Equilibrium dynamics of single DNA molecules confined to nanopit structures

Transcription

1 Equbum dynm of ng DNA mou onfnd o nnop uu Hugo B. Bndo* 1, W Rn 2 1,2 Dpmn of Phy, MG Unvy, 3600 u Unvy, Mon, Qub, Cnd H3A 2T8 ABSTRACT Inoduon: Of g n n h phy ody, h udy of ng mou n nno-fud dv. Th b-on--hp n povd h b fmwok fo qunfyng h bhvo of mou, uh poym, und onfnmn. Th udy n nvgon of ho f-ngy mod ud o pd hmodynm pop of DNA mou ud n dv d nnop y. Two pm n h mod, mou ngh nd nnop wdh, vd nd d gn xpmn d. Mhod: Vdo-fuo moopy w ud o mg ng DNA mou n h nnop y; ny ond of dmnng h vg numb of nnop oupd by ng DNA mou ov m. Ru: Good quv gmn w hd bwn hoy nd xpmn fo h nnop wdh von, bu mou-ngh von pdon w hown o nd mpovmn. A -qu f of h hoy o h d uggd h h nop pm, A, nd h xudd voum m, B, hv modfd dpnd on nno hgh nd nnop dph hn wh uny pdd by h mod. Duon: Th xpmn onfm h h ho mod dqu und n gm nd pd ondon und whh hoy nd xpmn my gnfny dvg. Modfon o h hoy popod. Kywod DNA, nnop y, fuo vdomoopy *Copondng uho: hugo.bndo@m.mg. Rvd: 2 Jnuy 2011 Rvd: 13 Mh 2011 Inoduon Sou ho mn of h fundmn bhvou of poym bgn n h 1960 nd y 1970 wh om goundbkng ng gumn by d Gnn (1) nd Edwd (2). I h ony bn n n y (3), wh h dv n nno/ mofbon hnqu, h mgng nno-fud dv uh nnopo, nnohnn, nd nno hv bn b o goouy om of h y ho mod (1,2). Rn xpmn hv pobd h ff of gom onfnmn on ndvdu DNA mou n on-dmnon nnohnn (3,4) nd n wo dmnon nno (5,6). Whn h w of h nno-fud dv onfn h DNA bow buk h z n ouon (.. h du of gyon), boh h nd dynm bhvou (6) of ndvdu mou d du o h on of h DNA wh onfnng w, w h hydodynm f-on. VOLUME 6 ISSUE 1 MARCH

