YCHEXOFEPOHT0/101/11/1 2001 • Bun. 8

© M.B. CO.TIOBbeB, 2001 r. YcnexM repowronormm.-2001.-Bun. 8.-C. 27-33

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

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cmepTHocTii (no romnepT4Y), BbImmiraercs rwnOTe3a o

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27

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nynosa.

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28

YCilEX1/1 rEPOHT01101 - 1/11/1 • 2001 • Bbin. 8 •

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•

•

4

momer CAyN4I4Tb Bum AHU.lb OAHH reH) H aKTI4BHp0BaHO B

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xapaKTep, 6A1431C14i1 K 3KCTIOHeH13Na.AbHOMy [30]. TaK, B

pa6oTe [19] Ha KHLUe9410r1 naAo9Ke 6bIAa npoitemoHcTpH-

portaHa npHmepHo 3KCHOHeHl1HaAbHaA 3aBHCHMOCTb mexc-

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aAbHOMy [23].

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HAM Y; «He» — reH A aKTHBeH, eCAH reH X HeaKTI4BeH.

Haptizty C 143rIeHHeM cereil C 6HHapHb1M14 COCTOAHHAMH

renou, 6bIAM HCCAeA0BaHIDI cerH, rAe COCTOBHHA reHou. MOP-

Al4 MeHATbCA HenpeptaaHo B AHanaaoHe OT 0 AO 1 (MONieT

6bITb HHTepnpemposarto KaK pa3AH9HaA creneHb DKC-

npecc“H reHa). 3TO COOTBeTCTByeT TaK Haabmaemoii He-geTKOii (HAH Hertpepbtaxort) AorHKe. B HeH 6HHapnbte AO-

ni9eckHe CPyHKUHI4 3aMeHAFOTCA Ha HX Henpepbtaxbie 3K-

BHBaAeHTbI. HamH 6bIA HCCACA0BaH Hart6oAee npoc-ro Ba-

pHaHT, B KOTOpOM «H» aamefuleTcx Ha «MHHI4MyM» (min),

«HAN» — Ha «maKcHmym» (max), H «He» — Ha oitonoA-HeHHe» (corn, rAe com(x)=1—x). FlpHmepbt BbIgHCAe1414R

COCTOAHHA reHa A, castaaHHoro C reHamit X, Y, Z moryT BbIrAAAeTb TaK: A=max[X, min(Y, com(Z)] HAH

A=min[X, max(Y, Z)].

C mo.aeAblo 6blA npoae.aeH cAe.apoloil mcnepHmeHT:

gepes onpe.aeAeHHbie npome)KyricH apemem Ha mo.aeAb BosileiicTsosaAa cArtarmast cpAywryagm — nptiHyAmeA8- HO H3MeHAA0Cb COCTOAHHe oAHoro HAH HeCK0AbKHX reHos. npH 3TOM H3y9.3.AHCb HameHemut AHHaMHKH moiteAH.

314 aKcnepHmeHrbt HoAraepAHAH pesyAbramt, HoAy-9eHH8te C. KayclimaHom. npH onpe,aeAemori CBS13140CTH

(cpe4Hee 414CAO reHOB, CBA3aHlibIX C AaHHbIM — 6oAee Aux) H CAWKHOCTH (HCCAeA0BaAHCb CHCTeMbl OT OAHOrt AO

AeCATH TbI019 reHOB) B OTBeT Ha AericrEsHe cpAyKTyagHil citcTema reHHOH peryAsigHH AemoHcrimposaAa HeyCT0i4911-

meracra6HAbitoe noBeAeHme, xapaKrepHoe AAA xamrpt-

• •

29

M.B. COTIOBbee

+.7

tleCK14X CHCTeM — He6oAbwHe Boammemx reHHOH aKTHB-

HOCTH npwao,AHAH K nepexoay B Apyroe CTa611AbH0e COCTO-

AHHe. npH 9TOM He 6bIAo o6HappKeHo KatleCTBeHHbIX pa3-

AHYHH 6yAeBbIMH H HetieTKHMH morteAamH.

