Home Modeling the spatiotemporal intracellular calcium dynamics in nerve cell with strong memory effects
Article
Licensed
Unlicensed Requires Authentication

Modeling the spatiotemporal intracellular calcium dynamics in nerve cell with strong memory effects

  • Hardik Joshi ORCID logo EMAIL logo and Brajesh Kumar Jha
Published/Copyright: August 12, 2021
Become an author with De Gruyter Brill
Author Information
International Journal of Nonlinear Sciences and Numerical Simulation
From the journal International Journal of Nonlinear Sciences and Numerical Simulation Volume 24 Issue 6

Abstract

Calcium signaling in nerve cells is a crucial activity for the human brain to execute a diversity of its functions. An alteration in the signaling process leads to cell death. To date, several attempts registered to study the calcium distribution in nerve cells like neurons, astrocytes, etc. in the form of the integer-order model. In this paper, a fractional-order mathematical model to study the spatiotemporal profile of calcium in nerve cells is assembled and analyzed. The proposed model is solved by the finite element method for space derivative and finite difference method for time derivative. The classical case of the calcium dynamics model is recovered by setting the fractional parameter and that validates the model for classical sense. The numerical computations have systematically presented the impact of a fractional parameter on nerve cells. It is observed that calbindin-D28k provides a significant effect on the spatiotemporal variation of calcium profile due to the amalgamation of the memory of nerve cells. The presence of excess amounts of calbindin-D28k controls the intracellular calcium level and prevents the nerve cell from toxicity.

Keywords: calcium; calcium concentration; finite element method; fractional derivative; fractional diffusion equation; nerve cells
Corresponding author: Hardik Joshi, Department of Mathematics, School of Technology, Pandit Deendayal Petroleum University, Gandhinagar, Gujarat, India, E-mail:

  1. Author contribution: All the authors have accepted responsibility for the entire content of this submitted manuscript and approved submission.

  2. Research funding: None declared.

  3. Conflict of interest statement: The authors declare no conflicts of interest regarding this article.

References

[1] B. Schwaller, “Cytosolic Ca2+ buffers,” Cold Spring Harbor Perspect. Biol., vol. 2, pp. 1–20, 2010. https://doi.org/10.1101/cshperspect.a004051.Search in Google Scholar PubMed PubMed Central

[2] J. Gliabert, “Cytoplasmic calcium buffering,” Adv. Exp. Med. Biol., vol. 740, no. 3, p. e304, 2012.Search in Google Scholar

[3] H. Schmidt, “Three functional facets of calbindin D-28k,” Front. Mol. Neurosci., vol. 5, p. 25, 2012. https://doi.org/10.3389/fnmol.2012.00025.Search in Google Scholar PubMed PubMed Central

[4] T. Yamada, P. McGeer, K. Baimbridge, and E. McGeer, “Relative sparing in Parkinson’s disease of substantia nigra dopamine neurons containing calbindin-D28K,” Brain Res., vol. 526, pp. 303–307, 1990. https://doi.org/10.1016/0006-8993(90)91236-a.Search in Google Scholar PubMed

[5] G. Lally, R. L. M. Faull, H. J. Waldvogel, S. Ferrari, and P. C. Emson, “Calcium homeostasis in ageing: studies on the calcium binding protein calbindin D28K,” J. Neural. Transm., vol. 104, pp. 1107–1112, 1997. https://doi.org/10.1007/bf01273323.Search in Google Scholar PubMed

[6] D. C. German, M. C. Ng, C. Liang, A. M. C. Mahon, and A. M. Iacopino, “Calbindin-D 28k in nerve cell nuclei,” Neuroscience, vol. 81, no. 3, pp. 735–743, 1997. https://doi.org/10.1016/s0306-4522(97)00206-6.Search in Google Scholar PubMed

[7] S. Sun, F. Li, X. Gao, et al.., “Calbindin-D28K inhibits apoptosis in dopaminergic neurons by activation of the PI3-kinase-Akt signaling pathway,” Neuroscience, vol. 199, pp. 359–367, 2011. https://doi.org/10.1016/j.neuroscience.2011.09.054.Search in Google Scholar PubMed

