The Mechanism and Properties of Electron Transfer in the Protein Molecules

Transcription

1 Joural of Proomcs & Boformacs ISSN: X Rsarch rcl rcl Joural of Proomcs & Boformacs Xao-Fg, J Proomcs Boform 7, :8 DOI: 47/jpb44 OMICS Op Iraoal ccss Th Mchasm ad Proprs of Elcro Trasfr h Pro Molculs Pag Xao-Fg Isu of Lf Scc ad Tchology, Uvrsy of Elcroc Scc ad Tchology of Cha, Chgdu, Cha bsrac Th mchasm ad proprs of lcro rasfr alog pro molculs a f mpraur T h lf sysms ar sudd usg olar hory of bo-rgy raspor ad Gr fuco mhod, whch h lcros ar rasfrrd from doors o accpors vru of h suprsoud o xcd h rgy rlasd TP hydrolyss Th lcro rasfr s, ssc, a procss of oxdao-rduco raco I hs sudy w frs gv h Hamloa ad wav fuco of h sysm ad fd ou h o uo of h dyamcal uao h pro molculs wh f mpraur, ad oba h dyamcal coffc of h lcro rasfr Th rsuls show ha h spd of h lcro rasfr s rlad o h amplud ad vlocy of h o, h lcro s dsrbuo h door ad accpor as wll as h raco amog hm Th srogr h couplg bw hm, h h largr h spd of lcro rasfr W fally ga h chagd rul of lcrc curr arsg from h lcro rasfr wh varyg m Ths rsuls ar usful molcular ad chmcal bology Kywords: Elcro rasfr; Solo; Pro molculs; No-lar hory; Door; ccpor; Dyamcal coffc PCS Numbrs: 768y; 4-; 78; 4kf Iroduco Bologcal xprms show ha hr ar a gra umbr of lcros or chargs rasfr h bologcal ssus ad procsss, such as h mochodra, chloroplass ad chromaoors, h coduco of h rv mpuls, c [,] s kow, wh h mochodra a srs of chmcal rasformaos, calld h crc acd (or Krbs) cycl, braks dow h carbo cha of glucos o carbo doxd ad producs coamd ad duclod (ND ) plus a proo (H ) ad wo lcros ( - ) Ths wo lcros mak hr rps across a rgo off rsc mmbra pro, carryg wo proos sd h mochodro o ousd o ach pass Th dyamcs of h wo lcros ( - ) hrough h rgo of rsc mmbra pro s of prmary rs Ths omo shows ha hr s rally a lcro or proo rasfr chas h mochodra, whch ar combd a hghly orgazd complx of pro molculs, h lar form h par of mmbra of mochodra s a mar of fac, h procss of h lcro rasfr occurs alog h rspraory cha s r mmbras of h mochodra Th lcro rasfr ca b carrd ou hrough dffr mchasms ad forms, such as h ulg rasfr of lcros ad h lcro raspor ovr larg dsacs vru of pro molculs [-5] Howvr, hr ar always h doors ad accpors of h lcros ad hr carrrs h rasfr procss of larg dsacs vru of pro molculs I hs modl h lcros ar rasfrrd by h xco or o pro molculs,, wh h xco s formd as o hrough dformao of cha, h lcros doors ar also aachd o h o hrough h raco bw h door ad o ad mov furhr followg h moo of h o alog h molcular chas Oc h o ms ad acs wh h accpors, h lcros ar rasfrrd o h accpors from h o ad aachd o h surfac of h accpor Ths procss ca b rprsd by D S D S, S S () Thrfor, h lcro rasfr s, ssc, a procss of oxdaorduco raco I