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Functional Modeling of the Shift in Cellular Calcium Dynamics at the Onset of Synchronization in Smooth Muscle Cells

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Abstract

In the present paper we address the nature of synchronization properties found in populations of mesenteric artery smooth muscle cells. We present a minimal model of the onset of synchronization in the individual smooth muscle cell that is manifested as a transition from calcium waves to whole-cell calcium oscillations. We discuss how different types of ion currents may influence both amplitude and frequency in the regime of whole-cell oscillations. The model may also explain the occurrence of mixed-mode oscillations and chaotic oscillations frequently observed in the experimental system.

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References

  • Aalkjaer, C., & Nilsson, H. (2005). Vasomotion: cellular background for the oscillator and for the synchronization of smooth muscle cells. Br. J. Pharmacol., 144, 605–616.

    Article  Google Scholar 

  • Balanov, A., Janson, N., Postnov, D., & Sosnovtseva, O. (2009). Synchronization: from simple to complex. Berlin: Springer.

    MATH  Google Scholar 

  • Bartlett, I. S., Crane, G. J., Neild, T. O., & Segal, S. S. (2000). Electrophysiological basis of arteriolar vasomotion in vivo. J. Vasc. Res., 37, 568–575.

    Article  Google Scholar 

  • Berridge, M. J. (1993). Inositol trisphosphate and calcium signalling. Nature, 361, 315–325.

    Article  Google Scholar 

  • Bindschadler, M., & Sneyd, J. (2001). A bifurcational analysis of two coupled calcium oscillators. Chaos, 11, 237–246.

    Article  MATH  Google Scholar 

  • Boedtkjer, D. M., Matchkov, V. V., Boedtkjer, E., Nilsson, H., & Aalkjaer, C. (2008). Vasomotion has chloride-dependency in rat mesenteric small arteries. Pflügers Arch., 457, 389–404.

    Article  Google Scholar 

  • Clapham, D. E. (1995). Calcium signaling. Cell, 80, 259–268.

    Article  Google Scholar 

  • Colantuoni, A., Bertuglia, S., & Intaglietta, M. (1984). Quantitation of rhythmic diameter changes in arterial microcirculation. Am. J. Phys., 246, H508–H517.

    Google Scholar 

  • Cornelisse, L. N., Scheenen, W. J., Koopman, W. J., Roubos, E. W., & Gielen, S. C. (2001). Minimal model for intracellular calcium oscillations and electrical bursting in melanotrope cells of Xenopus laevis. Neural Comput., 13, 113–137.

    Article  MATH  Google Scholar 

  • 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. Proc. Natl. Acad. Sci. USA, 89, 9895–9899.

    Article  Google Scholar 

  • Dupont, G., & Goldbeter, A. (1993). One-pool model for Ca2+ oscillations involving Ca2+ and inositol 1,4,5-trisphosphate as co-agonists for Ca2+ release. Cell Calcium, 14, 311–322.

    Article  Google Scholar 

  • Fabiato, A., & Fabiato, F. (1977). Calcium release from the sarcoplasmic reticulum. Circ. Res., 40, 119–129.

    Google Scholar 

  • Fujii, K., Heistad, D. D., & Faraci, F. M. (1990). Ionic mechanisms in spontaneous vasomotion of the rat basilar artery in vivo. J. Physiol., 430, 389–398.

    Google Scholar 

  • Griffith, T. M. (1996). Temporal chaos in the microcirculation. Cardiovasc. Res., 31, 342–358.

    Google Scholar 

  • Griffith, T. M., & Edwards, D. H. (1994). Fractal analysis of role of smooth muscle Ca2+ fluxes in genesis of chaotic arterial pressure oscillations. Am. J. Physiol., 266(35), H1801–H1811.

    Google Scholar 

  • Gustafsson, H. (1993). Vasomotion and underlying mechanisms in small arteries. Acta Physiol. Scand., 614, 2–44.

    Google Scholar 

  • Gustafsson, H., & Nilsson, H. (1993). Rhythmic contractions of isolated small arteries from rat: role of calcium. Acta Physiol. Scand., 149, 283–291.

    Article  Google Scholar 

  • Gustafsson, H., Bulow, A., & Nilsson, H. (1994). Rhythmic contractions of isolated, pressurized small arteries from rat. Acta Physiol. Scand., 152, 145–152.

    Article  Google Scholar 

  • Henning, G. W., Smith, C. B., O’Shea, D. M., & Smith, T. K. (2002). Patterns of intracellular and intercellular Ca2+ waves in the longitudinal muscle layer of the murine large intestine in vitro. J. Physiol., 543, 233–253.

    Article  Google Scholar 

  • Hilsson, H., & Aalkjaer, C. (2003). Vasomotion: mechanisms and physiological importance. Mol. Interv., 3, 79–89.

    Article  Google Scholar 

  • Höfer, T., Politi, A., & Heinrich, R. (2001). Intercellular Ca2+ wave propagation through gap-junctional Ca2+ diffusion: A theoretical study. Biophys. J., 80, 75–87.

    Article  Google Scholar 

  • Jacobsen, J. C. B., Aalkjaer, C., Nilsson, H., Matchkov, V., Freiberg, J., & Holstein-Rathlou, N.-H. (2007a). Activation of a cGMP-sensitive calcium-dependent chloride channel may cause transition from calcium waves to whole-cell oscillations in smooth muscle cells. Am. J. Physiol., Heart Circ. Physiol., 293, H215–H228.

    Article  Google Scholar 

  • Jacobsen, J. C., Aalkjaer, C., Nilsson, H., Matchkov, V. V., Freiberg, J., & Holstein-Rathlou, N.-H. (2007b). A model of smooth muscle cell synchronization in the arterial wall. Am. J. Physiol., Heart Circ. Physiol., 293, H229–H237.

