Abstract
A physiologically realistic quantitative description of the electrical behavior of a gastric smooth muscle (SM) cell is presented. The model describes the response of a SM cell when activated by an electrical stimulus coming from the network of interstitial cells of Cajal (ICC) and is mediated by the activation of different ion channels species in the plasma membrane. The conductances (predominantly Ca2+ and K+) that are believed to substantially contribute to the membrane potential fluctuations during slow wave activity have been included in the model. A phenomenological description of intracellular Ca2+ dynamics has also been included because of its primary importance in regulating a number of cellular processes. In terms of shape, duration, and amplitude, the resulting simulated smooth muscle depolarizations (SMDs) are in good agreement with experimentally recordings from mammalian gastric SM in control and altered conditions. This model has also been designed to be suitable for incorporation into large scale multicellular simulations.
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Akbarali H. I., Giles W. R. (1993) Ca2+ and Ca(2+)-activated Cl− currents in rabbit oesophageal smooth muscle. J. Physiol. 460:117–133
Aliev R. R., Richards W., Wikswo J. P. (2000) A simple nonlinear model of electrical activity in the intestine. J. Theor. Biol. 204:21–28
Amberg G. C., Baker S. A., Koh S. D., Hatton W. J., Murray K. J., Horowitz B., Sanders K. M. (2002) Characterization of the A-type potassium current in murine gastric antrum. J. Physiol. 544:417–428
Amberg G. C., Koh S. D., Imaizumi Y., Ohya S., Sanders K. M. (2003). A-type potassium currents in smooth muscle. Am. J. Physiol. Cell. Physiol. 284:C583–C595
Barrett J. N., Magleby K. L., Pallotta B. S. (1982) Properties of single calcium-activated potassium channels in cultured rat muscle. J. Physiol. 331:211–230
Boev K., Bonev A., Papasova M. (1985) 4-Aminopyridine-induced changes in the electrical and contractile activities of the gastric smooth muscle. Gen. Physiol. Biophys. 4:589–595
Bradley K. N., Flynn E. R., Muir T. C., McCarron J. G. (2002) Ca(2+) regulation in guinea-pig colonic smooth muscle: the role of the Na(+)–Ca(2+) exchanger and the sarcoplasmic reticulum. J. Physiol. 538:465–482
Carl A., Frey B. W., Ward S. M., Sanders K. M., Kenyon J. L. (1993) Inhibition of slow-wave repolarization and Ca(2+)-activated K+ channels by quaternary ammonium ions. Am. J. Physiol. 264:C625–C631
Carl A., Lee H. K., Sanders K. M. (1996) Regulation of ion channels in smooth muscles by calcium. Am J Physiol. 271:C9–C34
Casteels R. (1981) Membrane potential in smooth muscle. In: Bulbring E. B. A., Jones A. W., Tomita T. (eds) Smooth Muscle: An Assesment of Current Knowledge. Edward Arnold, London, pp 105–126
Cousins H. M., Edwards F. R., Hickey H., Hill C. E., Hirst G. D. (2003) Electrical coupling between the myenteric interstitial cells of Cajal and adjacent muscle layers in the guinea-pig gastric antrum. J. Physiol. 550:829–844
Edwards F. R., Hirst G. D. (2005) An electrical description of the generation of slow waves in the antrum of the guinea-pig. J. Physiol. 564:213–232
Farrugia G. (1999) Ionic conductances in gastrointestinal smooth muscles and interstitial cells of Cajal. Annu. Rev. Physiol. 61:45–84
Farrugia G., Rich A., Rae J. L., Sarr M. G., Szurszewski J. H. (1995) Calcium currents in human and canine jejunal circular smooth muscle cells. Gastroenterology 109:707–717
Forrest, A. S., T. Ordog, and K. M. Sanders. Neural regulation of slow wave frequency in the murine gastric antrum. Am. J. Physiol. Gastrointest. Liver Physiol. 290(3):G486–G495, 2005.
