bifurcating from a zero hopf bifurcation in systems with two slow and one fast variables, Appl Math Comput, 232, 1, 84-90, (2014) · Zbl 1410.34169 |
| [39] | Baldemir, H.; Avitabile, D.; Tsaneva-Atanasova, K., Pseudo-plateau bursting and mixed-mode oscillations in a model of developing inner hair cells, Commun Nonlinear Sci Numer Simul, 80, Article 104979 pp., (2020) · Zbl 1451.92109 |
| [40] | Chay, T. R., Chaos in a three-variable model of an excitable cell, Physica D, 16, 2, 233-242, (1985) · Zbl 0582.92007 |
| [41] | Fan, Y.-S.; Chay, T. R., Generation of periodic and chaotic bursting in an excitable cell model, Biol Cybernet, 71, 5, 417-431, (1994) · Zbl 0805.92005 |
| [42] | Borghans, J. A.M.; Dupont, G.; Goldbeter, A., Complex intracellular calcium oscillations a theoretical exploration of possible mechanisms, Biophys Chem, 66, 1, 25-41, (1997) |
| [43] | Belykh, V.; Belykh, I.; Colding-Jørgensen, M.; Mosekilde, E., Homoclinic bifurcations leading to the emergence of bursting oscillations in cell models, Eur Phys J E, 3, 205-219, (2000) |
| [44] | Perc, M.; Marhl, M., Different types of bursting calcium oscillations in non-excitable cells, Chaos Solitons Fractals, 18, 4, 759-773, (2003) · Zbl 1068.92017 |
| [45] | Tsumoto, K.; Kitajima, H.; Yoshinaga, T.; Aihara, K.; Kawakami, H., Bifurcations in Morris-Lecar neuron model, Neurocomputing, 69, 4-6, 293-316, (2006) |
| [46] | Channell, P.; Cymbalyuk, G.; Shilnikov, A., Applications of the poincare mapping technique to analysis of neuronal dynamics, Neurocomputing, 70, 10-12, 2107-2111, (2007) |
| [47] | Gu, H., Experimental observation of transition from chaotic bursting to chaotic spiking in a neural pacemaker, Chaos, 23, 2, Article 023126 pp., (2013) |
| [48] | Serrano, S.; Martínez, M. A.; Barrio, R., Order in chaos: Structure of chaotic invariant sets of square-wave neuron models, Chaos, 31, 4, Article 043108 pp., (2021) · Zbl 1460.92038 |
| [49] | Sekikawa, M.; Kousaka, T.; Tsubone, T.; Inaba, N.; Okazaki, H., Bifurcation analysis of mixed-mode oscillations and farey trees in an extended Bonhoeffer-van der Pol oscillator, Physica D, 433, Article 133178 pp., (2022) · Zbl 1513.70078 |
| [50] | Njitacke, Z. T.; Takembo, C. N.; Koumetio, B. N.; Awrejcewicz, J., Complex dynamics and autapse-modulated information patterns in memristive wilson neurons, Nonlinear Dynam, 1-12, (2022) |
| [51] | Song, J.; Liu, S.; Wen, Q., Geometric analysis of the spontaneous electrical activity in anterior pituitary corticotrophs, Chaos Solitons Fractals, 161, Article 112305 pp., (2022) |
| [52] | Sankaranarayanan, S.; Simasko, S., A role for a background sodium current in spontaneous action potentials and secretion from rat lactotrophs, Am J Physiol Cell Physiol, 271, 6, C1927-C1934, (1996) |
| [53] | Kwiecien, R.; Robert, C.; Cannon, R.; Vigues, S.; Arnoux, A.; Kordon, C., Endogenous pacemaker activity of rat tumour somatotrophs, J Physiol, 508, 3, 883-905, (1998) |
| [54] | Wulfsen, I.; Hauber, H.; Schiemann, D.; Bauer, C.; Schwarz, J., Expression of mRNA for voltage-dependent and inward-rectifying k channels in GH3/B6 cells and rat pituitary, J Neuroendocrinol, 12, 3, 263-272, (2000) |
| [55] | Tabak, J.; Toporikova, N.; Freeman, M. E.; Bertram, R., Low dose of dopamine may stimulate prolactin secretion by increasing fast potassium currents, J Comput Neurosci, 22, 211-222, (2007) |
