Normal mode analysis in dihedral angle space was carried out on two X-ray crystal structures and one model structure responded to the same sequence of duplex DNA: d(CGCGAATTCGCG). Comparing these results indicates that it is reliable and meaningful to carry out normal mode analysis on model structures. The reliability is greater except for the ends of helix

Liao, XL

Lin, DH

林东海

Chemical Research in Chinese Universities

Xiamen University Institutional Repository

Normal Mode Analysis on Three DifferentStructures of a Duplex DNA d( CGCGAATTCGCG) *LIN Dong-hai* *and LIAO Xin-li( Dep ar tment of Chemistry , The R esear ch L aboratory of SE DC of Analytical Sciencef or M ater ial and L if e Chemistry , X iamen University , X iamen, 361005)( Received May 14, 1997)* Suppor ted by the Natura l Science Foundation of Fujian and t he G rant s fr om JSPS Fellowship.* * To w hom cor respondence should be addressed.　　Normal mode analy sis in dihedr al ang le space w as car r ied out on two X-ray cr ystal st ructuresand one m odel structure r esponded to the same sequence of duplex DNA : d( CGCGAATT CGCG) .Compar ing these r esults indicates that it is r eliable and meaningful to car ry out normal mode analy-sis on model st ructures. T he reliability is g reater ex cept fo r t he ends of helix .Keywords　Normal mode analy sis, Duplex DNA , A tomic fluctuat ion, Molecular dynamicsIntroductionComputer simulat ion appro aches have been pro ved to be pow erful tools to determine andcharacterize dynamics of proteins and nucleic acids. Mo lecular dynam ics calculat ion, no rmalmode analysis and Monte Carlo simulat ion are three main types of computat ional methods.M olecular dynamics calculat ion is fr ee from the assumpt ion of the harmonicity o f mo tionmade by normal mode analysis, how ever, it s approach is lim ited to the study of conforma-tional phenomena occurring in the t ime range o f 10- 10s o r faster[ 1]. In a majority o f not-very-low-frequency modes the assumption of the harmonicity is valid[ 2], and normal mode analysisis useful for understanding dynamics of mo lecular conformations in these modes.　　Recent ly, normal mode analysis in DAS( Dihedral Angle Space) has been employed toreveal the conformat ional dynamics o f pr oteins[ 3～5]and nucleic acids[ 6]. In DAS, only r otat-able dihedral angles are t reated as independent v ar iables and bond leng ths and bond ang lesare f ixed. T he low-frequency modes from both analyses in DAS and CCS ( Car tesian Coordi-nate Space) span the same subspace[ 7]. How ever, the cho ice of DAS leads to considerable r e-duct ion of the number o f independent v ariables compared w ith that o f CCS. No rmal modeanaly sis starts usually f rom a X-r ay cr ystal str ucture. How ever, fo r many duplex DNAmolecules, it is dif f icult o r unavailable to obtain experimental st ructures f rom Protein DataBank( PDB) or other sour ces. In this w ork we carr ied out no rmal mode analysis in CAS ontw o X-ray st ructures f rom PDB and a model st ructure w hich responded to the same sequenceof a duplex DNA, and compared these results to understand the reliability of using a modelst ructure to carry out normal mode analysis.Normal Mode AnalysisBased on the harmonic assumption, normal mode analysis can be used express the con-fo rmat ional energy around a minimum as a multidimensional parabola[ 1] :Vo l. 14 No. 3　1 9 9 8 　　　　　　　　　Chem ical Resear ch in Chinese Univer sities　　　　　　　　 289～293　E = ( 1/ 2)∑i, jf ij$Hi$Hj ( 1)w here f ij is the second derivat ive of the conformat ional energ y funct ion at the minimum . $His the infinitesimal change o f dihedral angle H.　　By separating the external mot ions o f the molecule f rom internal mot ions with themethod of Eckart[ 8] , the kinet ic energ y Lagr ang ian of internal mo tions in a nucleic acidmolecule is g iven byT = ( 1/ 2)∑i, jh ij$Hõi$Hõj ( 2)　　Newton equat ion is given byH$Hb+ F$H= 0 ( 3)w here F , H are matrices w hose elements ar e f ij and h ij respect ively. To solve equat ion ( 3) ,$His expr essed as linear combinat ion of the mot ions of new variables $R( named as no rmalmode variables) as follow s:$H= V$R ( 4)w here matrix V transforms the posit ive def inite symmetr ic matrices F and H into a positivedef inite diagonal matrix 8 and an identical matrix I , r espect ively :VtFV = 8 ( 5)VtHV = I ( 6)　　The main st rategy of normal mode analy sis is to solv e simultaneously the tw o eig en-pr oblems( i . e. , the gener alized eig en-pr oblem ) . In the new collect ive variables, the equationof mot ion is decomposed into$Rb+ ( 2PMi ) 2$R = 0 ( 7)w here ( 2PMi) 2 is an element of the diagonal elements of matrix 8 . Equat ion ( 7) describes aharmonic oscillato r, i. e . , a no rmal mode w ith f requency Mi .　　