36 3 ( Vol 36 No3 22 5 Jourl of Jgx Norl Uversty (Nturl Scece My 22 文章编号 : -5862(223-22-9 : ( 5275 摘要 : ( RNA 关键词 : ; ; ; ; 中图分类号 : Q 4 文献标志码 : A 引言 DNA [-2] RNA 2 : (Crc 958 DNA DNA DNA RNA RNA 2 7 RNA DNA ; DNA RNA RNA DNA DNA DNA ; DNA RNA ( RNA DNA RNA ( RNA DNA ( DNA DNA ( DNA RNA ( RNA Prote ( ; RNA RNA ( RNA DNA ( 图 描述生物学中心法则的示意图 DNA RNA RNA RNA 5 cppg( 3 polya( 收稿日期 : 22-3-5 基金项目 : (673628 (397398 作者简介 : (962-
222 ( 22 RNA RNA RNA RNA trna RNA trna 5 : ( [3-5] : DNA RNA RNA DNA RNA DNA ( RNA ; ( [6-25] : ( ON ( OFF ON OFF DNA RNA RNA DNA RNA DNA ( RNA ; ( [26-28] : ON OFF ON OFF DNA RNA RNA DNA RNA DNA ( RNA (v [3-4 29-3] : 3 ; (v : 3 5 5 5 : RNA ( ; ; ( 4 5 ; RNA RNA 问题的格式 : 数学建模 ( (probblty desty fucto: PDF 2 : [32] N { X X2 XN } T x = ( x x2 x N x X M T s = s = ( x ( x ( x 2 M s X s = ( s s T ( N P x X t x ( [32-33] P( x; = M = ( ( x s P x s ; t x P x ; t ( x ( ( P ( x M = x s P x s x P x =
3 : : 223 ( (ODE ODE ( x ODE Ω ( Ω X ( = 2 N X s r s r s X rx _ = = c = Ω V Hoff = c s { } { r s} dc s = ( r s ( c = P( ; = c s X s ( ( 2 ( s =! s (( s! ( ( ; (( s r Ω Ε s P t = I P s = = Ω r (( r s Ε (2 Ω I P r = = Ω I Ε Ε Ε f = f ( f ( f Ε = (2 (2 2 A X 2X B 2 [ ] dp = ϕaω Ε I p 2 Ω Ε I ( p p = P ; t X t ϕ A A 2 * * * 2 E 2 E E 2 E E : [ ] * * E E E = E T ( NT P( = [ N ( T ( 2 2( NT ] P( [ ( ( NT 2( NT ] P( [ ( 2 ( ] P( (geertg fucto P( ; t G( z; t G( z; = P( ; z = P ; t ; = G( z z! z= P( ; t G( z z; = P( ; z z = P( ; = G( z z;!! z z 2 CK z = z= Chp-Kologorov (CK (
224 ( 22 S ( x P = A ( P( t x x x 2 B ( P( 2 x x W xz t P z t W zx t P x t d z A( xt B( xt : X ( t = x tδt t t B xt X X A( x W ( xz ( z x : ( B ( x = W ( x z = W( z x = CK (ouvlle ; ( A( x = B ( x = CK ; ( W ( xz = W ( zx = CK Foer-Plc ; (v B ( x t = CK CK A( xt B( xt W( xz CK : I λ I λ I λ I 2 3 2 3 λ 2 I ( λ ( = 2 3 λ 2 ( P x t RNA ( X I t x = 2 3 CK ( xp ( x P x t = λp( x λ3p3( x = λp x t 2P3 x t λ P P ( x xp2 ( x 2 P ( x xp3 ( x 3 2 2 3 ( λ ( ( x = λ λ λ P 2P2( x ( 3 2 ( x : ( ( ( ( P xt = P xt P2 xt P3 xt? 3 ( G( z; = P ( ; z = ( N 2 z z N z2 z N G( z; = z G( ; z z Hlbert H z ( : z { λ } { } { } ϕ z ϕ = λ ϕ z z z G( z; G( z G ( ϕ ( z ϕ z H ( ϕ ( z G( z; ϕ ( z { } H ; = d G ( t = λ G ( t { λ } t { G ( t } G ( t = Ae λ t { G ( t } G( z; ( z ; ( z { λ } { ϕ ( z } : [34] ( 5 2 概率密度的分析表达 2 (burs RNA RNA
3 : : 225 2 : = d ; b = d RNA RNA d d RNA x( t x( t P( x ( CK P( x = dxp ( x x w ( xx P( x dx x = V(V 2 ( = ( ( w x x w x x x x w( x x ( x - ( x ( x x ( x ( x x w x x = w x x = x x x x b d ( x e x b = b = [3] P( x = b Γ ( x x b e x G ( DNA DNA d d P = ( P P ( P P d ( P P d ( P P (3 RNA P G( z z; = z z P (3 G ( u γ b u G G = u G υ υ u υ τ υ = d b = d γ = d d τ = u = z υ = z (4 [7] τ b be P ( τ =! b b Γ b 2F ; ; e τ Γ b ( γ (4 τ > γ b F 2 bcz ; ; (4 τ Γ b b P = Γ Γ b b [35] 22 : ON OFF λ γ I A A I A A X X I A X RNA ( X ( x PA ( x PI ( x X P = PA PI x P PA JA = λpi γpa (5 PI JI = λpi γpa J A( xt = ( x PA( xt JI ( x = xpi ( x (5