r1100T030 0 CIMIN mexcRy xaocom N crapeemem eexoropme ee cnericreae

KaK BI421.140 H3 BbILLIeH3A0>KeHHOCO, C 0411140r4 CT0p0HbI,

11p0/1,0A/KHTeAbHOCTb /14143H14 MO?KeT 6bITb cyulecTaamo H3MeHeHa npocTbnw B03/1eACTBHAMH (HanpHmep, 143114eHe-

Hmem aKTHBHOCTH HeCK0AbKHX reHoB). 3T0 KOCBCHHO CBH-

liereAbcrayeT o TOM, tiTO B KOHTeKCTe 11HHaMHKI4 (T.e. 143-

meHefflia CBOHCTB BO apemem) OpraHH3M KaK QeAoe ABAA-

eTCA HeycTorimaoci, MeTaCTa611AbH0r4 CHCTeMOH. C Apyroil

CT0p0Hb1, HCCAeA0BaHHA morteAeil CHCTeMbI reHHoii pery-ARUHH (KOTOpall ABABeTCA KOHetIFIbIM 3BeHOM 60AbILIHHCT-

Ba (1)H3HOAOCHtleCKHX H 6HOXI4MH'IeCKHX 143MeHeHHA, CBA-

3aHlIbIX co cTapeHHem) noKaabmaioT, ATO oHa momeT yn-paBASITb03 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): HanpH- mep, AOKaAbHOe II0BbILLIeHHe TemnepaTypial HAM KOHgeHT-

pagHH HcAeAcTaHe TenAosoro ,aBH111eH1451 H «n06OYHbIX»

XHMHtleCKHX H itoAroapemeHHblmu (Heo6paTH-MbIMH HAH tlaCTHAHO 06paTI4MbIMH — penamyembimm): HartpHmep, MyTaW4H, HecnegHcimmecKHe mo,n,mimagHH cTpywrypb1 6eAKOB H AH11144,0B acAeAcTeme BO3ael4CTBKH

CB0604HbIX paAHKaA0B 14 -a-AucrpomarmiTHoro 143ArieHHA.

Tame qmywryagHH MOfyT 8p14801114Tb K HecnegwpmecKo- my 1,13MeHeH1-110 reHHoll aKTHBHOCTH, HanpHmep, BCAeACT- N- axe 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 aK-

THBHOCTH MO?KeT npimecTH K CTOHKHM OTKAOHeHHAM B naT-TepHe aKTHBHOCTH rams — T.e. ycToilmaomy OTKAOHe-

HHIO KAeTKH OT HopmaAbHoro COCTOAHHA, K yCT0114HBOMy

«HeHopmaAbHomy» CPyl4KUHOHI4p0BaHHIO KAeTKH. no mepe HaK011AeH1451 TaKHX «OTKAOHHBLIIHXCA» KAeTOK nocTenamo yxy4waeTcx cpywcumnwposame TKaHeci, opraHoe. H opra-HH3Ma B UeA0M.

npH 9TOM OTKAOHeHHA B aKTHBHOCTH Tex reHoa, KOTO-

pme 110A111HbI 6bITb yCTOrriHBbl K OTKAOHeHHIO (TaK KaK

OHH 4,0A/KHb1 pearHpoBaTb Ha TaKHe OTKAOHeHHA B xorte HopmaAbHoro (PyHKUHOHHp0BaH1451 — T.e. OHH 40AACHb1

H3MeHHTb CBOH aKTHBHOCTb, a noTom BepHyTbca K Hop-MaAbH0My ypOBH10 aKTHBHOCTH), He ae4yr K OTKAOHeHHIO

OT «TpaeKTopim» HOpMaAbHOil 214143HH KAeTOK. B TO apemst KaK He3HatIHTeAbHble OTKAOHeli1431 B Tex reHax, tlbA

aKTHBHOCTb B 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 OT-

CyTCTBHH 3H,a0reHHbIX H 91(301THHbIX noapemaemii MaK-

pomoAeHyA cTapeme B °pram-fame 6y4eT 11p0HCX0/1,HTb.