The mean-square amplitude of thermal fluctuat ions o f the normal mode variables is giv-en by〈$R2i〉= kT / ( 2PMi) 2 ( 8)　　The mean-square f luctuat ion o f atom ic coo rdinates is given by〈$ r2a〉= ∑iD2ai ( 9)Dai = ( kT )1/ 2/ ( 2PMi )∑jkajV j i ( 10)w here Dai is the displacement vector of the ath atom in the i th normal mode, k aj is an elementof matrix K , i . e. ,kaj = 5ra/ 5Hj ( 11)Results and Discussion1　Minimum StructuresWe chose the double-st randed dodecamer d( CGCGAATT CGCG) for our study becauseof the ex tensiv e cry stal st ructur al data and analy sis on this sequence[ 9—12]. The structuralperturbat ion at tr ibutable to cr ystal packing is a smooth 19°bend in the over al l helix ax is.The cry stal atomic coor dinates w ere taken from 9bna[ 12]and 7bna[ 11]in PDB w ith the sameresolut ions of 0. 19 nm respect ively. T he third str ucture is a model str ucture built by amolecule modeling so ftw are Insight Ⅱ. The to tal number of atoms is 758. T herefo re, thenumber of independent v ar iables in CCS is 2 274. In DA S the number o f independent vari-290 Chemica l Resear ch in Chinese Univ ersities　　　　　　　　　　　　Vol. 14　ables is 194 including 24 pseudo-rotat ion variables and 6 ex ter nal v ar iables betw een tw ost rands.Fig. 1　Ster eo drawing s of the thr ee super imposed str uc-tur es.( A) before min imizing ; ( B) af ter minimiz ing.　　From the three conformations we m inimized the conformat ional energ y. T he AMBERpo tent ial[ 13]was employed as an empirical conformat ional energ y funct ion. T he prog ramFEDER/ 2N [ 14] was used for the minim ization. T he distance-dependent dielect ric constantw as taken equal to 4r , i. e. fo ur t imes interatom ic distance. T he minimizat ion w as per formedin vacuum w ith New tonqs method. During the minimizat ion, the w eight parameters of PDBdata constr aints f rom the X-ray conformat ion w er e decreased g radually as increasing thesteps.　　Fig . 1 show s that the stereo draw ing s of the three superimpo sed st ructures befor e mini-mizing and af ter minim izing . T able 1 gives the ro ot-mean-square deviat ions ( rms D ) o fCartesian coordinates of all the atoms andthe backbone atoms betw een theminimum str uctures and the o riginalst ructures( those before minim izing ) . Af-ter m inimizing , the model st ructurechanges largely than the X-r ay st ructuresdo . Table 2 gives rms D of Cartesian co-ordinates of the heavy atoms among thethr ee st ructures, w hich indicates that thedif ferences among the model st ructureand the X-ray st ructures become smallerw ith r espect to tho se among the o riginalst ructures. T her efore, it may be expect-ed that the dif ferences between the resultof normal mode analysis on the modelst ructure and tho se on the X-ray str uc-tures are smaller.Table 1　rms D of Cart esian coordinates of the atoms bet weent he minimized st ructures and t he o rigina l str uctur e( in nm)St ructu re All atom s Backbone atoms9bna 0. 174 2 0. 179 27bna 0. 174 6 0. 181 3Model 0. 226 0 0. 226 1Table 2　rms D o f Cartesian coordinat es o f the heavy atom samong the thr ee st ructures( in nm )St ructu reBefore minimiz ing7bna m odelAf ter minimizing7bna model9b na 0. 030 9 0. 153 9 0. 069 3 0. 087 67bna 0. 151 6 0. 120 82　Frequency Histogram　　For each st ructure, 194 no rmal modes were obtained, which is the number o f indepen-dent variables in DAS. The dist ribut ions of the calculated fr equencies are illust rated inFig . 2. T he frequencies are show n by co rresponding light w ave numbers. The number o fnormal modes in each interv al of 5 cm- 1is show n. T he number o f normal modes with fr e-291　No . 3 L IN Dong-hai and LIAO Xin-li 　　quencies 200～450 cm- 1, is 6 for 9bna st ructure, 4 for 7bna structure and the model st ruc-ture, respect ively. F ig . 2 show s that the low-frequency modes ar e very similar to high-fr e-quency modes, the signif icant difference occurs in a few modes w ith f requencies 200～450cm- 1. It has been shown[ 7]that the atom ic f luctuat ions o f the duplex DNA are mainly deter-mined by a small number of low-fr equency normal modes, the no rmal modes w ith f requenciesbelow 30 cm- 1make major contr ibutions to the site-dependence of atomic fluctuat ions, thosew ith frequencies above 30 cm- 1contribute mainly to site-independent “background”motions.Therefo re the differences among the modes w ith f requencies 200～450 cm- 1are t rivial.F ig . 