Ganitkevich V., Shuba M. F., Smirnov S. V. (1987) Calcium-dependent inactivation of potential-dependent calcium inward current in an isolated guinea-pig smooth muscle cell. J. Physiol. 392:431–449
Hagiwara S., Kusano K., Saito N. (1961) Membrane changes of Onchidium nerve cell in potassium-rich media. J. Physiol. 155:470–489
Hirst G. D., Edwards F. R. (2004) Role of interstitial cells of Cajal in the control of gastric motility. J. Pharmacol. Sci. 96:1–10
Holm A. N., Rich A., Miller S. M., Strege P., Ou Y., Gibbons S., Sarr M. G., Szurszewski J. H., Rae J. L., Farrugia G. (2002) Sodium current in human jejunal circular smooth muscle cells. Gastroenterology 122:178–187
Huang S., Nakayama S., Iino S., Tomita T. (1999) Voltage sensitivity of slow wave frequency in isolated circular muscle strips from guinea pig gastric antrum. Am. J. Physiol. 276:G518–G528
Huizinga J. D. (2001) Physiology and pathophysiology of the interstitial cell of Cajal: from bench to bedside. II. Gastric motility: lessons from mutant mice on slow waves and innervation. Am Am. J. Physiol. Gastrointest. Liver Physiol. 281:G1129–G1134
Hurwitz L., Fitzpatrick D. F., Debbas G., Landon E. J. (1973) Localization of calcium pump activity in smooth muscle. Science 179:384–386
Inoue R., Isenberg G. (1990) Effect of membrane potential on acetylcholine-induced inward current in guinea-pig ileum. J. Physiol. 424:57–71
Inoue R., Isenberg G. (1990) Intracellular calcium ions modulate acetylcholine-induced inward current in guinea-pig ileum. J. Physiol. 424:73–92
Isaac L., McArdle S., Miller N. M., Foster R. W., Small R. C. (1996) Effects of some K(+)-channel inhibitors on the electrical behaviour of guinea-pig isolated trachealis and on its responses to spasmogenic drugs. Br. J. Pharmacol. 117:1653–1662
Kang T. M., Kim Y. C., Sim J. H., Rhee J. C., Kim S. J., Uhm D. Y., So I., Kim K. W. (2001) The properties of carbachol-activated nonselective cation channels at the single channel level in guinea pig gastric myocytes. Jpn. J. Pharmacol. 85:291–298
Kim S. J., Ahn S. C., Kim J. K., Kim Y. C., So I., Kim K. W. (1997) Changes in intracellular Ca2+ concentration induced by L-type Ca2+ channel current in guinea pig gastric myocytes. Am. J. Physiol. 273:C1947–C1956
Knot H., Brayden J., Nelson M. (1995) Calcium channels and potassium channels. In: Barany M., (eds). Biochemistry of Smooth Muscle Contraction. Academic Press, Chicago, pp. 203–217
Koh S. D., Monaghan K., Ro S., Mason H. S., Kenyon J. L., Sanders K. M. (2001) Novel voltage-dependent non-selective cation conductance in murine colonic myocytes. J. Physiol. 533:341–355
Koh S. D., Ward S. M., Dick G. M., Epperson A., Bonner H. P., Sanders K. M., Horowitz B., Kenyon J. L. (1999) Contribution of delayed rectifier potassium currents to the electrical activity of murine colonic smooth muscle. J. Physiol. 515(Pt 2):475–487
Lang, R. J. and C. A. Rattray-Wood. A simple mathematical model of the spontaneous electrical activity in a single smooth muscle myocyte. In: Smooth Muscle Excitation, edited by B. Bolton and T. Tomita. London: Academic Press, 1996, pp. 391–402.