226 ( 22 [36] λ γ γ λ Γ (( λ γ Γ P( x = x x Γ λ γ x Bet Γ ( G γ λ X P( x G γ ( e x P x x λ γ = γ Γ λ λ γ 2 ( P ( t RNA P ( t DNA RNA ( : d A I ( : I A d d 2 ( ( ( ( ( P τ = κ P κ P P P ( ( ( P ( ( ( P b P P γ P = P P P ( ( ( ( τ κ κ ( ( ( ( γ ( ( b( P P P P P P ( P (6 κ = d κ = d = d b= d γ = d d 2 ( ( ( ( ( ( ( = ( f z z = z z P f z z z z P (6 ( ( ( ( f κf κ f f = υ τ υ υ ( u f γ b( u υ u (7 ( ( f ( ( f = κf κ f υ τ υ υ ( u ( u f f γ b( u υ υ u u = z υ = z (7 [7] ( α ( β ( κ κ P ( α ( β ( κ κ Γ Γ b = Γ Γ Γ Γ b b b 2F α κ κ β; κ κ ; b b ( ( P = P P 2 α β = 2 4 2 κ κ ± κ κ κ 23 λ I I = 2 I A A I λ p A A M M M P p M P γ ( γ λ λ ( = 2 RNA p RNA p : = ( RNA ( RNA RNA P ( P ( t ( = 2 RNA t RNA ( d P d P t ( d P ( λ ( = γp t P t ( E I ( E I P ( λp( γp( ( E I P ( = ( λ ( = λ P t P t ( E I P ( ( = 2 (8 I E E ( f E f ( = f ( f = f ( (8 P ( ; E t
3 : : 227 G( z = z P( ( = = (8 G ( ; G ( z γg ( z λ G ( z z t = G ( z ( z ( z G ( z z G ( z = λg( z γg( z G ( z ( z z G ( z = λg ( z λ G ( z G ( z ( z ( = 2 z ( λ λ = γ t t G = G γ = ( 2 2 ( C G = G z F ; b b b ; z C C = ; F [37] z = Tylor G( z RNA [28] ( Γ ( Γ( b = = =! Γ( Γ ( b = = F ( b b P ; ; RNA 24 λ I A γ I P A P A A P P P P ( ; ( ; P t I A t ( λp( ; γp( ; P( ; ( P ( ; P ( ; d P ; = d P ; t P( ; γp( ; P( ; ( P( ; P( ; P ( ; P ( ; = λ [38] P F λ ; λ γ ; (9 (9 RNA 25 ; λ γ I A P t r A P I P A A P P P t I A ; t d P ( ; = λp( ; γp( ; rp( ; ( P( ; P( ; d P ( ; = λp( ; γp( ; rp( ; ( P( ; P( ; P( ; P( ; RNA ( λ ( λ β Γ λ Γ λ β P = Γ Γ r F λ ; β λ ; 2 ( r! r F λβ ; λ; 2 ( r r 3 讨论 RNA
228 ( 22 ( DNA RNA ( RNA ( Fo ( Nture Scece [4 39] : Y = f ( X X ( Y ( ( f ( : f X PI ( X Y PO ( Y 4 参考文献 [] Ble W J Kær M Colls J J Nose euryotc gee expresso [J] Nture 23 422: 633-637 [2] Rser J O She E Cotrol of stochstcty euryotc gee expresso [J] Scece 23 34: 8-84 [3] Boeger H Gresebec J Korberg R D Nucleosoe reteto d the stochstc ture of prooter chrot reodelg for trscrpto [J] Cell 28 33: 76-726 [4] rso D R Wht do expresso dycs tell us bout the echs of trscrpto? [J] Curr Op Geet Dev 2 2: 59-599 [5] Chubb J R Trce T Sger R H Trscrptol pulsg of developetl gee [J] Curr Bol 26 6: 8-25 [6] Pedrz J M Pulsso J Effects of oleculr eory d burstg o fluctutos gee expresso [J] Scece 28 39: 339-343 [7] Sáchez A Kodev J Trscrptol cotrol of ose gee expresso [J] Proc Ntl Acd Sc U S A 28 5: 58-586 [8] Schez A Grc H G Kodev J Effect of prooter rchtecture o the cell-to-cell vrblty gee expresso [J] PoS Coput Bol 2 7: e [9] Mo C Brow C R Boeger H Qutttve lyss of the trscrpto cotrol echs [J] Mol Syst Bol 2 6: 43-438 [] Mr Schulz E G Höfer T Short-ter eory gee ducto revels the regultory prcple behd stochstc I-4 expresso [J] Mol Syst Bol 2 6: 359-365 [] Mller-Jese K Dey S S Ar A P Vryg vrulece: epgeetc cotrol of expresso ose d dsese processes [J] Treds Botechol 2 29: 57-525 [2] 3 [J] : 28 32(: -5 [3] Fred N C Xe X S g stochstc dycs to populto-dstrbuto: lytcl frewor of gee expresso [J] Phys Rev ett 26 97: 6832 [4] Pulsso J Sug up the ose gee etwors [J] Nture 24 427: 45-48 [5] Thtt M V Ouderde A Itrsc ose gee regultory etwors [J] Proc Ntl Acd Sc U S A 2 98: 864-869 [6] Peccoud J Ycrt B Mrov odellg of gee product sythess [J] Theor Popul Bol 995 48: 222-234 [7] Shhreze V Sw P S Alytcl dstrbutos