[8] H.-H. Yuan, R.-J. Chen, Y.-H. Zhu, C.-L. Peng, and X.-R. Zhu, “The neuroprotective effect of overexpression of calbindin-D28k in an animal model of Parkinson’s disease,” Mol. Neurobiol., pp. 117–122, 2012. https://doi.org/10.1007/s12035-012-8332-3.Search in Google Scholar PubMed

[9] C. Wang, C. Jiang, H. Yuan, C. Xiao, and D. Gao, “Role of calbindin-D28K in estrogen treatment for Parkinson’s disease,” Neural Regener. Res., vol. 8, no. 8, pp. 702–707, 2013. https://doi.org/10.3969/j.issn.1673-5374.2013.08.004.Search in Google Scholar PubMed PubMed Central

[10] T. Calì, D. Ottolini, and M. Brini, “Calcium signaling in Parkinson’s disease,” Cell Tissue Res., vol. 357, no. 2, pp. 439–454, 2014. https://doi.org/10.1007/s00441-014-1866-0.Search in Google Scholar PubMed

[11] M. Brini, T. Calì, D. Ottolini, and E. Carafoli, “Neuronal calcium signaling: function and dysfunction,” Cell. Mol. Life Sci., vol. 71, no. 15, pp. 2787–2814, 2014. https://doi.org/10.1007/s00018-013-1550-7.Search in Google Scholar PubMed

[12] D. J. Surmeier, P. T. Schumacker, J. D. Guzman, E. Ilijic, B. Yang, and E. Zampese, “Calcium and Parkinson’s disease,” Biochem. Biophys. Res. Commun., vol. 483, no. 4, pp. 1013–1019, 2017. https://doi.org/10.1016/j.bbrc.2016.08.168.Search in Google Scholar PubMed PubMed Central

[13] S. V. Zaichick, K. M. McGrath, and G. Caraveo, “The role of Ca2+ signaling in Parkinson’s disease,” Dis. Models Mech., vol. 10, no. 5, pp. 519–535, 2017. https://doi.org/10.1242/dmm.028738.Search in Google Scholar PubMed PubMed Central

[14] S. Schrank, N. Barrington, and G. E. Stutzmann, “Calcium-handling defects and neurodegenerative disease,” Cold Spring Harbor Perspect. Biol., vol. 12, no. 7, pp. 1–25, 2020. https://doi.org/10.1101/cshperspect.a035212.Search in Google Scholar PubMed PubMed Central

[15] T. Glaser, V. Fernandes, A. Sampaio, C. Lameu, and H. Ulrich, “Calcium signalling : a common target in neurological disorders and neurogenesis,” Semin. Cell Dev. Biol., no. December, pp. 0–1, 2018.Search in Google Scholar

[16] R. Fairless, S. K. Williams, and R. Diem, “Calcium-binding proteins as determinants of central nervous system neuronal vulnerability to disease,” Int. J. Mol. Sci., vol. 20, no. 9, p. 2146, 2019. https://doi.org/10.3390/ijms20092146.Search in Google Scholar PubMed PubMed Central

[17] C. Catoni, T. Calì, and M. Brini, “Calcium, dopamine and neuronal calcium sensor 1: their contribution to Parkinson’s disease,” Front. Mol. Neurosci., vol. 12, no. 55, 2019. https://doi.org/10.3389/fnmol.2019.00055.Search in Google Scholar PubMed PubMed Central

[18] E. Pchitskaya, E. Popugaeva, and I. Bezprozvanny, “Calcium signaling and molecular mechanisms underlying neurodegenerative diseases,” Cell Calcium, vol. 70, pp. 87–94, 2018. https://doi.org/10.1016/j.ceca.2017.06.008.Search in Google Scholar PubMed PubMed Central

[19] E. Carafoli and M. Brini, Calcium Signalling and Disease, University of Padova, Italy, Springer Science and Business Media, 2007.10.1007/978-1-4020-6191-2Search in Google Scholar

[20] C. S. Chan, T. S. Gertler, and D. J. Surmeier, “Calcium homeostasis, selective vulnerability and Parkinson’s disease,” Trends Neurosci., vol. 32, no. 5, pp. 249–256, 2009. https://doi.org/10.1016/j.tins.2009.01.006.Search in Google Scholar PubMed PubMed Central

