Документ взят из кэша поисковой машины. Адрес оригинального документа : http://www.mce.biophys.msu.ru/archive/doc15426/doc.pdf Дата изменения: Wed Sep 26 14:50:28 2007 Дата индексирования: Mon Oct 1 20:05:27 2012 Кодировка: IBM-866

. ., . ., . ., . .

(, )
, н . - . , . . н , . н , . , Ca2+ . , Ca2+ [1н 3]. , , . , - - . , .
346


. . . -- -- 2006, . 2, . 346н370 Katsnelson L. B. at al -- MCE -- 2006, v. 2, p. 346н370

, , , , , . , , [4н7], - [4]. . , , . . . . , [8, 9]. : , . . [8], [10]. () : , 347


7. , Part 7. Mathematical Models In Biology, Ecology And Chemistry

; Noble'98, , , () (. 1, I, II). , , . , .

. 1. I. . (ix), ; II. ; III:

CaTnC
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. . . -- -- 2006, . 2, . 346н370 Katsnelson L. B. at al -- MCE -- 2006, v. 2, p. 346н370

, . : 1 . CaTnC , [11,12]. 2 . CaTnC CaTnC [11,12]. 3 . TnC л Ё , CaTnC [10,12,13]. CaTn CaTnC , , , / . , CaTnC. , CaTnC, - , .. - [14, 15], - , .. Ca2+ нн [12,15]. , . , Ca2+ , , [Ca2+]i. , CaTnC , , [Ca2+]i Na+-Ca2+ 349


7. , Part 7. Mathematical Models In Biology, Ecology And Chemistry

( ) [8]. , . (NA), , CaTnC:

dA = aon ( Atot - A) CaC - a off exp(-k A A) ( N A ) A, dt
A н CaTnC, NA н , CaTnC. , NA . () . [10]. , , . . , N, . CaTnC (A), LOZ(l1), l1, n1(l1) н , лЁ ; n1 l1 . N н н , 350


. . . -- -- 2006, . 2, . 346н370 Katsnelson L. B. at al -- MCE -- 2006, v. 2, p. 346н370

/ . , , /. NA N: NA=N/(LOZ*A). , (NA), , (N/(LOZ*A)), . , , (N/(LOZ*A)) , CaTnC, . () н , н [8,9,15]. , , . (. 1 3). н , , ( ), . , , . ( ). , 351


7. , Part 7. Mathematical Models In Biology, Ecology And Chemistry

. , , . in vivo. , [8,9,16]. . : , - . () , (40 н 120 ), . , н 60 : Fm ( ) = =6.662 ( , 0.95Lmax, Lmax , ); t30 ( 30% Fm) = =188 . , , ,
352


. . . -- -- 2006, . 2, . 346н370 Katsnelson L. B. at al -- MCE -- 2006, v. 2, p. 346н370

, ~ 0.95Lmax. , 0.95Lmax , . - .

2. Na+-K+ . L=0.95Lmax; 75 ./. I: , II: Ca2+ , III: Na+ 300

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7. , Part 7. Mathematical Models In Biology, Ecology And Chemistry

. 3. , .2. I. : (F), (2+) () 156 ? 179 . ( 0.8 .). 2 : (i) (ii). II. , (i) (ii).

() - Na+-K+ , : Na+, 65% Km,Na (40 mM -

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. . . -- -- 2006, . 2, . 346н370 Katsnelson L. B. at al -- MCE -- 2006, v. 2, p. 346н370

24.2 mM), , . (, ). . , 75 , . (60 ) : Fm = =7.126 (.. 107% ); t30= 227 (.. 120% ). , 75 (. .2, 0.95Lmax). ~200 , (. 3). , , . , 75 , , 0.95Lmax. , , Na+-K+ . Na+-K+ [Na+]i. , 75 , ( Na+-Ca2+ н reverse mode) Ca2+ . () Ca2+ .
355


7. , Part 7. Mathematical Models In Biology, Ecology And Chemistry

Ca2+ , ( Na+-Ca2+ н forward mode) , , . , , , , . Noble Varghese (1998) [4] ( ) Na+-K+ . EarmHilgeman-Noble [17, 18], Noble'98. , Ca2+. , , . , Na+-K+ , , Noble-Varghese 20 mM ~9 mM, . Ca2+ , . Ca2+ Ca2+ , . Ca2+ ( 1,5 , ) , , , . Earm-Hilgeman-Noble н , .
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. . . -- -- 2006, . 2, . 346н370 Katsnelson L. B. at al -- MCE -- 2006, v. 2, p. 346н370

. 4. , л Ё . 3. , (i) . 3 (II). . , (i) . 3 (II)

, (*) . 3, . 3 , , , . 2,3. . 4 . , . 4, . 3 (. II, (i)) л Ё Ca2+ , (*), ~ 745 357