Langton P. D., Burke E. P., Sanders K. M. (1989) Participation of Ca currents in colonic electrical activity. Am. J. Physiol. 257:C451–C460
Miftakhov R. N., Abdusheva G. R., Christensen J. (1999) Numerical simulation of motility patterns of the small bowel. 1. formulation of a mathematical model. J. Theor. Biol. 197:89–112
Monteith G. R., Kable E. P., Chen S., Roufogalis B. D. (1996) Plasma membrane calcium pump-mediated calcium efflux and bulk cytosolic free calcium in cultured aortic smooth muscle cells from spontaneously hypertensive and Wistar-Kyoto normotensives rats. J. Hypertens 14:435–442
Moore E. D., Etter E. F., Philipson K. D., Carrington W. A., Fogarty K. E., Lifshitz L. M., Fay F. S. (1993) Coupling of the Na+/Ca2+ exchanger, Na+/K+ pump and sarcoplasmic reticulum in smooth muscle. Nature 365:657–660
Muraki K., Imaizumi Y., Watanabe M. (1991) Sodium currents in smooth muscle cells freshly isolated from stomach fundus of the rat and ureter of the guinea-pig. J. Physiol. 442:351–375
Noack T., Deitmer P., Lammel E. (1992) Characterization of membrane currents in single smooth muscle cells from the guinea-pig gastric antrum. J. Physiol. 451:387–417
Noble D. (2004) Modeling the heart. Physiology (Bethesda) 19:191–197
Ohta T., Ito S., Nakazato Y. (1993) Chloride currents activated by caffeine in rat intestinal smooth muscle cells. J. Physiol. 465:149–162
Pullan A., Cheng L., Yassi R., Buist M. (2004) Modelling gastrointestinal bioelectric activity. Prog. Biophys. Mol. Biol. 85:523–550
Sanders K. M. (2001) Invited review: mechanisms of calcium handling in smooth muscles. J. Appl. Physiol. 91:1438–1449
Sanders, K., S. Koh, and S. Ward. Organization and electrophysiology of interstitial cells of cajal and smooth muscle cells in the gastrointestinal tract. In: Physiology of the gastrointestinal tract, edited by L.R. Johnson. Boston: Elsevier Academic Press, 2006, pp. 533–576.
Sanders K. M., Koh S. D., Ward S. M. (2006) Interstitial cells of cajal as pacemakers in the gastrointestinal tract. Annu. Rev. Physiol. 68:307–343
Sims S. M. (1992) Calcium and potassium currents in canine gastric smooth muscle cells. Am. J. Physiol. 262:G859–G867
Sims S. M. (1992) Cholinergic activation of a non-selective cation current in canine gastric smooth muscle is associated with contraction. J. Physiol. 449:377–398
Skinner F. K., Ward C. A., Bardakjian B. L. (1993) Pump and exchanger mechanisms in a model of smooth muscle. Biophys. Chem. 45:253–272
Smirnov S. V., Zholos A. V., Shuba M. F. (1992) A potential-dependent fast outward current in single smooth muscle cells isolated from the newborn rat ileum. J. Physiol. 454:573–589
Splawski I., Timothy K. W., Sharpe L. M., Decher N., Kumar P., Bloise R., Napolitano C., Schwartz P. J., Joseph R. M., Condouris K., Tager-Flusberg H., Priori S. G., Sanguinetti M. C., Keating M. T. (2004) Ca(V)1.2 calcium channel dysfunction causes a multisystem disorder including arrhythmia and autism. Cell 119:19–31
Suzuki H. (2000) Cellular mechanisms of myogenic activity in gastric smooth muscle. Jpn. J. Physiol. 50:289–301