[21] X. S. Yang, “Computational modelling of nonlinear calcium waves,” Appl. Math. Model., vol. 30, no. 2, pp. 200–208, 2006. https://doi.org/10.1016/j.apm.2005.03.013.Search in Google Scholar

[22] M. Marhl, M. Gosak, M. Perc, C. Jane Dixon, and A. K. Green, “Spatio-temporal modelling explains the effect of reduced plasma membrane Ca2+ efflux on intracellular Ca2+ oscillations in hepatocytes,” J. Theor. Biol., vol. 252, no. 3, pp. 419–426, 2008. https://doi.org/10.1016/j.jtbi.2007.11.006.Search in Google Scholar PubMed

[23] B. K. Jha, N. Adlakha, and M. N. Mehta, “Two-dimensional finite element model to study calcium distribution in astrocytes in presence of excess buffer,” Int. J. Biomath., vol. 7, no. 3, pp. 1–11, 2014. https://doi.org/10.1142/s1793524514500314.Search in Google Scholar

[24] S. Panday and K. R. Pardasani, “Finite element model to study the mechanics of calcium regulation in oocyte,” J. Mech. Med. Biol., vol. 14, no. 2, pp. 1–16, 2014. https://doi.org/10.1142/s0219519414500225.Search in Google Scholar

[25] A. Jha and N. Adlakha, “Two-dimensional finite element model to study unsteady state Ca2+ diffusion in neuron involving ER LEAK and SERCA,” Int. J. Biomath., vol. 8, no. 1, pp. 1–14, 2015.10.1142/S1793524515500023Search in Google Scholar

[26] A. Jha, N. Adlakha, and B. K. Jha, “Finite element model to study effect of Na+ - Ca2+ exchangers and source geometry on calcium dynamics in a neuron cell,” J. Mech. Med. Biol., vol. 16, no. 2, pp. 1–22, 2015.10.1142/S0219519416500184Search in Google Scholar

[27] X. Ding, X. Zhang, and L. Ji, “Contribution of calcium fluxes to astrocyte spontaneous calcium oscillations in deterministic and stochastic models,” Appl. Math. Model., vol. 55, no. November, pp. 371–382, 2018. https://doi.org/10.1016/j.apm.2017.11.002.Search in Google Scholar

[28] H. Kumar, P. A. Naik, and K. R. Pardasani, “Finite element model to study calcium distribution in T lymphocyte involving buffers and ryanodine receptors,” Proc. Natl. Acad. Sci. India A, vol. 88, no. 4, pp. 585–590, 2018. https://doi.org/10.1007/s40010-017-0380-7.Search in Google Scholar

[29] P. A. Naik and K. R. Pardasani, “Three-dimensional finite element model to study effect of RyR calcium channel, ER leak and SERCA pump on calcium distribution in oocyte cell,” Int. J. Comput. Methods, vol. 15, no. 3, pp. 1–19, 2018. https://doi.org/10.1142/s0219876218500913.Search in Google Scholar

[30] P. A. Naik and J. Zu, “Modeling and simulation of spatial-temporal calcium distribution in T lymphocyte cell by using a reaction-diffusion equation,” J. Bioinf. Comput. Biol., vol. 18, no. 02, p. 2050013, 2020. https://doi.org/10.1142/S0219720020500134.Search in Google Scholar PubMed

[31] B. K. Jha, H. Joshi, and D. D. Dave, “Portraying the effect of calcium-binding proteins on cytosolic calcium concentration distribution fractionally in nerve cells,” Interdiscip. Sci., vol. 10, no. 4, pp. 674–685, 2018. https://doi.org/10.1007/s12539-016-0202-7.Search in Google Scholar PubMed

[32] H. Joshi and B. K. Jha, “Fractionally delineate the neuroprotective function of calbindin-28k in Parkinson’s disease,” Int. J. Biomath., vol. 11, no. 08, p. 1850103, 2018. https://doi.org/10.1142/s1793524518501036.Search in Google Scholar

