[go: up one dir, main page]
Skip to main content
SpringerLink
Log in

Computational Model of Complex Calcium Dynamics: Store Operated Ca2+ Channels and Mitochondrial Associated Membranes in Pancreatic Acinar Cells

  • Original Paper
  • Published:
Cell Biochemistry and Biophysics Aims and scope Submit manuscript

Abstract

This proposed model explores the intricate Ca2+ dynamics within the pancreatic acinar cells (PACs) by emphasizing the role of store-operated Ca2+ entry (SOCE) and the mitochondrial-associated membranes (MAMs) in the secretory region (apical) of the PACs. Traditionally, Ca2+ releases from the endoplasmic reticulum (ER) via calcium-induced calcium release (CICR). It has been shown to be important in regulating functions such as secretion of digestive enzymes in PACs. However, this model posits that upon the depletion of Ca2+ in the ER, the signaling protein stromal interaction molecule (STIM1) is activated. Activated STIM1, then facilitates the opening of Orai channels, allowing Ca2+ influx through the store-operated calcium channels (SOCCs). The model highlights the complexity of the Ca2+ dynamics, and the importance of SOCE and MAMs in the PACs Ca2+ homeostasis. The numerical and bifurcation analysis illustrate how changes in agonist concentrations can lead to the diverse Ca2+ oscillation patterns, such as thin to broader oscillations, sinusoidal patterns, and baseline fluctuations, driven by the feedback mechanisms involving Ca2+ and inositol 1,4,5 trisphosphate (IP3). This understanding could have broader implications for cellular physiology and the development of therapies targeting Ca2+ signaling pathways.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Subscribe and save

Springer+ Basic
$34.99 /Month
  • Get 10 units per month
  • Download Article/Chapter or eBook
  • 1 Unit = 1 Article or 1 Chapter
  • Cancel anytime
Subscribe now

Buy Now

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8
Fig. 9

Similar content being viewed by others

References

  1. Berridge, M., Lipp, P. & Bootman, M. (1999). Calcium signalling. Current Biology, 9, R157–159. https://doi.org/10.1016/s0960-9822(99)80101-8.

    Article  CAS  PubMed  Google Scholar 

  2. Pallagi, P., Madácsy, T., Varga, Á. & Maléth, J. (2020). Intracellular Ca2+ signalling in the pathogenesis of acute pancreatitis: Recent advances and translational perspectives. International Journal of Molecular Sciences, 21, 4005. https://doi.org/10.3390/ijms21114005.

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  3. Gerasimenko, J. V., & Gerasimenko, O. V. (2023). The role of Ca2+ signalling in the pathology of exocrine pancreas. Cell Calcium, 112, 102740 https://doi.org/10.1016/j.ceca.2023.102740.

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  4. Gerasimenko, J. V., Flowerdew, S. E., Voronina, S. G., Sukhomlin, T. K., Tepikin, A. V., Petersen, O. H. & Gerasimenko, O. V. (2006). Bile acids induce Ca2+ release from both the endoplasmic reticulum and acidic intracellular calcium stores through activation of inositol trisphosphate receptors and ryanodine receptors. Journal of Biological Chemistry, 281, 40154–40163. https://doi.org/10.1074/jbc.M606402200.

    Article  CAS  PubMed  Google Scholar 

  5. Putney, J. W.(2011). The physiological function of store-operated calcium entry. Neurochemical Research, 36, 1157–1165. https://doi.org/10.1007/s11064-010-0383-0.

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  6. Zheng, S., Zhou, L., Ma, G., Zhang, T., Liu, J., Li, J., Nguyen, N. T., Zhang, X., Li, W., Nwokonko, R., Zhou, Y., Zhao, F., Liu, J., Huang, Y., Gill, D. L. & Wang, Y. (2018). Calcium store refilling and STIM activation in STIM- and Orai-deficient cell lines. Pflügers Archiv - European Journal of Physiology, 470, 1555–1567. https://doi.org/10.1007/s00424-018-2165-5.

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  7. Lunz, V., Romanin, C., & Frischauf, I. (2019). STIM1 activation of Orai1. Cell Calcium, 77, 29–38. https://doi.org/10.1016/j.ceca.2018.11.009.

