title: The emergence of subcellular pacemaker sites for calcium waves and oscillations.
abstract: Calcium (Ca(2+)) waves generating oscillatory Ca(2+) signals are widely observed in biological cells. Experimental studies have shown that under certain conditions, initiation of Ca(2+) waves is random in space and time, while under other conditions, waves occur repetitively from preferred locations (pacemaker sites) from which they entrain the whole cell. In this study, we use computer simulations to investigate the self-organization of Ca(2+) sparks into pacemaker sites generating Ca(2+) oscillations. In both ventricular myocyte experiments and computer simulations of a heterogeneous Ca(2+) release unit (CRU) network model, we show that Ca(2+) waves occur randomly in space and time when the Ca(2+) level is low, but as the Ca(2+) level increases, waves occur repetitively from the same sites. Our analysis indicates that this transition to entrainment can be attributed to the fact that random Ca(2+) sparks self-organize into Ca(2+) oscillations differently at low and high Ca(2+) levels. At low Ca(2+), the whole cell Ca(2+) oscillation frequency of the coupled CRU system is much slower than that of an isolated single CRU. Compared to a single CRU, the distribution of interspike intervals (ISIs) of the coupled CRU network exhibits a greater variation, and its ISI distribution is asymmetric with respect to the peak, exhibiting a fat tail. At high Ca(2+), however, the coupled CRU network has a faster frequency and lesser ISI variation compared to an individual CRU. The ISI distribution of the coupled network no longer exhibits a fat tail and is well-approximated by a Gaussian distribution. This same Ca(2+) oscillation behaviour can also be achieved by varying the number of ryanodine receptors per CRU or the distance between CRUs. Using these results, we develop a theory for the entrainment of random oscillators which provides a unified explanation for the experimental observations underlying the emergence of pacemaker sites and Ca(2+) oscillations.
authors.affiliation: Z. Qu: Department of Medicine, David Geffen School of Medicine at UCLA, A2-237 CHS, 650 Charles E. Young Drive South, Los Angeles, CA 90095. zqu@mednet.ucla.edu.
authors.forename: Michael
authors.initials: M
authors.lastname: Nivala
authors.forename: Christopher Y
authors.initials: CY
authors.lastname: Ko
authors.forename: Melissa
authors.initials: M
authors.lastname: Nivala
authors.forename: James N
authors.initials: JN
authors.lastname: Weiss
authors.forename: Zhilin
authors.initials: Z
authors.lastname: Qu
mesh_terms: D000200:Action Potentials; D000818:Animals; D020013:Calcium Signaling; D003198:Computer Simulation; D006352:Heart Ventricles / Q000166:cytology; D008297:Male; D008810:Mice, Inbred C57BL; D032383:Myocytes, Cardiac / Q000378:metabolism* / Q000502:physiology
references.citation: Circ Res. 1997 Oct;81(4):462-9
references.pmid: 9314826
references.citation: Cell. 1997 Oct 31;91(3):367-73
references.pmid: 9363945
references.citation: Circ Res. 2010 May 28;106(10):1582-91
references.pmid: 20378857
references.citation: Phys Rev Lett. 2011 Jun 24;106(25):254102
references.pmid: 21770642
references.citation: J Gen Physiol. 1999 Mar;113(3):469-89
references.pmid: 10051521
references.citation: Physiol Rev. 2007 Apr;87(2):457-506
references.pmid: 17429038
references.citation: Biophys J. 1998 Aug;75(2):595-600
references.pmid: 9675162
references.citation: J Physiol. 1998 May 15;509 ( Pt 1):81-91
references.pmid: 9547383
references.citation: Biophys J. 2011 Jan 19;100(2):271-83
references.pmid: 21244823
references.citation: Biophys J. 2003 Jan;84(1):42-56
references.pmid: 12524264
references.citation: Am J Physiol. 1985 Mar;248(3 Pt 2):H412-8
references.pmid: 4038857
references.citation: J Mol Cell Cardiol. 2009 Oct;47(4):456-74
references.pmid: 19573534
references.citation: J Cardiovasc Electrophysiol. 2006 May;17 Suppl 1:S64-S70
references.pmid: 16686684
references.citation: J Math Biol. 1982;14(1):1-23
references.pmid: 7077182
references.citation: Cell. 1993 Aug 27;74(4):669-77
references.pmid: 8395348
references.citation: Proc Natl Acad Sci U S A. 2007 Sep 18;104(38):14958-63
references.pmid: 17848521
