Main Article Content
Computational mathematical models have shown promise in the biological mechanism's reproduction. This work presents a computational mathematical model of the hormonal storage control applied to an endocrine cell. The model is based on a system of differential equations representing the internal cell dynamics and governed by the Lyapunov control function. Among the stages of these dynamics, we analyze the storage and degradation, which occur within some endocrine cells. The model’s evaluation considers, as an example, the synthesis–storage-release regulation of catecholamine in the adrenal medulla. Seven experiments, varying the input parameters, were performed to validate and evaluate the model. Different behaviors could be observed according to the numerical data used for future research and scientific contributions, besides confirming that Lyapunov control function is feasible to govern the cell dynamics.
This work is licensed under a Creative Commons Attribution-NoDerivatives 4.0 International License.
Submission of an article implies that the work described has not been published previously (except in the form of an abstract or as part of a published lecture or academic thesis), that it is not under consideration for publication elsewhere, that its publication is approved by all authors and tacitly or explicitly by the responsible authorities where the work was carried out, and that, if accepted, will not be published elsewhere in the same form, in English or in any other language, without the written consent of the Publisher. The Editors reserve the right to edit or otherwise alter all contributions, but authors will receive proofs for approval before publication.
Copyrights for articles published in IJIER journals are retained by the authors, with first publication rights granted to the journal. The journal/publisher is not responsible for subsequent uses of the work. It is the author's responsibility to bring an infringement action if so desired by the author.
A. Albillos, E. Neher, T. Moser. “R-type ca2+ channels are coupled to the rapid component of secretion in mouse adrenal slice chromaffin cells”. Journal of Neuroscience, Soc Neuroscience, 20.22 (2000): 8323–8330.
J. Axelrod. “Putification and propertities of phenylethanolamine-n-methyl transferase.” J. Biol. Chem. 237.5 (1962): 1657-1660.
R. Bellman. Dynamic Programming. NY: Dover Publications, Inc. 2003.
V.H. Borges Modelagem da dinâmica de armazenamento hormonal em uma célula endócrina. Dissertação de Mestrado. Programa de Pós-Graduação em Ciências Computacionais. 2018.
F. Brauer, C. Castillo-Chavez. (2000). Mathematical Models in Population Biology and Epidemiology. Springer-Verlag.
G.E. Briggs, J.B.S. Haldane. Biochem. J. 1925, 19, 338.
S. Burbridge, I. Stewart, M. Placzek. “Development of the Neuroendocrine Hypothalamus”. Compr Physiol. 2016;6(2):623-643. Published 2016 Mar 15. doi:10.1002/cphy.c150023
S. Bygdeman, U. Euler. “Resynthesis of catecliol hormones in the cat’s adrenal medulla”. Acta Physiologica, Wiley Online Library, v. 44, n. 3-4, p. 375–383, 1958.
J. Castillo-Armengol, L. Fajas, I.C. Lopez-Mejia. “Inter-organ communication: a gatekeeper for metabolic health”. EMBO Rep. 2019;20(9):e47903. doi:10.15252/embr.201947903
W.H. Chan, D.G. Gonsalvez, H.M. Young, E.M. Southard-Smith, K.N. Cane, C.R. Anderson. “Differences in CART expression and cell cycle behavior discriminate sympathetic neuroblast from chromaffin cell lineages in mouse sympathoadrenal cells”. Dev Neurobiol. 2016;76(2):137-149. doi:10.1002/dneu.22304.
D.A. Charlebois, G. Balázsi. “Modeling cell population dynamics”. In Silico Biol. 2019;13(1-2):21-39. doi:10.3233/ISB-180470
R. Comline, M. Silver. “Development of activity in the adrenal medulla of the foetus and new-born animal”. British Medical Bulletin 22:16–20 (1966).
C.M. Cortez, A. Pires Neto, A.A.E.A. Motta. “Dynamics for the storage control of a endocrine gland: A model for adrenal epinephrine.” AIP Conference Proceedings. Vol. 1790, 100004(2016). AIP Publishing LLC, 2016.
M.E. Davis, J.D. Madura, J. Sines, B.A. Luty, S.A. Allison, J.A. McCammon. “Diffusion-controlled enzymatic reactions”. Methods in enzymology 1991. v. 202, p. 473–497.
W. de Back, T. Zerjatke, I. Roeder. Statistical and Mathematical Modeling of Spatiotemporal Dynamics of Stem Cells. Methods Mol Biol. 2019, 2017:219‐243. doi:10.1007/978-1-4939-9574-5_17
H. Deng, F. Chen, Z. Zhenliang, L. Zhong. “Dynamic behaviors of Lokta-Volterra predator-prey model incorporating predator cannibalism”. Advances in Difference Equations 2019: 359 (2019).
J.D. Deupree, J.A. Weaver, D.A. Downs. “Catecholamine content of chromaffin granule ‘ghosts’ isolated from bovine adrenal glands.” Biochimica et Biophysica Acta (BBA)-General Subjects 714.3 (1982): 471-478.
M. Esler et al. Effects of aging on epinephrine secretion and regional release of epinephrine from the human heart. The Journal of Clinical Endocrinology & Metabolism, Oxford University Press, v. 80, n. 2, p. 435–442, 1995.
D.S. Goldstein et al. “Sympathoadrenal imbalance before neurocardiogenic syncope.” The American journal of cardiology 91.1 (2003): 53-58.