[33] H. Joshi and B. K. Jha, “Fractional-order mathematical model for calcium distribution in nerve cells,” Comput. Appl. Math., vol. 39, no. 2, pp. 1–22, 2020. https://doi.org/10.1007/s40314-020-1082-3.Search in Google Scholar

[34] P. A. Naik, “Modeling the mechanics of calcium regulation in T lymphocyte: a finite element method approach,” Int. J. Biomath., vol. 13, p. 2050038, 2020. https://doi.org/10.1142/s1793524520500382.Search in Google Scholar

[35] J. G. Aguilar, K. A. Abro, O. Kolebaje, and A. Yildirim, “Chaos in a calcium oscillation model via Atangana-Baleanu operator with strong memory,” Eur. Phys. J. Plus, vol. 134, pp. 1–9, 2019. https://doi.org/10.1140/epjp/i2019-12550-1.Search in Google Scholar

[36] R. Agarwal, S. D. Purohit, and Kritika, “A mathematical fractional model with nonsingular kernel for thrombin receptor activation in calcium signalling,” Math. Methods Appl. Sci., vol. 1, no. February, pp. 1–12, 2019. https://doi.org/10.1002/mma.5822.Search in Google Scholar

[37] S. L. Gao, “Fractional time scale in calcium ion channels model,” Int. J. Biomath., vol. 6, no. 4, 2013. https://doi.org/10.1142/s179352451350023x.Search in Google Scholar

[38] T. Comlekoglu and S. H. Weinberg, “Memory in a fractional-order cardiomyocyte model alters voltage- and calcium-mediated instabilities,” Commun. Nonlinear Sci. Numer. Simulat., vol. 89, p. 105340, 2020. https://doi.org/10.1016/j.cnsns.2020.105340.Search in Google Scholar

[39] R. Agarwal, Kritika, and S. D. Purohit, “Mathematical model pertaining to the effect of buffer over cytosolic calcium concentration distribution,” Chaos, Solit. Fractals, vol. 143, p. 110610, 2021. https://doi.org/10.1016/j.chaos.2020.110610.Search in Google Scholar

[40] N. Vu-Bac, T. Lahmer, X. Zhuang, T. Nguyen-Thoi, and T. Rabczuk, “A software framework for probabilistic sensitivity analysis for computationally expensive models,” Adv. Eng. Software, vol. 100, pp. 19–31, 2016. https://doi.org/10.1016/j.advengsoft.2016.06.005.Search in Google Scholar

[41] K. B. Oldham and J. Spanier, Theory and Applications of Differentiation and Integration of Arbitrary Order, New York, London, Academic Press, 2006.Search in Google Scholar

[42] K. Diethelm, The Analysis of Fractional Differential Equations: An Application-Oriented Exposition Using Differential Operators of Caputo Type, Berlin Heidelberg: Springer-Verlag, 2010.10.1007/978-3-642-14574-2Search in Google Scholar

[43] R. L. Magin, Fractional Calculus in Bioengineering, University of Illinois, Chicago, USA, Begell House, 2006.Search in Google Scholar

[44] D. Baleanu, K. Diethelm, E. Scalas, and J. J. Trujillo, “Fractional calculus: models and numerical methods,” World Sci., vol. 3, no. January, pp. 1–428, 2012.10.1142/8180Search in Google Scholar

[45] I. Podlubny, Fractional Differential Equations: An Introduction to Fractional Derivatives, Fractional Differential Equations, to Methods of Their Solution and Some of Their, 1st ed. San Diego, California, USA, Academic Press, Elsevier, 1998.Search in Google Scholar

[46] A. Kilbas, B. Columbia, and J. J. Trujillo, Theory and Applications of Fractional Differential Equations, New York, Elsevier, 2006.Search in Google Scholar

[47] D. Kumar, J. Singh, M. Al Qurashi, and D. Baleanu, “A new fractional SIRS-SI malaria disease model with application of vaccines, antimalarial drugs, and spraying,” Adv. Differ. Equ., vol. 2019, no. 1, p. 278, 2019. https://doi.org/10.1186/s13662-019-2199-9.Search in Google Scholar

