Skip to main content
NCBI home page
Biophysical Journal logoLink to Biophysical Journal
. 1996 Dec;71(6):3064–3072. doi: 10.1016/S0006-3495(96)79500-0

Analytical steady-state solution to the rapid buffering approximation near an open Ca2+ channel.

G D Smith 1
PMCID: PMC1233795  PMID: 8968577

Abstract

We derive an analytical steady-state solution for the Ca2+ profile near an open Ca2+ channel based on a transport equation which describes the buffered diffusion of Ca2+ in the presence of rapid stationary and mobile Ca2+ buffers (Wagner and Keizer, 1994). This steady-state rapid buffering approximation gives an upper bound on local Ca2+ elevations such as Ca2+ puffs or sparks when conditions for the validity of the rapid buffering approximation are met and is an alternative to approximations that assume that mobile buffers are unsaturable. This result also provides an analytical estimate of the cytosolic Ca2+ domain concentration ([Ca2+]d) near a channel pore and shows the dependence of [Ca2+]d on moderate concentrations of endogenous mobile buffer, Ca2+ indicator dye, and bulk cytosolic Ca2+. Assuming a simple relationship between [Ca2+]d and the lumenal depletion domain of an intracellular Ca2+ channel, lumenal and cytosolic Ca2+ profiles are matched to give an implicit analytical expression for the effect of bulk lumenal Ca2+ on [Ca2+]d.

Full text

PDF
3064

Selected References

These references are in PubMed. This may not be the complete list of references from this article.

