The role of calcium dynamics with amyloid beta on neuron-astrocyte coupling

Abstract

Amyloid beta ($A\beta$) plaques are associated with neurodegenerative diseases such as Alzheimer's disease. Due to the involvement of $A\beta$ plaques in the functioning of the brain; cognitive decline disrupts calcium homeostasis in nerve cells and causes abnormal calcium ions ($Ca^{2+}$) signaling patterns. In consequence, there is enhanced neuronal excitability, compromised synaptic transmission, and decreased astrocytic function. Neuron-astrocyte coupling through calcium dynamics with different neuronal functions has been studied. Key signaling molecules in this process include $Ca^{2+}$, which control several cellular functions, including neurotransmission and astrocytic regulation. The mathematical model for neuron-astrocyte communication has been developed to study the importance of calcium dynamics in signal transduction between the cells. To understand the wide role of mitochondria, NCX, and amyloid beta with various necessary parameters included in the model, $Ca^{2+}$ signaling patterns have been analyzed through amplitude modulation and frequency modulation. The results of the current model are simulated and analyzed using XPPAUT. The findings of the current study are contrasted with experimental data from an existing mathematical model that illustrates the impact of calcium oscillation frequency and amplitude modulations in nerve cells.

Keywords

• Neuron
• Astrocytes
• Calcium dynamics
• amyloid beta
• neurodegenerative diseases

References

1. [1] Ye, M. and Zuo, H. Stability analysis of regular and chaotic Ca2+ oscillations in astrocytes. Discrete Dynamics in Nature and Society, 2020, 1-9, (2020).
2. [2] Wade, J.J., McDaid, L.J., Harkin, J., Crunelli, V. and Kelso, J.S. Bidirectional coupling between astrocytes and neurons mediates learning and dynamic coordination in the brain: a multiple modeling approach. PloS One, 6(12), e29445, (2011).
3. [3] Dave, D.D. and Jha, B.K. Mathematical modeling of calcium oscillatory patterns in a neuron. Interdisciplinary Sciences: Computational Life Sciences, 13, 12-24, (2021).
4. [4] Falcke, M., Or-Guil, M. and Bär, M. Dispersion gap and localized spiral waves in a model for intracellular Ca2+ dynamics. Physical Review Letters, 84(20), 4753, (2000).
5. [5] Kalia, M., Meijer, H.G., van Gils, S.A., van Putten, M.J. and Rose, C.R. Ion dynamics at the energy-deprived tripartite synapse. PLoS Computational Biology, 17(6), e1009019, (2021).
6. [6] Keener, J. and Sneyd, J. The Heart. In Mathematical Physiology (pp. 523-626). New York, NY: Springer, (2009).
7. [7] 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).
8. [8] Jha, A. and Jha, B.K. Computational modelling of calcium buffering in a star shaped astrocyte. In Proceedings of the 2019 9th International Conference on Bioscience, Biochemistry and Bioinformatics (ICBBB), pp. 63-66, Singapore, (2019, January).