7. , Part 7. Mathematical Models In Biology, Ecology And Chemistry

() . н ( . 3, II (i)). (1) Noble'98 ( , ) R, Ca2+ . , . R : R, (. л Ca2+ Ё ). , R Ca2+. (2) [Ca2+] . Ca2+ , , , (. . 4, V). (3) Ca2+ ( ) , , н , ( (5) ). (4) [Ca2+]i R (. . 4, IV) , , , Ca2+. , Ca2+, , - [Ca2+]i. (5) , [Ca2+]i ,
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. . . -- -- 2006, . 2, . 346н370 Katsnelson L. B. at al -- MCE -- 2006, v. 2, p. 346н370

. , . 4, , 1 . , (N/(LOZ*A)) CaTnC (. , dA/dt CaTnC). . 4 , (N/(LOZ*A)). , CaTnC ( I) ( 745 ), N ( II) . , CaTnC, .. N/A ( III) . , . 4 ( N/A , ). (N/(LOZ*A)) (LOZ ). (N/(LOZ*A)) CaTnC, ( IV). , Ca2+, TnC 1 ((N/(LOZ*A))). лЁ лЁ . , Ca2+ , Ca2+, TnC, Na+-Ca2+ . Ca2+ . Na+-Ca2+ Ca2+, TnC. , Ca2+ , V. Ca2+
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7. , Part 7. Mathematical Models In Biology, Ecology And Chemistry

((1) н (4)), .

. 5. .

, N/A 1 ((N/(LOZ*A))) , , (ii) II . 3. н , (i), , (N/(LOZ*A)) min . (~330 ) (ii). , (N/(LOZ*A)) min , CaTnC , ,

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N/A CaTnC. , , , (i), . , ( н ) (). , (1) н (5) , , . 2 н 4, , , . 5. , 156.8 (.. , . 3, I). 23 136 . () ( ) - . . , , . , , - . - -. ( , ) , .. . -, 361


7. , Part 7. Mathematical Models In Biology, Ecology And Chemistry

Km,Na 57% , , 0.95Lmax. -, Na+-K+ (~5%), 360 . , . - ( ) -. . . . 6. 75 90% Lmax, ( Lmax) . 90% Lmax. / 0 360 . . I - ( (1)) ( (2)), 0.9Lmax (75 ). (1) , . II, III, IV , , ( ). II , III н 362


. . . -- -- 2006, . 2, . 346н370 Katsnelson L. B. at al -- MCE -- 2006, v. 2, p. 346н370

- 30 -, IV, , н - 30 -. , ( - 1, - 2). , , . I, - (140 н 147 ). , , . ( II) 2 . - - ( , - I, 140 155 ). н -, . ~160 ~180 , . ( III IV . 6) -. , - (.. Na+-K+ ) ( III): (~160 н ~180 ) , ( II); - (.. Na+-K+ ) (~112 ) (10 15 ), II . , Na+-K+ (-) , (-

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IV), , . , , - ~171 ~181 , - ~172 ~188 . , ( III IV).

. 6. , . I: ; II: ; III, IV: (‘30 )

, , , . , , IV . 6, 364


. . . -- -- 2006, . 2, . 346н370 Katsnelson L. B. at al -- MCE -- 2006, v. 2, p. 346н370

, , . , - . . () - - . , , , . - , 75 , ( 0 360 ), . 0.9Lmax -, . . 7 , : 0.9Lmax, 0.88Lmax, 0.85Lmax, 0.82Lmax (, , , ( SE, . . 1), ). . , . , I (2) . 6, - 0.9Lmax, .
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7. , Part 7. Mathematical Models In Biology, Ecology And Chemistry

, 0.88Lmax. , , 268 280 . , : 190 205 0.85Lmax 151 169 0.82Lmax.

. 7. , -, : I: 0.91Lmax ; II: 0.88Lmax; III: 0.85Lmax ; IV: 0.82Lmax

5 - , 0.5Fm 0.9Fm. 0.9Lmax, н 75
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. Fm -, ( , Fm , I . 7). , , / . 0.9Fm, 0.8Fm 0.7Fm. 0.6Fm 0.5Fm, , : 198 213 0.6Fm, 170 187 0.5Fm. . , , , Na+-K+ . , , . Na+K+ , Na+ , , , . , , , , , . , , , . , Na+-K+ , [19]. , , [19]. , 367


7. , Part 7. Mathematical Models In Biology, Ecology And Chemistry

Na+-K+ . [4н7,20] , , Na+нK+ [4]. , , . , (1) / CaTnC 1 ; (2) н ; (3) ; (4) , Na+-K+ / . , , .


1. Kihara Y. and Morgan J.P. Intracellular calcium and ventricular fibrillation. Studies in the aequorin-loaded isovolumic ferret heart // Circ Res. 1991. -- Vol. 68. -- 5. -- P. 1378н1389. 2. Lakatta E.G. and Guarnieri T. Spontaneous myocardial calcium oscillations: are they linked to ventricular fibrillation? // J Cardiovasc Electrophysiol, 1993. -- Vol. 4. -- 4. -- P. 473н489. 3. Thandroyen F.T., Morris A.C., Hagler H.K., Ziman B., Pai L., Willerson J.T. and Buja L.M. Intracellular calcium transients and arrhythmia in isolated heart cells // Circ Res, 1991. -- Vol. 69. -- 3. -- P. 810н819. 4. Noble D. and Varghese A. Modelling of sodium-overload arrhythmias and their suppression // Can J Cardiol, 1998. -- Vol. 14. -- 1. -- P. 97н 100.

