Numerical methods to determine calcium release flux from calcium transients in muscle cells

Biophysical Journal

Volumn 74, Issue 4, 1998, Pages 1694-1707

  Timmer, J ^a   Muller T ^a   Melzer, W ^b  

^a UNIVERSITY OF FREIBURG   (Germany)

^b UNIVERSITY OF ULM   (Germany)

Author keywords

[No Author keywords available]

Indexed keywords

ARTICLE; CALCIUM TRANSPORT; MATHEMATICAL ANALYSIS; MATHEMATICAL MODEL; MUSCLE CELL; SIMULATION; TRANSPORT KINETICS;

EID: 0344110505     PISSN: 00063495     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0006-3495(98)77881-6     Document Type: Article

References (49)

1. Baylor, S. M., W. K. Chandler, and M. W. Marshall. 1983. Sarcoplasmic reticulum calcium release in frog skeletal muscle fibres estimated from arsenazo III calcium transients. J. Physiol. (Lond.). 334:625-666.
2. Bock, H. G. 1981. Numerical treatment of inverse problems in chemical reaction kinetics. In Modelling of Chemical Reaction Systems. K. Ebert, P. Deutlhard, and W. Jäger, editors. Springer, Heidelberg and New York. 102-125.
3. Bock, H. G. 1983. Recent advances in parameteridentification techniques for o.d.e. In Numerical Treatment of Inverse Problems in Differential and Integral Equations. P. Deuflhard and E. Hairer, editors. Birkhäuser, Basel. 95-121.
4. Brum, G., E. Rios, and M. F. Schneider. 1988a. A quantitative model of calcium removal from the myoplasmic solution. J. Physiol. (Lond.). 398:467-473 (appendix to Brum et al., 1988b).
5. Brum, G., E. Ríos, and E. Stéfani. 1988b. Effects of extracellular calcium on calcium movements of excitation-contraction coupling in frog skeletal muscle fibres. J. Physiol. (Lond.). 398:441-473.
6. Chandler, W. K., D. Jong, P. C. Pape, and S. M. Baylor. 1995. Calcium inactivation of calcium release in frog skeletal muscle fibers. In Calcium as Cell Signal. K. Maruyama, Y. Nonomura, and K. Kohama, editors. Igaku-Shoin Medical Publishers, New York. 80-88.
7. 2+ release in rat skeletal muscle fibers. J. Membr. Biol. 146:91-99.
8. 2+ release in slow- and fast-twitch muscle. J. Membr. Biol. 151:123-130.
9. Delbono, O., K. S. O'Rourke, and W. H. Ettinger. 1995. Excitation-calcium release uncoupling in aged single human skeletal muscle fibers. J. Membr. Biol. 148:211-222.
10. Feldmeyer, D., W. Melzer, and B. Pohl. 1990. Effects of gallopamil on calcium release and intramembrane charge movements in frog skeletal muscle fibres. J. Physiol. (Lond.). 421:343-362.
11. García, J., and M. F. Schneider. 1993 Calcium transients and calcium release in rat fast-twitch skeletal muscle fibres. J. Physiol. (Lond.). 463:709-728.
12. Gasser, T., H.-G. Müller, and V. Mammitzsch. 1985. Kernels for nonparametric curve estimation. J. K. Statist. Soc. B. 47:238-252.
13. Gill, P. E., W. Murray, and M. H. Wright. 1981. Practical Optimization. Academic Press, London.
14. Gonzáles, A., and E. Ríos. 1993. Perchlorate enhances transmission in skeletal muscle excitation-contraction coupling. J. Gen. Physiol. 102:373-421.
15. Hairer, E., S. P. Nørsett, and G. Wanner. 1987. Solving Ordinary Differential Equations I. Springer, Heidelberg and New York.
16. Hall, P., and T. E. Wehrly. 1991. A geometrical method for removing edge effects from kernel-type nonparametric regression estimates. J. Am. Statist. Assoc. 86:665-672.
17. Honerkamp, J. 1994. Stochastic Dynamical Systems. VCH, Weinheim, Germany.
18. 2+ on calcium binding by parvalbumin and calcium uptake by the sarcoplasmic reticulum in frog skeletal muscle. J. Gen. Physiol. 100:115-135.
19. Jong, D.-S., P. C. Pape, S. M. Baylor, and W. K. Chandler. 1995. Calcium inactivation of calcium release in frog cut muscle fibres that contain millimolar EGTA or Fura-2. J. Gen. Physiol. 106:337-338.
20. Jong, D.-S., P. C. Pape, W. K. Chandler, and S. M. Baylor. 1993. Reduction of calcium inactivation of sarcoplasmic reticulum calcium release by fura-2 in voltage-clamped cut twitch fibres from frog muscle. J. Gen. Physiol. 102:333-370.
21. Jong, D.-S., P. C. Pape, J. Geibel, and W. K. Chandler. 1996. Sarcoplasmic reticulum calcium release in frog cut muscle fibers in the presence of a large concentration of EGTA. In Organellar Ion Channels and Transporters. D. E. Clapham, editor. The Rockefeller University Press, New York. 255-268.
