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Bulletin of Mathematical Biology

, Volume 81, Issue 5, pp 1394–1426 | Cite as

A Model of \(\hbox {Ca}^{2+}\) Dynamics in an Accurate Reconstruction of Parotid Acinar Cells

  • Nathan PagesEmail author
  • Elías Vera-Sigüenza
  • John Rugis
  • Vivien Kirk
  • David I. Yule
  • James Sneyd
Article

Abstract

We have constructed a spatiotemporal model of \(\hbox {Ca}^{2+}\) dynamics in parotid acinar cells, based on new data about the distribution of inositol trisphophate receptors (IPR). The model is solved numerically on a mesh reconstructed from images of a cluster of parotid acinar cells. In contrast to our earlier model (Sneyd et al. in J Theor Biol 419:383–393. https://doi.org/10.1016/j.jtbi.2016.04.030, 2017b), which cannot generate realistic \(\hbox {Ca}^{2+}\) oscillations with the new data on IPR distribution, our new model reproduces the \(\hbox {Ca}^{2+}\) dynamics observed in parotid acinar cells. This model is then coupled with a fluid secretion model described in detail in a companion paper: A mathematical model of fluid transport in an accurate reconstruction of a parotid acinar cell (Vera-Sigüenza et al. in Bull Math Biol. https://doi.org/10.1007/s11538-018-0534-z, 2018b). Based on the new measurements of IPR distribution, we show that Class I models (where \(\hbox {Ca}^{2+}\) oscillations can occur at constant [\(\hbox {IP}_3\)]) can produce \(\hbox {Ca}^{2+}\) oscillations in parotid acinar cells, whereas Class II models (where [\(\hbox {IP}_3\)] needs to oscillate in order to produce \(\hbox {Ca}^{2+}\) oscillations) are unlikely to do so. In addition, we demonstrate that coupling fluid flow secretion with the \(\hbox {Ca}^{2+}\) signalling model changes the dynamics of the \(\hbox {Ca}^{2+}\) oscillations significantly, which indicates that \(\hbox {Ca}^{2+}\) dynamics and fluid flow cannot be accurately modelled independently. Further, we determine that an active propagation mechanism based on calcium-induced calcium release channels is needed to propagate the \(\hbox {Ca}^{2+}\) wave from the apical region to the basal region of the acinar cell.

Keywords

Calcium dynamics Inositol triphosphate receptors Fluid secretion Finite-element modelling Parotid acinar cells 

Notes

Acknowledgements

This work was supported by the National Institutes of Health grant number RO1DE019245-10 and by the Marsden Fund of the Royal Society of New Zealand. High-performance computing facilities and support were provided by the New Zealand eScience Infrastructure (NeSI) funded jointly by NeSI’s collaborator institutions and through the Ministry of Business, Innovation and Employment’s Research Infrastructure programme. Thanks to NVIDIA Corporation for a K40 GPU grant.

Supplementary material

Supplementary material 1 (mp4 121237 KB)

11538_2018_563_MOESM2_ESM.pdf (8.4 mb)
Supplementary material 2 (pdf 8601 KB)