3. BHOXHMxveCKHe (pAywryawm He mom 6bITb I4C-

KAIOtleHbI (HanpHmep, nort ztelicTaHem ecrecTseHHoro OT-

6opa), TaK KaK 40A1KHa 14MeTbCA onpelteAeHHail 110/41314?K-

HOCTb 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 «3aCTbI-

BaH1410>> CHCTeMbl, HeB03MO2KHOCTI4 ee cpyrmun0mposa- HeCII0C06HOCTH ocytgecTaAemm ee peryAmpoaamm,

KoTopoe Bo MHoroM 06ecnemaaeTcs CAa6bIMH 3.AeKTpo- MarHHTHb1MH B3aHM0/1,ekTBIIAMH (HanpHmep, CB513131BaHHe

pery.wprowx (PaKTOpOB C 6eAKOM HAH reHom) — T.e. K

Hecnoco6HocTH noLa,epxcamx romeocTasa, a Taime ocy-WeCTBACHHA 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 cTape- Him ace paBHO 6y.ti,eT 8p0HCX0,414Tb H3-3a Apyrmx (HanpH- Mep, TenAoaboc) cpAyKTyaUHA H nocAe,a,rowero Haprue- Hag peryAxwin (T.e. OTKAOHelitia OT «HOpMaAbH0ii» TpaeK-Topm reHHoii aKTHBHOCTH).

4. B npmgme TO, tITO cTapeme ABASIeTCA XaOTHtleC-

KI4M npogeccom, cAeztyeT Ha ypatmemx FomnepTga. 3anx-wem 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 cAeApoweil:

4(0 = p.'(t) — µ„ (t) = (µ0, — µ0") exp(at) = exp(at).

ria sToro ypatmemx SHAH°, tITO pa3HOCTb HatlaAbHbIX

ycAosHri BeiteT K 3KCII0HeHUHaAbHal pasHHge COCTOAHHil

(MO/KHO CKa3aTb, YTO C BoapacTom oTpaeKTopm CHAbI

cmepTHocTH» paCX04ATCA no 3KCII0HeHUHaAbHOIVfy 3aK0-

Hy) — T.e. 3BOAIOUHA CHAbI CMepTHOCTH npoHcxwmT Tax-

KaK 3BOA1OUHA XaOTHtieCKHX CHCTeM.

5. alccnoliempaAbtme pacxomytemte «Tpaewroppdt CHAbI CMepTHOCTI4>> 1103BOAAeT Bb1ABHHyTb ripeimoxoace - }me, tITO 110Ka3aTeAb aticrrottexTbi (a) B ypasmemat Fom-

30

Bo3pacr nonoaoro co3peBaHt4R

YCF1EXV1rEPOHT0/101- 141/1 • 2001 Bun. 8

nepTga MO2KeT COOTBeTCTBOBaTb Il0Ka3aTeA10 .A.snyHosa

(X) — BeAH9HHe, KOTOpaA x.apaxTepH3yeT cpeAmwo CKO-

pOCTb 3a6bIBaHHH Ha9aAbH0r0 COCTOAHHA B xaoTHmecmx

CHCTeMaX. B cAymae CTaPeHHA aTomy MO2KeT COOTBeTCTBO-

BaTb 9KCI1OHCHUHaAbH0e 3a6bIBaHHe HaYaAbH0I -0 (3Aopo-

soro, HOpMaAbH0 peamprowero) COCTORHHA.

