The effect of amyloid beta, membrane, and ER pathways on the fractional behavior of neuronal calcium
DOI:
https://doi.org/10.59292/bulletinbiomath.2024009Keywords:
Fractional-order derivative, calcium ions, neuron, Alzheimer's diseaseAbstract
Calcium signal transduction is essential for cellular activities such as gene transcription, death, and neuronal plasticity. Dynamical changes in the concentration of calcium have a profound effect on the intracellular activity of neurons. The Caputo fractional reaction-diffusion equation is a useful tool for modeling the intricate biological process involved in calcium concentration regulation. We include the Amyloid Beta, STIM-Orai mechanism, voltage-dependent calcium entry, inositol triphosphate receptor (IPR), endoplasmic reticulum (ER) flux, SERCA pump, and plasma membrane flux in our mathematical model. We use Green's function and Hankel and Laplace integral transforms to solve the membrane flux problem. Our simulations investigate the effects of various factors on the spatiotemporal behavior of calcium levels, with a simulation on the buffers in Alzheimer's disease-affected neurons. We also look at the effects of calcium-binding substances like the S100B protein and BAPTA and EGTA. Our results demonstrate how important the S100B protein Amyloid beta and the STIM-Orai mechanism are, and how important they are to consider when simulating the calcium signaling system. As such, our research indicates that a more realistic and complete model for modeling calcium dynamics may be obtained by using a generalized reaction-diffusion technique.
References
Workgroup, A.A.C.H and Khachaturian, Z.S. Calcium hypothesis of Alzheimer’s disease and brain aging: a framework for integrating new evidence into a comprehensive theory of pathogenesis. Alzheimer’s & Dementia, 13(2), 178-182, (2017).
Ribe, E.M., Serrano-Saiz, E., Akpan, N. and Troy, C.M. Mechanisms of neuronal death in disease: defining the models and the players. Biochemical Journal, 415(2), 165-182, (2008).
Bezprozvanny, I. Calcium signaling and neurodegenerative diseases. Trends in Molecular Medicine, 15(3), 89-100, (2009).
Smith, G.D. Analytical steady-state solution to the rapid buffering approximation near an open Ca2+ channel. Biophysical Journal, 71(6), 3064-3072, (1996).
Dupont, G., Berridge, M.J. and Goldbeter, A. Signal-induced Ca2+ oscillations: properties of a model based on Ca2+-induced Ca2+ release. Cell Calcium, 12(2-3), 73-85, (1991).
Dupont, G., Houart, G. and De Koninck, P. Sensitivity of CaM kinase II to the frequency of Ca2+ oscillations: a simple model. Cell Calcium, 34(6), 485-497, (2003).
Sherman, A., Smith, G.D., Dai, L. and Miura, R.M. Asymptotic analysis of buffered calcium diffusion near a point source. SIAM Journal on Applied Mathematics, 61(5), 1816-1838, (2001).
Schmeitz, C., Hernandez-Vargas, E.A., Fliegert, R., Guse, A.H. and Meyer-Hermann, M. A mathematical model of T lymphocyte calcium dynamics derived from single transmembrane protein properties. Frontiers in Immunology, 4, 277, (2013).
Friedhoff, V.N., Ramlow, L., Lindner, B. and Falcke, M. Models of stochastic Ca2+ spiking. The European Physical Journal Special Topics, 230, 2911-2928, (2021).
Marhl, M., Haberichter, T., Brumen, M. and Heinrich, R. Complex calcium oscillations and the role of mitochondria and cytosolic proteins. BioSystems, 57(2), 75-86, (2000).
Dave, D.D. and Jha, B.K. Analytically depicting the calcium diffusion for Alzheimer’s affected cell. International Journal of Biomathematics, 11(7), 1850088, (2018).
Manhas, N., Sneyd, J. and Pardasani, K.R. Modelling the transition from simple to complex Ca2+ oscillations in pancreatic acinar cells. Journal of Biosciences, 39(3), 463-484, (2014).
Naik, P.A. and Pardasani, K.R. Finite element model to study calcium distribution in oocytes involving voltage gated Ca2+ channel, ryanodine receptor and buffers. Alexandria Journal of Medicine, 52(1), 43–49, (2016).
Jha, B.K., Joshi, H. and Dave, D.D. Portraying the effect of calcium-binding proteins on cytosolic calcium concentration distribution fractionally in nerve cells. Interdisciplinary Sciences: Computational Life Sciences, 10, 674-685, (2018).