hs procss h pro molculs play h brdg rol of rasfrrg h lcros h lf bods May scss sudd h lcro rasfr dffr sysms usg dffr mhods [6-9], for xampl, Davydov al sudd h lcro ad xcos olar molcular chas by a o hory [6], Saarc ad Zakula; Saarc al [7,8] sudd h lcro rasfr alog h uas-o-dmsoal molcular srucur by Davydov o modl, Goldma [9] sudd h log-rag lcro rasfr pro by a rormalzd-prurbao-xpaso approach I hs papr w wll sudy h proprs of h lcro rasfr h pro molculs by Pag s o modl [-], whch w hk h lcro rasfr pro molculs s carrd ou vru of h followg mchasm Wh h o s formd h pro molculs wh f mpraur udr aco of rgy rlasd TP hydrolyss, h dformao of h pro molculs occurs, h h lcros ca b adhrd o h o hrough a aracd raco bw hm ad movs owards h accpor o accompay h moo of h o alog h pro molcular chas Wh hy approach h accpors, h lcros ar raspord o h accpors du o h raco bw h lcros ad accpors Thus h lcros ar rasfrrd o h accpors from h doors vru of h o Our suds ar dscrbd as follows Mhods ad Rsuls Th Hamloa ad wav fuco of h sysm ad s o uo of dyamcal uao Basd o h abov mchasm of h lcro rasfr pro molculs proposd by us w ca gv h Hamloa of h gra sysm, whch s composd of pro molculs, door, accpor ad lcro, Pag s modl [9-], whch s as follows: Corrspodg auhor: Pag Xao-Fg, Isu of Lf Scc ad Tchology, Uvrsy of Elcroc Scc ad Tchology of Cha, Chgdu 654, Cha, Tl: 86886; Fax: ; E-mal: pagxf6@alyucom Rcvd Ju 7, 7; ccpd ugus, 7; Publshd ugus 7, 7 Cao: Xao-Fg P (7) Th Mchasm ad Proprs of Elcro Trasfr h Pro Molculs J Proomcs Boform : 9-97 do: 47/ jpb44 Copyrgh: 7 Xao-Fg P Ths s a op-accss arcl dsrbud udr h rms of h Crav Commos rbuo Lcs, whch prms ursrcd us, dsrbuo, ad rproduco ay mdum, provdd h orgal auhor ad sourc ar crdd J Proomcs Boform, a op accss joural ISSN: X Volum (8) 9-97 (7) - 9

2 Cao: Xao-Fg P (7) Th Mchasm ad Proprs of Elcro Trasfr h Pro Molculs J Proomcs Boform : 9-97 do: 47/jpb44 H H H( D, ) H () Whr x H H H H x x P {[ BB JBB ( B B)] [ λ( u u ) M λ( u u ) ] [ χ( u u ) B B () χ ( u u )( B BB I dscrbs h moos of h xco ad oo ad hr raco Pag s modl Th Hamloa of h door ad accpor s dod as: H ( D, ) D D m D m m ω a a d d ω lm lm lm lm (4) Whr Dm( Dm) ad m( m) ar h crav ad ahlao opraor of h lcro h door wh h rgy ad h lcro h accpor wh h rgy of, rspcvly a ( a ) ad dlm( dlm) h crav ad ahlao opraor of h Boso h door wh h rgy ω ad h lcro h accpor wh h rgy of ωlm arsg from h xcao of vbrao, rspcvly ( l) ( l) H [ V B a ] [ ] V Ba W ml m BDd m lm Wm DBd m lm [ Ym a BD m Ym DBa m ] [ ma ] Dd m lm d Da lm m ω ω m l Whr V s h marx lm of raco bw h xco ad vbraoal xcao (l) of h accpor a s, l s h marx lm of raco bw h xco ad vbraoal xcao (l) of h door a s m, hy hav a maxmum wh, V () l () l ad W W (6) V m Y m s h marx lm of