Pa3BHBaA aTy aHaAorHio AaAbwe, MO2KHO npeAnoAo-

2KHTb, 9TO opram43m He A0A2KeH 3a6bIBaTb csoe HaTlaAbH0e

COCTOHHIle B Tevefuie nepHoAa, AOCTaT09/10r0 AAA peripo-

Ayxgm (HHame roe.ops: 3a6b1BaTb COCTOAHHe 3A0p013b51

1103BOAHTeAbH0, Koma npoH3seAeHo IIOTOMCTB0). TOT-IHOe

mawHHe 9Toro nepHoAa 3aBHCHT OT 6H0A0114H Hower-

Horo 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 Apo3o-

CPHAbI (OpraHH3MOB, ‘IbH napameTpbi cTapemis H3BeCTHbI C

60AbIl1011 TO9HOCTb10) 9TH BeAHLIHHbI npHmepHo cosnaAa-

10T (Ta6A. 2). aTO Ha6mAeHHe corAacyeTcR C AaHHbIMII 0

TOM, 'ITO 60AbLIIHHCTBO C4H31,10A0r1V9eCKHX napameTpos Ha-

YHHalOT yxyAwaTbcs C MOMeHTa noAosoro CO3peBaHHA

(CM., HanpHmep, [4]).

Ta6m4Lta 2

Coomercreme mexpy BpemeHem 11nnyHoBa (T) H

H03pacrom nonortoro co3pesaHHB

BHA

genoeeK*

Mbiwb**

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

12-15

30-50***

9 [8]

[8]

* A wamepReTcs B 1 40A, ocranbsue Ber1W41411b1 — B ropax.

** HamepRercsi 8 %yr , ocranbHble aenw-RiHbi — B cyncax.

*** 30 — OT momeHra po(geHmq, 50 — OT momeHra onnoaorsopemnsi.

06o6Lgam npeAnoAomeHme o 3a6b1BaHliH COCTOAHHA

3,A0p0Bbfl, MOASHO npHATH K cAeAroigHm sbmoAam: a) C TOMKH spemis TeopHH impopmagHH, cTapefwe MONK-

HO omicaTb Kai( HameHeHHe peaxgHH cHcTembi Ha cnegHciam-mecnie CHI'HaAbI 110A, BAHAHHem Hecneguctimmecxxx cHrHaAos (cpApayagHii) — T.e. 3a6bwamie npasHAbHoro (PyHKUHOHH-

p0BaHHA (HAN 3a6bIBaHHe COCTOAHHA 3A0p0B1351);

6) C TemeHHem spemeHH B03M0HiHbIe TpaesTopHH reH-Hort peryARgsm pa36eraioTc.s (OTKAOHAIOTCH Apyr OT Apyra y pa3HbIX OpraHH3MOB HAH OT HOpMaAbH0r0 COCTOAHHA re-

HoperyAmTopHoil CHCTeMbI y oAHoro H Toro me OpraHH3Ma) noA AeiicTsHem cpAywryagml. CTeneHb HX pa36eraHHA pe-ryAmpyeTcs 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.Ao6-

HbIM spemeHHbim napameTpom, xapaxTepHapoLgfim 6H0A0IIP9eCKHA BHA) — T.e. B TemeHHe 9Toro nepHo-

Aa HY2KHO YAeP/KHBaTb TpaexTopHH B nrixe (He AOITYCKaTb

3HWIHTeAbH0r0 OTKAOHeHHA OT HOpMaAbH0r0 COCTOAHHA).

B Ka9eCTBe A0110AHeHHA K AaHHOMy flyway MACHO

npeA,AoncHTb o&bscHeHHe Tomy, KaK, C TO9KH apeHHa Teo-

pHH mwpopmagHH, npomcxoitmT 3a6bmaHHe HagaAbH0f0

(3A0p0B0r0) COCTOAHHHopraHH3ma. 1 I0A0HiliTeAbH0e 3Ha-

geHlie FlOKa3aTeAS ARnyHosa csHAeTeAbcTsyer 0 TOM, WO

1B cHcTeme ymeAmmxmaeTcH KOAH‘leCTBO HHCPOpMaQPIH (B pe- f3y.AbTaTe cpAyxTyagHil) — T.e. BospacTeT mHCAO cTeneHeil