Joshi, H. and Yavuz, M. Numerical analysis of compound biochemical calcium oscillations process in hepatocyte cells. Advanced Biology, 8(4), 2300647, (2024).
Vatsal, V.H., Jha, B.K. and Singh, T.P. To study the effect of ER flux with buffer on the neuronal calcium. The European Physical Journal Plus, 138, 494, (2023).
Vatsal, V.H., Jha, B.K. and Singh, T.P. Deciphering two-dimensional calcium fractional diffusion of membrane flux in neuron. Journal of Applied Mathematics and Computing, 70, 4133–4156, (2024).
Joshi, H. and Jha, B.K. Chaos of calcium diffusion in Parkinson’s infectious disease model and treatment mechanism via Hilfer fractional derivative. Mathematical Modelling and Numerical Simulation with Applications, 1(2), 84-94, (2021).
Vaishali and Adlakha, N. Model of calcium dynamics regulating IP3, ATP and insulin production in a pancreatic β-cell. Acta Biotheoretica, 72, 2, (2024).
Luchko, Y., Mainardi, F. and Povstenko, Y. Propagation speed of the maximum of the fundamental solution to the fractional diffusion–wave equation. Computers & Mathematics with Applications, 66(5), 774-784, (2013).
Pawar, A. and Pardasani, K.R. Computational model of interacting system dynamics of calcium, IP3 and β-amyloid in ischemic neuron cells. Physica Scripta, 99(1), 015025, (2024).
Lai, Y.M., Coombes, S. and Thul, R. Calcium buffers and L-type calcium channels as modulators of cardiac subcellular alternans. Communications in Nonlinear Science and Numerical Simulation, 85, 105181, (2020).
Luchko, Y. and Yamamoto, M. General time-fractional diffusion equation: some uniqueness and existence results for the initial-boundary-value problems. Fractional Calculus and Applied Analysis, 19(3), 676-695, (2016).
Agarwal, R., Kritika and Purohit, S.D. Mathematical model pertaining to the effect of buffer over cytosolic calcium concentration distribution. Chaos, Solitons & Fractals, 143, 110610, (2021).
Tewari, S.G., Camara, A.K.S., Stowe, D.F. and Dash, R.K. Computational analysis of Ca2+ dynamics in isolated cardiac mitochondria predicts two distinct modes of Ca2+ uptake. The Journal of Physiology, 592(9), 1917-1930, (2014).
Jagtap, Y. and Adlakha, N. Numerical model of hepatic glycogen phosphorylase regulation by nonlinear interdependent dynamics of calcium and IP3. The European Physical Journal Plus, 138, 399, (2023).
Singh, T. and Adlakha, N. Numerical investigations and simulation of calcium distribution in the alpha-cell. Bulletin of Biomathematics, 1(1), 40-57, (2023).
Vatsal, V.H., Jha, B.K. and Singh, T.P. Generalised neuronal calcium dynamics of membrane and ER in the polar dimension. Cell Biochemistry and Biophysics, (2024).
Jha, B.K., Vatsal, V.H. and Singh, T.P. Navigating the fractional calcium dynamics of Orai mechanism in polar dimensions. Cell Biochemistry and Biophysics, (2024).
Joshi, H. Mechanistic insights of COVID-19 dynamics by considering the influence of neurodegeneration and memory trace. Physica Scripta, 99(3), 035254, (2024).
Purohit, S.D., Baleanu, D. and Jangid, K. On the solutions for generalised multiorder fractional partial differential equations arising in physics. Mathematical Methods in the Applied Sciences, 46(7), 8139-8147, (2023).
Vaishali and Adlakha, N. Disturbances in system dynamics of Ca2+ and IP3 perturbing insulin secretion in a pancreatic β-cell due to type-2 diabetes. Journal of Bioenergetics and Biomembranes, 55, 151–167, (2023).
Naik, P.A., Eskandari, Z. and Shahraki, H.E. Flip and generalized flip bifurcations of a two-dimensional discrete-time chemical model. Mathematical Modelling and Numerical Simulation with Applications, 1(2), 95-101, (2021).
Manhas, N. Mathematical model for IP3 dependent calcium oscillations and mitochondrial associate membranes in non-excitable cells. Mathematical Modelling and Numerical Simulation with Applications, 4(3), 280–295, (2024).