    Article  CAS  PubMed  Google Scholar 

  8. Wang, Y., Deng, X., Zhou, Y., Hendron, E., Mancarella, S., Ritchie, M. F., Tang, X. D., Baba, Y., Kurosaki, T., Mori, Y., Soboloff, J. & Gill, D. L. (2009). STIM protein coupling in the activation of Orai channels. Proceedings of the National Academy of Sciences of the United States of America, 106, 7391–7396. https://doi.org/10.1073/pnas.0900293106.

    Article  PubMed  PubMed Central  Google Scholar 

  9. Petersen, O. H.(2009). Ca2+ signaling in pancreatic acinar cells: physiology and pathophysiology. The Brazilian Journal of Medical and Biological Research, 42, 9–16. https://doi.org/10.1590/S0100-879X2009000100003.

    Article  CAS  PubMed  Google Scholar 

  10. Putney, J. W., Steinckwich-Besançon, N., Numaga-Tomita, T., Davis, F. M., Desai, P. N., D’Agostin, D. M., Wu, S. & Bird, G. S. (2017). The functions of store-operated calcium channels. Biochimica et Biophysica Acta (BBA) - Molecular Cell Research, 1864, 900–906. https://doi.org/10.1016/j.bbamcr.2016.11.028.

    Article  CAS  PubMed  Google Scholar 

  11. Rosado, J. A. ed (2016). Calcium Entry Pathways in Non-excitable Cells. Cham: Springer International Publishing.

    Google Scholar 

  12. De Young, G. W. & Keizer, J. (1992). 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 of the United States of America, 89, 9895–9899. https://doi.org/10.1073/pnas.89.20.9895.

    Article  PubMed  PubMed Central  Google Scholar 

  13. Atri, A., Amundson, J., Clapham, D. & Sneyd, J. (1993). A single-pool model for intracellular calcium oscillations and waves in the Xenopus laevis oocyte. Biophysical Journal, 65, 1727–1739. https://doi.org/10.1016/S0006-3495(93)81191-3.

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  14. Shen, P., & Larter, R. (1995). Chaos in intracellular Ca2+ oscillations in a new model for non-excitable cells. Cell Calcium, 17, 225–232. https://doi.org/10.1016/0143-4160(95)90037-3.

    Article  CAS  PubMed  Google Scholar 

  15. LeBeau, A. P., Yule, D. I., Groblewski, G. E. & Sneyd, J. (1999). Agonist-dependent phosphorylation of the inositol 1,4,5-trisphosphate receptor. The Journal of General Physiology, 113, 851–872. https://doi.org/10.1085/jgp.113.6.851.

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  16. Giovannucci, D. R., Bruce, J. I. E., Straub, S. V., Arreola, J., Sneyd, J., Shuttleworth, T. J. & Yule, D. I. (2002). Cytosolic Ca(2+) and Ca(2+)-activated Cl(-) current dynamics: insights from two functionally distinct mouse exocrine cells. The Journal of Physiology, 540, 469–484. https://doi.org/10.1113/jphysiol.2001.013453.

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  17. Sneyd, J., Tsaneva-Atanasova, K., Bruce, J. I. E., Straub, S. V., Giovannucci, D. R. & Yule, D. I. (2003). A model of calcium waves in pancreatic and parotid acinar cells. Biophysical Journal, 85, 1392–1405. https://doi.org/10.1016/S0006-3495(03)74572-X.

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  18. Simpson, D., Kirk, V. & Sneyd, J. (2005). Complex oscillations and waves of calcium in pancreatic acinar cells. Physica D: Nonlinear Phenomena, 200, 303–324. https://doi.org/10.1016/j.physd.2004.11.006.

    Article  CAS  Google Scholar 

  19. Ventura, A. C. & Sneyd, J. (2006). Calcium oscillations and waves generated by multiple release mechanisms in pancreatic acinar cells. Bulletin of Mathematical Biology, 68, 2205–2231. https://doi.org/10.1007/s11538-006-9101-0.

    Article  PubMed  Google Scholar 

  20. Manhas, N., Sneyd, J. & Pardasani, K. R. (2014). Modelling the transition from simple to complex Ca2+ oscillations in pancreatic acinar cells. Journal of Biosciences, 39, 463–484. https://doi.org/10.1007/s12038-014-9430-3.