  1. Adler E. M., Augustine G. J., Duffy S. N., Charlton M. P. Alien intracellular calcium chelators attenuate neurotransmitter release at the squid giant synapse. J Neurosci. 1991 Jun;11(6):1496–1507. doi: 10.1523/JNEUROSCI.11-06-01496.1991. [DOI] [PMC free article] [PubMed] [Google Scholar]
  2. Allbritton N. L., Meyer T., Stryer L. Range of messenger action of calcium ion and inositol 1,4,5-trisphosphate. Science. 1992 Dec 11;258(5089):1812–1815. doi: 10.1126/science.1465619. [DOI] [PubMed] [Google Scholar]
  3. Bezprozvanny I., Ehrlich B. E. Inositol (1,4,5)-trisphosphate (InsP3)-gated Ca channels from cerebellum: conduction properties for divalent cations and regulation by intraluminal calcium. J Gen Physiol. 1994 Nov;104(5):821–856. doi: 10.1085/jgp.104.5.821. [DOI] [PMC free article] [PubMed] [Google Scholar]
  4. Bezprozvanny I., Ehrlich B. E. The inositol 1,4,5-trisphosphate (InsP3) receptor. J Membr Biol. 1995 Jun;145(3):205–216. doi: 10.1007/BF00232713. [DOI] [PubMed] [Google Scholar]
  5. Cannell M. B., Cheng H., Lederer W. J. Spatial non-uniformities in [Ca2+]i during excitation-contraction coupling in cardiac myocytes. Biophys J. 1994 Nov;67(5):1942–1956. doi: 10.1016/S0006-3495(94)80677-0. [DOI] [PMC free article] [PubMed] [Google Scholar]
  6. Cannell M. B., Cheng H., Lederer W. J. The control of calcium release in heart muscle. Science. 1995 May 19;268(5213):1045–1049. doi: 10.1126/science.7754384. [DOI] [PubMed] [Google Scholar]
  7. Cheng H., Lederer W. J., Cannell M. B. Calcium sparks: elementary events underlying excitation-contraction coupling in heart muscle. Science. 1993 Oct 29;262(5134):740–744. doi: 10.1126/science.8235594. [DOI] [PubMed] [Google Scholar]
  8. Clapham D. E. Calcium signaling. Cell. 1995 Jan 27;80(2):259–268. doi: 10.1016/0092-8674(95)90408-5. [DOI] [PubMed] [Google Scholar]
  9. DeFelice L. J. Molecular and biophysical view of the Ca channel: a hypothesis regarding oligomeric structure, channel clustering, and macroscopic current. J Membr Biol. 1993 May;133(3):191–202. doi: 10.1007/BF00232019. [DOI] [PubMed] [Google Scholar]
  10. Heinemann C., Chow R. H., Neher E., Zucker R. S. Kinetics of the secretory response in bovine chromaffin cells following flash photolysis of caged Ca2+. Biophys J. 1994 Dec;67(6):2546–2557. doi: 10.1016/S0006-3495(94)80744-1. [DOI] [PMC free article] [PubMed] [Google Scholar]
  11. Horne J. H., Meyer T. Luminal calcium regulates the inositol trisphosphate receptor of rat basophilic leukemia cells at a cytosolic site. Biochemistry. 1995 Oct 3;34(39):12738–12746. doi: 10.1021/bi00039a033. [DOI] [PubMed] [Google Scholar]
  12. Jafri M. S., Keizer J. On the roles of Ca2+ diffusion, Ca2+ buffers, and the endoplasmic reticulum in IP3-induced Ca2+ waves. Biophys J. 1995 Nov;69(5):2139–2153. doi: 10.1016/S0006-3495(95)80088-3. [DOI] [PMC free article] [PubMed] [Google Scholar]
  13. Mazzanti M., DeFelice L. J., Liu Y. M. Gating of L-type Ca2+ channels in embryonic chick ventricle cells: dependence on voltage, current and channel density. J Physiol. 1991 Nov;443:307–334. doi: 10.1113/jphysiol.1991.sp018835. [DOI] [PMC free article] [PubMed] [Google Scholar]
  14. Monck J. R., Robinson I. M., Escobar A. L., Vergara J. L., Fernandez J. M. Pulsed laser imaging of rapid Ca2+ gradients in excitable cells. Biophys J. 1994 Aug;67(2):505–514. doi: 10.1016/S0006-3495(94)80554-5. [DOI] [PMC free article] [PubMed] [Google Scholar]
  15. Nelson M. T., Cheng H., Rubart M., Santana L. F., Bonev A. D., Knot H. J., Lederer W. J. Relaxation of arterial smooth muscle by calcium sparks. Science. 1995 Oct 27;270(5236):633–637. doi: 10.1126/science.270.5236.633. [DOI] [PubMed] [Google Scholar]
  16. Parker I., Yao Y. Ca2+ transients associated with openings of inositol trisphosphate-gated channels in Xenopus oocytes. J Physiol. 1996 Mar 15;491(Pt 3):663–668. doi: 10.1113/jphysiol.1996.sp021247. [DOI] [PMC free article] [PubMed] [Google Scholar]
  17. Risso S., DeFelice L. J. Ca channel kinetics during the spontaneous heart beat in embryonic chick ventricle cells. Biophys J. 1993 Sep;65(3):1006–1018. doi: 10.1016/S0006-3495(93)81147-0. [DOI] [PMC free article] [PubMed] [Google Scholar]