Kumar, P. and Erturk, V.S. Dynamics of cholera disease by using two recent fractional numerical methods. Mathematical Modelling and Numerical Simulation with Applications, 1(2), 102-111, (2021).
Nakul, N., Mishra, V. and Adlakha, N. Finite volume simulation of calcium distribution in a cholangiocyte cell. Mathematical Modelling and Numerical Simulation with Applications, 3(1), 17-32, (2023).
Podlubny, I. Fractional Differential Equations (Vol. 198). Academic Press: New York, USA, (1999).
Miller, K.S. and Ross, B. An Introduction to The Fractional Calculus and Fractional Differential Equations. John Willey & Sons: New York, (1993).
Kilbas, A.A., Srivastava, H.M. and Trujillo, J.J. Theory and Applications of Fractional Differential Equations (Vol. 204). Elsevier: Amsterdam, (2006).
Diethelm, K. The Analysis of Fractional Differential Equations: An Application-Oriented Exposition using Differential Operators of Caputo Type. Springer: Heidelberg, (2010).
Mainardi, F. and Pagnini, G. The Wright functions as solutions of the time-fractional diffusion equation. Applied Mathematics and Computation, 141(1), 51-62, (2003).
Keener, J. and Sneyd, J. Mathematical Physiology (Vol. 8/1). Springer: New York, (2009).
Prista von Bonhorst, F., Gall, D. and Dupont, G. Impact of β-amyloids induced disruption of Ca2+ homeostasis in a simple model of neuronal activity. Cells, 11(4), 615, (2022).
Zhang, H., Sun, S., Wu, L., Pchitskaya, E., Zakharova, O., Tacer, K.F. and Bezprozvanny, I. Store-operated calcium channel complex in postsynaptic spines: a new therapeutic target for Alzheimer’s disease treatment. Journal of Neuroscience, 36(47), 11837-11850, (2016).
Gil, D., Guse, A.H. and Dupont, G. Three-dimensional model of sub-plasmalemmal Ca2+ microdomains evoked by the interplay between ORAI1 and InsP3 receptors. Frontiers in Immunology, 12, 659790, (2021).
Sneyd, J., Tsaneva-Atanasova, K., Bruce, J.I.E., Straub, S.V., Giovannucci, D.R. and Yule, D.I. A model of calcium waves in pancreatic and parotid acinar cells. Biophysical Journal, 85(3), 1392–1405, (2003).
Marambaud, P., Dreses-Werringloer, U. and Vingtdeux, V. Calcium signaling in neurodegeneration. Molecular Neurodegeneration, 4, 20, (2009).
Yagami, T., Kohma, H. and Yamamoto, Y. L-type voltage-dependent calcium channels as therapeutic targets for neurodegenerative diseases. Current Medicinal Chemistry, 19(28), 4816- 4827, (2012).
Bezprozvanny, I.B. Calcium signaling and neurodegeneration. Acta Naturae, 2(1), 72-80, (2010).
Jha, B.K., Adlakha, N. and Mehta, M.N. Finite volume model to study the effect of ER flux on cytosolic calcium distribution in astrocytes. Journal of Computing, 3(11), 74-80, (2011).
Downloads
Published
How to Cite
Issue
Section
License
Copyright (c) 2024 Brajesh Kumar Jha, Vora Hardagna Vatsal, Tajinder Pal Singh
This work is licensed under a Creative Commons Attribution 4.0 International License.
Articles published in the Bulletin of Biomathematics are made freely available online immediately upon publication, without subscription barriers to access. All articles published in this journal are licensed under the Creative Commons Attribution 4.0 International License (click here to read the full-text legal code). This broad license was developed to facilitate open access to, and free use of, original works of all types. Applying this standard license to your work will ensure your right to make your work freely and openly available.
Under the Creative Commons Attribution 4.0 International License, authors retain ownership of the copyright for their article, but authors allow anyone to download, reuse, reprint, modify, distribute, and/or copy articles in the Bulletin of Biomathematics, so long as the original authors and source are credited.
The readers are free to:
- Share — copy and redistribute the material in any medium or format
- Adapt — remix, transform, and build upon the material for any purpose, even commercially.
- The licensor cannot revoke these freedoms as long as you follow the license terms.
under the following terms:
- Attribution — You must give appropriate credit, provide a link to the license, and indicate if changes were made. You may do so in any reasonable manner, but not in any way that suggests the licensor endorses you or your use.
- No additional restrictions — You may not apply legal terms or technological measures that legally restrict others from doing anything the license permits.
