Study of calcium profile in neuronal cells with respect to temperature and influx due to potential activity

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dc.citation.epage252
dc.citation.issue2
dc.citation.spage241
dc.contributor.affiliationВасантрао Найк Махавідялая
dc.contributor.affiliationІнженерний коледж Пімпри Чінчвад
dc.contributor.affiliationТехаський університет
dc.contributor.affiliationVasantrao Naik Mahavidyalaya
dc.contributor.affiliationPimpri Chinchwad College of Engineering
dc.contributor.affiliationUniversity of Texas
dc.contributor.authorПатил, Дж. В.
dc.contributor.authorВазе, А. Н.
dc.contributor.authorШарма, Л.
dc.contributor.authorБачав, А.
dc.contributor.authorPatil, J. V.
dc.contributor.authorVaze, A. N.
dc.contributor.authorSharma, L.
dc.contributor.authorBachhav, A.
dc.coverage.placenameЛьвів
dc.coverage.placenameLviv
dc.date.accessioned2023-10-24T07:21:43Z
dc.date.available2023-10-24T07:21:43Z
dc.date.created2021-03-01
dc.date.issued2021-03-01
dc.description.abstractКальцій є важливим другим кур’єром передачі нервових імпульсів. Він надходить в клітини через керовані Ca2+ канали і регулює нейротрансмісію. Цей механізм контролюється за допомогою дифузії кальцію, буферного механізму та притоками кальцію в цитоплазму. Вивчення динаміки Ca2+ цікаве, оскільки концентрація Ca2+ демонструє дуже складну просторово-часову поведінку. Існує безліч засобів контролю концентрації Ca2+ в цитоплазмі; по-перше, він сильно буферизується (тобто зв’язується) великими білками, а по-друге, контроль здійснюється за допомогою змінного коефіцієнта дифузії. Коефіцієнт дифузії прямо пропорційний температурі та обернено пропорційний в’язкості. У цій роботі досліджено одновимірний випадок стаціонарного стану з граничними умовами для розуміння розподілу Ca2+ у нейронних клітинах, що включає дифузію кальцію, точкове джерело, надлишкове буферне наближення (НБН) та надходження кальцію через потік. Також вивчається залежність концентрації Ca2+ від різних значень коефіцієнта дифузії. Для отримання розв’язків застосовувався метод скiнченних елементів (МСЕ).
dc.description.abstractCalcium is a critically important second messenger in the nervous system. It enters through voltage-gated Ca2+ channels and regulates the release of the synaptic transmitter. This mechanism is monitored by calcium diffusion, buffering mechanism and calcium influx into the cytoplasm. The study of Ca2+ dynamics is interesting because the concentration of Ca2+ shows highly complex spatial-temporal behavior. There are many controls on the cytoplasmic Ca2+ concentration. First, it is heavily buffered (i.e., bound) by large proteins and second control is that of the variable diffusion coefficient. The diffusion coefficient is directly proportional to the temperature and inversely proportional to the viscosity. In this paper, the one-dimensional steady-state case with boundary conditions has been studied to understand the Ca2+ distribution in neuronal cells incorporating diffusion of calcium, point source, excess buffer approximation (EBA), an influx due to the calcium current. Moreover, the dependency of Ca2+ concentration based on the variable diffusion coefficient is studied. The finite element method (FEM) has been employed to obtain the solutions.
dc.format.extent241-252
dc.format.pages12
dc.identifier.citationStudy of calcium profile in neuronal cells with respect to temperature and influx due to potential activity / J. V. Patil, A. N. Vaze, L. Sharma, A. Bachhav // Mathematical Modeling and Computing. — Lviv : Lviv Politechnic Publishing House, 2021. — Vol 8. — No 2. — P. 241–252.
dc.identifier.citationenStudy of calcium profile in neuronal cells with respect to temperature and influx due to potential activity / J. V. Patil, A. N. Vaze, L. Sharma, A. Bachhav // Mathematical Modeling and Computing. — Lviv : Lviv Politechnic Publishing House, 2021. — Vol 8. — No 2. — P. 241–252.
dc.identifier.doidoi.org/10.23939/mmc2021.02.241
dc.identifier.urihttps://ena.lpnu.ua/handle/ntb/60380
dc.language.isoen
dc.publisherВидавництво Львівської політехніки
dc.publisherLviv Politechnic Publishing House
dc.relation.ispartofMathematical Modeling and Computing, 2 (8), 2021
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dc.relation.references[16] Shannon T. R., Wang F., Puglisi J., Weber C., Bers D. M. A mathematical treatment of integrated Ca dynamics within the ventricular myocyte. Biophysical Journal. 87 (5), P3351–P3371 (2004).
