Impact of Temperature Variation on Calcium Profiling in a Neuronal Cell Due to Cancer: A Steady-State Case




Calcium profile, Finite element method, Excess buffering approximation, Variable diffusion coefficient


A crucially vital second messenger for intracellular signaling in the nervous system is Calcium. It regulates the release of synaptic transmitters. The cellular metabolism is monitored by diffusion, the activity of buffering, and influx in the cytoplasm. The temperature of the cellular microenvironment rises as excess energy from cellular metabolism is transformed into heat. The addition of medications or other cancer-curing treatments leads cancer cells to heat up more than normal cells, according to numerous studies. The calcium concentration profile is impacted by the cellular metabolism’s elevated temperature. This research aims to examine calcium profiles in neurons brought on by temperature changes brought on by cancer treatment. When there is calcium current input, the Goldman-Hodgkin-Katz (GHK) current equation and mathematical modelling are employed to determine calcium diffusion in neuron cells. Also, the impact of the temperature of the cellular environment on calcium concentration is studied. This model has been proposed for a 1-D steady-state case with the right initial and boundary conditions. To obtain the solution, the finite element method has been used. The simulations have been used to identify the effect of buffers as well as the effect of temperature variation on calcium distribution.


Download data is not yet available.


G. J. Augustine, F. Santamaria and K. Tanaka, Local calcium signaling in neurons, Neuron 40(2) (2003), 331 – 346, DOI: 10.1016/S0896-6273(03)00639-1.

R. Bertram, G. D. Smith and A. Sherman, Modeling study of the effects of overlapping Ca2+ microdomains on neurotransmitter release, Biophysical Journal 76 (1999), 735 – 750, DOI: 10.1016/s0006-3495(99)77240-1.

A. Bettaieb, P. K. Wrzal and D. A. Averill-Bates, Hyperthermia: Cancer treatment and beyond, in: Cancer Treatment - Conventional and Innovative Approaches L. Rangel (editor), IntechOpen, 630 page (2013), DOI: 10.5772/55795.

A. H. L. Bong and G. R. Monteith, Calcium signaling and the therapeutic targeting of cancer cells, Biochimica et Biophysica Acta (BBA) - Molecular Cell Research 1865(11)(Part B) (2018), 1786 – 1794, DOI: 10.1016/j.bbamcr.2018.05.015.

G. Bormann, F. Brosens and E. De Schutter, Modeling molecular diffusion, Chapter 8, in: Computational Methods in Molecular and Cellular Biology: from Genotype to Phenotype, J. M. Bower and H. Bolouri (editors), Boston Reviews in the Neurosciences series, MIT Press (2002), URL:

C. Cárdenas, M. Müller, A. McNeal, A. Lovy, F. Jana, G. Bustos, F. Urra, N. Smith, J. Molgó, J. A. Diehl, T. W. Ridky and J. K. Foskett, Selective vulnerability of cancer cells by inhibition of Ca2+ transfer from endoplasmic reticulum to mitochondria, Cell Reports 14(10) (2016), 2313 – 2324, DOI: 10.1016/j.celrep.2016.02.030.

G. L. Fain, Molecular and Cellular Physiology of Neurons, 2nd Edition, Harvard University Press, 752 pages (2014), URL:

J. P. Keener and J. Sneyd, Mathematical Physiology, 1st edition, Springer, New York, xx + 767 pages (1998), DOI: 10.1007/b98841.

K. Luby-Phelps, Cytoarchitecture and physical properties of cytoplasm: volume, viscosity, diffusion, intracellular surface area, International Review of Cytology 192 (1999), 189 – 221, DOI: 10.1016/s0074-7696(08)60527-6.

M. Mantina, A. C. Chamberlin, R. Valero, C. J. Cramer and D. G. Truhlar, Consistent van der Waals radii for the whole main group, The Journal of Physical Chemistry 113(19) (2009), 5806 – 5812, DOI: 10.1021/jp8111556.

E. A. Matthews and D. Dietrich, Buffer mobility and the regulation of neuronal calcium domains, Frontiers in Cellular Neuroscience 9 (2015), Article number: 48, DOI: 10.3389/fncel.2015.00048.

J. M. McHugh and J. L. Kenyon, An Excel-based model of Ca2+ diffusion and fura 2 measurements in a spherical cell, American Journal of Physiology Cell Physiology 286(2) (2004), C342 – C348, DOI: 10.1152/ajpcell.00270.2003.

