YCHEXOFEPOHT0/101/11/1 2001 • Bun. 8 YcnexM repowronormm.-2001.-Bun. 8.-C. 27-33
© M.B. CO.TIOBbeB, 2001 r. YAK 612.67:575.113.001.573+577.23
M.B.
C0.110Bbef3
0 BO3MONCHOPI P0.11M XAOTWIECK0r0 1110BEAEHMSI CMCTEMbl rEHHOPI PErYllSILAYM B CTAPEHMM OPFAHM3MA Ht/11/1 OHK0/1011414 14M. npocp. H.H. fleTposa MinHaspaBa
CaHKT-ilerepoypr, 197758, flecovnuri, yn. flennnrpascxas, 68; an. nc-ra: msoloviev@mail.ru
Ha ocHoae: 1) (1)3KTOB H3 6vionortui crapemis, caltaeTenbcTerowinx o TOM, 4TO momilmiaawis aKTHBHOCTH HeCK011b KHX KI1104eBbIX reHOB moweT apHBOCTH K 3Ha41/1TerlbHOMy HsmeHemao npoppnaorreabHocTvi )1013HH; 2) sacnepHmeHTOR C KOMablOTepHb1MH MO/leflAMH reHHOA perynawni, nokasbusatowamm, 4T0 TaKWM cHcremam CBOACTBeHHO meTa-
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oTomcsecrsneHa C noaasaTenem CHabl cmepTHoctii B ypaaHamm romneprio, a BenwanHa, o6parHas noKaaaTenlo 11snyHoaa (spems IlanyHosa) H xapaKTeprisytowas neptio,q, 4epe3 KOTOpbIN cacTema 3a6bisaeT ceoe HavanbHoe (3Roposoe)COCTOSIHHe, HaXOAHTCA B xopowem COOTBeTCTBMW C sospacTom f10/101301-0 cospeearms (T.e. H01-0 sospacTa, AO KOT0p01-0 AOJ1)KHO coxpaHaTbcs 3,qopoBoa COCTOREMe) ABA •-ienoiseaa, MbIUM H AP030431111b1 (opramismoe, 4b1/1 napaMeTpbl cTapeHma 143BeCTHbl C 6036-
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me CHCTeMbI HrKHO OFIHCbIBaTb CTaTHCTIV-IeCKH, B Tepmn-
[9].
Hax aucam6Aeil TpaeKTOpH1). Pa36erarme TpaexTopA
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27
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coomeTcTsylowHe ozunim H TM ace HacoxpaHRer CMbICA (AonycxaeT B onpeAeAeHHoii mepe npeacxasaHHe). ,11eAcTsnTeAbHo, nocAe ,11,0CTaTO9H0 nportoAxinTeAbHoro no cpasHeHHto co apemeHem ARnyHosa nepHop,a 9B0A1-0QH14, HaMATb 0 HaHaAbHOM COCTOAH1411 CHCTeMbI 110AHOCTb10 yTpaRHHaeTcR: 3HaHHe HagaAbH0r0 COCTOAHHA He nossoAReT 6oAee onpezteARTb TpaeKTOpH10. 2. Xaoc no F. Lllycmepy [13]. Axxammecxxii xaOC — 9T0 HenepHosakriecxoe ,L113412KeHHe B iteTepmHHHpoBaHliblX cHcTemax (T.e. B TaKHX, rite 6y,argee 0/1H03HaT4H0 Hmelowee KOHeT4Hblr4 rOpH3014T onpe,aemeTcR nporHosa (onpeikeAsiemmii BpeMeHeM ARnyHosa). ripmRem, KaK npaBHAo, IIpOCTpaHCTBO COCTOAH14174 XaOTHTieCKI4X cHcTem Heo,n,Hopop,Ho. B Hem moryT cyLgecTsosaTb o6Aac TH, r.ae cpAylcryammg mwkeT cxaqkom nepesecni CHCTM B Apyrro 06AaCTb npocTpaHcTsa COCTORHHil. BmecTe C TeM, eCTb 06AaCTH HOBbILLICHHOli yCTOligHBOCTH K cpAyxTyagaRm. 3. Xaoc no 43fc. Hukaaucy [7]. 