2 Dynm of DNA mou n nnop y Th udy fuh xpoon of nw knd of nno-fud dv, h nnop y, dvopd ny by Rn. (7) n Nnop y nno, whh on of hn bwn wo wf wh of mbddd nnop on h boom wf, n n Fg. 1. A DNA mou onfnd o nnop w um b onfguon h mnmz f-ngy. In h fo of qubum, gvn DNA mou w h f ng nnop o pn mup nnop dpndng on onou ngh L nd gom pm uh hgh h, p dph d, p wdh, nd p png. Whn mou pn mup p, h moun of mou n gvn p fuu n m mou xhng onou bk nd foh du o Bownn fuuon (7). Fom hnoog pon of vw, nnop y povd mp wy o mnpu ng DNA mou on hp, povdng mo fxby nd pon hn onvnon nno, nd mo dg of fdom hn nnohnn. Fo xmp, pob o mgn - ung nnop y n onjuon wh mbddd nnopo n h p - h on oud pfom hghy ozd hmy on pu ppng gmn of DNA o om g poym. Fuhmo, nnop my b ufu n ppon uh ng-mou dnuon mppng n nno-fud hnn (8). Fo n, f nnop w hd no nnohnn, hy mgh v o vo fo mpoy unndd mou gmn, wh h gmn of DNA undgong ny xnd no h nnohnn. O gvn gmn h bn nyd, pu n b ppd o dv onou fom h vo no h nnohnn nd o hf h nyd onou gmn no n djn vo. Th m of h pp o h f-ngy mod pnd by Rn. (7). Wh h mod, pob o pd hmodynm qun fom hp gomy nd DNA mou pop. By py vyng h DNA mou ngh (L) nd nnop wdh (), xpmn d w ghd ung fuo vdo-moopy of ng λ-dna mou n h nnop y; h d w nyzd ung h num pogmmng pkg, MATLAB. Th v DNA mou (λ-dna) w ud n h xpmn o ow fo xpmn ompon o pvou wok don by Rn (7) nd o xnd h pvou wok. Mumn of h vg numb of nnop oupd by mou vu p wdh w d ou fo wdh ng of nm nd ompd o h mod pdon. A m ny w pfomd fo mou-ngh von ung λ-dna dg. Th ngd nny of h fgmn w ud o dmn mou ngh nd po of h vg nnop oupy vu mou z w md. Ung h mhod, oupy pobb w d gn h ho pdon fo wo dffn pm n h un mod. BACKGROUND Thoy fo Oupy S Cond DNA mou of ngh L onnd o oupy N nnop n 2D. Nx, um h h p onn n qu moun of DNA. A mou n ng f n v dffn wy on h dpndng on h numb N; h upp nd ow bound of N by h phy mon of hng nd ompng whn h nnop. Now, onqu of h d numb of oupd nnop, h numb of ngy b o mou ffvy qunzd. Fo pu gomy, h mou w fvou ngmn n n numb of N nnop mo hn oh. Povdd mod (7) o qunfy h f ngy ( F o ) of mou whn h nnop y fuon of N, h pobby, P N, h N p oupd n b ud fom Fo(N ) P N = Ω k B T N Fo(N ) k Ω N B T N Ω N, h dgy, h o numb of dffn wy of mbng mou, n f-vodng mnn, on qu wh N oupd p; pn h numb of wh h m ngy. Vu fo Ω N n b found n u (9) fo N=1 up o N=28. k B nd T Bozmnn onn nd mpu pvy. Th mou dynm houd b Bownn n h b of xn ou of fud fow uh ppd fd o pu gdn (10). H, n b onzd h djn nnop d, h p onn ppoxmy n qu moun of DNA. Thu, h o onou ngh L n b ubdvdd no h moun of onou whn h p (L p ), nd h moun n h nno-, n bwn h p, (L ) o obn L = N L p + (N-1)L Th hng n f ngy fom (7) hn gvn by ΔF o = N( F p F ) + ( N 1)F png (F p - F ) h dff f ngy of onou L p pd n nnop vu n nno, nd F png n ngy m [1] [2] [3] 24 MSURJ MG S Undgdu Rh Joun MSURJ.MCGILL.CA

