Mathematical model for IP$_{3}$ dependent calcium oscillations and mitochondrial associate membranes in non-excitable cells

Year 2024, Volume: 4 Issue: 3, 280 - 295, 30.09.2024

Neeraj Manhas

https://doi.org/10.53391/mmnsa.1503948

Abstract

Theoretical studies on calcium oscillations within the cytosolic [Ca$^{2+}$], and mitochondria [Ca$^{2+}$]$_{mit}$ have been conducted using a mathematical model-based approach. The model incorporates the mechanism of calcium-induced calcium release (CICR) through the activation of inositol-trisphosphate receptors (IPR), with a focus on the endoplasmic reticulum (ER) as an internal calcium store. The production of 1,4,5 inositol-trisphosphate (IP$_{3}$) through the phospholipase \(C\) isoforms and its degradation via Ca$^{2+}$ are considered, with IP$_{3}$ playing a crucial role in modulating calcium release from the ER. The model includes a simple kinetic mechanism for mitochondrial calcium uptake, release and physical connections between the ER and mitochondria, known as mitochondrial associate membrane complexes (MAMs), which influence cellular calcium homeostasis. Bifurcation analysis is used to explore the different dynamic properties of the model, identifying various regimes of oscillatory behavior and how these regimes change in response to different levels of stimulation, highlighting the complex regulatory mechanisms governing intracellular calcium signaling.

Keywords

Mitochondria-associated membranes, Hopf bifurcation, periodic doubling bifurcation, calcium oscillation

Ethical Statement

NIL

Supporting Institution

The author thanks Department of Mathematics, NIT, Raipur, to provide facilities to do this research.