9. [9] Dave, D.D. and Jha, B.K. 2D finite element estimation of calcium diffusion in Alzheimer’s affected neuron. Network Modeling Analysis in Health Informatics and Bioinformatics, 10, 43, (2021).
10. [10] 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).
11. [11] Nadkarni, S. and Jung, P. Spontaneous oscillations of dressed neurons: a new mechanism for epilepsy?. Physical Review Letters, 91(26), 268101, (2003).
12. [12] Lenk, K., Satuvuori, E., Lallouette, J., Ladrón-de-Guevara, A., Berry, H. and Hyttinen, J.A. A computational model of interactions between neuronal and astrocytic networks: the role of astrocytes in the stability of the neuronal firing rate. Frontiers in Computational Neuroscience, 13, 92, (2020).
13. [13] Zuo, H. and Ye, M. Bifurcation and numerical simulations of Ca2+ oscillatory behavior in astrocytes. Frontiers in Physics, 8, 258, (2020).
14. [14] Zhou, A., Liu, X. and Yu, P. Bifurcation analysis on the effect of store-operated and receptor-operated calcium channels for calcium oscillations in astrocytes. Nonlinear Dynamics, 97, 733-748, (2019).
15. [15] Pankratova, E.V., Kalyakulina, A.I., Stasenko, S.V., Gordleeva, S.Y., Lazarevich, I.A. and Kazantsev, V.B. Neuronal synchronization enhanced by neuron–astrocyte interaction. Nonlinear Dynamics, 97, 647-662, (2019).
16. [16] Oku, Y., Fresemann, J., Miwakeichi, F. and Hülsmann, S. Respiratory calcium fluctuations in low-frequency oscillating astrocytes in the pre-Bötzinger complex. Respiratory Physiology & Neurobiology, 226, 11-17, (2016).
17. [17] Naji, R. and Abdulateef, B. The dynamics of model with nonlinear incidence rate and saturated treatment function. Science International, 29(6), 1223-1236, (2017).
18. [18] Li, J.J., Du, M.M., Wang, R., Lei, J.Z. and Wu, Y. Astrocytic gliotransmitter: diffusion dynamics and induction of information processing on tripartite synapses. International Journal of Bifurcation and Chaos, 26(08), 1650138, (2016).
19. [19] Matrosov, V.V. and Kazantsev, V.B. Bifurcation mechanisms of regular and chaotic network signaling in brain astrocytes. Chaos: An Interdisciplinary Journal of Nonlinear Science, 21(2), 023103, (2011).
20. [20] Faramarzi, F., Azad, F., Amiri, M. and Linares-Barranco, B. A neuromorphic digital circuit for neuronal information encoding using astrocytic calcium oscillations. Frontiers in Neuroscience, 13, 998, (2019).
21. [21] Singh, T. and Adlakha, N. Numerical investigations and simulation of calcium distribution in the alpha-cell. Bulletin of Biomathematics, 1(1), 40-57, (2023).
22. [22] 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).
23. [23] 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).
24. [24] Naik, P.A. Modeling the mechanics of calcium regulation in T lymphocyte: a finite element method approach. International Journal of Biomathematics, 13(05), 2050038, (2020).
25. [25] Naik, P.A. and Pardasani, K.R. Finite element model to study calcium signalling in oocyte cell. International Journal of Modern Mathematical Sciences, 15(01), 58-71, (2017).
26. [26] Naik, P.A. and Pardasani, K.R. Three-dimensional finite element model to study calcium distribution in oocytes. Network Modeling Analysis in Health Informatics and Bioinformatics, 6, 16, (2017).
27. [27] Joshi, H., Yavuz, M. and Stamova, I. Analysis of the disturbance effect in intracellular calcium dynamic on fibroblast cells with an exponential kernel law. Bulletin of Biomathematics, 1(1), 24-39, (2023).
28. [28] 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).
29. [29] Marambaud, P., Dreses-Werringloer, U. and Vingtdeux, V. Calcium signaling in neurodegeneration. Molecular Neurodegeneration, 4, 20, (2009).
30. [30] Latulippe, J., Lotito, D. and Murby, D. A mathematical model for the effects of amyloid beta on intracellular calcium. PLoS One, 13(8), e0202503, (2018).
31. [31] Manninen, T., Havela, R. and Linne, M.L. Reproducibility and comparability of computational models for astrocyte calcium excitability. Frontiers in Neuroinformatics, 11, 11, (2017).
32. [32] Schampel, A. and Kuerten, S. Danger: high voltage-the role of voltage-gated calcium channels in central nervous system pathology. Cells, 6(4), 43, (2017).
33. [33] Grubelnik, V., Larsen, A.Z., Kummer, U., Olsen, L.F. and Marhl, M. Mitochondria regulate the amplitude of simple and complex calcium oscillations. Biophysical Chemistry, 94(1-2), 59-74, (2001).
34. [34] Jha, B.K., Jha, A. and Adlakha, N. Three-dimensional finite element model to study calcium distribution in astrocytes in presence of VGCC and excess buffer. Differential Equations and Dynamical Systems, 28, 603-616, (2020).
35. [35] Nazari, S., Faez, K., Amiri, M. and Karami, E. A digital implementation of neuron-astrocyte interaction for neuromorphic applications. Neural Networks, 66, 79-90, (2015).
36. [36] Gao, H., Liu, L. and Chen, S. Simulation of Ca2+ oscillations in astrocytes mediated by amyloid beta in Alzheimer’s disease. BioRxiv, 2020-03, (2020).
37. [37] Liu, L., Gao, H., Li, J. and Chen, S. Probing microdomain Ca2+ activity and synaptic transmission with a node-based tripartite synapse model. Frontiers in Network Physiology, 3, 1111306, (2023).
38. [38] Zeng, S., Li, B., Zeng, S. and Chen, S. Simulation of spontaneous Ca2+ oscillations in astrocytes mediated by voltage-gated calcium channels. Biophysical Journal, 97(9), 2429-2437, (2009).
39. [39] Ermentrout, B. and Mahajan, A. Simulating, analyzing, and animating dynamical systems: a guide to XPPAUT for researchers and students. Applied Mechanics Reviews, 56(4), B53, (2003).