The role of astrocytes in physiological processes is always a matter of interest for biologists, mathematicians and computer scientists. Similar to neurons, astrocytes propagate Ca2+ over long distances in response to stimulation and release gliotransmitters in a Ca2+-dependent manner to modulate various important brain functions. There are various processes and parameters that affect the cytoplasmic calcium concentration level of astrocytes like calcium buffering, influx via calcium channels, etc. Buffers bind with calcium ion (Ca2+) and makes calcium bound buffers. Thus, it decreases the calcium concentration [Ca2+] level. Ca2+ enters into the cytosol through voltage gated calcium channel (VGCC) and thus it increases the concentration level. In view of above, a three-dimensional mathematical model is developed for combined study of the effect of buffer and VGCC on cytosolic calcium concentration in astrocytes. Finite element method is applied to find the solution using hexagonal elements. A computer programme is developed for entire problem to simulate the results. The obtained results show that high affinity buffer reveals the effect of VGCC and at low buffer concentration VGCC effects more significantly.
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Deitmer, J.W., Verkhratsky, A.J., Lohr, C.: Calcium signalling in glial cells. Cell Calcium 24, 405–416 (1998)
Verkhratsky, A., Butt, A.: Glial Neurobiology: A Textbook. Wiley, New York (2007)
Fellin, T.: Communication between neuron and astrocytes: relevance to the modulation of synaptic and network activity. J. Neurochem. 108(3), 533–544 (2009)
Nedergaard, M., Rodriguez, J.J., Verkhratsky, A.: Glial calcium and disease of the nervous system. Cell Calcium 47, 140–149 (2010)
Liu, Q.S., Xu, Q., Kang, J., Nedergaard, M.: Astrocyte activation of presynaptic metabotropic glutamate receptors modulates hippocampal inhibitory synaptic transmission. Neuron Glia Biol. 1, 307–316 (2004)
Fiacco, T.A., Agulhon, C., McCarthy, K.D.: Sorting out astrocyte physiology from pharmacology. Annu. Rev. Pharmacol. Toxicol. 49, 151–174 (2009)
Cornell-Bell, A., Finkbeiner, S.M.: Ca2+ waves in astrocytes. Cell Calcium 12, 185–204 (1991)
Zeng, S., Li, B., Zeng, S., Chen, S.: Simulation of spontaneous Ca2+ oscillations in astrocytes mediated by voltage-gated calcium channels. Biophys. J. 97, 2429–2437 (2009)
Jha, A., Adlakha, N., Jha, B.: Finite element model to study effect of Na+–Ca2+ exchangers and source geometry on calcium dynamics in a neuron cell. J. Mech. Med. Biol. 16(2), 1–22 (2015)
Jha, A., Adlakha, N.: Finite element model to study the effect of exogenous buffer on calcium dynamics in dendritic spines. Int. J. Model. Simul. Sci. Comput. 5(2), 1–12 (2014)
Jha, A., Adlakha, N.: Analytical solution of two dimensional unsteady state problem of calcium diffusion in a neuron cell. J. Med. Imaging Health Inform. 4(4), 547–553 (2014)
Tewari, S.G., Pardasani, K.R.: Modeling effect of sodium pump on calcium oscillations in neuron cells. J. Multiscale Model. 4(3), 1–16 (2012)
Tewari, S.G., Pardasani, K.R.: Finite element model to study two dimensional unsteady state cytosolic calcium diffusion in presence of excess buffers. IAENG Int. J. Appl. Math. 40(3), 108–112 (2010)
Jha, B.K., Adlakha, N., Mehta, M.N.: Two-dimensional finite element model to study calcium distribution in astrocytes in presence of excess buffer. Int. J. Biomath. 7(3), 1–11 (2014)
Jha, B.K., Adlakha, N., Mehta, M.: Two-dimensional finite element model to study calcium distribution in astrocytes in presence of VGCC and excess buffer. Int. J. Model. Simul. Sci. Comput. 4(2), 1250030-1–1250030-15 (2016)
Naik, P.A., Pardasani, K.: Finite element model to study calcium distribution in oocytes involving voltage gated calcium channel, ryanodine receptor and buffers. Alex. J. Med. 52(1), 43–49 (2016)
Naik, P.A., Pardasani, K.: 2D finite element analysis of calcium distribution in oocytes. Netw. Model. Anal. Health Inform. Bioinform. 7, 1–11 (2018)
Kumar, H., Naik, P.A., Pardasani, K.: Finite element model to study calcium distribution in T lymphocyte involving buffers and ryanodine receptors. Proc. Natl. Acad. Sci. India Sect. A 88(4), 585–590 (2018)
Naik, P.A., Pardasani, K.: 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 16(1), 1–19 (2019)
Dave, D.D., Jha, B.K.: Analytically depicting the calcium diffusion for Alzheimer’s affected cell. Int. J. Biomath. 11(7), 1–17 (2018)
Jha, B.K., Joshi, H., Dave, D.D.: Portraying the effect of calcium-binding proteins on cytosolic calcium concentration distribution fractionally in nerve cells. Interdiscip. Sci. Comput. Life Sci. 10(4), 674–685 (2018)
Adler, E., Augustine, G., Duffy, S., Charlton, M.: Alien intracellular calcium chelators attenuate neurotransmitter release at the squid giant synapse. J. Neurosci. 11(6), 1496–1507 (1991)
Wang, Z., Tymianski, M., Jones, O.T., Nedergaard, M.: Impact of calcium buffering on the spatial and temporal characteristics of intercellular calcium signals in astrocytes. J. Neurosc. 17(19), 7359–7371 (1997)
Smith, G.D., Dai, L., Miura, R.M., Sherman, A.: Asymptotic analysis of buffered calcium diffusion near a point source. SIAM J. Appl. Math. 61, 1816–1838 (2000)
Smith, G.D.: Analytical steady-state solution to the rapid buffering approximation near an open Ca2+ channel. Biophys. J. 71, 3064–3072 (1996)
Keener, J., Sneyd, J.: Mathematical physiology, vol. 8, pp. 53–56. Springer, Berlin (1998)
Verkhratsky, A., Rodríguez, J.J., Parpura, V.: Molecular and cellular endocrinology calcium signalling in astroglia. Mol. Cell. Endocrinol. 353(1–2), 45–56 (2012)
Hofmann, F., Biel, M., Flockerzi, V.: Molecular basis for Ca2+ channel diversity. Annu. Rev. Neurosci. 17, 399–418 (1994)
Huguenard, J.R.: Low threshold calcium currents in central nervous system. Annu. Rev. Physiol. 58, 329–348 (1996)
Macvicar, B.A.: Voltage-dependent calcium channels in glial cells. Science 226, 1345–1347 (1984)
Rao, S.S.: Finite element method in engineering. Books. Elsevier Science and Technology, New York (2004)
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Jha, B.K., Jha, A. & Adlakha, N. Three-Dimensional Finite Element Model to Study Calcium Distribution in Astrocytes in Presence of VGCC and Excess Buffer. Differ Equ Dyn Syst 28, 603–616 (2020). https://doi.org/10.1007/s12591-019-00502-x
- Ca2+ concentration
- Voltage gated calcium channel
- Finite element method
Mathematics Subject Classification