41,A51 xapaxTepHcTHK14 nose,aeHHA XaOTH‘leCK0ii CHCTeMbI peataiolgee sHaReHme HmeeT ,lyBCTBHTeAbHOCTb K MaAbIM CPAyKTyaUHAM, T.e. K HexoToport Hcxo4Hoii Heonpe,aeAeHHocTH B Ha4aAbHbIX ycA0BHFIX (B 3a4aHHH HAH HsmepeHHH COCTOAHHA). 4A51 TaKHX CHCTeM HagaAbHaff Heonpe4eAeHHocTb 9KCII0HeHUHaAbH0 BospacTaeT co spemeHem AO Tex nop, noxa cAeztylowee COCTOAHHe CHCTeMbl He CTaHOBHTC51 Henpe,acxasyeMbIM. FIOTepA HHCPOpMaUHH 0 HagaAbHOM COCTOAHHH CHCTeMbI nponcxo,n,HT sa xoHenHoe spew' (HpemR ARnyHosa), T.e. no HcTeReHHH aToro HpemeHH CHCTeMa CTaHOEHTC51 npaKTHIleCKH Henpe,ackasyemoii (mo?xHo cxasaTb, Wc0 owH6xa npe,acKasaHas HexoToporo napameTpa cTaHospiTcR comsmepHma co sHameHHem camoro napameTpa). napameTpom, 011HCb1Bal0LEHM cpe,aincao AOKaAbHp0 yCT0174'4HBOCTb, HAH Cpe4111010 CKOpOCTb, C KOTOpOH yrpaRHHaeTcR HHcpopMaWili 0 HagaAbHOM COCTOAHHH, ABAAeTCA 1-10Ka3aTeAb AAnynosa. .me»)
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npoHsoiiiteT op,Ha TaKa5I myragHR, TO, cxopee scero, oHa He AacT 3HaT414TeAbH0r0 scpcpexTa H 6yaeT yCTpaHeHa H3 11011y.A51U11H. HaH6oAee Bep051THO, YTO MyragHH, B pesyAbTaTe KOTOpbIX 11p0HCX0AHT ybeAHReHne r1p021,0A2KHTeAbHOCTI4 TKH3HH, nporicxoART B HeCK0AbKHX KAIOYeBbIX reHax, KOTOpbie yripasAinoT ApyrHmH reHaMH. HHTepecHo, tITO B HeKO" TOpb1X cAyRasix yHeAHReHrie 11p0,40A2KHTeAbHOCTH 2KH3HH AocmraeTcH sa cReT myTaullii B reHax, xoTophie cynpeccHpyioT 6HoxiimHHecime npogeccu, cnoco6cTspoigHe
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cArtaritible 6yAexbi 433,14KQHH TpyAno parrepnperHposam. AAA yAyqutexHB ruirepnperripyemocTH pe3yAbTaTOB MOzteAb C. Kaycpmaxa HaMH 6bIAa momcpHuHposaHa cAeArowpm o6paBoM. ByAeBbl LpyHKUHH Bbl6HpaAHCb He 143 xcero BO3MO1SHOr0 mHomecrsa TaKHX (pp-n(4mA, a TOAbK0 143 'Tex BO3MONCliblX BapHaHTOB: «H», «HAM», «He». ilpH 3TOM BO3M01KHa raKast Hwrepnperawm 3THX (13),HKaHil: «H» — rem A aKTHBeH, eCAH aKTFIBHbl o6a rem X H Y; «HAM» — reH A aKTHBeH, ecAH aKTHBeH OAHH H3 reHOB X HAM Y; «He» — reH A aKTHBeH, eCAH reH X HeaKTI4BeH. Haptizty C 143rIeHHeM cereil C 6HHapHb1M14 COCTOAHHAMH renou, 6bIAM HCCAeA0BaHIDI cerH, rAe COCTOBHHA reHou. MOPAl4 MeHATbCA HenpeptaaHo B AHanaaoHe OT 0 AO 1 (MONieT 6bITb HHTepnpemposarto KaK pa3AH9HaA creneHb DKCnpecc“H reHa). 3TO COOTBeTCTByeT TaK Haabmaemoii HegeTKOii (HAH Hertpepbtaxort) AorHKe. B HeH 6HHapnbte AOni9eckHe CPyHKUHI4 3aMeHAFOTCA Ha HX Henpepbtaxbie 3KBHBaAeHTbI. HamH 6bIA HCCACA0BaH Hart6oAee npoc-ro BapHaHT, B KOTOpOM «H» aamefuleTcx Ha «MHHI4MyM» (min), «HAN» — Ha «maKcHmym» (max), H «He» — Ha oitonoA-