Project Number

NiL

References

• [1] Berridge, M.J. Smooth muscle cell calcium activation mechanisms. The Journal of Physiology, 586(21), 5047-5061, (2008).
• [2] Südhof, T.C. Neurotransmitter release: the last millisecond in the life of a synaptic vesicle. Neuron, 80(3), 675-690, (2013).
• [3] Berridge, M., Lipp, P. and Bootman, M. Calcium signalling. Current Biology, 9(5), R157-R159, (1999).
• [4] Gerasimenko, J.V., Peng, S., Tsugorka, T. and Gerasimenko, O.V. Ca2+ signalling underlying pancreatitis. Cell Calcium, 70, 95-101, (2018).
• [5] Bartlett, P.J., Cloete, I., Sneyd, J. and Thomas, A.P. IP3-dependent Ca2+ oscillations switch into a dual oscillator mechanism in the presence of PLC-linked hormones. Iscience, 23(5), 101062, (2020).
• [6] Yule, D.I. and Gallacher, D.V. Oscillations of cytosolic calcium in single pancreatic acinar cells stimulated by acetylcholine. FEBS Letters, 239(2), 358-362, (1988).
• [7] Petersen, O.H. Local calcium spiking in pancreatic acinar cells. Ciba Foundation Symposium, 188, 85-103, (1995).
• [8] Raturi, A. and Simmen, T. Where the endoplasmic reticulum and the mitochondrion tie the knot: the mitochondria-associated membrane (MAM). Biochimica et Biophysica Acta (BBA)- Molecular Cell Research, 1833(1), 213-224, (2013).
• [9] Yang, M., Li, C., Yang, S., Xiao, Y., Xiong, X., Chen, W. et al. Mitochondria-associated ER membranes–the origin site of autophagy. Frontiers in Cell and Developmental Biology, 8, 595, (2020).
• [10] De Young, G.W. and Keizer, J. A single-pool inositol 1, 4, 5-trisphosphate-receptor-based model for agonist-stimulated oscillations in Ca2+ concentration. Proceedings of the National Academy of Sciences, 89(20), 9895-9899, (1992).
• [11] Atri, A., Amundson, J., Clapham, D. and Sneyd, J. A single-pool model for intracellular calcium oscillations and waves in the Xenopus laevis oocyte. Biophysical Journal, 65(4), 1727- 1739, (1993).
• [12] Dupont, G. and Swillens, S. Quantal release, incremental detection, and long-period Ca2+ oscillations in a model based on regulatory Ca2+-binding sites along the permeation pathway. Biophysical Journal, 71(4), 1714-1722, (1996).
• [13] Li, Y.X. and Rinzel, J. Equations for InsP3 receptor-mediated [Ca2+] i oscillations derived from a detailed kinetic model: a Hodgkin-Huxley like formalism. Journal of Theoretical Biology, 166(4), 461-473, (1994).
• [14] Bezprozvanny, I. Theoretical analysis of calcium wave propagation based on inositol (1, 4, 5)-trisphosphate (InsP3) receptor functional properties. Cell Calcium, 16(3), 151-166, (1994).
• [15] Cuthbertson, K.S.R. and Chay, T.R. Modelling receptor-controlled intracellular calcium oscillators. Cell Calcium, 12(2-3), 97-109, (1991).
• [16] Meyer, T. and Stryer, L. Molecular model for receptor-stimulated calcium spiking. Proceedings of the National Academy of Sciences, 85(14), 5051-5055, (1988).
• [17] 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).
• [18] Manhas, N. and Pardasani, K.R. Modelling mechanism of calcium oscillations in pancreatic acinar cells. Journal of Bioenergetics and Biomembranes, 46, 403-420, (2014).
• [19] 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, 463-484, (2014).
• [20] Manhas, N. and Anbazhagan, N. A mathematical model of intricate calcium dynamics and modulation of calcium signalling by mitochondria in pancreatic acinar cells. Chaos, Solitons & Fractals, 145, 110741, (2021).
• [21] Dupont, G., Falcke, M., Kirk, V. and Sneyd, J. Models of Calcium Signalling (Vol. 43). Springer: Switzerland, (2016).
• [22] Dupont, G., Swillens, S., Clair, C., Tordjmann, T. and Combettes, L. Hierarchical organization of calcium signals in hepatocytes: from experiments to models. Biochimica et Biophysica Acta (BBA)-Molecular Cell Research, 1498(2-3), 134-152, (2000).
• [23] Kummer, U., Olsen, L.F., Dixon, C.J., Green, A.K., Bornberg-Bauer, E. and Baier, G. Switching from simple to complex oscillations in calcium signaling. Biophysical Journal, 79(3), 1188-1195, (2000).
• [24] Ullah, G., Jung, P. and Machaca, K. Modeling Ca2+ signaling differentiation during oocyte maturation. Cell Calcium, 42(6), 556-564, (2007).
• [25] 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).
• [26] Naik, P.A. and Pardasani, K.R. Three-dimensional finite element model to study effect of RyR calcium channel, ER leak and SERCA pump on calcium distribution in oocyte cell. International Journal of Computational Methods, 16(01), 1850091, (2019).
• [27] Zhang, H., Zhang, S., Wang, W., Wang, K. and Shen, W. A mathematical model of the mouse atrial myocyte with inter-atrial electrophysiological heterogeneity. Frontiers in Physiology, 11, 972, (2020).
• [28] Greenstein, J.L. and Winslow, R.L. An integrative model of the cardiac ventricular myocyte incorporating local control of Ca2+ release. Biophysical Journal, 83(6), 2918-2945, (2002).
• [29] Bers, D.M. Cardiac excitation–contraction coupling. Nature, 415, 198-205, (2002).
• [30] Bhattacharyya, R. and Jha, B.K. Analyzing fuzzy boundary value problems: a study on the influence of mitochondria and ER fluxes on calcium ions in neuron cells. Journal of Bioenergetics and Biomembranes, 56, 15-29, (2024).
• [31] Jethanandani, H., Jha, B.K. and Ubale, M. The role of calcium dynamics with amyloid beta on neuron-astrocyte coupling. Mathematical Modelling and Numerical Simulation with Applications, 3(4), 376-390, (2023).
• [32] 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).
• [33] Ishii, K., Hirose, K. and Iino, M. Ca2+ shuttling between endoplasmic reticulum and mitochondria underlying Ca2+ oscillations. EMBO Reports, 7, 390-396, (2006).
• [34] Johnson, P.R., Dolman, N.J., Pope, M., Vaillant, C., Petersen, O.H., Tepikin, A.V. and Erdemli, G. Non-uniform distribution of mitochondria in pancreatic acinar cells. Cell and Tissue Research, 313, 37-45, (2003).