raco bw h xco ad lcro h lcro mgrao from h door o accpor s s kow, hr ar sll h cohr faurs of collcv xcaos of h xco ad oo arsg from h rgy rlasd TP hydrolyss h pro molculs, alhough h doors ad accpors xs hs sysm, whch ar vry small Thus h wav fuco of h sysm coag small doors, accpors ad lcros ca sll b rprsd by: () () () () B ϕ α ϕ ( ϕ() ) x λ! B Φ > > > > ' / / xp (/ N) α () a α () a ( ν ) ( a ) > (7) Whr (!) v v v ( a ) > > m Is h ooc compl s whch rprss h lmary xcao sa of sgl oo du o h f mpraur T I hs mawhl, w hr usd h followg rlaos: r r ω ω R ( / MN ) ( a a ), P ( M / M ) ( a a ), - whr ω (W/M) / s(r /) s h frucy of a oo wh wav vcor, N s h umbr of amo acd h molcular cha, r s h dsac bw wo amo acds, a ( a ) s h ahlao (5) (8) (crao) opraors of oo () H From uaos ()-(6) ad ϕ ϕ () ad α () H α () (hr H Φ() H Φ () ) I couy approxmao ad o dmsoal cas [6-] w ca oba: () (,) ( ) (, ) ϕ ϕ ( JB( T )) (,) x Jr B( T ) x χ χ ϕ Qx ϕ(,) x x x (9) 4 Qx (,) Qx (,) vr Qx (,) r( χ χ) λr v ϕ(,) x Qx (,) 4 x x M x M x x () Whr Qx (,) Φ() ux (,) Φ(), x B( T ) xp{ ch( ω / k T ) α s( r / ) B Usg a approxma mhod w ca oba h uos of uaos (8 ad 9) as follows: M( ν ' v ) v Q( x, ) sc h [ ν '( x v),( v > v, ν ' ( )) () λ r v ϕ( x, ) '( T )sc h[ ν '( x x v) xp[ ( kx ω ], k m v /, () / Whr '( T) (4 Wm( T)/ v ), m( T) / JB( T) r W ca fd ou h uos of Es (8 ad 9) h cas of al codo of Q () ( ϕ) ϕ usg h rav mhod [6-], whch ca b rprsd by: 6 ν ' 4( χ χ) Q( x, ) sc h [ ν '( x x v),( v > v),( ρ ) ρ Jr B( T ) () ϕ ν ω / ( x, ) ( '/ 4) sc h[ k'( xx v) xp{ [ k'( xx) ]}, (4) / / Whr ( k ' v / Jr, k ' (6 ρ ) Clarly, h abov o uos uaos () ad (4) ar h suprsoud os ad sabl, whch hus ca srv as h carrr of h lcro rasfr lvg sysms Th dyamcal coffc of lcro rasfr ad s proprs W ow calcula rao of h lcro rasfr from h door o accpor by vru of h abov suprsoud os I h sysm of lcro rasfr h umbr opraors of h o, door ad accpor ar dod by: NB BB, N, ND DD m m m m rspcvly Obvously, whol parcl umbr N N( B) N N( Dm), whch s rlad o Hamloa of h sysm E (), s cosrvav,, N [ N, H] Ths umbr opraors sasfy h followg Hasbrg uaos N [ N, H],( k' B,, D ) (5) k' k' m Usg E () w ca oba: [ ] N B V B a V a B l l [ WmBDd m m WmdlmDB m ] m [ ] N V a B V B a J Proomcs Boform, a op accss joural ISSN: X Volum (8) 9-97 (7) - 94

3 Cao: Xao-Fg P (7) Th Mchasm ad Proprs of Elcro Trasfr h Pro Molculs J Proomcs Boform : 9-97 do: 47/jpb44 l l [ m lm m m m m] m ND W d DB W BDd (6) I hs sysm of lcro rasfr h umbr currs formd ar ulbrum sa ad sasfy h followg rlaoshp N( B) [ N N( D)] (7) Basd o hs faur w ca us h sasc hory of uasulbrum sa sablshd by Zubarv [4] o sudy h lcro rasfr Corrspodg sasc opraor of h uas-ulbrum sa ca b rprsd by: ˆ xp{ [ ]} xp( ˆ ) H N N ρ β µ a a a d a