(cpe4Hee
Aux)
9ro6b1
414CAO
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CBA3aHlibIX C AaHHbIM —
6oAee
H CAWKHOCTH (HCCAeA0BaAHCb CHCTeMbl OT OAHOrt AO
reHOB) B OTBeT Ha AericrEsHe cpAyKTyagHil citcTema reHHOH peryAsigHH AemoHcrimposaAa HeyCT0i4911meracra6HAbitoe noBeAeHme, xapaKrepHoe AAA xamrptAeCATH TbI019
Apyroe COCTORHI4e. axcriepHmeHToB, OH BbIC14.33aA 29
M.B. COTIOBbee
CHCTeM — He6oAbwHe Boammemx reHHOH aKTHBHOCTH npwao,AHAH K nepexoay B Apyroe CTa611AbH0e COCTOAHHe. npH 9TOM He 6bIAo o6HappKeHo KatleCTBeHHbIX pa36yAeBbIMH H HetieTKHMH morteAamH. AHYHH
OT
tleCK14X
BI421.140 H3 BbILLIeH3A0>KeHHOCO, C 0411140r4 CT0p0HbI,
cyulecTaamo H3MeHeHa npocTbnw B03/1eACTBHAMH (HanpHmep, 143114eHeHmem aKTHBHOCTH HeCK0AbKHX reHoB). 3T0 KOCBCHHO CBHliereAbcrayeT o TOM, tiTO B KOHTeKCTe 11HHaMHKI4 (T.e. 143meHefflia CBOHCTB BO apemem) OpraHH3M KaK QeAoe ABAAeTCA HeycTorimaoci, MeTaCTa611AbH0r4 CHCTeMOH. C Apyroil CT0p0Hb1, HCCAeA0BaHHA morteAeil CHCTeMbI reHHoii peryARUHH (KOTOpall ABABeTCA KOHetIFIbIM 3BeHOM 60AbILIHHCT11p0/1,0A/KHTeAbHOCTb /14143H14 MO?KeT 6bITb
Ba (1)H3HOAOCHtleCKHX H 6HOXI4MH'IeCKHX 143MeHeHHA, CBA-
co cTapeHHem) noKaabmaioT, ATO oHa momeT ynpaBASITb03 3aKOHaMH xaoca. nO3TOMy npeAcTaaAaeTcx anoAHe 060CHOBaHHbIM npe,anoAoHmTb, ATO 3aKOHbI Xa0Ca HrpalOT KA109eBy10 p0Ab B CTapeHHH Opta1843Ma. BoAee IteTanbno aTa rHnoTe3a momeT 6-bITb 01114CaHa cAe4pww4m o6paaom. 1. HopmaAkHosgHorniposame opramama H, 13 Oco6eHHOCTH, ero peaKgHH Ha cTpeccopnbie B03/1eACTBHA C011150B0Maa1-OTC51 6110X1,1M1,19eCKI4M14 cpAyKTyagaxmH. VHH moryT 6bITb KpancoapemeHHbima (o6paTHmbimH): HanpHmep, AOKaAbHOe II0BbILLIeHHe TemnepaTypial HAM KOHgeHTpagHH HcAeAcTaHe TenAosoro ,aBH111eH1451 H «n06OYHbIX» XHMHtleCKHX H itoAroapemeHHblmu (Heo6paTHMbIMH HAH tlaCTHAHO 06paTI4MbIMH — penamyembimm): HartpHmep, MyTaW4H, HecnegHcimmecKHe mo,n,mimagHH cTpywrypb1 6eAKOB H AH11144,0B acAeAcTeme BO3ael4CTBKH CB0604HbIX paAHKaA0B 14 -aA - ucrpomarmiTHoro 143ArieHHA. Tame qmywryagHH MOfyT 8p14801114Tb K HecnegwpmecKomy 1,13MeHeH1-110 reHHoll aKTHBHOCTH, HanpHmep, BCAeACTNaxe noapeacileom cpparmeErra 4HK HAH OTC0e,(84HeHHA (113-3a AOKaAbHOil TeI1A0B011 (pAyKTyagHH), moAeKy.Abi 6eAKa, 6AompylotEero TpaHcKpHrugHto 4HK. B CBOIO ogepe4b, /twice KpaTKoapememoe Hama-lame reHHoil aKTHBHOCTH MO?KeT npimecTH K CTOHKHM OTKAOHeHHAM B naTTepHe aKTHBHOCTH rams — T.e. ycToilmaomy OTKAOHeHHIO KAeTKH OT HopmaAbHoro COCTOAHHA, K yCT0114HBOMy «HeHopmaAbHomy» CPyl4KUHOHI4p0BaHHIO KAeTKH. no mepe HaK011AeH1451 TaKHX «OTKAOHHBLIIHXCA» KAeTOK nocTenamo yxy4waeTcx cpywcumnwposame TKaHeci, opraHoe. H opraHH3Ma B UeA0M. npH 9TOM OTKAOHeHHA B aKTHBHOCTH Tex reHoa, KOTO3aHlIbIX