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dc.relation.references[20] Luby-Phelps K. Cytoarchitecture and physical properties of cytoplasm: volume, viscosity, diffusion, intra cellular surface area. International Review of Cytology. 192, 189–221 (1999).
dc.relation.references[21] Puchkov E. O. Intracellular viscosity: Methods of measurement and role in metabolism. Biochemistry (Moscow) Supplement Series A: Membrane and Cell Biology. 7 (4), 270–279 (2013).
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dc.relation.references[23] Vogel H. Das Temperaturabhangigkeitsgesetz der Viskosit¨at von Fl¨ussigkeiten. Physikalische Zeitschrift. 22, 645–646 (1921).
dc.relation.references[24] Tanimoto R., Hiraiwa T., Nakai Y., Shindo Y., Oka K., Hiroi N., Funahashi A. Detection of Temperature Difference in Neuronal Cells. Scientific Reports. 6, 22071 (2016).
dc.relation.references[25] Van Hook M. J. Temperature effects on synaptic transmission and neuronal function in the visual thalamus. PloS one. 15 (4), e0232451 (2020).
dc.relation.references[26] Bertram R., Smith G. D., Sherman A. Modeling Molelling study of the effects of overlapping Ca2+ microdomains on neurotransmitter release. Biophysical Journal. 76 (2), 735–750 (1999).
dc.relation.references[27] Sherman A., Smith G. D., Dai L., Miura R. M. Asymptotic analysis of buffered calcium diffusion near a point source. SIAM Journal on Applied Mathematics. 61 (5), 1816–1838 (2001).
dc.relation.references[28] Mantina M., Chamberlin A. C., Valero R., Cramer C. J., Truhlar D. G. Consistent van der Waals radii for the whole main group. Journal of Physical Chemistry A. 113 (19), 5806–5812 (2009).
dc.relation.referencesen[1] Augustine G. J., Santamaria F., Tanaka K. Local calcium signaling in neurons. Neuron. 40 (2), 331–346 (2003).
dc.relation.referencesen[2] Matthews E. A., Dietrich D. Buffer mobility and the regulation of neuronal calcium domains. Frontiers in Cellular Neuroscience. 9, 48 (2015).
dc.relation.referencesen[3] Bormann G., Brosens F., De Schutter E. Chapter 8: Modeling molecular diffusion. In: Bower J. M., Bolouri H. (eds.) Computational Methods in Molecular and Cellular Biology: from Genotype to Phenotype. MIT Press, Boston Reviews in the Neurosciences (2001).
dc.relation.referencesen[4] Carnevale N. T. Modeling intracellular ion diffusion. Abstr. Soc. Neurosci. 15, 1143 (1989).
dc.relation.referencesen[5] Crank J. The mathematics of diffusion. Clarendon Press, Oxford, UK (1975).
dc.relation.referencesen[6] Naraghi M., Neher E. Linearized buffered Ca2+ diffusion in microdomains and its implications for calculation of Ca2+ at the mouth of a calcium channel. Journal of Neuroscience. 17 (18), 6961–6973 (1997).
dc.relation.referencesen[7] Nasi E., Tillotson D. The rate of diffusion of Ca2+ and Ba2+ in a nerve cell body. Biophysical Journal. 47 (5), 735–738 (1985).
dc.relation.referencesen[8] Smith G. D. Analytical steady-state solution to the rapid buffering approximation near an open Ca2+ channel. Biophysical Journal. 71 (6), 3064–3072 (1996).
dc.relation.referencesen[9] Fain G. L. Molecular and cellular physiology of neurons. Harvard Uni. press (1999).
dc.relation.referencesen[10] Sharma L. A Numerical Model to Study Excess Buffering Approximation near an Open Ca2+ Channel for an Unsteady State Case. Elixir Appl. Math. 73, 26214–26217 (2014).