    Article  CAS  PubMed  Google Scholar 

  21. Manhas, N. & Pardasani, K. R. (2014). Modelling mechanism of calcium oscillations in pancreatic acinar cells. Journal of Bioenergetics and Biomembranes, 46, 403–420. https://doi.org/10.1007/s10863-014-9561-0.

    Article  CAS  PubMed  Google Scholar 

  22. Tsaneva-Atanasova, K., Yule, D. I. & Sneyd, J. (2005). Calcium oscillations in a triplet of pancreatic acinar cells. Biophysical Journal, 88, 1535–1551. https://doi.org/10.1529/biophysj.104.047357.

    Article  CAS  PubMed  Google Scholar 

  23. Manhas, N. & Anbazhagan, N. (2021). A mathematical model of intricate calcium dynamics and modulation of calcium signalling by mitochondria in pancreatic acinar cells. Chaos Solitons Fractals, 145, 110741 https://doi.org/10.1016/j.chaos.2021.110741.

    Article  Google Scholar 

  24. Bertram, R., Gram Pedersen, M., Luciani, D. S. & Sherman, A. (2006). A simplified model for mitochondrial ATP production. Journal of Theoretical Biology, 243, 575–586. https://doi.org/10.1016/j.jtbi.2006.07.019.

    Article  CAS  PubMed  Google Scholar 

  25. Magnus, G. & Keizer, J. (1998). Model of β-cell mitochondrial calcium handling and electrical activity. I. Cytoplasmic variables. The American Journal of Physiology-Cell Physiology, 274, C1158–C1173. https://doi.org/10.1152/ajpcell.1998.274.4.C1158.

    Article  CAS  Google Scholar 

  26. Magnus, G. & Keizer, J. (1998). Model of β-cell mitochondrial calcium handling and electrical activity. II. Mitochondrial variables. The American Journal of Physiology-Cell Physiology, 274, C1174–C1184. https://doi.org/10.1152/ajpcell.1998.274.4.C1174.

    Article  CAS  Google Scholar 

  27. Han, J. M. & Periwal, V. (2019). A mathematical model of calcium dynamics: Obesity and mitochondria-associated ER membranes. PLOS Computational Biology, 15, e1006661. https://doi.org/10.1371/journal.pcbi.1006661.

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  28. Qi, H., Li, L. & Shuai, J. (2015). Optimal microdomain crosstalk between endoplasmic reticulum and mitochondria for Ca2+ oscillations. Scientific Reports, 5, 7984. https://doi.org/10.1038/srep07984.

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  29. Marhl, M., Schuster, S. & Brumen, M. (1998). Mitochondria as an important factor in the maintenance of constant amplitudes of cytosolic calcium oscillations. Biophysical Chemistry, 2, 125–132.

    Article  CAS  PubMed  Google Scholar 

  30. Marhl, M., Schuster, S., Brumen, M. & Heinrich, R. (1997). Modeling the interrelations between the calcium oscillations and ER membrane potential oscillations. Biophysical Chemistry, 63, 221–239. https://doi.org/10.1016/s0301-4622(96)02248-x.

    Article  CAS  PubMed  Google Scholar 

  31. Dyzma, M., Szopa, P. & Kaźmierczak, B. (2012). Membrane associated complexes: New approach to calcium dynamics modelling. The Mathematical Modelling of Natural Phenomena, 7, 167–186. https://doi.org/10.1051/mmnp/20127608.

    Article  CAS  Google Scholar 

  32. Li, Y. X., Stojilković, S. S., Keizer, J. & Rinzel, J. (1997). Sensing and refilling calcium stores in an excitable cell. Biophysical Journal, 72, 1080–1091. https://doi.org/10.1016/S0006-3495(97)78758-7.

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  33. Wiesner, T. F., Berk, B. C. & Nerem, R. M. (1996). A mathematical model of cytosolic calcium dynamics in human umbilical vein endothelial cells. The American Journal of Physiology-Cell Physiology, 270, C1556–C1569. https://doi.org/10.1152/ajpcell.1996.270.5.C1556.