    Article  Google Scholar 

  • Jacobsen, J. C., Aalkjaer, C., Matchkov, V. V., Nilsson, H., Freiberg, J., & Holstein-Rathlou, N. H. (2008). Heterogeneity and weak coupling may explain the synchronization characteristics of cells in the arterial wall. Philos. Trans. R. Soc., Math. Phys. Eng. Sci., 366, 3483–3502.

    Article  Google Scholar 

  • Keener, J., & Sneyd, J. (1998). Mathematical physiology. Berlin: Springer.

    MATH  Google Scholar 

  • Koenigsberger, M., Sauser, R., & Meister, J.-J. (2005). Emergent properties of electrically coupled smooth muscle cells. Bull. Math. Biol., 67, 1253–1272.

    Article  MathSciNet  Google Scholar 

  • Matchkov, V., Aalkjaer, C., & Nilsson, H. (2004). A cyclic GMP-dependent calcium-activated chloride current in smooth-muscle cells from rat mesenteric resistance arteries. J. Gen. Physiol., 123, 121–134.

    Article  Google Scholar 

  • Miriel, V. A., Mauban, J. R., Blaustein, M. P., & Wier, W. G. (1999). Local and cellular Ca2+ transients in smooth muscle of pressurized rat resistance arteries during myogenic and agonist stimulation. J. Physiol., 518, 815–824.

    Article  Google Scholar 

  • Parthimos, D., Haddock, R. E., Hill, C. E., & Griffith, T. M. (2007). Dynamics of a three-variable nonlinear model of vasomotion: comparison of theory and experiment. Biophys. J., 93, 1534–1556.

    Article  Google Scholar 

  • Peng, H., Matchkov, V., Ivarsen, A., Aalkjaer, C., & Nilsson, H. (2001). Hypothesis for the initiation of vasomotion. Circ. Res., 88, 810–815.

    Article  Google Scholar 

  • Piper, A. S., & Large, W. A. (2004). Direct effect of Ca2+-calmodulin on cGMP-activated Ca2+-dependent Cl channels in rat mesenteric artery myocytes. J. Physiol., 559, 449–457.

    Article  Google Scholar 

  • Postnov, D. E., Han, S. K., Yim, T., & Sosnovtseva, O. V. (1999). Experimental observation of coherence resonance in cascaded excitable systems. Phys. Rev. E, 59, 3791–3794.

    Article  Google Scholar 

  • Rahman, A., Matchkov, V., Nilsson, H., & Aalkjaer, C. (2005). Effect of cGMP on coordination of vascular smooth muscle cells of rat mesenteric small arteries. J. Vasc. Res., 42, 301–311.

    Article  Google Scholar 

  • Rahman, A., Hughes, A., Matchkov, V., Nilsson, H., & Aalkjaer, C. (2007). Antiphase oscillations of endothelium and smooth muscle [Ca2+]i in vasomotion of rat mesenteric small arteries. Cell Calcium, 42, 536–547.

    Article  Google Scholar 

  • Ruehlmann, D. O., Lee, C. H., Poburko, D., & van Breemen, C. (2000). Asynchronous Ca2+ waves in intact venous smooth muscle. Circ. Res., 86, E72–E79.

    Google Scholar 

  • Sanders, K. M. (2001). Mechanisms of calcium handling in smooth muscles. J. Appl. Physiol., 91, 1438–1449.

    Google Scholar 

  • Schiff, L. (1854). Ein accessorisches Arterienherz bei Kaninchen. Arch. Physiol. Heilk, 13, 523–527.

    Google Scholar 

  • Sell, M., Boldt, W., & Markwardt, F. (2002). Desynchronising effect of the endothelium on intracellular Ca2+ concentration dynamics in vascular smooth muscle cells of rat mesenteric arteries. Cell Calcium, 32, 105–120.

    Article  Google Scholar 

  • Sneyd, J., Wetton, B. T., Charles, A. C., & Sanderson, M. J. (1995). Intercellular calcium waves mediated by diffusion of inositol trisphosphate: A two-dimensional model. Am. J. Physiol., 268, C1537–C1545.

    Google Scholar 

  • Somlyo, A. P. (1985). Excitation-contraction coupling and the ultrastructure of smooth muscle. Circ. Res., 57, 497–507.

    Google Scholar 

  • Zucchi, R., & Ronca-Testoni, S. (1997). The sarcoplasmic reticulum Ca2+ channel/ryanodine receptor: Modulation by endogenous effectors, drugs and disease states. Pharmacol. Rev., 49, 1–51.

    Google Scholar 

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Authors and Affiliations

  1. Department of Physics, Saratov State University, Astrakhanskaya Str. 83, Saratov, 410026, Russia

    D. E. Postnov

  2. Department of Biomedical Sciences, Copenhagen University, Blegdamsvej 3, 2200, Copenhagen N, Denmark

    J. C. Brings Jacobsen, N.-H. Holstein-Rathlou & O. V. Sosnovtseva

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  1. D. E. Postnov
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  2. J. C. Brings Jacobsen
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  3. N.-H. Holstein-Rathlou
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  4. O. V. Sosnovtseva
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Correspondence to O. V. Sosnovtseva.

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Postnov, D.E., Brings Jacobsen, J.C., Holstein-Rathlou, NH. et al. Functional Modeling of the Shift in Cellular Calcium Dynamics at the Onset of Synchronization in Smooth Muscle Cells. Bull Math Biol 73, 2507–2525 (2011). https://doi.org/10.1007/s11538-011-9636-6

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  • DOI: https://doi.org/10.1007/s11538-011-9636-6

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