[48] V. Gill, Y. Singh, D. Kumar, and J. Singh, “Analytical study for fractional order mathematical model of concentration of Ca2 in astrocytes cell with a composite fractional derivative,” J. Multiscale Model., vol. 11, no. 3, 2020. https://doi.org/10.1142/s1756973720500055.Search in Google Scholar

[49] P. A. Naik, M. Yavuz, and J. Zu, “The role of prostitution on HIV transmission with memory: a modeling approach,” Alexandria Eng. J., vol. 59, no. 4, pp. 2513–2531, 2020. https://doi.org/10.1016/j.aej.2020.04.016.Search in Google Scholar

[50] M. Yavuz and A. Yokus, “Analytical and numerical approaches to nerve impulse model of fractional‐order,” Numer. Methods Part. Differ. Equ., vol. 36, no. 6, pp. 1348–1368, 2020. https://doi.org/10.1002/num.22476.Search in Google Scholar

[51] P. A. Naik, J. Zu, and K. M. Owolabi, “Modeling the mechanics of viral kinetics under immune control during primary infection of HIV-1 with treatment in fractional order,” Phys. A: Stat. Mech. Appl., vol. 545, p. 123816, 2020. https://doi.org/10.1016/j.physa.2019.123816.Search in Google Scholar

[52] S. Kumar, R. Kumar, J. Singh, K. S. Nisar, and D. Kumar, “An efficient numerical scheme for fractional model of HIV-1 infection of CD4+ T-cells with the effect of antiviral drug therapy,” Alexandria Eng. J., vol. 59, pp. 2053–2064, 2020.10.1016/j.aej.2019.12.046Search in Google Scholar

[53] M. Yavuz and E. Bonyah, “New approaches to the fractional dynamics of schistosomiasis disease model,” Phys. A: Stat. Mech. Appl., vol. 525, pp. 373–393, 2019. https://doi.org/10.1016/j.physa.2019.03.069.Search in Google Scholar

[54] P. A. Naik, K. M. Owolabi, M. Yavuz, and J. Zu, “Chaotic dynamics of a fractional order HIV-1 model involving AIDS-related cancer cells,” Chaos, Solit. Fractals, vol. 140, pp. 1–13, 2020. https://doi.org/10.1016/j.chaos.2020.110272.Search in Google Scholar

[55] V. M. Nguyen-Thanh, X. Zhuang, and T. Rabczuk, “A deep energy method for finite deformation hyperelasticity,” Eur. J. Mech. Solid., vol. 80, p. 103874, 2020. https://doi.org/10.1016/j.euromechsol.2019.103874.Search in Google Scholar

[56] E. Samaniego, C. Anitescu, S. Goswami, et al.., “An energy approach to the solution of partial differential equations in computational mechanics via machine learning: concepts, implementation and applications,” Comput. Methods Appl. Mech. Eng., vol. 362, p. 112790, 2020. https://doi.org/10.1016/j.cma.2019.112790.Search in Google Scholar

[57] J. Wagner and J. Keizer, “Effects of rapid buffers on Ca2+ diffusion and Ca2+ oscillations,” Biophys. J., vol. 67, no. 1, pp. 447–456, 1994. https://doi.org/10.1016/s0006-3495(94)80500-4.Search in Google Scholar PubMed PubMed Central

[58] M. Naraghi and E. Neher, “Linearized buffered Ca2+ diffusion in microdomains and its implications for calculation of [Ca2+] at the mouth of a calcium channel,” J. Neurosci., vol. 17, no. 18, pp. 6961–6973, 1997. https://doi.org/10.1523/jneurosci.17-18-06961.1997.Search in Google Scholar

[59] G. D. Smith, L. Dai, R. M. Miura, and A. Sherman, “Asymptotic analysis of buffered calcium diffusion near a point source,” SIAM J. Appl. Math., vol. 61, no. 5, pp. 1816–1838, 2001.10.1137/S0036139900368996Search in Google Scholar

[60] J. Keener and J. Sneyd, “Mathematical physiology,” in Interdisciplinary Applied Mathematics, 2nd ed., US: Springer, 2009.10.1007/978-0-387-75847-3Search in Google Scholar

[61] J. Crank, The Mathematics of Diffusion, 2nd ed. London, WI, Oxford University Press, Ely House, 1975.Search in Google Scholar