    Article  CAS  Google Scholar 

  34. Kowalewski, J. M., Uhlén, P., Kitano, H. & Brismar, H. (2006). Modeling the impact of store-operated Ca2+ entry on intracellular Ca2+ oscillations. Mathematical Biosciences, 204, 232–249. https://doi.org/10.1016/j.mbs.2006.03.001.

    Article  CAS  PubMed  Google Scholar 

  35. Liu, W., Tang, F. & Chen, J. (2010). Designing dynamical output feedback controllers for store-operated Ca2+ entry. Mathematical Biosciences, 228, 110–118. https://doi.org/10.1016/j.mbs.2010.08.013.

    Article  CAS  PubMed  Google Scholar 

  36. Croisier, H., Tan, X., Perez-Zoghbi, J. F., Sanderson, M. J., Sneyd, J., & Brook, B. S. (2013). Activation of store-operated calcium entry in airway smooth muscle cells: insight from a mathematical model. PLoS ONE, 8, e69598 https://doi.org/10.1371/journal.pone.0069598.

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  37. Yoast, R. E., Emrich, S. M., Zhang, X., Xin, P., Johnson, M. T., Fike, A. J., Walter, V., Hempel, N., Yule, D. I., Sneyd, J., Gill, D. L. & Trebak, M. (2020). The native ORAI channel trio underlies the diversity of Ca2+ signaling events. Nature Communications, 11, 2444. https://doi.org/10.1038/s41467-020-16232-6.

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  38. Emrich, S. M., Yoast, R. E., Xin, P., Arige, V., Wagner, L. E., Hempel, N., Gill, D. L., Sneyd, J., Yule, D. I. & Trebak, M. (2021). Omnitemporal choreographies of all five STIM/Orai and IP3Rs underlie the complexity of mammalian Ca2+ signaling. Cell Reports, 34, 108760. https://doi.org/10.1016/j.celrep.2021.108760.

    Article  CAS  PubMed  Google Scholar 

  39. Octors, C., Yoast, R. E., Emrich, S. M., Trebak, M. & Sneyd, J. (2024). Calcium oscillations in HEK293 cells lacking SOCE suggest the existence of a balanced regulation of IP3 production and degradation. Frontiers in Systems Biology, 4, 1343006. https://doi.org/10.3389/fsysb.2024.1343006.

    Article  Google Scholar 

  40. Sneyd, J. & Dufour, J.-F. (2002). A dynamic model of the type-2 inositol trisphosphate receptor. Proceedings of the National Academy of Sciences of the United States of America, 99, 2398–2403. https://doi.org/10.1073/pnas.032281999.

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  41. Keizer, J. & Levine, L. (1996). Ryanodine receptor adaptation and Ca2+(-)induced Ca2+ release-dependent Ca2+ oscillations. Biophysical Journal, 71, 3477–3487. https://doi.org/10.1016/S0006-3495(96)79543-7.

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  42. Politi, A., Gaspers, L. D., Thomas, A. P. & Höfer, T. (2006). Models of IP3 and Ca2+ oscillations: Frequency encoding and identification of underlying feedbacks. Biophysical Journal, 90, 3120–3133. https://doi.org/10.1529/biophysj.105.072249.

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  43. Doedel EJ: A programe for the automatic bifurcation analysis of autonomus systems. 30, 263–385 (1981)

  44. Dingsdale, H., Voronina, S., Haynes, L., Tepikin, A. & Lur, G. (2012). Cellular geography of IP3 receptors, STIM and Orai: a lesson from secretory epithelial cells. Biochemical Society Transactions, 40, 108–111. https://doi.org/10.1042/BST20110639.

    Article  CAS  PubMed  Google Scholar 

  45. Hong, J. H., Li, Q., Kim, M. S., Shin, D. M., Feske, S., Birnbaumer, L., Cheng, K. T., Ambudkar, I. S. & Muallem, S. (2011). Polarized but differential localization and recruitment of STIM1, Orai1 and TRPC channels in secretory cells. Traffic, 12, 232–245. https://doi.org/10.1111/j.1600-0854.2010.01138.x.