dc.relation.referencesen[11] McHugh J. M., Kenyon J. L. An Excel-based model of Ca2+ diffusion and fura 2 measurements in a spherical cell. American Journal of Physiology-Cell Physiology. 286 (2), P.342–P.348 (2004).
dc.relation.referencesen[12] Neher E. Concentration profiles of intracellular Ca2+ in presense of diffusible cheltors. Exp. Brain Res. 14, 80–96 (1986).
dc.relation.referencesen[13] Sharma L. A Numerical Model to Study the Rapid Buffering Approximation near an Open Ca2+ Channel for an Unsteady State Case. International Journal of Physical and Mathematical Sciences. 8 (2), 445–449 (2014).
dc.relation.referencesen[14] Sharma L. A Numerical Model to Study Effect of Potential-Dependent Influx on Calcium Diffusion in Neuron Cells. Research & Reviews: Journal of Neuroscience. 4 (1), 1–8 (2014).
dc.relation.referencesen[15] Rao S. S. The Finite Element Method in Engineering. Elsevier Sci. Technol. (2004).
dc.relation.referencesen[16] Shannon T. R., Wang F., Puglisi J., Weber C., Bers D. M. A mathematical treatment of integrated Ca dynamics within the ventricular myocyte. Biophysical Journal. 87 (5), P3351–P3371 (2004).
dc.relation.referencesen[17] Rao S. S. The finite element method in engineering. Butterworth–Heinemann (2017).
dc.relation.referencesen[18] Reddy J. N. An introduction to the finite element method. New York, McGraw-Hill (2004).
dc.relation.referencesen[19] Keener J. P., Sneyd J. Mathematical physiology. New York, Springer (1998).
dc.relation.referencesen[20] Luby-Phelps K. Cytoarchitecture and physical properties of cytoplasm: volume, viscosity, diffusion, intra cellular surface area. International Review of Cytology. 192, 189–221 (1999).
dc.relation.referencesen[21] Puchkov E. O. Intracellular viscosity: Methods of measurement and role in metabolism. Biochemistry (Moscow) Supplement Series A: Membrane and Cell Biology. 7 (4), 270–279 (2013).
dc.relation.referencesen[22] Viswanath D. S, Natarajan G. Data book on the viscosity of liquids. New York, Hemisphere Pub. Corp. (1989).
dc.relation.referencesen[23] Vogel H. Das Temperaturabhangigkeitsgesetz der Viskosit¨at von Fl¨ussigkeiten. Physikalische Zeitschrift. 22, 645–646 (1921).
dc.relation.referencesen[24] Tanimoto R., Hiraiwa T., Nakai Y., Shindo Y., Oka K., Hiroi N., Funahashi A. Detection of Temperature Difference in Neuronal Cells. Scientific Reports. 6, 22071 (2016).
dc.relation.referencesen[25] Van Hook M. J. Temperature effects on synaptic transmission and neuronal function in the visual thalamus. PloS one. 15 (4), e0232451 (2020).
dc.relation.referencesen[26] Bertram R., Smith G. D., Sherman A. Modeling Molelling study of the effects of overlapping Ca2+ microdomains on neurotransmitter release. Biophysical Journal. 76 (2), 735–750 (1999).
dc.relation.referencesen[27] Sherman A., Smith G. D., Dai L., Miura R. M. Asymptotic analysis of buffered calcium diffusion near a point source. SIAM Journal on Applied Mathematics. 61 (5), 1816–1838 (2001).
dc.relation.referencesen[28] Mantina M., Chamberlin A. C., Valero R., Cramer C. J., Truhlar D. G. Consistent van der Waals radii for the whole main group. Journal of Physical Chemistry A. 113 (19), 5806–5812 (2009).
dc.rights.holder© Національний університет “Львівська політехніка”, 2021
dc.subjectдифузія кальцію
dc.subjectзмінний коефіцієнт дифузії
dc.subjectНБН
dc.subjectМСЕ
dc.subjectcalcium diffusion
dc.subjectvariable diffusion coefficient
dc.subjectEBA
dc.subjectFEM
dc.titleStudy of calcium profile in neuronal cells with respect to temperature and influx due to potential activity
dc.title.alternativeДослідження профілю кальція в нейронних клітинах залежно від температури та стану за наявності притоку потенційно активного кальція
dc.typeArticle

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Mathematical Modeling And Computing. – 2021. – Vol. 8, No. 2