ten Tusscher K. H., Noble D., Noble P. J., Panfilov A. V. (2004) A model for human ventricular tissue. Am. J. Physiol. Heart. Circ. Physiol. 286:H1573–H1589
Thornbury K. D., Ward S. M., Sanders K. M. (1992) Participation of fast-activating, voltage-dependent K currents in electrical slow waves of colonic circular muscle. Am. J. Physiol. 263:C226–236
Tiwari J. K., Sikdar S. K. (1999) Temperature-dependent conformational changes in a voltage-gated potassium channel. Eur. Biophys. J. 28:338–345
Vivaudou M. B., Clapp L. H., Walsh J. V., Jr., Singer J. J. (1988) Regulation of one type of Ca2+ current in smooth muscle cells by diacylglycerol and acetylcholine. Faseb. J. 2:2497–2504
Vogalis F., Sanders K. M. (1990) Cholinergic stimulation activates a non-selective cation current in canine pyloric circular muscle cells. J. Physiol. 429:223–236
Vogalis F., Publicover N. G., Hume J. R., Sanders K. M. (1991) Relationship between calcium current and cytosolic calcium in canine gastric smooth muscle cells. Am. J. Physiol. 260:C1012–C1018
Vogalis F., Publicover N. G., Sanders K. M. (1992) Regulation of calcium current by voltage and cytoplasmic calcium in canine gastric smooth muscle. Am. J. Physiol. 262:C691–C700
Wang Q., Akbarali H. I., Hatakeyama N., Goyal R. K. (1996) Caffeine- and carbachol-induced Cl- and cation currents in single opossum esophageal circular muscle cells. Am. J. Physiol. 271:C1725–C1734
Ward S. M., Dixon R. E., de Faoite A., Sanders K. M. (2004) Voltage-dependent calcium entry underlies propagation of slow waves in canine gastric antrum. J. Physiol. 561:793–810
White C., McGeown J. G. (2000) Regulation of basal intracellular calcium concentration by the sarcoplasmic reticulum in myocytes from the rat gastric antrum. J. Physiol. 529(Pt 2):395–404
Wu C., Fry C. H. (2001) Na(+)/Ca(2+) exchange and its role in intracellular Ca(2+) regulation in guinea pig detrusor smooth muscle. Am. J. Physiol. Cell. Physiol. 280:C1090–C1096
Xiong Z., Sperelakis N., Noffsinger A., Fenoglio-Preiser C. (1995) Ca2+ currents in human colonic smooth muscle cells. Am. J. Physiol. 269:G378–G385
Xu W. X., Kim S. J., So I., Kang T. M., Rhee J. C., Kim K. W. (1997) Volume-sensitive chloride current activated by hyposmotic swelling in antral gastric myocytes of the guinea-pig. Pflugers Arch. 435:9–19
Yamamoto Y., Hu S. L., Kao C. Y. (1989) Inward current in single smooth muscle cells of the guinea pig taenia coli. J. Gen. Physiol. 93:521–550
Yoshino M., Someya T., Nishio A., Yabu H. (1988) Whole-cell and unitary Ca channel currents in mammalian intestinal smooth muscle cells: evidence for the existence of two types of Ca channels. Pflugers Arch. 411:229–231
Yunker A. M., McEnery M. W. (2003) Low-voltage-activated ("T-Type") calcium channels in review. J. Bioenerg. Biomembr. 35:533–575
Acknowledgments
The authors are grateful to Dr. K. Sanders and Dr. G. Farrugia for their advice.
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A sample implementation of the model is available from the authors upon request.