CB060A,b1 CHCTeMbI [7]. B KOHTeKCTe reHHoii peryAsgHH 3T0 0311agaeT, 9TO yBeAHYHBatTCA 9HC.A0 BO3MO2KFIbIX pe-axgHii Ha OAHO H TO Am B03AefICTBHe — T.e. K ■KIIpal3flAb-

Hb1M)) (HOpMaAbHbIM, 3Aoposbim, H3Ha‘laAbH0 3anporpam-MHp0BaHHb1M) peaKUHRM 71,06aBASHOTCH «HenpasHAbHbie» e

(6oAe3HeHHble, naToAorHmecKHe) pealugm. 6. 143 xaoTHmecxoft npmpoAbi reHHoil peryARgHH He

nocpeAcTseHHo cAeAyeT, Tro cTapeHHe A0A2KHO 6bITb MHO-'

FOCTaAHAFIbIM npogeccom (KaKOBbIM OHO, no 'Keil useposT-HOCTH, 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-

ReHm=1 B cHcTeme reHHoli peryARgHH, ynpasAsembix 3axo- HaMH xaoca, MO/KHO npeAAommTb 0673ACHeHHe H TaKOMy

MHBble COCTOAHHH (meHee yCTOrP-IHBble OHa IIOKHAaeT 110A

BAHAHHeM (pAyxTyagHii). C soapacTom BepOATHOCTb Ha-

X01KAeHHSI CHCTeMbI B 6oAee yCTOiNHBOM COCTOAHHH yse-AH914BaeTCH. BbIBeCTH cHcTemy H3 ycToilmHsoro COCTOAHHH

Tpy4Hee. noaTomy AAA Toro, 91•06bI meAosex 3a60AeA,

Hy2KHO 6oAee CHAbH0e someiicTsHe, mem paHbuie. COOT-

BeTCTBeHHO, KTO He HaX0AHT TaK0I-0 yCTOAIIHBOI*0 COCTOA-

HHA K AaHHOMy so3pacTy — yMHpaeT. C Apyroil CT0p0HbI, nepHoA pocTa momeT conposom-

A9TbC5i 110BbILLIeHHOff noTpe6HocTb10 B reHHoii peryugHH, *ITO BeAeT K yse.AHmeHlis) cTeneHeil cmo60,abi reHoperyAH-

TopHog CHCTeMbI. 3THM momeT 6bITb 06'bACHeHO nommen-Has! CHAR CMepTHOCTH B M.AaAIIIHX BO3paCTHbIX rpynnaX.

8. TaxAce, C TO9K143pems xaommectwii npHpoAbi reH-HOH MO2KHO nonbrraTbcs TIOHATb, nomemy CTa-

palm HmeeT mHoro o6wHx mepT y pa3HbIX BHAOB mHoro-KAeTOHFIbIX ?KHBOTHbIX. &AMMO, BO mmorom 9T0 MO2KeT

6bITb CBH3aHO C 061MHOCTb10 B OpraHH3aUHH renoMa: CPO CAO2KHOCTH, KOMPleCTBa reHOB, crenemi C13513HOCTH, xa-paxTepa C13513HOCTH. nO9TOMy npH B03,AerICTBHH cpAyicrya-

wig (KoTopme TaK2Ke CX0A,Hbl — BBHAy CX0ACTBa 6HOXH-

(\.'+ 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 pe- ryAsigHH. npH 3TOM CHCTeMa KaK 6bI oHlMeTD 6oAee clu

31

M.B. Conoabea

MHH) ,zatHammxa reHHar peryABUHH B o6wem 9B0.110UHOHH-

pyeT 4110CTaT09H0 e4HH006pa3Ho. XOTH rippi 3TOM B HaCT-

HbIX cArraax KOHKpeTHbIe Aerami 1-13MeHeHHAreHHori pery-

ASIgHH (T.e. KaKHe HMeHHO reubi MeHAFOT caoe COCTOAHHe y

4a.HHOr0 BH,aa) ripm cTaperwrx moryT pa3A1riaTbC51 BecbMa

3Has-IHTeAbHO.