references.citation: EMBO J. 2001 Jan 15;20(1-2):65-76
references.pmid: 11226156
references.citation: Front Physiol. 2012 May 08;3:114
references.pmid: 22586402
references.citation: Cell Calcium. 1996 Aug;20(2):105-21
references.pmid: 8889202
references.citation: Proc Natl Acad Sci U S A. 2003 Jan 21;100(2):506-10
references.pmid: 12518049
references.citation: Am J Physiol. 1996 Jan;270(1 Pt 1):C148-59
references.pmid: 8772440
references.citation: Nature. 1996 Sep 26;383(6598):323-7
references.pmid: 8848043
references.citation: Circ Res. 2000 Jun 9;86(11):1140-5
references.pmid: 10850965
references.citation: Am J Physiol Heart Circ Physiol. 2009 Jul;297(1):H171-80
references.pmid: 19429830
references.citation: Chaos. 2009 Sep;19(3):037111
references.pmid: 19792036
references.citation: J Biol Chem. 1990 Jun 25;265(18):10792-6
references.pmid: 2113061
references.citation: J Biol Chem. 1997 Sep 5;272(36):22654-61
references.pmid: 9278423
references.citation: Circ Res. 2010 Oct 29;107(9):1117-26
references.pmid: 20829511
references.citation: PLoS Comput Biol. 2010 Aug 05;6(8):
references.pmid: 20700497
references.citation: Circ Res. 2012 Feb 17;110(4):569-77
references.pmid: 22223353
references.citation: Biophys J. 1998 Mar;74(3):1149-68
references.pmid: 9512016
references.citation: Proc Natl Acad Sci U S A. 2009 Dec 29;106(52):22275-80
references.pmid: 20018773
references.citation: Biophys J. 1994 Jul;67(1):447-56
references.pmid: 7919018
references.citation: Biophys J. 2008 Oct;95(8):3767-89
references.pmid: 18676655
references.citation: Biophys J. 2008 Mar 15;94(6):2404-11
references.pmid: 18065468
references.citation: Biophys J. 2011 Dec 7;101(11):2638-44
references.pmid: 22261051
references.citation: Circ Res. 2010 Sep 17;107(6):767-75
references.pmid: 20651285
references.citation: Circ Res. 2010 Mar 5;106(4):659-73
references.pmid: 20203315
references.citation: Nat Rev Mol Cell Biol. 2000 Oct;1(1):11-21
references.pmid: 11413485
references.citation: J Mol Cell Cardiol. 2011 Oct;51(4):468-73
references.pmid: 21276796
references.citation: Biophys J. 2007 May 15;92(10):3734-52
references.pmid: 17325022
references.citation: Biophys J. 2008 Jan 15;94(2):392-410
references.pmid: 18160660
references.citation: Biophys J. 2002 Jul;83(1):59-78
references.pmid: 12080100
references.citation: Physiol Rev. 2008 Oct;88(4):1491-545
references.pmid: 18923188
references.citation: IEEE Trans Biomed Eng. 1982 Jun;29(6):456-7
references.pmid: 7106796
references.citation: Am J Physiol Heart Circ Physiol. 2007 Oct;293(4):H2409-17
references.pmid: 17630346
references.citation: J Physiol. 2012 Sep 15;590(18):4403-22
references.pmid: 22495592
references.citation: Science. 1991 Jul 26;253(5018):390-5
references.pmid: 17746394
references.citation: Cardiovasc Res. 2011 Sep 1;91(4):598-605
references.pmid: 21613275
references.citation: J Gen Physiol. 1986 Nov;88(5):589-613
references.pmid: 3783125
references.citation: Proc Natl Acad Sci U S A. 2005 Feb 22;102(8):3099-104
references.pmid: 15710901
references.citation: Circ Res. 2008 Aug 29;103(5):509-18
references.pmid: 18635824
references.citation: Biophys J. 2006 Jul 1;91(1):95-112
references.pmid: 16603499
references.citation: Biophys Chem. 1998 May 5;72(1-2):87-100
references.pmid: 9652087
references.citation: EMBO J. 1999 Oct 1;18(19):5285-99
references.pmid: 10508162
references.citation: Cell. 1993 Aug 27;74(4):661-8
references.pmid: 8395347
references.citation: Circ Res. 1991 Oct;69(4):1022-33
references.pmid: 1934330
references.citation: J Physiol. 2012 Aug 1;590(15):3403-6
references.pmid: 22855048
references.citation: Circ Res. 1999 Feb 19;84(3):266-75
references.pmid: 10024300
references.citation: Biophys J. 2010 Sep 8;99(5):1408-15
references.pmid: 20816052
references.citation: Nature. 2002 Jan 10;415(6868):198-205
references.pmid: 11805843
references.citation: Biophys J. 2012 Jun 6;102(11):2433-42
references.pmid: 22713558
references.citation: Phys Rev E Stat Nonlin Soft Matter Phys. 2001 Mar;63(3 Pt 1):031905
references.pmid: 11308676
references.citation: Am J Physiol Heart Circ Physiol. 2001 Feb;280(2):H535-45
references.pmid: 11158949
references.citation: Am J Physiol Heart Circ Physiol. 2005 Oct;289(4):H1692-701
references.pmid: 15937096