a M M (8) Whr ˆ, ˆ M β H µ [ a a Na M β R B d N RDB d N( Dm), β / KBT Z s sasc sum of h sysm, µ a s h chmcal poal of ah compo s a small paramr, RB ad R DB do h chmcal affy h chmcal raco E(), hr rlaoshp wh chmcal poal ar as follows: R ( µ µ ), R ( µ µ ) (9) B B DB D B Sc ˆM s small ad h rus of ormalzao,, SP( ˆ ρ ), h E () ca xprss as: ˆ Mτ ˆ [ ˆ Mτ Mτ Mτ ρ dτ M dτ < M > ] ρ () whr ˆ ρ s a localzd ulbrum dsy marx, whch ca b dod by: Mˆ Mˆ ˆ ρ / Sp( ) () Th h umbr curr of accpor ca b xprssd by N sp( N ˆ ρ ), hus w yld Mˆ τ ˆ Mτ Mτ Mτ N N dτ N M N M { < > < > } () Thr s h rlao of N h localzd ulbrum sa whou dsspao, h h umbr curr of accpor ca b xprssd by: N βr βr Q( N, N( D)) () B Whr h dyamc coffcs hs procss ar of h forms: Mˆτ Mˆτ d dτ{ < N N( ) > (4) Mˆ τ Mτ Q( N, N( D)) d dτ{ < N N( D) > (5) Ths coffcs characrz h szs of chag of parcls ad faurs of parcl curr formd, rspcvly Thy rprs h umbr of parcls of rasformao u m h procss of lcro rasfr If h uadrc rms E() ar oly cosdrd, h opraor ˆM ca rprs as ˆ [ M M H N BB β µ β µ µ ) ( µ ) DD) ω aa ) ωlmd d )] ff a a a ff a m D D m m lm lm lm DB (6) Ulzg E (6) ad sparag h fucos rlad o τ ad complg hs graos h w do E (4) as: ( ) V V ( ) d a B B' () ' () a '' () ( ) V V ( ) ( ') ' ' ' ' ' ( ') ' ' '' ' d B a a () B () () ' ' ' ' Whr w usd h followg rlaoshps: (7) ± Mˆ ff Mff ± ± Mff M ff ± ( ), ( ) B a B a a B a B a B B() () a () B() () a () a B ' ' '' ' ' '' E Ba a () B() a () B() Ba, '' ' ' '' ' ' ω µ µ B Ths dyamcal coffcs ca bcom h followg Osagr rprsaos vru of Boso pospod Gr fuco [6-7,4] ( ') V r V ' ' d a B B' () ' () a'' () CC ( ) '' ' (8) whr r ϑ ab B' () ' () a'' () ab B' () ' () a'' () whr h sp fuco (f <), or (f >) Bcaus h dyamcal coffc coas odd Frm opraors, hus s avrag s zro I ordr o fd ou h xplc rprsao of w mus calcula h Gr fuco of hr parcls as abov mod W hr do approxmaly by Gr fuco of sgal parcl Sc H(,D) s oly rlad o suars of ad a, h h followg uaos hold () (), () H/ H/ / / ' ' ' a a (), a a () ω' ' ω' ' ' ' ' ' ' ' ' ' Ulzg hs rlaoshps, h Euao (8) ca b xprssd by h Gr fuco of sgal parcl for h Boso opraor B of h xco, whch s as follows: V V dxp[ ( ω ) ] ( ) ' ( ') ' ' ' ' '' ' B ( o) B () N ( a) CC (9) Whr ( a) {xp[( β ω ) ]} ( a) {xp[( β ω ) ]} W ow sudy h rols of h abov suprsoud o h procss of lcro rasfr I hs cas, l h abov Gr fuco dos as: r ϑ B ( o) B [ B ( o), B ] ' ' coh For h cohr wav fuco E(7) h Boso opraor B () has h faur B () ϕ ϕ ϕ pplyg hs faurs ad Wojzak s mhod [5] ad furhr cosdrg h fluc of mpraur of h sysm, h h Gr fuco of sgal parcl ca b foud ou, whch s: ϑ B( o) B' ϕ() ϕ' xp[ β ( µ B)] J Proomcs Boform, a op accss joural ISSN: X Volum (8) 9-97 (7) - 95