3 H. B. Bndo nd W. Rn ounng fo h f-ngy qud o h h DNA mou bwn nnop. Fom of poym hoy ng gumn, F p - F n b -wn F p F = A L p + BL p 2 [4] Th pm A nd B dpnd on h gom on of h nnop y h, d,, (Fg. 2A) nd pop of h DNA mou, udng p ngh P (h mnmum ngh fo whh gmn of DNA nno f-) nd h wdh of h mou w. Th png ngy (7) gvn by, ΔF png = PL 2(1 /L ) [5] Mnmzon of h f ngy n Eq.3 f h ppop ubuon of quon 2, 4, nd 5, yd h qubum vu of L p. Subuon of h vu bk no Eq.3 dmn h qubum f ngy; uv fo h oupy pobby n hn b gnd by vyng on pm (uh L o ). Fny, h vg p oupy fo mou w b gvn by Fg. 1. Th-dmnon hm dgm of nnop y. In d pnon of DNA mou n h nnop. Th nnop y w onud on fud wf ung ombnon of on bm nd UV o hogphy. n vg = N N P N [6] EXPERIMENTAL METHODS Expmn Podu D w od fo fuo vdo-moopy ung Nkon Ep T-U nvd moop quppd wh n Ando XON m pb of ng-phoon don nd N.A. o-mmon objv n. Nnop dph nd hgh of mp nnop y w mud o b 71±2 nm nd 69±2 nm pvy wh pofom. SEM mogph of h nnofud hp v h p wdh o b 250nm, 300nm, 350nm, 400nm, 500nm, 600nm nd 1000nm. Th mumn hd 4.4% fon o h 95% onfd v dmnd fom mg ny of h SEM mogph. Spng n bwn p w fxd 1 μm fo xpmn ondud. Fgu 2B nd 2C how mp nnng on moop (SEM) mg of n y of nnop onng of 1 μm p-o-p png nd 300nm p wdh n yp qu gomy. A nno-fud hp onnng of nnop y of vyng gomy w hd on huk by n umnum nng ng. Appon of pnum pu o un h DNA fom h odng vo no h nnop y w nud by h O-ng. Fgu 3 how hm dgm of h xpmn up. Fg. 2. Co-up vw of nnop n hp. A) Oun of h mpon gom pm qud n h hoy o pd DNA oupy : hgh (h), p wdh (), p dph (d), nd p png (). B,C) SEM mogph of n y of nnop wh 1μm p-o-p png nd 300nm p wdh. Th DNA w upndd n 10 mm T buff mud ph of 7.92±0.02 nd onduvy of 0.53±0.02 ms. Th xpmn w un ung λ-phg DNA (48.5kbp) fom Nw Engnd BoLb nd wh YOYO-1 fuon dy (Invogn) wh DNA b p o dy onon of 5:1. Du o h nng po, h ngh of h DNA mou w md o fom 16.5μm o 21μm w mud by Rn. n 2007 (4). To p phoobhng of h dy nd phookkng, β-mpohno w ddd o h buff o 2% voum/voum ouon. Bfo ondung h xpmn, boh h buff ouon nd buff-fd hp onnng h nnop y w f o d-g ovngh. Thu, fow-ndung bubb n h mohnn of h hp w ffvy movd. Appoxmy 20μ of h VOLUME 6 ISSUE 1 MARCH

4 Dynm of DNA mou n nnop y nf mod, wh nggb dy bwn mg quon. Expmn w ondud oom mpu. Fg 3. Shm dgm of huk nd hp. DNA odd no h u odng vo ung mopp nd un wh pnum pu nud v o-ng. Sm bu of pu n b ppd o dv DNA fom h nnohnn no h nnop y o b mgd. Dgm podud bu modfd fom (4) wh pmon by h uho. D Any Img of h DNA mou w nyd ung MATLAB. A ngu of qu box w gnd o h nnop by h u v gph u nf. Oupy of nnop w hn bhd by dmnng h vg px nny vu whn h box; f h mn nny whn box w bov n hhod, hn h p w dmd fd. Th hhod pm w djud mnuy fo h mg qu; h fxby owd h u o ho h mo ppop vu fo gvn xpmn ondon nd quy of mg. Fgu 4A how yp vdo-moopy mg of h DNA mou n h nnop y. Oupd nnop hv bn dnfd nd h nnop gd o pu mou (ndd by h numbng of h p). To dnguh bwn wo mou n djn nnop, h pogm d on n dg-dng fuon vb n h MATLAB by. Th fuon wokd by ppyng Gun f o h mg v ndd onvouon mhod nd Lpn opo o d of pd nny hng. Th gohm woud oupu n mg wh h boundy of mou y dfnd. If wo djn nnop w od by uh boundy, hn ng mou oupd boh p; ohw, h p w oupd by dffn mou. Fg 4. Compon of vou dg-don hnqu vb fo mg ny. A) Unpod fuo vdo-moopy mg kn of λ-dna mou; xpou m 0.1. B) Edg found v h Lpn of Gun mhod ung n unpod mg. C) Edg found v h Lpn of Gun mhod ung pod mg vgd ov h fm. D) Edg found v h Sob dg-don mhod. ppd DNA/buff ouon w mnuy odd h nx dy wh mopp no h of h fou vo on h hp mb of pnum pu w ud o dv DNA fom h vo no h nno o vod fgmnon of h mou. Sho bu of mb of pu w hn ppd o h of h fou vo ndvduy o quz h fud v nd o mnmz unwnd fow. Mou w owd o x n h nnop fo ond f bng dvn no h nno. D w qud onnuouy by h CCD m wh m xpou m, n fm Th Lpn of Gun mhod of dg don pfomd vy w oy. Du o o nu, quky nhd no vdn n fgu 4B nd 4C; nvh, mnd h pfd mhod of dg don. Oh dg-fndng mhod w ondd udng h Rob nd Sob mhod (11). Wh hy ofn found h DNA mou dg nd dd no nh no, hy fd o podu mooh, od onou of h who mou n b n n ompng fgu 4D o fgu 4B nd 4C. An u nhn n h ho xpou m of 100 m (ud o qu dd pof of h p-o-p onou fuuon of mou) w h mou gmn n bwn p oony dppd fom n fm. Fo n, h boom f nnop oupd by mou 7 n fgu 4B ppd dond fom h oh wo p. Howv, npon of qu of mg vd h h nnop bongd o h m mou. An ppoh h povd o b vy ffv o mdy h knd of pobm w o pfom mg vgng: Eh mg fom h vdo w vgd wh h mg n h fm bfo nd 26 MSURJ MG S Undgdu Rh Joun MSURJ.MCGILL.CA