+.7
pme 110A111HbI 6bITb yCTOrriHBbl K OTKAOHeHHIO (TaK KaK
pearHpoBaTb Ha
HopmaAbHoro
(PyHKUHOHHp0BaH1451 —
B TO apemst
Tex reHax, tlbA HOpMe He noiwep2Kena OTKAOHeH1410, MO?KeT «ysecTH» KAeTtcy B 06AaCTb Xa0Ca. 2. Hs npe,abuytmero nyuKTa, B tlaCTHOCTH, cAe,ayeT, YTO itaxie npH a6COAIOTHO TO4H0f4 penapagm HAH npH OTCyTCTBHH 3H,a0reHHbIX H 91(301THHbIX noapemaemii MaKpomoAeHyA cTapeme B °pram-fame 6y4eT 11p0HCX0/1,HTb. 3. B HOXHMxveCKHe (pAywryawm He mom 6bITb I4CKAIOtleHbI (HanpHmep, nort ztelicTaHem ecrecTseHHoro OT6opa), TaK KaK 40A1KHa 14MeTbCA onpelteAeHHail 110/41314?KHOCTb moAeKyA 14 14X gacTert (a TaKafl 110,1/13142EHOCTb ae4eT K Bocnomm‘wocTH K ,AdicTakno (pArcryawn1). Be/Lb ecAH 01114 6y,ayT <<CHaAHHbI HamepTaoD, 3TO npimeiteT K «3aCTbIBaH1410>> CHCTeMbl, HeB03MO2KHOCTI4 ee cpyrmun0mposaHeCII0C06HOCTH ocytgecTaAemm ee peryAmpoaamm, KoTopoe Bo MHoroM 06ecnemaaeTcs CAa6bIMH 3.AeKTpoMarHHTHb1MH B3aHM0/1,ekTBIIAMH (HanpHmep, CB513131BaHHe pery.wprowx (PaKTOpOB C 6eAKOM HAH reHom) — T.e. K Hecnoco6HocTH noLa,epxcamx romeocTasa, a Taime ocyWeCTBACHHA oHToreHesa H 9BOA1OUHH. 143 aToro cAeAyeT, tITO apemeHHbie H3MeHeHHA noA 4alcTimem 80TOKa CPAyKTyaUHil HMMaHeHTHbl cHcTeme reHHol-I per-yAxgm. 4pyroe cAeltcTme — He cytgecTayeT oCTHMyA0BD (3130A104HOHH01-0 AaBAeH1451), HanpaaAeHHbot Ha TO, ATO6b1 MHHHMH3Hp0BaTb nospeautems moAeKyA HAM yBeA14.414Tb TOYHOCTb HX penapawm, BOCKOAbKy cTapeHim ace paBHO 6y.ti,eT 8p0HCX0,414Tb H3-3a Apyrmx (HanpHMep, TenAoaboc) cpAyKTyaUHA H nocAe,a,rowero HaprueHag peryAxwin (T.e. OTKAOHelitia OT «HOpMaAbH0ii» TpaeKTopm reHHoii aKTHBHOCTH). 4. B npmgme TO, tITO cTapeme ABASIeTCA XaOTHtleCKI4M npogeccom, cAeztyeT Ha ypatmemx FomnepTga. 3anxwem era B cAe,a,pormem Bpute: µ(t)=µ 0 exp(at), rzte f.t(t) — CHAa CMepTHOCTH B MOMeHT apemeHH t, o HatlaAbHa51 CHAR CMepTHOCTH, a — 110Ka3aTeAb CHAbI cmepTHocTH. Flycrb 2 opraHxama He3HatIHTeAbH0 pa3AHtlaIOTCA B HattaAbHbni MOMeHT apeman.' no po Ha BeAHAHHy 41.0 . Torita gepes spew t pasmtga B HX cHAe CMepTHOCTH L1,1 aKTHBHOCTb B
mexcRy xaocom N crapeemem eexoropme ee cnericreae
OHH 4,0A/KHb1
HOpMaAbHOil 214143HH KAeTOK.