4 Cao: Xao-Fg P (7) Th Mchasm ad Proprs of Elcro Trasfr h Pro Molculs J Proomcs Boform : 9-97 do: 47/jpb44 Thus, E (9) ca rprs as: V V ϑ β( µ d xp[ ( ω ) ] ϕ () ϕ' N () Whr ϕ() ad ϕ () ar h ampluds of h suprsoud o Es ( ad 4) Isrg E () o E () w ca oba ' T β d ( V ) N ( ) E cosh [ ν '( X X )] cos Ω β( µ cosh [ ν '( X X v / r)] Whr Xx/r, X x /r, Ω ω ω / W ow fd ou h grao of E (), whch s: () β( µ ) B cos Ω πωr () d cosh [ ν '( X X v / r)] ν ' v πωr cosh [ ν '( X X)]sh ν ' v ν ' v πωr πωr πω r πω r { h[ ν '( X X )][ h[ B ] h [ '( X X )]( )] ν ' ' πωr ν ' v ν ' v ν v ν v Whr B s Brooll umbr Th h abov dyamc coffc ca fally do as: πωr ' ( ) β( µ sh ( T) πωr ( V ) N ν ' v ' β( 4 µ B) βω βν v E [ ][ ] cosh [ ν '( X X )] ν ' v πωr πωr πω r πω r { h[ ν '( X X )][ h[ B ] h [ '( X X )]( ' ν ' πωr ν ' v ν ' v ν v ν v )} () Euao () s jus h dyamcal coffc of lcro rasfr alog h pro molculs by h suprsoud o E () Obvously, h spd of h lcro rasfr s rlad o h amplud ad vlocy of h o, h lcro s dsrbuo h door ad accpor as wll as h raco amog h o, door ad accpor I gral, h srogr h couplg bw hm, h h largr h spd of lcro rasfr bcaus h lar s drcly proporoal o h suar of h raco poal V Ths s corrspodd wh praccal cas ad rasoabl Thrfor, h abov rsul s corrc I ordr o xhb clarly h faurs of h lcro rasfr w ow sudy som spcal suaos Dscusso Th faurs of h lcro rasfr h cas of hghr ' ' cocrao of door ad accpor I hs cas νd ν N Ths mas ha N ad ar o rlad o, ad h sum, dz, ca b rplacd by h grao dz Thus w ca oba from E () ( ) β( µ ( V ) N πωr ' ' πωr () ( T) βν vesh ν ' v Ths shows clarly ha h dyamc coffc s also drcly proporoal o h suar of h raco poal V ( ) ad dcrasd wh crasg h vlocy ad amplud of h o Ths mas ha h spd of lcro rasfr by largr ad fas o s small ha ha by small ad slow o hs cas If w furhr ak accou of hs cas of πω r << ν ' v, h E () bcoms as: ( V ) NπΩr (4) ( ) β( µ ' ' Tβν ve Thus w kow ha h dyamcal coffc wll cras sly h cas E ad µ B I h cas of v Ths mas ha h suprsoud o s sac sa From E () w ca oba: ' β( µ ( T) U N( ) ( a) () 4 β E ( ω µ B ) cosh [ ν '( X X)] (5) Whr π () () V [ ( ω ω ) ], ω ω U If h faurs of dyamc coffcs amog Es (, ad 5) ar compard w ca fd ha h dyamc coffc h cas of v s largr ha hos ohr cass Ths rsmbl h lcro rasfr by h bll-yp magc-o ad h rsul of rasfr spd of rgy of frromagc rsoa h frromag obad by Wojzak ad Sukck [5] Ohrws, w ca also oba h dyamc coffc of door, QN (, ND ), f oly h paramrs of h accpor Es (- 5) ar rplacd by corrspodg paramrs of h door Howvr, o fd rprsao of QN (, ND ) s dffculy W mus aga add h raco bw h accpor ad door, whch s H D V D a d CC lm lm lm lm, o h abov Hamloa Th s calculao s complcad, whch s sudd ohr papr Th rlaxao m of h lcro rasfr, whch dos h sz of spd of lcro rasfr from h door o h accpor, s a vrs masur of h dyamcal