Appendix
Appendix
The main equations of the model are:
• Steady state parameters
Activation: \(\frac{1}{1+e^{-\frac{V_{0.5} +V}{k}}}\) Inactivation: \(\frac{1}{1+e^{\frac{V_{0.5} +V}{k}}}\)
Activation | Inactivation | ||||
---|---|---|---|---|---|
Variable name | V 0.5 (mV) | k | Variable name | V 0.5 (mV) | k |
d | 17 | 4.3 | f | 43 | 8.9 |
d LVA | 27.5 | 10.9 | f LVA | 15.8 | 7 |
x r1 | 27 | 5 | x r2* | 58 | 10 |
x a1 | 26.5 | 7.9 | x a2** | 65 | 6.2 |
d Na | 47 | 4.8 | f Na | 78 | 3 |
m NSCC | 25 | 20 |
• Time constants
Variable name | Time constants (ms) |
---|---|
d | 0.47 |
f | 86 |
d LVA | 3 |
f LVA | \(7.58\ast e^{0.00817\ast V_{\rm m}} \) |
x r1 | 80 |
x r2 | \(-707.0+1481\ast e^\frac{V_{\rm m} +36}{95}\) |
x a1 | \(31.8+175\ast e^{-0.5\ast (\frac{V_{\rm m} +44.4}{22.3})^{2}}\) |
x a2 | 90 |
d Na | −0.017* V m+0.44 |
f Na | −0.25* V m+5.5 |
m NSCC | \(\frac{150}{1+e^{-\frac{V_{\rm m} +66}{26}}}\) |
Model parameters
Parameter name | Description | Value | Units |
---|---|---|---|
R | Ideal gas constant | 8.314 | J/(mol*K) |
T | Temperature | 310 | K |
F | Faraday constant | 96486.7 | C/mol |
C m | Cell membrane capacitance | 77 | pF |
A m | Cell surface | 0.000041 | cm2 |
V c | Total cytoplasmic volume | 3500 | μm3 |
Cao | Extracellular Ca2+ concentration | 2.5 | mM |
Nao | Extracellular sodium concentration | 137 | mM |
Na i | Intracellular sodium concentration | 10 | mM |
K o | Extracellular potassium concentration | 5.9 | mM |
K i | Intracellular potassium concentration | 164 | mM |
Ach | Acetylcholine concentration in absence of muscarinic stimulation | 10 | nM |
G CaL | Maximal conductance for L-type Ca2+ channels | 65 | nS |
G LVA | Maximal conductance for low-voltage activated Ca2+ channels | 0.18 | nS |
G Kr | Maximal conductance for delayed rectifier potassium channels | 35 | nS |
G Ka | Maximal conductance for A-type potassium channels | 9 | nS |
G BK | Maximal conductance for Ca2+-activated potassium channels | 45.7 | nS |
G Kb | Maximal background potassium conductance | 0.014 | nS |
G Na | Maximal conductance for sodium channels | 3 | nS |
G NSCC | Maximal conductance for non-selective cationic channels | 50 | nS |
G couple | Coupling conductance between ICC and SM | 1.3 | nS |
h | Steepness for Ca2+ activation for BK channels | 2 | – |
K bk | Steepness for voltage activation for BK channels | −17 | mV |
Caset | Ca2+ set point for BK channels | 0.001 | mM |
h Ca | Half concentration for the fCa variable | 201.4 | nM |
s Ca | Slope factor for the steady state fCa variable | 13.1 | nM |
E NSCC | Reversal potential for NSCC channels | −28 | mV |
K m-NSCC | Half activation value for Ach activation of NSCC channels | 10 | μM |
n Ach | Hill coefficient for Ach activation of NSCC channels | 1 | – |
K Ca-NSCC | Half activation value for Ca2+ facilitation of NSCC channels | 200 | nM |
n Ca | Hill coefficient for Ca2+ facilitation of NSCC channels | −4 | – |
Q10-Ca | Q10 value for Ca2+ channels | 2.1 | – |
Q10-K | Q10 value for potassium channels | 1.5 | – |
Q10-Na | Q10 value for sodium channels | 2.45 | – |
ΔV ICC | Membrane potential fluctuation in an ICC | 59 | mV |
t ICCpeak | Peak time of the slow wave in an ICC | 98 | ms |
t ICCplateau | Plateau time of the slow wave in the ICC | 7582 | ms |
t ICC | Total time of the slow wave in the ICC | 10,000 | ms |
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Corrias, A., Buist, M.L. A Quantitative Model of Gastric Smooth Muscle Cellular Activation. Ann Biomed Eng 35, 1595–1607 (2007). https://doi.org/10.1007/s10439-007-9324-8
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DOI: https://doi.org/10.1007/s10439-007-9324-8