for stochstc gee expresso [J] Proc Ntl Acd Sc U S A 28 5: 7256-726 [8] Pulsso J Models of stochstc gee expresso [J] Phys fe Rev 25 2: 57-75 [9] Kepler T B Elsto T C Stochstcty trscrptol regulto: orgs cosequeces d thetcl represettos [J] Bophys J 2 8: 36-336 [2] Pulsso J Ehreberg M Rdo sgl fluctutos c reduce rdo fluctutos regulted copoets of checl regultory etwors [J] Phys Rev ett 2 84: 5447-545 [2] Krr R Bose I Grded d bry resposes stochstc gee expresso [J] Phys Bol 24 : 97-24 [22] Iyer-Bsws S Hyot F Jyprsh C Stochstcty of gee products fro trscrptol pulsg [J] Phys Rev E 29 79: 39 [23] Mugler A Wlcz A M Wggs C H Spectrl solutos to stochstc odels of gee expresso wth bursts d regulto [J] Phys Rev E 29 8: 492 [24] Mcey M C Tyr-Kńs M Yvec R Moleculr dstrbutos gee regultory dycs [J] J Theor Bol 2 274: 84-96
3 : : 229 [25] Assf M Roberts E uthey-schulte Z Deterg the stblty of geetc swtches: explctly ccoutg for RNA ose [J] Phys Rev ett 2 6: 2482 [26] Suter D M Mol N Nef F Ml gees re trscrbed wth wdely dfferet burstg etcs [J] Scece 2 332: 472-474 [27] Hrper C V Festä B Whte M R Dyc lyss of stochstc trscrpto cycles [J] PoS Bol 2 9: e67 [28] Zhg Ju Zhou Tshou Alytcl dstrbuto d tublty of ose odel of prooter progress [J] Bophys J 22 2: 247-257 [29] Zhg Ju Yu Zhg Zhou Tshou Physcl lts of feedbc ose-suppresso bologcl etwors [J] Phys Bol 29 6: 469 [3] [J] 2 26(6: 457-47 [3] Zhg Ju Yu Zhg Hxog et l Archtecture-depedet robustess d bstblty clss of geetc crcuts [J] Bophys J 2 99: 34-42 [32] Ullh M Wolehuer O Fly tree of Mrov odels systes bology [J] IET Syst Bol 27 (4: 247-254 [33] V Kpe N G Stochstc process physcs d chestry [M] Asterd: North-Holld 992 [34] Sur J Moder qutu echcs [M] Id: Perso Educto 985 [35] McAds H H Ar A Stochstc echss gee expresso [J] Proc Ntl Acd Sc U S A 997 94(3: 84-89 [36] R A Pes C S Trch D et l Stochstc RNA sythess l cells [J] PoS Bol 26 4(: e39 [37] Slter J Cofluet hypergeoetrc fuctos [M] Cbrdge: Cbrdge Uversty Press 96 [38] Iyer-Bsws S Jyprsh C Mxed posso dstrbuto exct soluto of stochstc uto-regulto odels [J] rxv 284v [q-boqm] 2 Oct 2 [39] Tse-Ncol S Wrre P B Te Wolde P R Sgl detecto odulrty d the correlto betwee extrsc d trsc ose bochecl etwors [J] Phys Rev ett 26 97: 682 Revew o Gee Expresso Models: Probblty Dstrbuto ZHOU T-shou (School of Mthetcs d Coputtol Sceces Su Yt-Se Uversty Gugzhou Gugdog 5275 Ch Abstrct: Qutfyg gee expresso (cludg thetcl odelg d qulttve d qutttve lyss s ot oly portt step towrd to uderstdg trcellulr processes but lso the core of the curret systes bology Gee expresso odels hve bee developed to coplcted ult-stte odels cosderg detled bologcl processes d uber of bologcl fctors fro the tl sple sgle-stte odels Bsed o cetrl dog bology The proceedg the study of gee expresso odels focusg o proveet of thetcl odels probblty dstrbuto of RNAs d protes etc re sply revewed Cosequetly soe geerl lws relted to gee expresso re surzed I ddto soe ssues to deserve further studes re dscussed d potetl drectos re poted out Key words: gee expresso; gee stte; bochecl ster equto; probblty desty; geertg fucto ( 责任编辑 : 王金莲