KaK He3HatIHTeAbHble OTKAOHeli1431 B
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xorte T.e. OHH 40AACHb1 H3MeHHTb CBOH aKTHBHOCTb, a noTom BepHyTbca K HopMaAbH0My ypOBH10 aKTHBHOCTH), He ae4yr K OTKAOHeHHIO TaKHe OTKAOHeHHA B
—
cAeApoweil: 4(0 = p.'(t) — µ„ (t) = (µ0, — µ0") exp(at) = exp(at). ria sToro ypatmemx
ycAosHri BeiteT
SHAH°, tITO pa3HOCTb HatlaAbHbIX
pasHHge COCTOAHHil BoapacTom oTpaeKTopm CHAbI cmepTHocTH» paCX04ATCA no 3KCII0HeHUHaAbHOIVfy 3aK0Hy) — T.e. 3BOAIOUHA CHAbI CMepTHOCTH npoHcxwmT TaxK 3KCII0HeHUHaAbHal
(MO/KHO CKa3aTb, YTO C
KaK 3BOA1OUHA XaOTHtieCKHX CHCTeM.
5. alccnoliempaAbtme pacxomytemte «Tpaewroppdt CHAbI CMepTHOCTI4>> 1103BOAAeT Bb1ABHHyTb ripeimoxoace }me, tITO 110Ka3aTeAb aticrrottexTbi (a) B ypasmemat Fom30
YCF1EXV1rEPOHT0/101 - 141/1 • 2001 Bun. 8
.A.snyHosa BeAH9HHe, KOTOpaA x.apaxTepH3yeT cpeAmwo CKOpOCTb 3a6bIBaHHH Ha9aAbH0r0 COCTOAHHA B xaoTHmecmx CHCTeMaX. B cAymae CTaPeHHA aTomy MO2KeT COOTBeTCTBOBaTb 9KCI1OHCHUHaAbH0e 3a6bIBaHHe HaYaAbH0I -0 (3Aoposoro, HOpMaAbH0 peamprowero) COCTORHHA. Pa3BHBaA aTy aHaAorHio AaAbwe, MO2KHO npeAnoAo2KHTb, 9TO opram43m He A0A2KeH 3a6bIBaTb csoe HaTlaAbH0e COCTOHHIle B Tevefuie nepHoAa, AOCTaT09/10r0 AAA peripoAyxgm (HHame roe.ops: 3a6b1BaTb COCTOAHHe 3A0p013b51 1103BOAHTeAbH0, Koma npoH3seAeHo IIOTOMCTB0). TOT-IHOe mawHHe 9Toro nepHoAa 3aBHCHT OT 6H0A0114H HowerHoro sHAa. ELAN (B IlepBOM npH6AHmeHHH) II0A02KPITb ero npHmepso paBHbIM so3pacTy noAosoro CO3peBaHHA H cpasHHTb 3TO 3i-1w9el-we CO spemeHem ABIlyHOBa (1 / ), TO MO2KHO o6HappsHTb, ‘ITO AAA meAosexa, MbILUH H Apo3oCPHAbI (OpraHH3MOB, ‘IbH napameTpbi cTapemis H3BeCTHbI C 60AbIl1011 TO9HOCTb10) 9TH BeAHLIHHbI npHmepHo cosnaAa10T (Ta6A. 2). aTO Ha6mAeHHe corAacyeTcR C AaHHbIMII 0 TOM, 'ITO 60AbLIIHHCTBO C4H31,10A0r1V9eCKHX napameTpos HaYHHalOT yxyAwaTbcs C MOMeHTa noAosoro CO3peBaHHA (CM., HanpHmep, [4]).
nepTga (X) —
spemeHHbim napameTpom, xapaxTepHapoLgfim 6H0A0IIP9eCKHA BHA) — T.e. B TemeHHe 9Toro nepHoAa HY2KHO YAeP/KHBaTb TpaexTopHH B nrixe (He AOITYCKaTb HbIM
MO2KeT COOTBeTCTBOBaTb Il0Ka3aTeA10
3HWIHTeAbH0r0 OTKAOHeHHA OT HOpMaAbH0r0 COCTOAHHA).