| [56] | Tsaneva-Atanasova, K.; Sherman, A.; Van Goor, F.; Stojilkovic, S. S., Mechanism of spontaneous and receptor-controlled electrical activity in pituitary somatotrophs: Experiments and theory, J Neurophysiol, 98, 1, 131-144, (2007) |
| [57] | Hayashi, H.; Ishizuka, S., Chaotic nature of bursting discharges in the onchidium pacemaker neuron, J Theoret Biol, 156, 3, 269-291, (1992) |
| [58] | Elbert, T.; Ray, W. J.; Kowalik, Z. J.; Skinner, J. E.; Graf, K. E.; Birbaumer, N., Chaos and physiology: deterministic chaos in excitable cell assemblies, Physiol Rev, 74, 1, 1-47, (1994) |
| [59] | Shahhosseini, A.; Tien, M.-H.; D’Souza, K., Poincare maps: a modern systematic approach toward obtaining effective sections, Nonlinear Dynam, 1-20, (2022) |
| [60] | Gutiérrez, J. M.; Iglesias, A., Mathematica package for analysis and control of chaos in nonlinear systems, Comput Phys, 12, 6, 608-619, (1998) |
| [61] | Rubin, J. E.; Signerska-Rynkowska, J.; Touboul, J. D.; Vidal, A., Wild oscillations in a nonlinear neuron model with resets:(I) bursting, spike adding and chaos, (2016), arXiv preprint arXiv:1611.02740 · Zbl 1371.37032 |
| [62] | Huang, L.; Zhang, Z.; Xiang, J.; Wang, S., A new 4D chaotic system with two-wing, four-wing, and coexisting attractors and its circuit simulation, Complexity, 2019, 1-13, (2019) |
| [63] | Dong, Y.; Wang, G.; Chen, G.; Shen, Y.; Ying, J., A bistable nonvolatile locally-active memristor and its complex dynamics, Commun Nonlinear Sci Numer Simul, 84, Article 105203 pp., (2020) · Zbl 1451.78032 |
| [64] | Vijay, S. D.; Thamilmaran, K.; Ahamed, A. I., Superextreme spiking oscillations and multistability in a memristor-based Hindmarsh-Rose neuron model, Nonlinear Dynam, 1-11, (2022) |
| [65] | Vo, T.; R., B.; Wechselberger, M., Multiple geometric viewpoints of mixed mode dynamics associated with pseudo-plateau bursting, SIAM J Appl Dyn Syst, 12, 2, 789-830, (2013) · Zbl 1295.37022 |
| [66] | Liu, Y.; Liu, S.; Lu, B.; Kurths, J., Mixed-mode oscillations for slow-fast perturbed systems, Phys Scr, 96, 12, Article 125258 pp., (2021) |
| [67] | Neiman, A. B.; Dierkes, K.; Lindner, B.; Han, L.; Shilnikov, A. L., Spontaneous voltage oscillations and response dynamics of a hodgkin-huxley type model of sensory hair cells, J Math Neurosci, 1, 1, 1-24, (2011) · Zbl 1259.92009 |
| [68] | Malykh, S.; Bakhanova, Y.; Kazakov, A.; Pusuluri, K.; Shilnikov, A., Homoclinic chaos in the Rössler model, Chaos, 30, 11, Article 113126 pp., (2020) · Zbl 1451.34060 |
| [69] | Kolomiets, M. L.; Shilnikov, A. L., Poincaré return maps in neural dynamics: three examples, (Progress on difference equations and discrete dynamical systems: 25th ICDEA, London, UK, June 24-28, 2019 25, (2020), Springer), 45-57 · Zbl 1471.37078 |
| [70] | Xing, T.; Pusuluri, K.; Shilnikov, A. L., Ordered intricacy of shilnikov saddle-focus homoclinics in symmetric systems, Chaos, 31, 7, Article 073143 pp., (2021) · Zbl 1481.37053 |
| [71] | Gonchenko, S.; Kazakov, A.; Turaev, D.; Shilnikov, A. L., Leonid shilnikov and mathematical theory of dynamical chaos, Chaos, 32, 1, Article 010402 pp., (2022) · Zbl 07867638 |
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.