References

  1. Boltcheva D, Yvinec M, Boissonnat J (2009) Mesh generation from 3d multi-material images. In: International conference on medical image computing and computer-assisted intervention, pp 283–290.  https://doi.org/10.1007/978-3-642-04271-3_35
  2. Bruce JI, Shuttleworth TJ, Giovannucci DR, Yule DI (2002) Phosphorylation of inositol 1, 4, 5-trisphosphate receptors in parotid acinar cells. A mechanism for the synergistic effects of cAMP on \(\text{ Ca }^{2+}\) signaling. J Biol Chem 277(2):1340–1348.  https://doi.org/10.1074/jbc.M106609200 CrossRefGoogle Scholar
  3. De Young GW, Keizer J (1992) A single-pool inositol 1, 4, 5-trisphosphate-receptor-based model for agonist-stimulated oscillations in \(\text{ Ca }^{2+}\) concentration. Proc Natl Acad Sci 89(20):9895–9899.  https://doi.org/10.1073/pnas.89.20.9895 CrossRefGoogle Scholar
  4. Desbrun M, Meyer M, Schröder P, Barr A (1999) Implicit fairing of irregular meshes using diffusion and curvature flow. In: Proceedings of the 26th annual conference on computer graphics and interactive techniques SIGGRAPH ’99, pp 317–324.  https://doi.org/10.1145/311535.311576
  5. Dickinson GD, Ellefsen KL, Dawson SP, Pearson JE, Parker I (2016) Hindered cytoplasmic diffusion of inositol trisphosphate restricts its cellular range of action. Sci Signal 9(453):ra108CrossRefGoogle Scholar
  6. Dupont G, Erneux C (1997) Simulations of the effects of inositol 1, 4, 5-trisphosphate 3-kinase and 5-phosphatase activities on \(\text{ Ca }^{2+}\) oscillations. Cell Calcium 22(5):321–331.  https://doi.org/10.1016/S0143-4160(97)90017-8 CrossRefGoogle Scholar
  7. Dupont G, Goldbeter A (1993) One-pool model for \(\text{ Ca }^{2+}\) oscillations involving \(\text{ Ca }^{2+}\) and inositol 1, 4, 5-trisphosphate as co-agonists for \(\text{ Ca }^{2+}\) release. Cell Calcium 14(4):311–322CrossRefGoogle Scholar
  8. Dupont G, Falcke M, Kirk V, Sneyd J (2016) Models of calcium signalling, vol 43. Springer, New YorkzbMATHGoogle Scholar
  9. Friel D (1995) [\(\text{ Ca }^{2+}\)]\(_i\) oscillations in sympathetic neurons: an experimental test of a theoretical model. Biophys J 68(5):1752–1766.  https://doi.org/10.1016/S0006-3495(95)80352-8 CrossRefGoogle Scholar
  10. Gaspers LD, Bartlett PJ, Politi A, Burnett P, Metzger W, Johnston J, Joseph SK, Höfer T, Thomas AP (2014) Hormone-induced calcium oscillations depend on cross-coupling with inositol 1, 4, 5-trisphosphate oscillations. Cell Rep 9(4):1209–1218.  https://doi.org/10.1016/j.celrep.2014.10.033 CrossRefGoogle Scholar
  11. Geuzaine C, Remacle J (2009) Gmsh: a 3-d finite element mesh generator with built-in pre- and post-processing facilities. Int J Numer Methods Eng 79:1309–1331.  https://doi.org/10.1002/nme.2579 MathSciNetCrossRefzbMATHGoogle Scholar
  12. Harootunian AT, Kao JP, Paranjape S, Tsien RY (1991) Generation of calcium oscillations in fibroblasts by positive feedback between calcium and IP\(_3\). Science 251:75–78.  https://doi.org/10.1126/science.1986413 CrossRefGoogle Scholar
  13. Kasai H, Li YX, Miyashita Y (1993) Subcellular distribution of \(\text{ Ca }^{2+}\) release channels underlying \(\text{ Ca }^{2+}\) waves and oscillations in exocrine pancreas. Cell 74(4):669–677.  https://doi.org/10.1016/0092-8674(93)90514-Q CrossRefGoogle Scholar
  14. Keizer J, Levine L (1996) Ryanodine receptor adaptation and \(\text{ Ca }^{2+}\) (-) induced \(\text{ Ca }^{2+}\) release-dependent \(\text{ Ca }^{2+}\) oscillations. Biophys J 71(6):3477–3487.  https://doi.org/10.1016/S0006-3495(96)79543-7 CrossRefGoogle Scholar