B
1
Apoaocfmna**
0,087-0,118 [2] 0,023-0,038 [15] 0,093-0,131 [2]
8,5-11,5 26,3-43,5 7,6-10,8
KaK, C TO9KH
apeHHa Teo-
pHH mwpopmagHH, npomcxoitmT 3a6bmaHHe
HagaAbH0f0
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ARnyHosa csHAeTeAbcTsyer 0
cHcTeme ymeAmmxmaeTcH
TOM, WO
KOAH‘leCTBO HHCPOpMaQPIH (B
(6oAe3Hbl,naTrmecKH)plug. 6. 143 xaoTHmecxoft npmpoAbi reHHoil peryARgHH He nocpeAcTseHHo cAeAyeT, Tro cTapeHHe A0A2KHO 6bITb MHO-' FOCTaAHAFIbIM npogeccom (KaKOBbIM OHO, no 'Keil useposTHOCTH, H ABASIeTCA [14]). n0A, BAHHHHeM cpAperyagnii 11p0HCX0AHT 9BOAIOVA TpaexTopml reHHbix COCTOAHHH OT OAHOFO ycTortmmaoro COCTOAHHA (T.e. CTaAHH) K Apyromy. CKopee stem, 110406HbIii 2fie MHOrOCTaAH1111bIii npogecc AenniT H B ocHose pa3BHTHSI paKOBbIX 3a60AesaHHil. 7.
PaCCMaTpHBaS1
cTapeHme
KaK COBOKyIIHOCTb H3Me-
cHcTeme reHHoli peryARgHH, ynpasAsembix 3axoHaMH xaoca, MO/KHO npeAAommTb 0673ACHeHHe H TaKOMy (\.'+ cpeHomeHy, KaK ymeHbateHHe CHAbI cmepTHocTH B cTapumx so3pacTHbix rpynnax (6oAee Rn ACT). nO.A BAHAHmem r 4 i"p )r.,. 4 cpAyKTyagHil npoHcxoAHT DEIOAIOQHA CHCTeMbI TeHHOii peryAsigHH. npH 3TOM CHCTeMa KaK 6bI oHlMeTD 6oAee clu MHBble COCTOAHHH (meHee yCTOrP-IHBble OHa IIOKHAaeT 110A BAHAHHeM (pAyxTyagHii). C soapacTom BepOATHOCTb HaX01KAeHHSI CHCTeMbI B 6oAee yCTOiNHBOM COCTOAHHH yseAH914BaeTCH. BbIBeCTH cHcTemy H3 ycToilmHsoro COCTOAHHH Tpy4Hee. noaTomy AAA Toro, 91•06bI meAosex 3a60AeA, Hy2KHO 6oAee CHAbH0e someiicTsHe, mem paHbuie. COOTBeTCTBeHHO, KTO He HaX0AHT TaK0I-0 yCTOAIIHBOI*0 COCTOAHHA K AaHHOMy so3pacTy — yMHpaeT. C Apyroil CT0p0HbI, nepHoA pocTa momeT conposomA9TbC5i 110BbILLIeHHOff noTpe6HocTb10 B reHHoii peryugHH, *ITO BeAeT K yse.AHmeHlis) cTeneHeil cmo60,abi reHoperyAHTopHog CHCTeMbI. 3THM momeT 6bITb 06'bACHeHO nommenHas! CHAR CMepTHOCTH B M.AaAIIIHX BO3paCTHbIX rpynnaX. 8. TaxAce, C TO9K143pems xaommectwii npHpoAbi reHHOH MO2KHO nonbrraTbcs TIOHATb, nomemy CTapalm HmeeT mHoro o6wHx mepT y pa3HbIX BHAOB mHoroKAeTOHFIbIX ?KHBOTHbIX. &AMMO, BO mmorom 9T0 MO2KeT 6bITb CBH3aHO C 061MHOCTb10 B OpraHH3aUHH renoMa: CPO CAO2KHOCTH, KOMPleCTBa reHOB, crenemi C13513HOCTH, xapaxTepa C13513HOCTH. nO9TOMy npH B03,AerICTBHH cpAyicryaReHm=1 B
12-15 30-50*** [8] 9 [8]
* A wamepReTcs B 1 40A, ocranbsue Ber1W41411b1 — B ropax. ** HamepRercsi 8 ocranbHble aenw-RiHbi — B cyncax. *** 30 — OT momeHra po(geHmq, 50 — OT momeHra onnoaorsopemnsi.
