Abstract
Computational cell models appear as necessary tools for handling the complexity of intracellular cell dynamics, especially calcium dynamics. However, while oscillating intracellular calcium oscillations are well documented and modelled, a simple enough virtual cell taking into account the mechano-chemical coupling between calcium oscillations and cell mechanical properties is still lacking. Considering the spontaneous periodic contraction of isolated cardiac myocytes, we propose here a virtual cardiac cell model in which the cellular contraction is modelled using an hyperelastic description of the cell mechanical behaviour. According to the experimental data, the oscillating cytosolic calcium concentrations trigger the spatio-temporal variation of the anisotropic intracellular stresses. The finite element simulations of the virtual cell deformations are compared to the self-sustained contractions of isolated rat cardiomyocytes recorded by time-lapse video-microscopy.
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References
Bourdarias, C., S. Gerbi and J. Ohayon (2003). A three dimensional finite element method for biological active soft tissue-Formulation in cylindrical polar coordinates. Mathematical Modelling and Numerical Analysis 37(4): 725–739.
Caille, N., O. Thoumine, Y. Tardy and J.J. Meister (2002). Contribution of the nucleus to the mechanical properties of endothelial cells. Journal of Biomechanics 35: 177–187.
Cazorla, O., A. Lacampagne, J. Fauconnier and G. Vassort (2003). SR 33805 a Ca2+ antagonist with length-dependent Ca2+-sensitizing properties in cardiac myocytes. British Journal of Pharmacology 139: 99–108.
Dhooge, A., W. Govaerts and Yu, A. Kuznetsov (2003). MATCONT: A MATLAB package for numerical bifurcation analysis of ODEs. ACM Transactions in mathematical software 29: 141–164.
Fabiato, A. (1983). Calcium-induced release of calcium from the cardiac sarcoplasmic reticulum, American Journal of Physiology 245: C1–C14.
Fabiato, A. and F. Fabiato (1975). Contraction induced by a calcium-triggered release of calcium from the sarcoplasmic reticulum of single skinned cardiac cell. Journal of Physiology London 249: 469–495.
Goldbeter, A., G. Dupont and M.J. Berridge (1990). Minimal model for signal-induced Ca2+ oscillations and for their frequency encoding through protein phosphorylation. Proceedings of the National Academy of Sciences, USA 87: 1461–1465.
Grouselle, M., B. Stuyvers, S. Bonoron-Adele, P. Besse and D. Georges-Cauld (1991). Digital imaging microscopy analysis of calcium release from sarcoplasmic reticulum in single rat cardiac myocytes. Pfluegers Archives 418: 109–119.
Holzapfel, G.A. (2001). Nonlinear Solid Mechanics. Ed. Wiley & Sons, NY.
Ishida, H., C. Genka, Y. Hirota, H. Nakazawa and W.H. Barry (1999). Formation of planar and spiral Ca2+ waves in isolated cardiac myocytes Biophysical Journal 77: 2114– 2122
Keener, J. and J. Sneyd (1998). Mathematical Physiology, Springer Verlag. NewYork.
Lakatta, E. (1992). Functional implications of spontaneous sarcoplasmic reticulum Ca2+ release in the heart. Cardiovascular Research 26: 193–214.
Ohayon, J. and P. Tracqui (2005). An extended method for computing the apparent stiffness of individual cell probed by magnetic twisting cytometry. Annals of Biomedical Engineering 33(2): 131–141.
Olivares, J., I. Dubus, A. Barrieux, J.L. Samuel, L. Rappaport and A. Rossi (1992). Pyrimidine nucleotide synthesis is preferentially supplied by exogenous cytidine in adult rat cultured cardiomyocytes. Journal of Molecular and Cellular Cardiology 24: 1349– 1359.
Slepchenko, B.M., J.C. Schaff, I. Macara and L.M. Loew (2003). Quantitative cell biology with the Virtual Cell. Trends in Cell Biology 13: 570–576.
Sneyd, J., S. Girard and D. Clapham (1993). Calcium wave propagation by calcium-induced calcium release: An unusuable excitable system. Bulletin of Mathematical Biology 55: 315– 344.
Stern, M.D., M.C. Capogrossi and E.G. Lakatta (1988). Spontaneous calcium release from the sarcoplasmic reticulum in myocardial cells: Mechanisms and consequences. Cell Calcium 9: 247–256.
Stuyvers, B.D, A.D. McCulloch, J. Guo, H.J. Duff and H.E.D.J. ter Keurs (2002). Effect of stimulation rate, sarcomere length and Ca2+ on force generation by mouse cardiac muscle. Journal of Physiology 544(3): 817–830.
Subramanian, S., S. Viatchenko-Karpinski, V. Lukyanenko, S. Györk and T.F. Wiesner (2001). Underlying mechanisms of symmetric calcium wave propagation in rat ventricular myocytes. Biophysical. Journal 80: 1–11.
Takamatsu, T. and W. Wier (1990). Calcium waves in mammalian heart: Quantification of origin, magnitude, waveform and velocity. FASEB Journal 4: 1519–1525.
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Pustoc'h, A., Ohayon, J., Usson, Y. et al. An Integrative Model of the Self-Sustained Oscillating Contractions of Cardiac Myocytes. Acta Biotheor 53, 277–293 (2005). https://doi.org/10.1007/s10441-005-4880-5
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DOI: https://doi.org/10.1007/s10441-005-4880-5