CTOHT 3aMeTHTb, 4TO cyrgecTayroT Teoppm (cm. [21]),

o6bacHaragme aaamogwo H orrorelles mepea Teopmo xao-

ca - T.e. H 3130AIOUHOHHOe npomcxors,a,efare craperima MO-

aceT 6bITb o6si3aHo xaocy. KpoMe Toro, xaoc HposisA.HeTcH

He TOAbKO B remoii perynagmi, HO H B ApyriAx 6HOXI4MIrie-

CKHX peaKuHax, a TaK1Ke H Ha KAeTOHHOM ypoBHe, ripmgem

3TH npogeccbi Taicaie moryT HrpaTb Ba2KHyto poAb B npo-

gecce cTapeHHa H pa3WITHH aCCOUHI1p0BaHHbIX C HHM

TOAOrHH [27, 31]. 143 Bcero 3Tor0 MO2KHO 3aKAIOHHTb, HTO

cTapeHHe moaleT 11BAHTbCH cAe.acT8Hem XaOTHHeCKOil rippr-

po,abr 1K1480171 maTeow B UeAoro.

3aKmogeHme

AAA noitTHepmaeHasi rHnoTe3bi 0 XaOTH4eCK011 npH-

po,ae craperwa Heo6xwwmo Bb1511311Tb OCHOBHbIe xapakTe-

pliCTHKH renoperyAaTopHbix CHCTeM YeA0BeKa H 211HBOT-

HbIX. aTO 1/101KHO 6y,/1eT C,I1eAaTb nyTeM co ,reTaHma KOM-

nbxyrepHoro moz(eAmposarwa C coapememmimH meTwiamm

Bbl.HBAeHHA ypOSHA aKcnpeccHH reHoa (4T06b1 BbIRBliTb

Boapacmpo Z1HHaMHKy rem-loci aKTIIBHOCTH) H aHaAH3a

HyKAeOTH.4HbIX nocAe.aoaaTeAaHocTeil, B OCO6eHHOCTH

rlaCTKOB, OTBeTCTBeHHbIX 3a peryAsigHlo aKTHBHOCTH AaH-

HOrO reHa (3Toro morceT OKa3aTbC51 ./10CTaTO4HO, HT06b1

BOCCTaHOBHTb 110AHyFO xapTHHy B3aHMOCBABH reHOB). H

eCAH moiteAb peaAbHOH CHCTeMbl reHHOLI peryArrupw 6yzteT

,aeMOHCTpHp0BaTb CBOVICTBa, xaparcreprible 4A21 xaoTwiec-

KHX cHcTem, MONSHO 6yAeT flpaKTHHeCKH HasepHsno yT-

HepmaaTb, 'TO crapeEme - BTO cyr.gecTseimo xaommec-

KIfil npouecc.