coffc Thus ca b rprsd by τ cosa/ Usg E (5) w ca oba ' ' πωr ( T) βν vesh τ cosa ν ' v (6) ( ) β( µ ( V ) N πωr Th h lcrc curr formd h lcro rasfr procss h pro molcul ca b rprsd by: N N xp[ / τ ] (7) Ths rprsao s vry usful molcular ad chmcal bology Cocluso I hs papr w sudd h mchasm ad proprs of lcro rasfr alog pro molculs wh f mpraur T h lf sysms usg olar hory of bo-rgy raspor ad Gr fuco mhod Th mchasm of h lcro rasfr ca b dscrbd as follows Wh h suprsoud o s formd udr aco of rgy rlasd TP hydrolyss, whch dformao of pro molculs occurs, h lcros ar adhrd o h o hrough a aracd raco bw hm ad movs owards h accpor o follow h moo of h o alog h pro molcular chas Wh hy approach h accpors, h lcros ar raspord o h accpors du o h raco bw h lcros ad accpors Thus h lcros ar rasfrrd from doors o accpors vru of h suprsoud o Thrfor h mchasm of h J Proomcs Boform, a op accss joural ISSN: X Volum (8) 9-97 (7) - 96

5 Cao: Xao-Fg P (7) Th Mchasm ad Proprs of Elcro Trasfr h Pro Molculs J Proomcs Boform : 9-97 do: 47/jpb44 lcro rasfr s, ssc, jus a procss of oxdao -rduco raco Basd o hs mchasm w frs gv h Hamloa ad wav fuco of h sysm ad fd ou h o uo of h dyamcal uao h pro molculs wh f mpraur, ad oba fally h dyamcal coffc of h lcro rasfr ad s faurs of rasfr Th rsuls obad show ha h spd of h lcro rasfr s rlad o h amplud ad vlocy of h o, h lcro s dsrbuo h door ad accpor as wll as h raco amog h o, door ad accpor I gral, h srogr h couplg bw hm, h h largr h spd of lcro rasfr bcaus h lar s drcly proporoal o h suar V of h raco poal Mawhl, w fally g h chagd rul of lcrc curr arsg from h lcro rasfr wh varyg m Ths rsuls ar usful molcular ad chmcal bology ckowldgm Th auhors would lk o ackowldg h Naoal 97 projc of Cha for facal suppor (Gra No: CB57) Rfrcs Xao-Fg P (7) Boyscs Th Prss of Uvrsy of Elcroc Scc & Tchology of Cha, Chgdu, Cha Hul C, Moush L, Yusog Z (999) Th srucurs ad fucos of bo macromolculs Shagha Prss of Mdcal Scc, Shagha, Cha pp: 4-54 Davydov S (98) Bology ad uaum mchacs Prgamo, NY, US 4 Davydov S (99) Th os molcular sysms Rdl, Dordrch 5 Davydov S (98) Solos uas-o-dmsoal molcular srucurs Sov Phys Usp 5: Davydov S, Zoloaruk V (98) Elcro ad xcos olar molcular chas Physca Scrpa 8: Saarc M, Zakula R (98) O h rol of h o mchasm h lcro rasfr alog h uas-o dmsoal molcular srucurs Phys Sa Sol 6: 67-8 Saarc M, Ivc Z, Zakula R (986) Th kc coffc of h lcro rasfr alog a o dmsoal molcular cha achvd by h mchasm of suprsoc Davydov o Physca Scrpa 4: Goldma C (99) Log-rag lcro rasfr pro by a rormalzdprurbao-xpaso approach Phys Rv 4: Pag XF () Improvm of h Davydov hory of borgy raspor pro molcular sysms Phys Rv E6: 6989 Pag XF () Th lfm of h o h mprovd Davydov modl a h bologcal mpraur K for pro molculs Europa