  18. Rizzuto R., Brini M., Murgia M., Pozzan T. Microdomains with high Ca2+ close to IP3-sensitive channels that are sensed by neighboring mitochondria. Science. 1993 Oct 29;262(5134):744–747. doi: 10.1126/science.8235595. [DOI] [PubMed] [Google Scholar]
  19. Roberts W. M. Localization of calcium signals by a mobile calcium buffer in frog saccular hair cells. J Neurosci. 1994 May;14(5 Pt 2):3246–3262. doi: 10.1523/JNEUROSCI.14-05-03246.1994. [DOI] [PMC free article] [PubMed] [Google Scholar]
  20. Roberts W. M. Spatial calcium buffering in saccular hair cells. Nature. 1993 May 6;363(6424):74–76. doi: 10.1038/363074a0. [DOI] [PubMed] [Google Scholar]
  21. Sherman A., Keizer J., Rinzel J. Domain model for Ca2(+)-inactivation of Ca2+ channels at low channel density. Biophys J. 1990 Oct;58(4):985–995. doi: 10.1016/S0006-3495(90)82443-7. [DOI] [PMC free article] [PubMed] [Google Scholar]
  22. Silver R. A., Lamb A. G., Bolsover S. R. Calcium hotspots caused by L-channel clustering promote morphological changes in neuronal growth cones. Nature. 1990 Feb 22;343(6260):751–754. doi: 10.1038/343751a0. [DOI] [PubMed] [Google Scholar]
  23. Simon S. M., Llinás R. R. Compartmentalization of the submembrane calcium activity during calcium influx and its significance in transmitter release. Biophys J. 1985 Sep;48(3):485–498. doi: 10.1016/S0006-3495(85)83804-2. [DOI] [PMC free article] [PubMed] [Google Scholar]
  24. Smith G. D., Wagner J., Keizer J. Validity of the rapid buffering approximation near a point source of calcium ions. Biophys J. 1996 Jun;70(6):2527–2539. doi: 10.1016/S0006-3495(96)79824-7. [DOI] [PMC free article] [PubMed] [Google Scholar]
  25. Stern M. D. Buffering of calcium in the vicinity of a channel pore. Cell Calcium. 1992 Mar;13(3):183–192. doi: 10.1016/0143-4160(92)90046-u. [DOI] [PubMed] [Google Scholar]
  26. Swillens S., Combettes L., Champeil P. Transient inositol 1,4,5-trisphosphate-induced Ca2+ release: a model based on regulatory Ca(2+)-binding sites along the permeation pathway. Proc Natl Acad Sci U S A. 1994 Oct 11;91(21):10074–10078. doi: 10.1073/pnas.91.21.10074. [DOI] [PMC free article] [PubMed] [Google Scholar]
  27. Thorn P., Lawrie A. M., Smith P. M., Gallacher D. V., Petersen O. H. Local and global cytosolic Ca2+ oscillations in exocrine cells evoked by agonists and inositol trisphosphate. Cell. 1993 Aug 27;74(4):661–668. doi: 10.1016/0092-8674(93)90513-p. [DOI] [PubMed] [Google Scholar]
  28. Tripathy A., Meissner G. Sarcoplasmic reticulum lumenal Ca2+ has access to cytosolic activation and inactivation sites of skeletal muscle Ca2+ release channel. Biophys J. 1996 Jun;70(6):2600–2615. doi: 10.1016/S0006-3495(96)79831-4. [DOI] [PMC free article] [PubMed] [Google Scholar]
  29. Tucker T., Fettiplace R. Confocal imaging of calcium microdomains and calcium extrusion in turtle hair cells. Neuron. 1995 Dec;15(6):1323–1335. doi: 10.1016/0896-6273(95)90011-x. [DOI] [PubMed] [Google Scholar]
  30. Wagner J., Keizer J. Effects of rapid buffers on Ca2+ diffusion and Ca2+ oscillations. Biophys J. 1994 Jul;67(1):447–456. doi: 10.1016/S0006-3495(94)80500-4. [DOI] [PMC free article] [PubMed] [Google Scholar]
  31. Yao Y., Choi J., Parker I. Quantal puffs of intracellular Ca2+ evoked by inositol trisphosphate in Xenopus oocytes. J Physiol. 1995 Feb 1;482(Pt 3):533–553. doi: 10.1113/jphysiol.1995.sp020538. [DOI] [PMC free article] [PubMed] [Google Scholar]
  32. Zhou Z., Neher E. Mobile and immobile calcium buffers in bovine adrenal chromaffin cells. J Physiol. 1993 Sep;469:245–273. doi: 10.1113/jphysiol.1993.sp019813. [DOI] [PMC free article] [PubMed] [Google Scholar]
  33. Zucker R. S., Fogelson A. L. Relationship between transmitter release and presynaptic calcium influx when calcium enters through discrete channels. Proc Natl Acad Sci U S A. 1986 May;83(9):3032–3036. doi: 10.1073/pnas.83.9.3032. [DOI] [PMC free article] [PubMed] [Google Scholar]
  34. Zweifach A., Lewis R. S. Rapid inactivation of depletion-activated calcium current (ICRAC) due to local calcium feedback. J Gen Physiol. 1995 Feb;105(2):209–226. doi: 10.1085/jgp.105.2.209. [DOI] [PMC free article] [PubMed] [Google Scholar]

Articles from Biophysical Journal are provided here courtesy of The Biophysical Society

RESOURCES