EcAH 3Ta rHnoTesa OKa1KeTCH sepia, TO cAe,apoto-rm

IllarOM ,710J1KeH CTaTb HOHCK MeTOHOB B0311e1ICTEH51 Ha re-

HoperyAsiTopfibie CHCTeMbI C UeAblo 3aMe4AeHRH, a B nep-

cneKTHBe H npeztoTapargeHaa crapelma. B DTOii CB.113H

Ope./1,CTaBASIEOTC51 KpaiiHe HHTepecHbrmH KAHHH4eCKHe H

aKcnepHmeHTaAbHbre il,a111-1bIe 110 npnmeHeHmo meTozwa

6HoperyAmppoweil TepanHH [5, 12, 16]. [Jo Hceil HepoHT-

HOCTH, aCIXIXKTHBHOCTb nenTap,Hoii 6HoperyAsigHH 110 3a-

Me4ACHHIO erapanw MO/KHO 06bACHHTb cAeztyboigmm o6-

pasom. MHHOpHble peryAaTopHbre B03,/leciCTBH.11 moryT

aosapargarb naTrepH remwil aKTHBHOCTI4 B 06AaCTb, COOT-

BeTcTBylotgyio HopmaAbitomy ipp-murformposaiiwo opra-

HHBMa (HHarie rosopa, He6oAbwoe peryArropHoe B034erl-

CTBHe Ha reHbl abrHymileHHo <OlpHB0,11,14T>> OTKAOHeHHy10

TpaexTopmo B «szoposoe» COCTOAHHe). Ha ceroxisuumil

ileHb B 6HoperyAHpyrorgeii repanHH AomHHkrpyer ammipm-

necxHii no4xo4. itonoAHeHHe ero meTozwmH aHaA133a merc-

reHHbix aaammortericTaHil, 6asupyrorgHxca Ha CO9eTaHHH

KOMIIIDIOTepH0r0 M0411,eAHIJOBaHHSI (B TOM HHCAe HCII0Ab3y-

lowero ocHombre 110A0211eHI-151 TeopHH xaoca) H moAexy-

AapHo-reHeTpNeckoro aHaA113a, nomomeT Bb1511:314Tb (npezt-

CKaBaTb) HOBbIe TOHK11 (reHbI), B034,efiCTBH51 Ha aoTopbre

cmwEeT 60Aee 3C10CpeKTI3BHO H 110AHO BO3BpaIgaTb TpaekTo-

pwo reHHog peryAaww B sztopoaoe COCTOH1114e.

Mcreparypa

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, repoH-

Ton.-2000.-Bun. 4. -C. 153- 159.

2. raspmnoa Faapvinoaa H.C. Smonorma nponorpkvi- TenaHocni xmaym.-M.: HayKa, 1986.-168 c.

3. rponakimckm BOOTDHKO B.fl., KmaxameA0B KoribToaep B.K. Ha,qexHocm M cTapemme 61,10/101-W-OCKI4X CHO-

Tem.-Kmes: Haykoaa nymka, 1987.-176 c.

4. Avinbmam B.M. LleTbipe moilenvi menvimmu.-11.: MeLlyakw-Ha, 1987.-288 C.

5. M0p03013 BT., XaBOHCOH B.X. flenTyguible 6,4operynsro-obi (25-neTHHH 0116IT aKcnepvimeHranbHoro M KTEIHAVOCKOM MC-

cne,a0BaHfr1A).-C116.: HayKa, 1996.-74 c.

6. FIVIKI4THH B.H. akcnepmmemTanembie nonxonbi K npo,arie-

HMO XGA3H14 //. &Armory's, c -rapeHms, / OTB. pen. B. B. Opona-kmc.-11.: HayKa, 1982.-C. 548-568.

7. H144(01114C 4,4Hamywa HepapxmecKmx cmcrem: 38onio- umomioe npeAcTaanerime.-M.: Mmp, 1989.-488 c.

8. 06beKT61 emonoryw paaeynAs, / OTB. pen. T. A. „fleT-nacp.-M.: HayKa, 1975.-579 c.

9. flpinro*mm M., Crearepc H. Bpema, xaoc, KBaHT.-M.:

flporpecc, 1994.-272 c.

10. Oporibkpic B. B. PerynopoaaHme, npmcnoco6nemme crapeame.-11.: HayKa, 1970.-432 c.

11. cIpponbkinc B. B., MypaHHH X. K. CTapaHlle, 3130/110L1H51

npo,rmeyme AcHaym.-KineH: HayKoea AyMKa, 1992.-336 c.

12. Xaammcom B.X., Mopoaoe B.F. FlenTmamap perynpuval

romeocTaaa nppi cTapeFaiiii // Ycnexm repowron.-2000.- Bun. 4.-C. 75-79.