G. R. Monteith, N. Prevarskaya and S. J. Roberts-Thomson, The calcium–cancer signalling nexus, Nature Reviews Cancer 17 (2017), 373 – 380, DOI: 10.1038/nrc.2017.18.

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, Journal of Neuroscience 17(18) (1997), 6961 – 6973, DOI: 10.1523/JNEUROSCI.17-18-06961.1997.

E. Nasi and D. Tillotson, The rate of diffusion of Ca2+ and Ba2+ in a nerve cell body, Biophysical Journal 47(5) (1985), 735 – 738, DOI: 10.1016/S0006-3495(85)83972-2.

K. Pathak and N. Adlakha, Finite element model to study two dimensional unsteady state calcium distribution in cardiac myocytes, Alexandria Journal of Medicine 52(3) (2016), 261 – 268, DOI: /10.1016/j.ajme.2015.09.007.

J. V. Patil, A. N. Vaze, L. Sharma and A. Bachhav, Study of calcium profile in neuronal cells with respect to temperature and influx due to potential activity, Mathematical Modeling and Computing 8(2) (2021), 241 – 252, DOI: 10.23939/mmc2021.02.241.

E. O. Puchkov, Intracellular viscosity: Methods of measurement and role in metabolism, Biochemistry (Moscow) Supplement Series A: Membrane and Cell Biology 7 (2013), 270 – 279, DOI: 10.1134/S1990747813050140.

S. S. Rao, The Finite Element Method in Engineering, Elsevier Butterworth-Heinemann, Amsterdam (2005).

J. N. Reddy, An Introduction to the Finite Element Method, McGraw-Hill Higher Eduction, Boston (2006).

R. Rizzuto, P. Pinton, D. Ferrari, M. Chami, G. Szabadkai, P. J. Magalhães, F. Di Virgilio and T. Pozzan, Calcium and apoptosis: facts and hypotheses, Oncogene 22 (2003), 8619 – 8627, DOI: 10.1038/sj.onc.1207105.

T. R. Shannon, F. Wang, J. Puglisi, C. Weber and B. D. Bers, A mathematical treatment of integrated Ca dynamics within the ventricular myocyte, Biophysical Journal 87(5) (2004), 3351 – 3371, DOI: 10.1529/biophysj.104.047449.

G. Shapovalov, A. Ritaine, R. Skryma and N. Prevarskaya, Role of TRP ion channels in cancer and tumorigenesis, Seminars in Immunopathology 38 (2016), 357 – 369, DOI: 10.1007/s00281-015-0525-1.

A. Sherman, G. D. Smith, L. Dai and R. M. Miura, Asymptotic analysis of buffered calcium diffusion near a point source, SIAM Journal on Applied Mathematics 61(5) (2001), 1816 – 1838, DOI: 10.1137/S0036139900368996.

R. Tanimoto, T. Hiraiwa, Y. Nakai, Y. Shindo, K. Oka, N. Hiroi and A. Funahashi, Detection of temperature difference in neuronal cells, Scientific Reports 6 (2016), Article number: 22071, DOI: 10.1038/srep22071.

S. G. Tewari and K. R. Pardasani, Finite element model to study two dimensional unsteady state cytosolic calcium diffusion in presence of excess buffers, IAENG International Journal of Applied Mathematics 40(3) (2010), 5 pages, URL:

V. Tewari, S. Tewari and K. R. Pardasani, Model to study the effect of excess buffers and Na+ions on Ca2+ diffusion in neuron cell, World Academy of Science, Engineering and Technology 5(4) (2011), 803 – 804.

M. J. Van Hook, Temperature effects on synaptic transmission and neuronal function in the visual thalamus, PLOS ONE 15(4) (2020), e0232451, DOI: 10.1371/journal.pone.0232451.

D. S. Viswanath and G. Natavajan, Data Book on the Viscosity of Liquids, 1st edition, CRC Press, USA (1989).




How to Cite

Patil, J., Vaze, A., Sharma, L., & Bachhav, A. (2023). Impact of Temperature Variation on Calcium Profiling in a Neuronal Cell Due to Cancer: A Steady-State Case. Communications in Mathematics and Applications, 14(3), 1229–1243.



Research Article