C.C. Feltrin, M. Rafikov. “Aplicação da Função de Lyapunov num Problema de Controle Ótimo de Pragas”. Trends App Comp Math 3, 83–92 (2002).
McC Goodall, B. W. Haynes. “Adrenal medullary insufficiency in severe thermal burn.” The Journal of clinical investigation 39.12 (1960): 1927-1932.
J.E. Hall. Guyton and Hall Textbook of Medical Physiology. Saundres-Elsevier, BIOS Sci Publishers, 2010.
F. Hoppensteadt. (2006). Predator-prey model. Scholarpedia 1(10):1563.
W.J. Kovacs, S.R. Ojeda. Textbook of Endocrine Physiology. Sixth edition. NY: Oxford Univ. Press, 2012.
J. Liang, J. Wei. “Lyapunov functional for virus infection model with diffusion and state-dependent delays”. Math Biosci Eng. 2019;16(2):947-966. doi:10.3934/mbe.2019044
A.J. Lotka. Analytical Theory of Biological Populations. NY: Plenun Press, 1998.
A.M. Lyapunov. “The General Problem of the Stability of Motion”. Int J Control 55:531-773, 1992.
E.N. Marieb, K. Hoehn. Human Anatomy & Physiology. 9th Ed. (2010).
L.K. Mccorry. “Physiology of the autonomic nervous system. American Journal of Pharmaceutical Education”, AJPE, v. 71, n. 4, p. 78, 2007.
G.G. Nair, J.S. Liu, H.A. Russ, S. Tran, M.S. Saxton, R. Chen, C. Juang, M.L. Li, V.Q. Nguyen, S. Giacometti, S. Puri, Y. Xing, Y. Wang , G.L. Szot, J. Oberholzer, A. Bhushan, M. Hebrok. “Recapitulating endocrine cell clustering in culture promotes maturation of human stem-cell-derived β cells”. Nat Cell Biol. 2019 Feb;21(2):263-274. doi: 10.1038/s41556-018-0271-4.
S.F. Perry, A. Capaldo. “The autonomic nervous system and chromaffin tissue: neuroendocrine regulation of catecholamine secretion in non-mammalian vertebrates”. Autonomic neuroscience, Elsevier, v. 165, n. 1, p. 54–66, 2011.
J.H. Phillips. “Transport of catecholamines by resealed chromaffin-granule ‘ghosts’”. Biochemical Journal 144.2 (1974): 311-318.
T.C. Rao, Z. Santana Rodriguez, M.M. Bradberry et al. “Synaptotagmin isoforms confer distinct activation kinetics and dynamics to chromaffin cell granules”. J Gen Physiol. 2017;149(8):763‐780. doi:10.1085/jgp.201711757
W.J. Schwartz, H. Gainer. “Suprachiasmatic nucleus: use of 14C-labeled deoxyglucose uptake as a functional marker.” Science 197.4308 (1977): 1089-1091.
N. Spasojevic, P. Jovanovic, S. Dronjak. “Differential regulation of catecholamine synthesis and transport in rat adrenal medulla by fluoxetine treatment”. Anais da Academia Brasileira de Ciências, v. 87, n. 1, p. 343–350, 2015.
M. Stroppolo et al. “Superefficient enzymes”. Cellular and Molecular Life Sciences CMLS, Springer, v. 58, n. 10, p. 1451–1460, 2001.
K. Tsaneva-Atanasova, H.M. Osinga, J. Tabak, M.G. Pedersen. “Modeling mechanisms of cell secretion.” Acta biotheoretica 58.4 (2010): 315-327.
S. Tseng, J.P. Hsu. “A comparison of the parameter estimating procedures for the michaelis-menten model”. Journal of theoretical biology, Elsevier, v. 145, n. 4, p. 457–464, 1990.
P. Unni, P. Seshaiyer. “Mathematical Modeling, Analysis, and Simulation of Tumor Dynamics with Drug Interventions”. Comput Math Methods Med. 2019;2019:4079298. Published 2019 Oct 8. doi:10.1155/2019/407929
J. Villanueva, C.J. Torregrosa-Hetland, V. García-Martínez, M. del Mar Francés, S. Viniegra, L.M. Gutiérrez. “The F-actin cortex in chromaffin granule dynamics and fusion: a minireview”. J Mol Neurosci. 2012;48(2):323‐327. doi:10.1007/s12031-012-9718-4
X. Wang, H. Ma. (2012) Lyapunov Function and Global Stability for a Class of Predator-Prey Models Discrete Dynamics in Nature and Society 2012:218785. doi:10.1155/2012/218785
D.P. Westfall, L.D. Todorov, S.T. Mihaylova-Todorova. “Atp as a cotransmitter in sympathetic nerves and its inactivation by releasable enzymes”. Journal of Pharmacology and Experimental Therapeutics, ASPET, v. 303, n. 2, p. 439–444, 2002.
X. Zhang, H. Zhao. “Dynamics analysis of a delayed reaction-diffusion predator-prey system with non-continuous threshold harvesting”. Math Biosci.2017;289:130-141. doi:10.1016/j.mbs.2017.05.007
C. Zhu, G. Yin. “On competitive Lotka–Volterra model in random environments”. J. Math Anal Applic 357:154-17- (2009).