[62] P. Paradisi, R. Cesari, F. Mainardi, and F. Tampieri, “Fractional Fick’s law for non-local transport processes,” Phys. A: Stat. Mech. Appl., vol. 293, nos 1–2, pp. 130–142, 2001. https://doi.org/10.1016/s0378-4371(00)00491-x.Search in Google Scholar

[63] X. Jiang, M. Xu, and H. Qi, “The fractional diffusion model with an absorption term and modified Fick’s law for non-local transport processes,” Nonlinear Anal. R. World Appl., vol. 11, no. 1, pp. 262–269, 2010. https://doi.org/10.1016/j.nonrwa.2008.10.057.Search in Google Scholar

[64] B. Aksoylu and Z. Unlu, “Conditioning analysis of nonlocal integral operators in fractional Sobolev spaces,” SIAM J. Numer. Anal., vol. 52, no. 2, pp. 653–677, 2014. https://doi.org/10.1137/13092407x.Search in Google Scholar

[65] V. J. Ervin, N. Heuer, and J. P. Roop, “Numerical approximation of a time dependent, nonlinear, space-fractional diffusion equation,” SIAM J. Numer. Anal., vol. 45, no. 2, pp. 572–591, 2007. https://doi.org/10.1137/050642757.Search in Google Scholar

[66] L. B. Feng, P. Zhuang, F. Liu, I. Turner, and Y. T. Gu, “Finite element method for space-time fractional diffusion equation,” Numer. Algorithm., vol. 72, no. 3, pp. 749–767, 2016. https://doi.org/10.1007/s11075-015-0065-8.Search in Google Scholar

[67] L. Feng, F. Liu, I. Turner, Q. Yang, and P. Zhuang, “Unstructured mesh finite difference/finite element method for the 2D time-space Riesz fractional diffusion equation on irregular convex domains,” Appl. Math. Model., vol. 59, pp. 441–463, 2018. https://doi.org/10.1016/j.apm.2018.01.044.Search in Google Scholar

[68] Y. Jiang and J. Ma, “High-order finite element methods for time-fractional partial differential equations,” J. Comput. Appl. Math., vol. 235, no. 11, pp. 3285–3290, 2011. https://doi.org/10.1016/j.cam.2011.01.011.Search in Google Scholar

[69] Z. Liu, A. Cheng, X. Li, and H. Wang, “A fast solution technique for finite element discretization of the space–time fractional diffusion equation,” Appl. Numer. Math., vol. 119, no. April, pp. 146–163, 2017. https://doi.org/10.1016/j.apnum.2017.04.003.Search in Google Scholar

[70] Y. Lin and C. Xu, “Finite difference/spectral approximations for the time-fractional diffusion equation,” J. Comput. Phys., vol. 225, no. 2, pp. 1533–1552, 2007. https://doi.org/10.1016/j.jcp.2007.02.001.Search in Google Scholar

[71] N. Manhas and K. R. Pardasani, “Modelling mechanism of calcium oscillations in pancreatic acinar cells,” J. Bioenerg. Biomembr., vol. 46, no. 5, pp. 403–420, 2014. https://doi.org/10.1007/s10863-014-9561-0.Search in Google Scholar PubMed