Phys J B9: 97-6 Pag XF () Calculao of vbraoal rgy-spcra of α-hlcal pro molculs ad s proprs Commu Thor Phys 5: Pag XF () Th Faurs of Ifrard bsorpo of h Pro Molculs h Lvg Sysm Commu Thor Phys 6: 78 4 Pag XF () Vbraoal rgy-spcra of pro molculs ad ohrmally bologcal ffc of frard lgh J I If Mll Wavs : Pag XF () Quaum vbraoal rgy spcra of molcular chas crysall acald J Phys Chm Solds 6: 79 6 Pag XF (999) Ivsgao o molcular mchasm curd sckss for frard mdcal-srum Ch J BoMd Eg 8: 9 7 Pag XF () Th bologcal ffc ad mdcal fucos of h frard rays Ch J BoMd Eg : 6 8 Pag XF, Fg YP (5) Quaum mchacs olar sysms World Scc Publshg Co, NJ, US, pp: Pag XF, Zhag HW, Yu JF, Fg YP (5) Sas ad proprs of h o raspord bo-rgy ouform pro molculs a yogcal mpraur Phys L 5: 48 Pag XF, Luo YH (4) Sablzao of h o raspord bo-rgy pro molculs h mprovd modl Commu Thor Phys 4: 47 Pag XF, Yu JF, Luo YH (5) Iflucs of uaum ad dsordr ffcs o os xcd pro molculs mprovd modl Commu Thor Phys 4: 67 Pag XF, Zhag HW (5) Chags of h Mössbaur ffc causd by h xcao of h os h orgac molcular crysals a f mpraur J Phys Chm Solds 66: Pag XF, Zhag HW, Yu JF, Luo YH (5) Thrmal sably of h w o raspord bo-rgy udr fluc of flucuaos of characrsc paramrs a bologcal mpraur h pro molculs I J Modr Physcs B 9: Pag XF, Zhag HW, Yu JF (6) Th fluc of h ha bah ad srucural dsordr pro molculs o o raspord bo-rgy a mprovd modl J Phys Codsd Mar 8: Pag XF, Zhag HW, Yu JF, Luo YH (6) Iflucs of varaos of characrsc paramrs of pro molculs o sas of o raspord bo-rgy I J Modr Physcs B : Pag XF, Yu JF, Lao YH (7) Combao ffcs of srucur ouformy of pros o h o raspord bo-rgy Ir J Mod Phys B : -4 7 Pag XF, Lu MJ (7) Proprs of o-raspord bo-rgy α-hlx pro molculs wh hr chals Commu Thor Phys 48: Pag XF (8) Ifluc of srucur dsordrs ad mpraurs of sysms o h bo-rgy raspor pro molculs (II) Frors of Physcs Cha : Pag XF, Lu MJ (9) Faurs of moo of o raspord bo-rgy aprodc α-hlx pro molculs wh hr chals Commu Thor Phys 5: 7-8 Pag XF, Yu JF, Lu MJ () Chags of proprs of h o wh mpraur udr flucs of srucur dsordr h α-hlx pro molculs wh hr chals Mol Phys 8: 97-5 Pag XF () Th hory of bo-rgy raspor h pro molculs ad s proprs Physcs of Lf Rvw 8: Pag XF () Corrcss ad complss of h hory of bo-rgy raspor Phys Lf Rv 8: -5 Pag XF () Th proprs of bo rgy raspor ad fluc of srucur o-uformy ad mpraur of sysms o rgy raspor alog polyppd cha Progrss of Boyscs Mol Bol 8: Zubarv NT (97) No-ulbrum sascal hrmodyacs ( s d) Nauka, Moskow, Russa pp: Wojozak L, Sukck (98) Frromagc rsoac for o-dmsoal mags wh os Z Phys B Codsd Ma 47: -6 Cao: Xao-Fg P (7) Th Mchasm ad Proprs of Elcro Trasfr h Pro Molculs J Proomcs Boform : 9-97 do: 47/jpb44 J Proomcs Boform, a op accss joural ISSN: X Volum (8) 9-97 (7) - 97