Incorporation of sarcolemmal calcium transporters into the Shorten et al. (2007) model of skeletal muscle: equations, coding, and stability

Noble, P. J. , Garny, A. , Shorten, P. R. , Tasaki, K. , Afshar, N. , Noble, D.

View publication

To cite this Physiome article, cite the whole collection at the DOI: 10.36903/physiome.12885590, and the Primary Publication at the DOI: https://doi.org/10.1007/s10974-007-9125-6. All Physiome articles are published as a collection containing the manuscript as a PDF file and the model implementation as an OMEX file.

Abstract: We describe a major development of the Shorten et al. (Shorten et al., 2007) model of skeletal muscle electrophysiology, biochemistry, and mechanics. The model was developed by incorporating equations for sarcolemmal transport of calcium ions, including L-type calcium channel, sodium-calcium exchange, calcium pump, and background calcium channel. The extended model also includes an addition to the equations for extracellular potassium ion movements to enable the exchange of potassium ions between bulk (plasma) concentration and the interstitial and tubular compartments to be modeled. In further research in an accompanying paper (Tasaki et al, 2019), we succeeded in reproducing muscle cramp, as well as its prevention and reversal, by investigating muscle contraction and cramp using this extended model in comparison with the original model.

1. A mathematical model of fatigue in skeletal muscle force contraction. Journal: Journal of muscle research and cell motility. Shorten, Paul R and O’Callaghan, Paul and Davidson, John B and Soboleva, Tanya K. Volume: 28. Year: 2007.
2. Role of extracellular [Ca2+] in fatigue of isolated mammalian skeletal muscle. Journal: Journal of applied physiology. Cairns, Simeon P and Hing, Wayne A and Slack, John R and Mills, Roland G and Loiselle, Denis S. Volume: 84. Year: 1998.
3. Changes of action potentials and force at lowered [Na+] o in mouse skeletal muscle: implications for fatigue. Journal: American Journal of Physiology-Cell Physiology. Cairns, Simeon P and Buller, Sarah J and Loiselle, Denis S and Renaud, Jean-Marc. Volume: 285. Year: 2003.
4. Do multiple ionic interactions contribute to skeletal muscle fatigue?. Journal: The Journal of physiology. Cairns, SP and Lindinger, MI. Volume: 586. Year: 2008.
5. On the role of calcium in the excitation-contraction process of frog sartorius muscle. Journal: The Journal of physiology. Edman, KAP and Grieve, DW. Volume: 170. Year: 1964.
6. How and why are calcium currents curtailed in the skeletal muscle voltage-gated calcium channels?. Journal: The Journal of physiology. Flucher, Bernhard E and Tuluc, Petronel. Volume: 595. Year: 2017.
7. The CaV 1.2 Ca2+ channel is expressed in sarcolemma of type I and IIa myofibers of adult skeletal muscle. Journal: Muscle \& Nerve: Official Journal of the American Association of Electrodiagnostic Medicine. Jeftinija, Du{\v{s}}an M and Wang, Qing Bo and Hebert, Sadie L and Norris, Christopher M and Yan, Zhen and Rich, Mark M and Kraner, Susan D. Volume: 36. Year: 2007.
8. Riluzole-induced block of voltage-gated Na+ current and activation of BKCa channels in cultured differentiated human skeletal muscle cells. Journal: Life sciences. Wang, Ya-Jean and Lin, Ming-Wei and Lin, An-An and Wu, Sheng-Nan. Volume: 82. Year: 2008.
9. The Role of Sodium-Calcium Exchange during the Cardiac Action Potential a. Journal: Annals of the New York Academy of Sciences. Noble, D and Noble, SJ and Bett, GCL and Earm, YE and Ho, WK and So, IK. Volume: 639. Year: 1991.
10. Identification of sodium-calcium exchange current in single ventricular cells of guinea-pig.. Journal: The Journal of Physiology. Kimura, JUNKO and Miyamae, SHUNICH and Noma, AKINORI. Volume: 384. Year: 1987.
11. Function and regulation of the Na+-Ca2+ exchanger NCX3 splice variants in brain and skeletal muscle. Journal: Journal of Biological Chemistry. Michel, Lauriane YM and Verkaart, Sjoerd and Koopman, Werner JH and Willems, Peter HGM and Hoenderop, Joost GJ and Bindels, Ren{\'e} JM. Volume: 289. Year: 2014.
12. A model of cardiac electrical activity incorporating ionic pumps and concentration changes. Journal: Philosophical Transactions of the Royal Society of London. B, Biological Sciences. Di Francesco, Dario and Noble, Denis. Volume: 307. Year: 1985.
13. A model of the action potential and underlying membrane currents in a rabbit atrial cell. Journal: American Journal of Physiology-Heart and Circulatory Physiology. Lindblad, DS and Murphey, CR and Clark, JW and Giles, WR. Volume: 271. Year: 1996.
14. OpenCOR: a modular and interoperable approach to computational biology. Journal: Frontiers in physiology. Garny, Alan and Hunter, Peter J. Volume: 6. Year: 2015.
15. Sodium/calcium exchange in amphibian skeletal muscle fibers and isolated transverse tubules. Journal: American Journal of Physiology-Cell Physiology. Cifuentes, Fredy and Vergara, Julio and Hidalgo, Cecilia. Volume: 279. Year: 2000.
16. Colocalization of the dihydropyridine receptor, the plasma-membrane calcium ATPase isoform 1 and the sodium/calcium exchanger to the junctional-membrane domain of transverse tubules of rabbit skeletal muscle. Journal: European journal of biochemistry. Sacchetto, Roberta and Margreth, Alfredo and Pelosi, Michele and Carafoli, Ernesto. Volume: 237. Year: 1996.