Received: 2020-11-15
Accepted: 2021-07-20
Published Online: 2021-08-12

© 2021 Walter de Gruyter GmbH, Berlin/Boston

Articles in the same Issue

  1. Frontmatter
  2. Original Research Articles
  3. Frequency responses for induced neural transmembrane potential by electromagnetic waves (1 kHz to 1 GHz)
  4. Investigating existence results for fractional evolution inclusions with order r ∈ (1, 2) in Banach space
  5. Optimal control of non-instantaneous impulsive second-order stochastic McKean–Vlasov evolution system with Clarke subdifferential
  6. Generalized forms of fractional Euler and Runge–Kutta methods using non-uniform grid
  7. Controllability of coupled fractional integrodifferential equations
  8. A new generalized approach to study the existence of solutions of nonlinear fractional boundary value problems
  9. Rational soliton solutions in the nonlocal coupled complex modified Korteweg–de Vries equations
  10. Buoyancy driven flow characteristics inside a cavity equiped with diamond elliptic array
  11. Analysis and numerical effects of time-delayed rabies epidemic model with diffusion
  12. Two occurrences of fractional actions in nonlinear dynamics
  13. Multiwave interaction solutions for a (3 + 1)-dimensional B-type Kadomtsev–Petviashvili equation in fluid dynamics
  14. Effects of mixed time delays and D operators on fixed-time synchronization of discontinuous neutral-type neural networks
  15. Solvability and stability of nonlinear hybrid ∆-difference equations of fractional-order
  16. Weak and strong boundedness for p-adic fractional Hausdorff operator and its commutator
  17. Simulation and modeling of different cell shapes for closed-cell LM-13 alloy foam for compressive behavior
  18. Pandemic management by a spatio–temporal mathematical model
  19. Adaptive ADI difference solution of quenching problems based on the 3D convection–reaction–diffusion equation
  20. Null controllability of Hilfer fractional stochastic integrodifferential equations with noninstantaneous impulsive and Poisson jump
  21. Application of modified Mickens iteration procedure to a pendulum and the motion of a mass attached to a stretched elastic wire
  22. Modeling the spatiotemporal intracellular calcium dynamics in nerve cell with strong memory effects
  23. Switched coupled system of nonlinear impulsive Langevin equations involving Hilfer fractional-order derivatives
  24. Improving the dynamic behavior of the plate under supersonic air flow by using nonlinear energy sink
https://doi.org/10.1515/ijnsns-2020-0254
Keywords for this article
calcium; calcium concentration; finite element method; fractional derivative; fractional diffusion equation; nerve cells

Articles in the same Issue

  1. Frontmatter
  2. Original Research Articles
  3. Frequency responses for induced neural transmembrane potential by electromagnetic waves (1 kHz to 1 GHz)
  4. Investigating existence results for fractional evolution inclusions with order r ∈ (1, 2) in Banach space
  5. Optimal control of non-instantaneous impulsive second-order stochastic McKean–Vlasov evolution system with Clarke subdifferential
  6. Generalized forms of fractional Euler and Runge–Kutta methods using non-uniform grid
  7. Controllability of coupled fractional integrodifferential equations
  8. A new generalized approach to study the existence of solutions of nonlinear fractional boundary value problems
  9. Rational soliton solutions in the nonlocal coupled complex modified Korteweg–de Vries equations
  10. Buoyancy driven flow characteristics inside a cavity equiped with diamond elliptic array
  11. Analysis and numerical effects of time-delayed rabies epidemic model with diffusion
  12. Two occurrences of fractional actions in nonlinear dynamics
  13. Multiwave interaction solutions for a (3 + 1)-dimensional B-type Kadomtsev–Petviashvili equation in fluid dynamics
  14. Effects of mixed time delays and D operators on fixed-time synchronization of discontinuous neutral-type neural networks
  15. Solvability and stability of nonlinear hybrid ∆-difference equations of fractional-order
  16. Weak and strong boundedness for p-adic fractional Hausdorff operator and its commutator
  17. Simulation and modeling of different cell shapes for closed-cell LM-13 alloy foam for compressive behavior
  18. Pandemic management by a spatio–temporal mathematical model
  19. Adaptive ADI difference solution of quenching problems based on the 3D convection–reaction–diffusion equation
  20. Null controllability of Hilfer fractional stochastic integrodifferential equations with noninstantaneous impulsive and Poisson jump
  21. Application of modified Mickens iteration procedure to a pendulum and the motion of a mass attached to a stretched elastic wire
  22. Modeling the spatiotemporal intracellular calcium dynamics in nerve cell with strong memory effects
  23. Switched coupled system of nonlinear impulsive Langevin equations involving Hilfer fractional-order derivatives
  24. Improving the dynamic behavior of the plate under supersonic air flow by using nonlinear energy sink
Sign up now to receive a 20% welcome discount
Institutional Access
How does access work?
Have an idea on how to improve our website?
Please write us.
© 2025 De Gruyter Brill
Downloaded on 27.10.2025 from https://www.degruyterbrill.com/document/doi/10.1515/ijnsns-2020-0254/pdf
Scroll to top button