13. WycTep F. AeTepmviHvipoeammuci xaoc.-M.:

1988.-240 c.

14. Anisimov V.N. Age as a risk factor in multistage carcino-genesis // Comprehensive Geriatric Oncology / Eds.: Balducci

L., Lyman G.H., Ershler W.B.-Amsterdam: Harwood Academic Publishers, 1998.-P. 157-178.

15. Anisimov V.N., Khavinson V.Kh., Mikhalski A.I., Yashin A.I. Effect of synthetic thymic and pineal peptides on biomarkers

of ageing, survival and spontaneous tumour incidence in female CBA mice // Mech. Ageing Dev.-2001.-Vol. 122.-P. 41-61.

16. Anisimov V.N., Mylnikov S.V., Khavinson V.Kh. Pineal

peptide preparation Epithalamin increase the life span of fruit flies, mice and rats // Ibid.-1998.-Vol. 103.-P. 123-132.

17. Austad S.N. Retarded senescense in aninsular popula-tion of Virginia opossums (Didelphis virginiana) // J.

Zoology.-1993.-Vol. 229.-P. 695-708.

18. Brown-Borg H.M., Borg K.E., Meliska C.J., Bartke A. Dwarf mice and the ageing process // Nature.-1996.-Vol. 384.-p. 33.

19. Elena S. F., Lenski R. E. Test of synergistic interactions among deleterious mutations in bacteria // Nature.-1997.-Vol.

390.-P. 395-398.

20. Johnson T.E. Increased life-span of age-1 mutants in

Caenorhabditis elegans and lower Gompertz rate of aging // Science.-1990.-Vol. 249.-P. 908-912.

21. Kauffman S.A. The Origins of Order: Self-Organization

and Selection in Evolution.-Oxford etc.: Oxford University Press, 1993.-709 p.

32

YCIIEXI'I rEPOHT01101-101 • 2001 • Bun. 8

22. Lin Y.J., Seroude L., Benzer S. Extended life-span and stress resistance in the Drosophila mutants methuselah // Science.-1998.-Vol. 282.-P. 943-946.

23. Martin G.M. Genetic and environmental modulations of chromosomal stability: their roles in aging and oncogenesis // Ann. N. Y. Acad. Sci.-1991.-Vol. 621.-P. 401-417.

24. Mattison J.M. Ames dwarf mice: A model for delayed aging // Ycnexw repoi-ron.-2000.-Bbin. 4.-C. 141-146.

25. Migliacchio E., Giorgio M., Mele S. et al. The p66shc adaptor protein controls oxidative stress response and life span in mammals // Nature.-1999.-Vol. 402.-P. 309-313.

26. Miller R.A. Kleemeier Award Lecture: Are There Genes for Aging? // J. Gerontol.: Biological Sciences.-1999.-Vol. 54A, Ns 7.-P. B297-B307.

27. Rossor M.N. Catastrophe, chaos and Alzheimer's dis-ease. The F. E. Williams lecture // Journal of the Royal College of Physicians (London).-1995.-Vol. 29.-P. 412-418.

28. Rudolph K.L., Chang S., Lee H.W. et al. Longevity, stress response, and cancer in aging telomerase-deficient mice // Cell.-1999.-Vol. 96.-P. 701-712.

29. Sohal R. S., Weindruch R. Oxidative stress, caloric restriction, and aging // Science.-1996.-Vol. 273.-P. 59-63.

30. Vijg J. Somatic mutations and aging: a re-evaluation // Mutat. Res.-2000.-Vol. 447.-P. 117-135.

31. Waliszewski P., Molski N1., Konarski J. On the holistic approach in cellular and cancer biology: nonlinearity, complexi-ty, and quasi-determinism of the dynamic cellular network // J. Surg. Oncol.-1998.-Vol. 68.-P. 70-78.

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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