    Article  CAS  PubMed  Google Scholar 

  46. Ishii, K., Hirose, K. & Iino, M. (2006). Ca2+ shuttling between endoplasmic reticulum and mitochondria underlying Ca2+ oscillations. EMBO Reports, 7, 390–396. https://doi.org/10.1038/sj.embor.7400620.

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  47. Tinel, H. (1999). Active mitochondria surrounding the pancreatic acinar granule region prevent spreading of inositol trisphosphate-evoked local cytosolic Ca2+ signals. EMBO Journal, 18, 4999–5008. https://doi.org/10.1093/emboj/18.18.4999.

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  48. Patterson, R.L., van Rossum, D.B., Gill, D.L.: Store-operated Ca2+Entry: Evidence for a secretion-like coupling model. Cell. 98, https://doi.org/10.1016/s0092-8674(00)81977-7

  49. Bolotina, V. M. & Csutora, P. (2005). CIF and other mysteries of the store-operated Ca2+-entry pathway. Trends in Biochemical Sciences, 30, 378–387. https://doi.org/10.1016/j.tibs.2005.05.009.

    Article  CAS  PubMed  Google Scholar 

  50. Feske, S.(2012). Physiological and pathophysiological functions of SOCE in the immune system. Frontiers in Bioscience, E4, 2253–2268. https://doi.org/10.2741/e540.

    Article  Google Scholar 

  51. Li, J., Zhou, R., Zhang, J. & Li, Z.-F. (2014). Calcium signaling of pancreatic acinar cells in the pathogenesis of pancreatitis. World Journal of Gastroenterol., 20, 16146. https://doi.org/10.3748/wjg.v20.i43.16146.

    Article  CAS  Google Scholar 

  52. Núñez, L., Bird, G. S., Hernando-Pérez, E., Pérez-Riesgo, E., Putney, J. W. & Villalobos, C. (2019). Store-operated Ca2+ entry and Ca2+ responses to hypothalamic releasing hormones in anterior pituitary cells from Orai1−/− and heptaTRPC knockout mice. Biochimica et Biophysica Acta (BBA) - Molecular Cell Research, 1866, 1124–1136. https://doi.org/10.1016/j.bbamcr.2018.11.006.

    Article  CAS  PubMed  Google Scholar 

  53. Parekh, A. B.(2006). On the activation mechanism of store-operated calcium channels. Pflügers Archiv: European Journal of Physiology, 453, 303–311. https://doi.org/10.1007/s00424-006-0089-y.

    Article  CAS  PubMed  Google Scholar 

  54. Zhang, I. & Hu, H. (2020). Store-operated calcium channels in physiological and pathological states of the nervous system. Frontiers in Cellular Neuroscience, 14, 600758. https://doi.org/10.3389/fncel.2020.600758.

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  55. Petersen, O. H. (2005). Ca2+ signalling and Ca2+-activated ion channels in exocrine acinar cells. Cell Calcium, 38, 171–200. https://doi.org/10.1016/j.ceca.2005.06.024.

    Article  CAS  PubMed  Google Scholar 

  56. Halangk, W. & Lerch, M. M. (2009). A unique pancreatic mitochondrial response to calcium and its role in apoptosis. Gut, 58, 328–330. https://doi.org/10.1136/gut.2008.160069.

    Article  PubMed  Google Scholar 

  57. Low, J. T., Shukla, A. & Thorn, P. (2010). Pancreatic acinar cell: new insights into the control of secretion. The International Journal of Biochemistry & Cell Biology, 42, 1586–1589. https://doi.org/10.1016/j.biocel.2010.07.006.

    Article  CAS  Google Scholar 

  58. Petersen, O. H., Gerasimenko, J. V., Gerasimenko, O. V., Gryshchenko, O. & Peng, S. (2021). The roles of calcium and ATP in the physiology and pathology of the exocrine pancreas. Physiological Reviews, 101, 1691–1744. https://doi.org/10.1152/physrev.00003.2021.

    Article  PubMed  Google Scholar 

  59. Ashby, M. C., Craske, M., Park, M. K., Gerasimenko, O. V., Burgoyne, R. D., Petersen, O. H. & Tepikin, A. V. (2002). Localized Ca2+ uncaging reveals polarized distribution of Ca2+-sensitive Ca2+ release sites. Journal of Cell Biology, 158, 283–292. https://doi.org/10.1083/jcb.200112025.