%yr,
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MACHO
pef3y.AbTaTe cpAyxTyagHil) — T.e. BospacTeT mHCAO cTeneHeil CB060A,b1 CHCTeMbI [7]. B KOHTeKCTe reHHoii peryAsgHH 3T0 0311agaeT, 9TO yBeAHYHBatTCA 9HC.A0 BO3MO2KFIbIX peaxgHii Ha OAHO H TO Am B03AefICTBHe — T.e. K ■KIIpal3flAbHb1M)) (HOpMaAbHbIM, 3Aoposbim, H3Ha‘laAbH0 3anporpamMHp0BaHHb1M) peaKUHRM 71,06aBASHOTCH «HenpasHAbHbie» e
Bo3pacr nonoaoro co3peBaHt4R
M bi wb**
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(3A0p0B0r0) COCTOAHHHopraHH3ma. 1 I0A0HiliTeAbH0e 3Ha-
Ta6m4Lta 2
genoeeK*
A0110AHeHHA K AaHHOMy
npeA,AoncHTb o&bscHeHHe Tomy,
Coomercreme mexpy BpemeHem 11nnyHoBa (T) H H03pacrom nonortoro co3pesaHHB BHA
Ka9eCTBe
3a6b1BaHliH COCTOAHHA
npHATH K cAeAroigHm sbmoAam: a) C TOMKH spemis TeopHH impopmagHH, cTapefwe MONKHO omicaTb Kai( HameHeHHe peaxgHH cHcTembi Ha cnegHciammecnie CHI'HaAbI 110A, BAHAHHem Hecneguctimmecxxx cHrHaAos (cpApayagHii) — T.e. 3a6bwamie npasHAbHoro (PyHKUHOHHp0BaHHA (HAN 3a6bIBaHHe COCTOAHHA 3A0p0B1351); 6) C TemeHHem spemeHH B03M0HiHbIe TpaesTopHH reHHort peryARgsm pa36eraioTc.s (OTKAOHAIOTCH Apyr OT Apyra y pa3HbIX OpraHH3MOB HAH OT HOpMaAbH0r0 COCTOAHHA reHoperyAmTopHoil CHCTeMbI y oAHoro H Toro me OpraHH3Ma) noA AeiicTsHem cpAywryagml. CTeneHb HX pa36eraHHA peryAmpyeTcs eCTeCTBCHHbIM oT6opom; B) npH 3TOM spems AHITyHOBa ABAHeTCH nepHoAom, KorAa MO2KHO CHHTaTb, tITO TpaexTopm4 reHHoii peryAmumm HaX0ASITCH B nymice — T.e. HX pa36eraHHe He3HWIHTeAbH0. saHanasoH 3Ha9eHHA T momer onpeAemincm nepHo4om noAosoro coapeaainim (HAH KaKHM-HH6yA,b Apyrnm no.Ao63,A0p0Bbfl, MOASHO
wig (KoTopme
31
TaK2Ke CX0A,Hbl — BBHAy CX0ACTBa 6HOXH-
M.B. Conoabea
MHH) ,zatHammxa reHHar peryABUHH B o6wem 9B0.110UHOHH-
KOMIIIDIOTepH0r0 M0411,eAHIJOBaHHSI (B TOM HHCAe HCII0Ab3y-
pyeT 4110CTaT09H0 e4HH006pa3Ho. XOTH rippi 3TOM B HaCT-
lowero ocHombre 110A0211eHI-151 TeopHH xaoca) H moAexy-
HbIX cArraax KOHKpeTHbIe Aerami 1-13MeHeHHAreHHori pery-
AapHo-reHeTpNeckoro aHaA113a, nomomeT Bb1511:314Tb (npezt-
ASIgHH (T.e. KaKHe HMeHHO reubi MeHAFOT caoe COCTOAHHe y
CKaBaTb) HOBbIe TOHK11 (reHbI), B034,efiCTBH51 Ha aoTopbre
4a.HHOr0 BH,aa) ripm cTaperwrx moryT pa3A1riaTbC51 BecbMa
cmwEeT 60Aee 3C10CpeKTI3BHO H 110AHO BO3BpaIgaTb TpaekTo-
3Has-IHTeAbHO.
pwo reHHog peryAaww B sztopoaoe COCTOH1114e.