  15. Krane CM, Melvin JE, Nguyen H-V, Richardson L, Towne JE, Doetschman T, Menon AG (2001) Salivary acinar cells from aquaporin 5-deficient mice have decreased membrane water permeability and altered cell volume regulation. J Biol Chem 276(26):23,413–23,420.  https://doi.org/10.1074/jbc.M008760200 CrossRefGoogle Scholar
  16. Lee MG, Xu X, Zeng W, Diaz J, Wojcikiewicz RJ, Kuo TH, Wuytack F, Racymaekers L, Muallem S (1997) Polarized expression of \(\text{ Ca }^{2+}\) channels in pancreatic and salivary gland cells. Correlation with initiation and propagation of [\(\text{ Ca }^{2+}\)]\(_i\) waves. J Biol Chem 272(25):15,765–15,770.  https://doi.org/10.1074/jbc.272.25.15765 CrossRefGoogle Scholar
  17. Leite MF, Burgstahler AD, Nathanson MH (2002) \(\text{ Ca }^{2+}\) waves require sequential activation of inositol trisphosphate receptors and ryanodine receptors in pancreatic acini. Gastroenterology 122(2):415–427.  https://doi.org/10.1053/gast.2002.30982 CrossRefGoogle Scholar
  18. MacLennan DH, Rice WJ, Green NM (1997) The mechanism of \(\text{ Ca }^{2+}\) transport by sarco (endo) plasmic reticulum \(\text{ Ca }^{2+}\)-ATPases. J Biol Chem 272(46):28,815–28,818.  https://doi.org/10.1074/jbc.272.46.28815 CrossRefGoogle Scholar
  19. Means S, Smith AJ, Shepherd J, Shadid J, Fowler J, Wojcikiewicz RJ, Mazel T, Smith GD, Wilson BS (2006) Reaction diffusion modeling of calcium dynamics with realistic ER geometry. Biophys J 91(2):537–557CrossRefGoogle Scholar
  20. Nathanson MH, Fallon MB, Padfield PJ, Maranto AR (1994) Localization of the type 3 inositol 1, 4, 5-trisphosphate receptor in the \(\text{ Ca }^{2+}\) wave trigger zone of pancreatic acinar cells. J Biol Chem 269(7):4693–4696Google Scholar
  21. Nezu A, Morita T, Tanimura A (2015) In vitro and in vivo imaging of intracellular \(\text{ Ca }^{2+}\) responses in salivary gland cells. J Oral Biosci 57(2):69–75.  https://doi.org/10.1016/j.job.2015.02.003 CrossRefGoogle Scholar
  22. Palk L, Sneyd J, Shuttleworth TJ, Yule DI, Crampin EJ (2010) A dynamic model of saliva secretion. J Theor Biol 266(4):625–640.  https://doi.org/10.1016/j.jtbi.2010.06.027 CrossRefzbMATHGoogle Scholar
  23. Penny CJ, Kilpatrick BS, Han JM, Sneyd J, Patel S (2014) A computational model of lysosome-ER \(\text{ Ca }^{2+}\) microdomains. J Cell Sci 127(13):2934–2943.  https://doi.org/10.1242/jcs.149047 CrossRefGoogle Scholar
  24. Politi A, Gaspers LD, Thomas AP, Höfer T (2006) Models of IP\(_3\) and \(\text{ Ca }^{2+}\) oscillations: frequency encoding and identification of underlying feedbacks. Biophys J 90(9):3120–3133.  https://doi.org/10.1529/biophysj.105.072249 CrossRefGoogle Scholar
  25. Rugis J (2005) Surface curvature maps and Michelangelo’s David. Image Vis Comput N Z 2005:218–222Google Scholar
  26. Rugis J, Klette R (2006a) A scale invariant surface curvature estimator. LNCS Adv Image Video Technol 4319:138–147CrossRefGoogle Scholar
  27. Rugis J, Klette R (2006b) Surface registration markers from range scan data. LNCS Comb Image Anal 4040:430–444MathSciNetGoogle Scholar
  28. Savitzky A, Golay M (1964) Smoothing and differentiation of data by simplified least squares procedures. Anal Chem 36:1627–1639.  https://doi.org/10.1021/ac60214a047 CrossRefGoogle Scholar
  29. Sneyd J, Tsaneva-Atanasova K, Bruce J, Straub S, Giovannucci D, Yule D (2003) A model of calcium waves in pancreatic and parotid acinar cells. Biophys J 85(3):1392–1405.  https://doi.org/10.1016/S0006-3495(03)74572-X CrossRefGoogle Scholar
  30. Sneyd J, Tsaneva-Atanasova K, Reznikov V, Bai Y, Sanderson M, Yule D (2006) A method for determining the dependence of calcium oscillations on inositol trisphosphate oscillations. Proc Natl Acad Sci USA 103(6):1675–1680.  https://doi.org/10.1073/pnas.0506135103 CrossRefGoogle Scholar