5 H. B. Bndo nd W. Rn f bfo undgong ny by h dg-don gohm. A n xmp of h ffvn of h hnqu, omp mou 7 n fgu 4B o fgu 4C: h nk h w pvouy no ppn h bn nnfd nd pkd up by h Lpn of Gun dg-don gohm. To jufy h u of fm-vgng, w nvgd h m fo h onou fuuon of mou n bwn wo nnop: vgng w wnd ong h m- w bow h oon m of p-o-p onou fuuon. By ngng h px nn of h nnop gd o of u-dfnd box, h fuo of h p w found. Thn, h oon offn w ompud of m g ung h GARCH mod (11) fo h o-oon of ngd nny bwn wo djn p. Th o-oon po fo h ngd nny of h nnop w ud o dmn h, 95% onfd, k bwn fv o n fm ( ) fo onou fuuon o bom uod. Wh h gnf h k 5-10 fm fo h onou gmn n on p o hv no mmoy of gnfn fuuon h oud n h djn p. Ou fm-vgng ombnd mg fo 0.3, whh 40% hn h m obvd oon m, uggng h w n u fm-vgng whou muh woy. Fgu 5 how mp of h u. RESULTS AND DISCUSSION Jufon of h umpon of qu onou p nnop In Son II, h qunzon of h ngy of mou w nodud by umng qu moun of mou p nnop. Th ho umpon w ny jufd by mng h h nnop w d; hu, DNA mou houd f nnop quy. Expmn ny of vn ndomy d mou how h fo m nv kn n m g hn h vg oon m fo p-o-p fuuon, nnop do ndd onn n qu moun of onou o whn 4%. Th png o bwn h mn p nny (whn ng u-dfnd box, ) nd h vgd mn nny fo nnop oupd by mou w ompud by: Von of mou ngh I known h mou nny houd vy ny wh onou ngh f h DNA unfomy nd wh n ppop dy (8). Conquny, whn nyng h vdo-moopy mg fo λ-(mono) DNA dg (Nw Engnd BoLb), w pob o m h ngh of h fgmn by ung mp o. Th nnop y gomy und ny ond of 1 μm p-o-p png, 100 nm p dph nd hgh, nd 300 nm p wdh. Th xpmn fuo vdo-moopy mg w od by Rn h Th Unvy of Dnmk nd w pod nd nyd wh h pmon. Fg 5. Smp o-oon po of p-o-p onou fuuon of DNA mou n nnop y wh gomy =1μm, =300nm, h=d=100nm. Coon offn whn h hozon bu b dm uod d o whn 95% onfd v. %o() = X X X X h mn nny of nnop nd h vgd mn nny. 100% [7] N X = X /N =1 Fg 6. Avg nnop oupy of dg of λ-dna fgmn n nnop y of dmnon =300nm, h=d=100nm, =1μm. Eo b pod fo boh h nny nd oupy 68% onfd. Th od n h ho pdon fo n vg fuon of onou ngh. VOLUME 6 ISSUE 1 MARCH