CTOHT 3aMeTHTb, 4TO cyrgecTayroT Teoppm (cm. [21]),
o6bacHaragme aaamogwo H orrorelles mepea Teopmo xao-
Mcreparypa
ca - T.e. H 3130AIOUHOHHOe npomcxors,a,efare craperima MO-
1. Bakaea B.B., TmxoHoaa 0.B., KOXVIH E.M. Hccnenoaaame B03,11e6CTBMS1 pa3/11,14HbIX rtarropoe Ha 11p0gOIDKVITellbHOCT6 *143Hti HemaTo,abi Caenorhabditis elegans // Ycnexv, repoHTon.-2000.-Bun. 4. - C. 153 - 159.
aceT 6bITb o6si3aHo xaocy. KpoMe Toro, xaoc HposisA.HeTcH He TOAbKO B remoii perynagmi, HO H B ApyriAx 6HOXI4MIrieCKHX peaKuHax, a TaK1Ke H Ha KAeTOHHOM ypoBHe, ripmgem
2. raspmnoa Faapvinoaa H.C. Smonorma nponorpkviTenaHocni xmaym.-M.: HayKa, 1986.-168 c.
3TH npogeccbi Taicaie moryT HrpaTb Ba2KHyto poAb B npo-
3. rponakimckm BOOTDHKO B.fl., KmaxameA0B KoribToaep B.K. Ha,qexHocm M cTapemme 61,10/101- W-OCKI4X CHOTem.-Kmes: Haykoaa nymka, 1987.-176 c.
gecce cTapeHHa H pa3WITHH aCCOUHI1p0BaHHbIX C HHM TOAOrHH [27, 31]. 143 Bcero 3Tor0 MO2KHO 3aKAIOHHTb, HTO
cTapeHHe moaleT 11BAHTbCH cAe.acT8Hem XaOTHHeCKOil rippr-
4. Avinbmam B.M. LleTbipe moilenvi menvimmu.-11.: MeLlyakwHa, 1987.-288 C.
po,abr 1K1480171 maTeow B UeAoro.
5. M0p03013 BT., XaBOHCOH B.X. flenTyguible 6,4operynsroobi (25-neTHHH 0116IT aKcnepvimeHranbHoro M KTEIHAVOCKOM MCcne,a0BaHfr1A).-C116.: HayKa, 1996.-74 c.
3aKmogeHme
6. FIVIKI4THH B.H. akcnepmmemTanembie nonxonbi K npo,arieHMO XGA3H14 //. &Armory's, c -rapeHms, / OTB. pen. B. B. Opona-
AAA noitTHepmaeHasi rHnoTe3bi 0 XaOTH4eCK011 npHpo,ae craperwa Heo6xwwmo Bb1511311Tb OCHOBHbIe xapakTe-
kmc.-11.: HayKa, 1982.-C. 548-568.
pliCTHKH renoperyAaTopHbix CHCTeM YeA0BeKa H 211HBOT-
7. H144(01114C 4,4Hamywa HepapxmecKmx cmcrem: 38onioumomioe npeAcTaanerime.-M.: Mmp, 1989.-488 c.
HbIX. aTO 1/101KHO 6y,/1eT C,I1eAaTb nyTeM co ,reTaHma KOM-
8. 06beKT61 emonoryw paaeynAs, / OTB. pen. T. A. „fleTnacp.-M.: HayKa, 1975.-579 c.
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Adv. Gerontol.-2001.-Vol. 8.-P. 27-33
M. V. Soloviev ON POSSIBLE ROLE OF CHAOTIC BEHAVIOR OF THE GENE REGULATION SYSTEM IN AGING N.N. Petrov Research Institute of Oncology, 197758, St. Petersburg, Pesochny-2, Leningradskaya, 68; e-mail: msoloviev@mail.ru 1. The facts of biology of aging say that the modification of activity of few key genes may lead to the significant increase of life span. 2. The experiments with computational models of gene regulation show that these models are characterized by metastable behavior typical for the chaotic systems. 3. The force of mortality in Gompertz equation grows exponentially in time. It allows to hypothesize that at least at the level of gene regulation aging can be a chaotic process (here implied that chaos is a kind of the complex systems dynamics controlled by strictly determined rules). This approach allows to describe aging from the view point of the information theory — as the forgetting of the right functioning of the Organism (i.e. forgetting the state of health) caused by fluctuations (weak nonspecific influencies on the system). Average rate of such forgetting (described by parameter, named Lyapunov exponent) could be identified with the exponent of mortality rate in Gompertz equation. And the parameter inverse to Lyapunov's exponent (Lyapunov time), that describes the time of the initial (healthy) state forgetting, well corresponds to the time of the puberty beginning (i.e. the minimal time for the healthy state to be kept) for human beings, mice, and fruit flies (organisms whose parameters of aging are most perfectly known). Key words: aging, gene regulation, chaos.
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