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  60. Lur, G., Sherwood, M. W., Ebisui, E., Haynes, L., Feske, S., Sutton, R., Burgoyne, R. D., Mikoshiba, K., Petersen, O. H. & Tepikin, A. V. (2011). Ins P 3 receptors and Orai channels in pancreatic acinar cells: co-localization and its consequences. Biochemical Journal, 436, 231–239. https://doi.org/10.1042/BJ20110083.

    Article  CAS  PubMed  Google Scholar 

  61. Williams, J. A.(2019). Cholecystokinin (CCK) regulation of pancreatic acinar cells: Physiological actions and signal transduction mechanisms. Comprehensive Physiology, 9, 535–564. https://doi.org/10.1002/cphy.c180014.

    Article  PubMed  Google Scholar 

  62. Dupont, G., Falcke, M., Kirk, V. & Sneyd, J. (2016). Models of Calcium Signalling. Cham: Springer International Publishing.

    Book  Google Scholar 

  63. Keener, J. & Sneyd, J. (1998). Mathematical Physiology. New York, NY: Springer New York.

    Book  Google Scholar 

  64. Perc, M., Rupnik, M., Gosak, M. & Marhl, M. (2009). Prevalence of stochasticity in experimentally observed responses of pancreatic acinar cells to acetylcholine. Chaos: An Interdisciplinary Journal of Nonlinear Science, 19, 037113. https://doi.org/10.1063/1.3160017.

    Article  CAS  Google Scholar 

Download references

Acknowledgements

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

Author contributions:

N.M.: Conceptualization, Methodology, Software, Investigation, Writing-original draft preparation, Writing-reviewing and editing.

Author information

Authors and Affiliations

  1. Department of Mathematics, National Institute of Technology, Raipur, Chhattisgarh, 492010, India

    Neeraj Manhas

Authors
  1. Neeraj Manhas
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Neeraj Manhas.

Ethics declarations

Conflict of interest

The author declares no competing interests.

Additional information

Publisher’s note Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Appendix A

Appendix A

$$\frac{d[C{a}^{2+}]}{dt}={J}_{rel}+\delta ({J}_{in}-{J}_{Pmca})-{J}_{Serca}-{J}_{Uni}+{J}_{NCX}-{J}_{RaM}$$
(A1)
$$\frac{d{[C{a}^{2+}]}_{er}}{dt}=\gamma (-{J}_{rel}+{J}_{Serca})-\rho {J}_{MAM}$$
(A2)
$$\frac{d{[C{a}^{2+}]}_{m}}{dt}=\tau ({J}_{Uni}-{J}_{ncx}+{J}_{RaM})+\rho {J}_{MAM}$$
(A3)
$$\frac{d[{\rm{I}}{{\rm{P}}}_{3}]}{dt}=({J}_{I{P}_{3}prod}-\,{J}_{I{P}_{3}{\rm{deg}} })$$
(A4)
$$\frac{d[{{\rm{P}}}_{SO}]}{dt}=({P}_{SO}^{\infty }-\,{P}_{SO})/{\tau }_{s}$$
(A5)

Also, here

$${J}_{rel}\,=\,{J}_{\begin{array}{c}IPR\end{array}}\,+{J}_{RyR}\,+{J}_{er}$$
(A6)
$$\frac{dR}{dt}={\phi }_{-2}O-{\phi }_{2}[I{P}_{3}]R+({k}_{-1}+{l}_{-2}){I}_{1}-{\phi }_{1}R$$
(A7)
$$\frac{dO}{dt}={\phi }_{2}[I{P}_{3}]R-({\phi }_{-2}+{\phi }_{4}+{\phi }_{3})O+{\phi }_{-4}A+{k}_{-3}S$$
(A8)
$$\frac{dA}{dt}={\phi }_{4}O-{\phi }_{-4}A-{\phi }_{5}A+({k}_{-1}+{l}_{-2}){I}_{2}$$
(A9)
$$\frac{d{I}_{1}}{dt}={\phi }_{1}R-({k}_{-1}+{l}_{-2}){I}_{1}$$
(A10)
$$\frac{d{I}_{2}}{dt}={\phi }_{5}A-({k}_{-1}+{l}_{-2}){I}_{2}$$
(A11)
$$\frac{dw}{dt}=\frac{{k}_{c}^{-}({w}^{\infty }[C{a}^{2+}]-w)}{{w}^{\infty }[C{a}^{2+}]}$$
(A12)
$${P}_{IPR}={(0.1O+0.9A)}^{4}:{\rm{open}}\,{\rm{probability}}\,{\rm{of}}\,{\rm{IPR}}$$
(A13)
$$S+A+O+{I}_{1}+{I}_{2}=1$$
(A14)
$${J}_{IPR}={k}_{IPR}{P}_{IPR}({[C{a}^{2+}]}_{er}-[C{a}^{2+}])$$
(A15)

