Journals / Communications Faculty of Sciences University of Ankara Series A2-A3 Physical Sciences and Engineering / 2018 / Cilt: 60 - Sayı: 1

COMPUTATIONAL BIFURCATION ANALYSIS TO FIND DYNAMIC TRANSITIONS OF THE CORTICOTROPH MODEL

Pages
41–64
Publication Date
2018-07-31
DOI
—
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AI Summary & Key Takeaways

AI Insight
⚡ TL;DR(Too Long; Didn't Read)

Finally, we discuss how some of the described bifurcations affect dynamic behavior and can be tested experimentally.

📌 3 Key Takeaways

🎯
Objective & Hypothesis:Öz The corticotroph model is a 7th order nonlinear differential equation system derived for representing the action potential dynamics of corticotrophs; one of the endocrine cells that is responsible for stress regulation.
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Key Findings & Data:Furthermore, we find that there are two routes to bursting, one is the experimentally observed BK-channel dynamics and the other is Ca2+ channel conductance only.
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Conclusion & Impact:Finally, we discuss how some of the described bifurcations affect dynamic behavior and can be tested experimentally.
🔬Design:Modeling & Simulation
📍Scope:Comprehensive Sample
⚙️Variables:Anahtar Kelimeler Dynamical System · Bifurcation analysis · Corticotroph Model

Özet

Öz The corticotroph model is a 7th order nonlinear differential equation system derived for representing the action potential dynamics of corticotrophs; one of the endocrine cells that is responsible for stress regulation. Here we use numerical continuation methods to perform bifurcation analysis since controlling bifurcations in the hormonal dynamics may bring some new insights in the treatment of stress related disorders. We study the bifurcation structure of the system as a function of the BK-channel dynamic parameters and the all maximal conductances. We identify the regions of bistability and bifurcations that shape the transitions between resting, bursting and spiking behaviors, and which lead to the appearance of bursting which is directly connected to stress regulation. Furthermore, we find that there are two routes to bursting, one is the experimentally observed BK-channel dynamics and the other is Ca2+ channel conductance only. Finally, we discuss how some of the described bifurcations affect dynamic behavior and can be tested experimentally.

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Cite This Article

AYAN, S. Ş., KURT, A. (2018). COMPUTATIONAL BIFURCATION ANALYSIS TO FIND DYNAMIC TRANSITIONS OF THE CORTICOTROPH MODEL. Communications Faculty of Sciences University of Ankara Series A2-A3 Physical Sciences and Engineering, Cilt: 60 - Sayı: 1, 41–64. https://ajindex.com/articles/51166

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References (12)

  1. Hodgkin, A. L., Huxley, A. F., “A quantitative description of membrane current and its application to conduction and excitation in nerve”, Journal of Physiology, 117(4) (1952) 500–544.[
  2. Duncan, P. J., Sengul, S., Tabak, J., Ruth, P., Bertram, R., Shipston, M. J., “Large conductance Ca2+-activated K+ channels (BK) promote secretagogue-induced transition from spiking to bursting in murine anterior pituitary corticotrophs”, Journal of Physiology, 593(5) (2015) 1197–1211.
  3. Murphy, H., Jaafari, H., Dobrovolny, H. M., “Differences in predictions of ODE models of tumor growth: a cautionary example”, BMC Cancer, 16 (2016) 163. Mary Celin Sharmila, D., Praveen, T., Rajendran, L., “Mathematical Modeling and Analysis of Nonlinear Enzyme Catalyzed Reaction Processes”, Journal of Theoretical Chemistry, (2013) 2013:7. Schaff, J. C., Gao, F., Li, Y., Novak, I. L., Slepchenko, B. M., “Numerical Approach to Spatial Deterministic-Stochastic Models Arising in Cell Biology”, PLoS Comput Biol., 12(12) (2016) e1005236. Rinzel, J., A Formal Classification of Bursting Mechanisms in Excitable Systems, Springer Berlin Heidelberg, 1987.
  4. Sherman, A., “Dynamical systems theory in physiology”, The Journal of General Physiology, 138(1) (2011) 13–19.
  5. Strogatz, S. H., Nonlinear Dynamics and Chaos, Addison-Wesley Publishing Company, 2001.
  6. Morris, C., Lecar, H., “Voltage oscillations in the barnacle giant muscle fiber”, Biophys J., 35(1) (1981) 193–213.
  7. Plant, R. E., Kim, M., “Mathematical descriptions of a bursting pacemaker neuron by a modification of the Hodgkin-Huxley equations”, Biophys. J., 16(3) (1976) 227–244.
  8. Braun, H. A., Bade, H., Hensel, H., “Static and dynamic discharge patterns of bursting cold fibers related to hypothetical receptor mechanisms”, Pflügers Arch., 386(1) (1980) 1–9.
  9. Clewley, R. H., Sherwood, W. E., Lamar, M. D., Guckenheimer, J. M., “PyDSTool, a software environment for dynamical systems modeling, URL=http://pydstool.sourceforge.net”, (2007).
  10. Atherton, L. A., Prince, L. Y., Tsaneva-Atanasova, K., “Bifurcation analysis of a two-compartment hippocampal pyramidal cell model”, J Comput Neuroscience, 41 (2016) 91–106.
  11. Ananthkrishnan, N., Gupta, N. K., Sinha, N. K., “Computational Bifurcation Analysis of Multiparameter Dynamical Systems”, Journal of Guidance Control and Dynamics, 32(5) (2009) 1651-1653.
  12. Tsaneva-Atanasova, K., Osinga, H. M., Rieb, T., Sherman, A., “Full System Bifurcation Analysis of Endocrine Bursting Models”, J Theor Biol., 264(4) (2010) 1133–1146. Ču