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5. Luo C.H. and Rudy Y. A dynamic model of the cardiac ventricular action potential. II. Afterdepolarizations, triggered activity, and potentiation // Circ Res, 1994. -- Vol. 74. -- 6. -- P. 1097н1113. 6. Noble D. Modeling the heart - from genes to cells to the whole organ // Science, 2002. -- Vol. 295. -- 5560. -- P. 1678н1682. 7. Noble D. Modelling the heart: insights, failures and progress // Bioessays,. 2002. -- Vol. 24. -- 12. -- P. 1155н1163. 8. Solovyova O., Vikulova N., Katsnelson L.B., Markhasin V.S., Noble P.J., Garny A.F., Kohl P. and Noble D. Mechanical interaction of heterogeneous cardiac muscle segments in silico: effects on Ca2+ handling and action potential // International Journal of Bifurcation and Chaos, 2003. -- Vol. 13. -- 12. -- P. 3757н3782. 9. Markhasin V.S., Solovyova O., Katsnelson L.B., Protsenko Y., Kohl P. and Noble D. Mechano-electric interactions in heterogeneous myocardium: development of fundamental experimental and theoretical models // Prog Biophys Mol Biol, 2003. -- Vol. 82. -- 1н3. -- P. 207н220. 10. Katsnelson L.B., Nikitina L.V., Chemla D., Solovyova O., Coirault C., Lecarpentier Y. and Markhasin V.S. Influence of viscosity on myocardium mechanical activity: a mathematical model // J Theor Biol, 2004. -- Vol. 230. -- 3. -- P. 385н405. 11. Gordon A.M., Regnier M. and Homsher E. Skeletal and cardiac muscle contractile activation: tropomyosin "rocks and rolls" // News Physiol Sci., 2001. -- Vol. 16. -- P. 49н55. 12. Katsnelson L.B. and Markhasin V.S. Mathematical modeling of relations between the kinetics of free intracellular calcium and mechanical function of myocardium // J Mol Cell Cardiol, 1996. -- Vol. 28. -- 3. -- P. 475н486. 13. Murray J.M. and Weber A. Cooperativity of the calcium switch of regulated rabbit actomyosin system // Mol Cell Biochem, 1981. -- Vol. 35. -- 1. -- P. 11н15. 14. Izakov V., Katsnelson L.B., Blyakhman F.A., Markhasin V.S. and Shklyar T.F. Cooperative effects due to calcium binding by troponin and their consequences for contraction and relaxation of cardiac muscle under various conditions of mechanical loading // Circ Res, 1991. -- Vol. 69. -- 5. -- P. 1171н1184. 15. Solovyova O., Katsnelson L., Guriev S., Nikitina L., Protsenko Y., Routkevitch S. and Markhasin V. Mechanical inhomogeneity of myocardium studied in parallel and serial cardiac muscle duplexes: experiments and

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models // Chaos Solitons Fractals. 2002. Vol. 13, 8. P. 1685-1711. 16. Solovyova O., Katsnelson L.B., Konovalov P., Lookin O., Moskvin A.S., Protsenko Y.L., Vikulova N., Kohl P. and Markhasin V.S. Activation sequence as a key factor in spatio-temporal optimization of myocardial function // Phil Trans R Soc Lond A, 2006. (submitted). 17. Hilgemann, D.W. and Noble D. Excitation-contraction coupling and extracellular calcium transients in rabbit atrium: reconstruction of basic cellular mechanisms // Proc R Soc Lond B Biol Sci, 1987. -- Vol. 230. -- 1259. -- P. 163н205. 18. Earm, Y.E. and Noble D. A model of the single atrial cell: relation between calcium current and calcium release // Proc R Soc Lond B Biol Sci, 1990. -- Vol. 240. -- 1297. -- P. 83н96. 19. Charlemagne D., Orlowski J., Oliviero P., Rannou F., Sainte Beuve C., Swynghedauw B. and Lane L.K. Alteration of Na,K-ATPase subunit mRNA and protein levels in hypertrophied rat heart // J Biol Chem, 1994. -- Vol. 269. -- 2. -- P. 1541н1547. 20. DiFrancesco, D. and Noble D. A model of cardiac electrical activity incorporating ionic pumps and concentration changes // Philos Trans R Soc Lond B Biol Sci, 1985. -- Vol. 307. -- 1133. -- P. 353н98.

MATHEMATICAL MODELING OF SOME ELECTROMECHANICAL FUNCTION DISTORBANCES OF VENTRICLE CARDIOMYOCYTES Katsnelson L. B., Sulman T. B., Solovyova O. E., Markhasin V. S.

(Russia, Ekaterinburg)
Calcium overload of cardiomyocytes may result in their spontaneous electrical activity, not rarely leading to extra-contractions нн extrasystoles. One of the prevalent causes of calcium overload is attenuation of the sodium-potassium pump activity. We studied this phenomenon by means of mathematical modeling, particularly being focused on the contribution of the mechanical factors to the arrhythmia arising and development.
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