  31. Sneyd J, Han JM, Wang L, Chen J, Yang X, Tanimura A, Sanderson MJ, Kirk V, Yule DI (2017a) On the dynamical structure of calcium oscillations. Proc Natl Acad Sci 14:201614613.  https://doi.org/10.1073/pnas.1614613114 Google Scholar
  32. Sneyd J, Means S, Zhu D, Rugis J, Won JH, Yule DI (2017b) Modeling calcium waves in an anatomically accurate three-dimensional parotid acinar cell. J Theor Biol 419:383–393.  https://doi.org/10.1016/j.jtbi.2016.04.030 CrossRefGoogle Scholar
  33. Stern MD, Pizarro G, Ríos E (1997) Local control model of excitation–contraction coupling in skeletal muscle. J Gen Physiol 110(4):415–440.  https://doi.org/10.1085/jgp.110.4.415 CrossRefGoogle Scholar
  34. Tanimura A, Morita T, Nezu A, Tojyo Y (2009) Monitoring of IP\(_3\) dynamics during \(\text{ Ca }^{2+}\) oscillations in HSY human parotid cell line with FRET-based IP\(_3\) biosensors. J Med Investig 56:357–361.  https://doi.org/10.2152/jmi.56.357 (Supplement)CrossRefGoogle Scholar
  35. Thorn P, Lawrie AM, Smith PM, Gallacher DV, Petersen OH (1993) Local and global cytosolic \(\text{ Ca }^{2+}\) oscillations in exocrine cells evoked by agonists and inositol trisphosphate. Cell 74(4):661–668.  https://doi.org/10.1016/0092-8674(93)90513-P CrossRefGoogle Scholar
  36. Vera-Sigüenza E, Catalàn MA, Peña-Münzenmayer G, Melvin JE, Sneyd J (2018a) A mathematical model supports a key role for Ae4 (Slc4a9) in salivary gland secretion. Bull Math Biol 80(2):255–282.  https://doi.org/10.1007/s11538-017-0370-6
  37. Vera-Sigüenza E, Pages N, Rugis J, Yule DI, Sneyd J (2018b) A mathematical model of fluid transport in an accurate reconstruction of parotid acinar cell. Bull Math Biol.  https://doi.org/10.1007/s11538-018-0534-z
  38. Tojyo Y, Tanimura A, Matsumoto Y (1997) Imaging of intracellular \(\text{ Ca }^{2+}\) waves induced by muscarinic receptor stimulation in rat parotid acinar cells. Cell Calcium 22(6):455–462.  https://doi.org/10.1016/S0143-4160(97)90073-7 CrossRefGoogle Scholar
  39. Wang IY, Bai Y, Sanderson MJ, Sneyd J (2010) A mathematical analysis of agonist-and KCl-induced \(\text{ Ca }^{2+}\) oscillations in mouse airway smooth muscle cells. Biophys J 98(7):1170–1181.  https://doi.org/10.1016/j.bpj.2009.12.4273 CrossRefGoogle Scholar
  40. Yule DI, Ernst SA, Ohnishi H, Wojcikiewicz RJ (1997) Evidence that zymogen granules are not a physiologically relevant calcium pool. Defining the distribution of inositol 1, 4, 5-trisphosphate receptors in pancreatic acinar cells. J Biol Chem 272(14):9093–9098.  https://doi.org/10.1074/jbc.272.14.9093 CrossRefGoogle Scholar
  41. Zhang X, Wen J, Bidasee KR, Besch HR, Rubin RP (1997) Ryanodine receptor expression is associated with intracellular \(\text{ Ca }^{2+}\) release in rat parotid acinar cells. Am J Physiol Cell Physiol 273(4):C1306–C1314.  https://doi.org/10.1152/ajpcell.1997.273.4.C1306 CrossRefGoogle Scholar
  42. Zhang X, Wen J, Bidasee KR, Besch HR, Wojcikiewicz RJH, Lee B, Rubin RP (1999) Ryanodine and inositol trisphosphate receptors are differentially distributed and expressed in rat parotid gland. Biochem J 340(2):519–527.  https://doi.org/10.1042/bj3400519 CrossRefGoogle Scholar

Copyright information

© Society for Mathematical Biology 2019

Authors and Affiliations

  1. 1.Department of MathematicsThe University of AucklandAucklandNew Zealand
  2. 2.School of Medicine and DentistryUniversity of Rochester Medical CenterRochesterUSA

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