6 Dynm of DNA mou n nnop y Th o of px nny o onou ngh w bd ung vu fom pvou xpmn (7), wh hown h fu-ngh λ-dna mou oup on vg 3.2±0.1 nnop. In h xpmn, h mou xhbng h g vg oupy fo h DNA dg (n vg = 3.01±0.05) w kn o b 21 μm ong. Th wo u no ompb whn o; howv, fo h pupo of quv ompon of h d o h hoy, h dff m nough o gno. Avg p oupy w pod gn onou ngh fo 82 dffn mou ogh wh h ho pdon. Th ho uv w obnd fom ung h vu fo h p ngh P, hn hkn w, nd gom pm of h hp ud by Rn. n h 2008 udy (7). A obvd n fgu 6, h vg oupy v vy non-ny wh onou ngh n wh pp o b of p. Wh h ho uv m o foow h gn nd of h mou dbuon, m o f undm hn ovm h vg oupy h non bwn n vg oung L=7.5 μm nd L=17 μm pvy. Moov, h vg nnop oupy ound 17μm vy uddny fom n vg =2 o n vg =3. Th hp non n h xpmn d no vdn n h ho ompuon, wh nd how mooh uv xndng fom 10 μm o 20 μm. Th o b n fgu 6 ompud fom h ndd dvon of h ngd nny nd vg oupy. Fg 7. Hogm of h xpmn d fo h vg onou ngh of mou. Pk dy opond o h fgmn z obvd fo h go-g opho u of λ-mono DNA dg. G-opho mg podud by pmon fom Nw Engnd BoLb. To ommod qunv duon fo ngh-von ny woud qu h w b b o dmn y bwn h dffn fgmn z n h DNA dg. Th λ-mono DNA dg fom Nw Engnd BoLb onn vn d fgmn z fo DNA. W n mk hogm of h vg oupy vu onou ngh nd ook fo wh h onou ngh pk. Th pk houd ou h onou-ngh vu of h fgmn z n h dg. Fgu 7 dpy u of hogm don fo h pon of fgu 6. Fo n, h pk ound L 14.5 μm n fgu 7 y opond o h mou fgmn of ngh 33,498 b p; mny of h oh fgmn ngh n b dnfd n h wy. Wh mo d pon, Gun f o h bnnd d n gv b d of h of h fgmn z, nd w ow u o b m h vg oupy o fo vou dffn mou ngh. To du h o n h xpmn du o wh no, pob o ub h vg bkgound fom h mg bfo px ngon; bd ng h gn o no o, h fuh nu h u fom dffn xpmn n b ompd ogh, whou off du o dffn xpmn ondon. Fg 8. L-qu-f of d o hoy nd ompon o h pdd u obnd fom h un dfnon of pm A o nd B o. Eo b on h d pon h ndd o on h vgd mn oupy fo 4, 15, 18, 4, 27, 35 nd 21 mou opondng o p wdh 250nm, 300nm, 350nm, 400nm, 500nm, 600nm nd 1000nm pvy. C.Von of p wdh An xpmn w ondud fo L fxd 21 μm, h=d=70nm, =1 μm. A o of 124 mou w nyd fo h vg nnop oupy wh p o nnop wdh. Th u w pod wh h od o n fgu 8. To gn h -qu-f uv h foowng o fuon w mnmzd by vyng pm A o nd B o. χ = ( n vg (A o,b o ) n xp ) 2 [8] 28 MSURJ MG S Undgdu Rh Joun MSURJ.MCGILL.CA

7 Iw h o h nkp of.w R n f oh g n ou ndg u d h oug hou h p oj.a o,iw h h nkq ku n Zhou ndand éb ndã of o h n g h f u nd n ngd u ononhow o k h ng hyp og mm ngf o hd n y, nda xk o zf oh ondu ng h x p m n.f n y,iw h o know dg NSERC ndm G Un v yf o hf n uppo p ov d d of und h h.

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