2　Histo gr ams of ca lculat ed v ibra tion fr equencies o f no rmal modes in this dodecamer for 9bna str uc-ture ( A ) , 7bna st ructure ( B) and the model str uctur e ( C) .　　Table 3 gives the f requencies of four very-low-frequency modes LFM 1, LFM 2, LFM 3,LFM 4 and the highest frequencies HFM fo r the thr ee st ructures. T able 3 tog ether w ithFig . 2 indicates that the f requency dist ribut ions o f the three st ructures ar e very similar.T able 3　The four ver y-low -fr equency modes and the highestfrequencies fo r t he t hr ee str uctur es(M~/ cm - 1)St ructure L FM 1 L FM 2 LFM 3 LFM 4 HFM9bn a 2. 13 2. 36 3. 58 4. 35 485. 937bn a 2. 10 2. 29 3. 74 5. 05 496. 84model 2. 19 2. 41 3. 81 4. 96 486. 143　Fluctuations of Positions of AtomsF ig . 3　Site-dependencies o f rms fluctuations o f po-sit ions of all atoms fo r 9bna str uctur es( Sol-id line ) , 7bna str uctur e ( broken line ) andthe model str uct ur e( dot ted line) .Fig. 4　Ster eo drawing s o f at omic displacement v ec-to rs in the second low est fr equency modeLFM 2 o f 9bna str ucture ( A ) , 7bna str uc-ture ( B) and t he model str uctur e( C) .　　Fig . 3 shows the site-dependencies o f rm s f luctuat ions of positions o f all the atoms for292 Chemica l Resear ch in Chinese Univ ersities　　　　　　　　　　　　Vol. 14　the three structures. Solid line is for 9bna st ructure, broken line for 7bna str ucture, dot tedline fo r the model st ructur e. Except for the terminal nucleo tide G12, the dif ferences amongrms atomic fluctuations of the thr ee str uctures ar e much small . By examining the threest ructures, w e observed a larger base-pair bucking between G12-C13 in these m inimumstructure. F ig . 3 illust rates the similarity between the atomic fluctuat ions of st rand A andtho se o f st rand B, w hich suggests the presence of a tw o-fold pseudo-symmetry ax is w ith it sorig in located at the center of the molecule. T he ideal tw o-fold symmetry is dest roy ed by the19°bend in the helix ax is. F ig. 3 also exhibits that the atoms at the ends of helix move morethan in the center , possibly due to the incompleteness o f base-stacking at the ends of helix .Fig . 4 show s the stereo draw ing s o f atomic displacement vectors in the second lowest fr e-quency mode LFM 2 o f the three st ructures. T hese plo ts ar e sim ilar to each other on thew ho le.4　Conclusions　　T he similarit ies among the results of normal mode analy sis on two X-ray cry stal st ruc-tures( 9bna and 7bna) and a model st ructure suggest that w e can carry out normal mode anal-ysis on a model str ucture o f duplex DNA if the experimentally obtained st ructure is unavail-able. T he reliability is greater ex cept for the ends o f helix. T his is ex cepted to be meaning fulfo r some bigger DNA molecules, in which the influences o f term inal nucleot ides are t rivial.Acknowledgement　　This w or k w as car ried out in the L aboratory of Quantum Chemist ry , Department ofChemistry , Kyoto University . The authors w ant to thank P rof essor N . Go f or his v aluableguiding. A lso, w e w ould like to thank Mr . A . Matsumoto, Dr . A . K idera and Dr . A . K i-tao f or helpf ul discussions.References[ 1]　Nishikawa , T . and Go, N . , P r oteins, 2, 308( 1987)[ 2]　Nogut i, T . and Go , N . , Nature, 296, 776( 1982)[ 3]　Yamato , T . , Hig o , J. , Seno , Y . and Go , N . , Pr oteins, 16, 327( 1993)[ 4]　Levit t, A . , Sander , C. and Stern, P . S. , J. Mo l. Biol. , 181, 423( 1985)[ 5]　Brooks, B. and Karplus, M . , P ro c. Natl. Sci. USA . , 80, 6 571( 1983)[ 6]　L in, D . H. , Matsumoto , A . and Go , N . , J. Chem. Phys. , 107, 3 684-3 690( 1997)[ 7]　Tomimo to, M . , K itao , A . and Go , N . , Elect ronic. J. Theo . Chem. , 1, 122-134( 1996)[ 8]　Eckar t, C. , Phys. Rev. , 47, 552( 1935)[ 9]　Dicker son, R . E. and Drew , H. R. , J. Mo l. Bio . , 151, 535( 1981)[ 10]　Stephen, R. H. and K im, S. H. , J. Mo l. Biol. , 173, 361( 1984)[ 11]　Holbr ook, S. R. , Dicker son, R . E. , Kim, S. H. , Acta Crystalog r . , Sect . B. , 41, 255( 1985)[ 12]　Westho f, E. , J. Biom ol. Str uct . Dyn. , 5, 581( 1987)[ 13]　Weiner , S . J. , Ko llman, P . A . , Case, D. A . et al. , J. Am. Chem. Soc. , 106, 765( 1984)[ 14]　Tomimo to, M . , Wako , H. and Go , N . , J. Comput. Chem . , 17, 910( 1996)293　No . 3 L IN Dong-hai and LIAO Xin-li 　　

Normal mode analysis on three different structures of a duplex DNA d(CGCGAATTCGCG)

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Normal mode analysis on three different structures of a duplex DNA d(CGCGAATTCGCG)

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