22. Klein, M. G., B. J. Simon, G. Szücs, and M. F. Schneider. 1988. Simultaneous recording of calcium transients in skeletal muscle using high-and low-affinity calcium indicators. Biophys. J. 53:971-988.
23. 2+ ions in excitation-contraction coupling of skeletal muscle fibres. Biochim. Biophys. Acta. 1241:59-116.
24. Melzer, W., E. Ríos, and M. F. Schneider. 1984. Time course of calcium release and removal in skeletal muscle fibers. Biophys. J. 45:637-641.
25. Melzer, W., E. Ríos, and M. F. Schneider. 1986. The removal of myoplasmic free calcium following calcium release in frog skeletal muscle. J. Physiol. (Lond.). 372:261-292.
26. Melzer, W., E. Rios, and M. F. Schneider. 1987. A general procedure for determining the rate of calcium release from the sarcoplasmic reticulum in skeletal muscle fibers. Biophys. J. 51:849-863.
27. Müller, H.-G. 1988. Nonparametric Regression Analysis of Longitudinal Data. Springer, Heidelberg and New York.
28. Müller, H.-G., and U. Stadtmüller. 1987. Variable bandwidth kernel estimators of regression curves. Ann. Statist. 15:182-201.
29. Pape, P. C., D.-S. Jong, and W. K. Chandler. 1993. Effect of Fura-2 on action potential-stimulated calcium release in cut twitch fibers from frog muscle. J. Gen. Physiol. 102:295-332.
30. Pape, P. C., D.-S. Jong, and W. K. Chandler. 1995. Calcium release and its voltage dependence in frog cut muscle fibers equilibrated with 20 mM EGTA. J. Gen. Physiol. 106:259-336.
31. Press, W. H., S. A. Teukolsky, W. T. Vetter, and B. P. Flannery. 1992. Numerical Recipes in C, 2nd Ed. Cambridge University Press, Cambridge.
32. Ratzlaff, K. L. 1987. Introduction to Computer-Assisted Experimentation. Wiley, New York.
33. Ríos, E., and G. Pizarro. 1991. Voltage sensor of excitation-contraction coupling in skeletal muscle. Physiol. Rev. 71:849-907.
34. Rios, E., and M. D. Stern. 1997. Calcium in close quarters: Microdomain feedback in excitation-contraction coupling and other cell biological phenomena. Annu. Rev. Biophys. Biomol. Struct. 26:47-82.
35. Savitzky, A., and M. J. E. Golay. 1964. Curve smoothing by local polynomial fits. Anal. Chem. 36:1627-1639.
36. Schittkowski, K. 1995. Parameter estimation in differential equations. In Recent Trends in Optimization Theory and Applications. R. Agarwal, editor. World Scientific, Singapore. 353-370.
37. Schneider, M. F. 1994. Control of calcium in functioning skeletal muscle fibers. Annu. Rev. Physiol. 56:463-484.
38. Schneider, M. F., E. Ri'os, and W. Melzer. 1985. Use of a metallochromic indicator to study intracellular calcium movements in skeletal muscle. Cell Calcium. 6:109-118.
39. Schneider, M. F., and B. J. Simon. 1988. Inactivation of calcium release from the sarcoplasmic reticulum in frog skeletal muscle. J. Physiol. (Lond.). 405:727-745.
40. Schneider, M. F., B. J. Simon, and G. Szücs. 1987. Depletion of calcium from the sarcoplasmic reticulum during calcium release in frog skeletal muscle. J. Physiol. (Lond.). 392:167-192.
41. Seather, S. J. 1992. The performance of six popular bandwidth selection methods on some real data sets. Comp. Statist. 7:225-250.
42. +release from the sarcoplasmic reticulum compared in amphibian and mammalian skeletal muscle. J. Gen. Physiol. 107:1-18.
43. Simon, B. J., M. G. Klein, and M. F. Schneider. 1991. Calcium dependence of inactivation of calcium release from the sarcoplasmic reticulum in skeletal muscle fibers. J. Gen. Physiol. 97:437-471.
44. Simon, B. J., and M. F. Schneider. 1988. Time course of activation of calcium release from sarcoplasmic reticulum in skeletal muscle. Biophys. J. 54:1159-1163.
45. 2+ across the sarcoplasmic reticulum of guinea pig cardiac cells during excitation-contraction coupling. J. Physiol. (Lond.). 435:605-630.
46. Stoer, J. 1971. On the numerical solution of constrained least-squares problems. SIAM J. Numer. Anal. 8:382-411.
47. Stoer, J., and R. Bulirsch. 1993. Introduction to Numerical Analysis, 2nd Ed. Springer, Heidelberg and New York.
48. Stortelder, W. J. H. 1996. Parameter estimation in chemical engineering, a case study for resin production. In Scientific Computing in Chemical Engineering. F. Keil, W. Mackens, H. Voss, and J. Werther, editors. Springer, Heidelberg and New York. 226-238.
49. van Domselaar, B., and P. W. Hemker. 1975. Nonlinear parameter estimation in initial value problems. Technical Report NW 18/75, Mathematical Centre, Amsterdam.