All ∅’s are saturating binding rate and are function of [Ca2+] derived from [40].

$${\phi }_{1}[C{a}^{2+}]=\frac{({k}_{1}{L}_{1}+{l}_{2})[C{a}^{2+}]}{{L}_{1}+[C{a}^{2+}]\left(1+\frac{{L}_{1}}{{L}_{3}}\right)}$$
(A16)
$${\phi }_{2}[C{a}^{2+}]=\frac{{k}_{2}{L}_{3}+{l}_{4}[C{a}^{2+}]}{{L}_{3}+[C{a}^{2+}]\left(1+\frac{{L}_{3}}{{L}_{1}}\right)}$$
(A17)
$${\phi }_{-2}[C{a}^{2+}]=\frac{{k}_{-2}+{l}_{-4}[C{a}^{2+}]}{\left(1+\frac{[C{a}^{2+}]}{{L}_{5}}\right)}$$
(A18)
$${\phi }_{3}[C{a}^{2+}]=\frac{{k}_{3}{L}_{5}}{{L}_{5}+[C{a}^{2+}]}$$
(A19)
$${\phi }_{4}[C{a}^{2+}]=\frac{({k}_{4}{L}_{5}+{l}_{6})[C{a}^{2+}]}{{L}_{5}+[C{a}^{2+}]}$$
(A20)
$${\phi }_{-4}[C{a}^{2+}]=\frac{{L}_{1}({k}_{-4}+{l}_{-6})}{{L}_{1}+[C{a}^{2+}]}$$
(A21)
$${\phi }_{5}[C{a}^{2+}]=\frac{({k}_{1}{L}_{1}+{l}_{2})[C{a}^{2+}]}{{L}_{1}+[C{a}^{2+}]}$$
(A22)
$${P}_{RyR}=\frac{w\left(1+{([C{a}^{2+}]/{K}_{b})}^{3}\right)}{\left(1+{({K}_{a}/[C{a}^{2+}])}^{4}+{([C{a}^{2+}]/{K}_{b})}^{3}\right)};{\rm{RyR}}\,{\rm{open}}\,{\rm{probability}}$$
(A23)
$${w}^{\infty }[C{a}^{2+}]=\frac{\left(1+{({K}_{a}/[C{a}^{2+}])}^{4}+{([C{a}^{2+}]/{K}_{b})}^{3}\right)}{\left(1+(1/{K}_{c})+{({K}_{a}/[C{a}^{2+}])}^{4}+{([C{a}^{2+}]/{K}_{b})}^{3}\right)}$$
(A24)