• [35] Tinel, H., Cancela, J.M., Mogami, H., Gerasimenko, J.V., Gerasimenko, O.V., Tepikin, A.V. and Petersen, O.H. Active mitochondria surrounding the pancreatic acinar granule region prevent spreading of inositol trisphosphate-evoked local cytosolic Ca2+ signals. The EMBO Journal, 18, 4999-5008, (1999).
• [36] Dyzma, M., Szopa, P. and Ka´zmierczak, B. Membrane associated complexes: new approach to calcium dynamics modelling. Mathematical Modelling of Natural Phenomena, 7(6), 167-186, (2012).
• [37] Marhl, M., Schuster, S. and Brumen, M. Mitochondria as an important factor in the maintenance of constant amplitudes of cytosolic calcium oscillations. Biophysical Chemistry, 71(2-3), 125-132, (1998).
• [38] Moshkforoush, A., Ashenagar, B., Tsoukias, N.M. and Alevriadou, B.R. Modeling the role of endoplasmic reticulum-mitochondria microdomains in calcium dynamics. Scientific Reports, 9, 17072, (2019).
• [39] Wacquier, B., Combettes, L., Van Nhieu, G.T. and Dupont, G. Interplay between intracellular Ca2+ oscillations and Ca2+-stimulated mitochondrial metabolism. Scientific Reports, 6, 19316, (2016).
• [40] Han, J.M. and Periwal, V. A mathematical model of calcium dynamics: Obesity and mitochondria-associated ER membranes. PLoS Computational Biology, 15(8), e1006661, (2019).
• [41] Doedel, E.J. AUTO: A program for the automatic bifurcation analysis of autonomous systems. In Proceedings, 10th Manitoba Conference on Numerical Mathematics and Computing, (Vol. 30) pp. 265-284, Winnipeg, Canada, (1981, September).
• [42] Sneyd, J. and Dufour, J.F. A dynamic model of the type-2 inositol trisphosphate receptor. Proceedings of the National Academy of Sciences, 99(4), 2398-2403, (2002).
• [43] Tsaneva-Atanasova, K., Yule, D.I. and Sneyd, J. Calcium oscillations in a triplet of pancreatic acinar cells. Biophysical Journal, 88(3), 1535-1551, (2005).
• [44] Politi, A., Gaspers, L.D., Thomas, A.P. and Höfer, T. Models of IP3 and Ca2+ oscillations: frequency encoding and identification of underlying feedbacks. Biophysical Journal, 90(9), 3120-3133, (2006).
• [45] Csordás, G., Várnai, P., Golenár, T., Roy, S., Purkins, G., Schneider, T. G. et al. Imaging interor-ganelle contacts and local calcium dynamics at the ER-mitochondrial interface. Molecular Cell, 39(1), 121-132, (2010).
• [46] Szopa, P., Dyzma, M. and Ka´zmierczak, B. Membrane associated complexes in calcium dynamics modelling. Physical Biology, 10(3), 035004, (2013).
• [47] Li, X., Zhang, S., Liu, X., Wang, X., Zhou, A. and Liu, P. Important role of MAMs in bifurcation and coherence resonance of calcium oscillations. Chaos, Solitons & Fractals, 106, 131-140, (2018).
• [48] Cloete, I., Bartlett, P.J., Kirk, V., Thomas, A.P. and Sneyd, J. Dual mechanisms of Ca2+ oscillations in hepatocytes. Journal of Theoretical Biology, 503, 110390, (2020).
• [49] Ventura, A.C. and Sneyd, J. Calcium oscillations and waves generated by multiple release mechanisms in pancreatic acinar cells. Bulletin of Mathematical Biology, 68, 2205-2231, (2006).
• [50] LeBeau, A.P., Yule, D.I., Groblewski, G.E. and Sneyd, J. Agonist-dependent phosphorylation of the inositol 1, 4, 5-trisphosphate receptor: a possible mechanism for agonist-specific calcium oscillations in pancreatic acinar cells. The Journal of General Physiology, 113(6), 851-872, (1999).
• [51] Heiske, M., Letellier, T. and Klipp, E. Comprehensive mathematical model of oxidative phosphorylation valid for physiological and pathological conditions. The FEBS Journal, 284(17), 2802-2828, (2017).
• [52] Zhang, J., Wang, X., Vikash, V., Ye, Q., Wu, D., Liu, Y. and Dong, W. ROS and ROS-mediated cellular signaling. Oxidative Medicine and Cellular Longevity, 2016, 4350965, (2016).
• [53] Murphy, M.P. How mitochondria produce reactive oxygen species. Biochemical Journal, 417(1), 1-13, (2009).
• [54] Criddle, D.N. Reactive oxygen species, Ca2+ stores and acute pancreatitis; a step closer to therapy?. Cell Calcium, 60(3), 180-189, (2016).
• [55] Chouchani, E.T., Pell, V.R., James, A.M., Work, L.M., Saeb-Parsy, K., Frezza, C. et al. A unifying mechanism for mitochondrial superoxide production during ischemia-reperfusion injury. Cell Metabolism, 23(2), 254-263, (2016).
• [56] Mazat, J.P., Devin, A. and Ransac, S. Modelling mitochondrial ROS production by the respiratory chain. Cellular and Molecular Life Sciences, 77, 455-465, (2020).
• [57] Quinlan, C.L., Orr, A.L., Perevoshchikova, I.V., Treberg, J.R., Ackrell, B.A. and Brand, M.D. Mitochondrial complex II can generate reactive oxygen species at high rates in both the forward and reverse reactions. Journal of Biological Chemistry, 287(32), 27255-27264, (2012).
• [58] Duong, Q.V., Levitsky, Y., Dessinger, M.J., Strubbe-Rivera, J.O. and Bazil, J.N. Identifying site-specific superoxide and hydrogen peroxide production rates from the mitochondrial electron transport system using a computational strategy. Function, 2(6), zqab050, (2021).
• [59] Manhas, N., Duong, Q.V., Lee, P., Richardson, J.D., Robertson, J.D., Moxley, M.A. and Bazil, J.N. Computationally modeling mammalian succinate dehydrogenase kinetics identifies the origins and primary determinants of ROS production. Journal of Biological Chemistry, 295(45), 15262-15279, (2020).
• [60] Manhas, N., Duong, Q.V., Lee, P. and Bazil, J.N. Analysis of mammalian succinate dehydro-genase kinetics and reactive oxygen species production. bioRxiv, 870501, (2019).
• [61] Chenna, S., Koopman, W.J., Prehn, J.H. and Connolly, N.M. Mechanisms and mathematical modeling of ROS production by the mitochondrial electron transport chain. American Journal of Physiology-Cell Physiology, 323(1), C69-C83, (2022).