Here

$${K}_{a}=\root4\of{{k}_{a}^{-}/{k}_{a}^{+}};\,{K}_{b}=\root3\of{{k}_{b}^{-}/{k}_{b}^{+}};{K}_{c}={k}_{c}^{-}/{k}_{c}^{+}$$
(A25)
$${J}_{RyR}={k}_{RyR}{P}_{RyR}({[C{a}^{2+}]}_{er}-[C{a}^{2+}])$$
(A26)
$${J}_{in}\,=\,{J}_{\begin{array}{c}leak\end{array}}\,+{J}_{Rocc}\,+\,{J}_{socc}\,$$
(A27)
$${J}_{leak}={\alpha }_{0}$$
(A28)
$${J}_{Rocc}={\alpha }_{1}{v}_{PLC}$$
(A29)
$${J}_{Soce}={V}_{Soce}{P}_{So}$$
(A30)
$${P}_{SO}^{\infty }=\frac{{K}_{Soce}^{4}}{{K}_{Soce}^{4}+{[C{a}^{2+}]}_{er}^{4}}$$
(A31)
$${J}_{er}=0.002{s}^{-1},$$
(A32)
$${J}_{Pmca}={V}_{Pmca}\frac{{[C{a}^{2+}]}^{2}}{{K}_{Pmca}^{2}+{[C{a}^{2+}]}^{2}}$$
(A33)
$${J}_{Serca}={V}_{Serca}\frac{[C{a}^{2+}]}{{K}_{Serca}+[C{a}^{2+}]}\times \frac{1}{{[C{a}^{2+}]}_{er}}$$
(A34)
$${J}_{I{P}_{3},prod}=\,\left({v}_{PLC}\frac{{[C{a}^{2+}]}^{2}}{{[C{a}^{2+}]}^{2}+{k}_{PLC}^{2}}\right)$$
(A35)
$${J}_{I{P}_{3},{\rm{deg}} }=\,\left(\,{k}_{{\rm{deg}} }\,(\frac{{[C{a}^{2+}]}^{2}}{{[C{a}^{2+}]}^{2}\,+\,{K}_{{\rm{deg}} }^{2}})[I{P}_{3}]\right)$$
(A36)
$${J}_{Uni}={V}_{Uni}\left(\frac{{[C{a}^{2+}]}^{4}}{{K}_{Uni}^{4}+{[C{a}^{2+}]}^{4}}\right)$$
(A37)
$${J}_{NCX}={v}_{NCX}\frac{{[N{a}^{+}]}_{cyto}^{3}}{{k}_{Na}^{3}+{[N{a}^{+}]}_{cyto}^{3}}\frac{{[C{a}^{2+}]}_{m}}{{k}_{NCX}+{[C{a}^{2+}]}_{m}}$$
(A38)
$${J}_{MAM}={V}_{MAM}\left(\frac{{[C{a}^{2+}]}_{er}^{4}}{{K}_{MAM}^{4}+{[C{a}^{2+}]}_{er}^{4}}\right)$$
(A39)
$${J}_{RaM}=\,{V}_{RaM}\left(\frac{{[C{a}^{2+}]}^{8}}{{K}_{RaM}^{8}+{[C{a}^{2+}]}^{8}}\right)$$
(A40)

Model without SOCC and mitochondria, and MAMs: Appendix B

For model without SOCC, Mitochondria and MAMs, the Eq. A1 is modified as

$$\begin{array}{l}\frac{d[C{a}^{2+}]}{dt}={J}_{rel}+\delta ({J}_{in}-{J}_{Pmca})-{J}_{Serca}\,;\,{\rm{here}}\,{J}_{in}=J_{leak}+{J}_{Rocc}\,;\\ \frac{d{[C{a}^{2+}]}_{er}}{dt}=\gamma (-{J}_{rel}+{J}_{Serca})\end{array}$$
(B1)

And the model is simulated without A3, A5, A29, A30, A36, A37, A38 and A39.

Model with SOCC, without mitochondria and MAMs: Appendix C

Model with SOCC and without Mitochondria, the Eq. A1 is modified as

$$\begin{array}{l}\frac{d[C{a}^{2+}]}{dt}={J}_{rel}+\delta ({J}_{in}-{J}_{Pmca})-{J}_{Serca}\,;\,{\rm{here}}\,{J}_{in}={J}_{\begin{array}{c}leak\end{array}}+{J}_{Rocc}+{J}_{socc};\\ \frac{d{[C{a}^{2+}]}_{er}}{dt}=\gamma (-{J}_{rel}+{J}_{Serca})\end{array}$$
(C1)

And the model is simulated without A3, A36, A37 A38 and A39.

Rights and permissions

Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Manhas, N. Computational Model of Complex Calcium Dynamics: Store Operated Ca2+ Channels and Mitochondrial Associated Membranes in Pancreatic Acinar Cells. Cell Biochem Biophys (2024). https://doi.org/10.1007/s12013-024-01484-6

Download citation

  • Accepted:

  • Published:

  • DOI: https://doi.org/10.1007/s12013-024-01484-6

Keywords

Search

Navigation