Canuto, Sylvio

Chaudhuri, Puspitapallab

IACS Institutional Repository

Illfl I  phys. 76B (4), 577-580 (2002)U P  Man international journalC o r r e l a t i o n  e f f e c t s  o n  p e p t i f t e  m o l e c u l e sP u sp ita p a lla b  C h au d h u ri and  S y lv lo  C a n u teInstitute dc Fisica, Universidade dc Sao Paulo, CP 66318, (»315-Q70 Sfto Paulo. SP, BrazilK-mail puspila@ift.unesp.lrfAbstract : Ab mitio methods are used to study the four possible dipcptidcs that can be formed from alanine and glycine in gas phase \Vc calculate the geometry, binding energy and rotational spectra of alanylalaninc, alanylglycinc, glycylalaninc and glycylglycinc. The scometnes are optimized using Hartrcc-Fock (HF) and second-order Mollcr-Plessct perturbation theory (MP2). Single-point energy .alculatjons with high-level CCSD(T) arc performed on MP2 geometries. Both electron correlation and zero-point vibrational energy .(Erections arc found to be very important and increase the calculated binding energy. Most of the correlation effects are obtained in ,aond-order The inclusion of zero-point correction is found to be essentialkevHords Correlation effects, peptide molecules.'\(S  No. 33.15.RyIntroductionicie bonds a re  o f  e n o n n o u s  s c ie n tif ic  in te re s t as it is th e  lary req u irem en t fo r  th e  s tru c tu re  o f  a ll th e  p ro te in s  and  equently, fo r th e  o r ig in  a n d  c o n tin u a tio n  o f  life. W ith  » c ic n i d e tec tio n  o f  m o re  th a n  1 0 0  sp ec ie s  o f  a m in o  s in  in te rs te lla r  sp a c e  [ I ]  a n d  w ith  th e  c o n tin u in g  dies for m o re , th e re  is a lw a y s  a p o ss ib ility  to  f in d  wins m th e  c o o l in te rs te lla r  sp ace . In th is  s itu a tio n  th e  y of pep tide  b o n d  fo rm a tio n  fro m  n e u tra l am in o  ac id s  ►nies o f  in te rest.be fo rm ation  o f  a  p e p tid e  b o n d  is an  ex am p le  o f  a Icnsation re a c tio n . T h e  tw o  m o le c u le s  o f  a m in o  ac id s  c o v a le n tly  to  fo r m  th e  b o n d  to g e th e r  w ith  th e  iTipanying re m o v a l o f  a  m o le c u le  o f  w a te r. S in ce  g ly c in e  alanine a re  th e  tw o  m o s t  s im p le  a m in o  a c id s , th e  ide bonds in v o lv in g  a la n in e  o r  g ly c in e  a re  th e  m o s t dy s tu d ie d  o n e s  b y  th e  th e o re t ic ia n s  [2 - 6 ]. In th e  -ni paper w e  in v e s tig a te  th e  s tru c tu re  a n d  e n e rg e tic s  o f  pep tid e  m o le c u le s  th a t m a y  be  fo rm e d  from  th e  ^re o f  a lan in e  a n d  g ly c in e  in g a s  p h ase . W hen  th e y  sp lit vater to  fo rm  a  d ip e p tid e , e ith e r  c o u ld  be  th e  d o n o r fo r a h y d r o g e n  o r  a  h y d r o x y l  g r o u p  a n d  h e n c e ,th eo re tic a lly , it g iv es  rise  to  fo u r  p o ss ib ilitie s  fo r th e  p ro d u c t (see  F ig u re  l a ) :H H/ ' v  I " i"  » > ■# "AUnylglyaiM- (ALA-GLY)NV  IIIoI \ :cCGlycyblaniiir (CLY-ALA) HM H1\ r6IIoAlanylaUniiic (ALA-ALA) Glycylclyruic (CLY-CLV)Figure U . The fout peptide molecules considered in the present study(1) A lany l g ly c in e  (A L A -G L Y ):C H ,-C H (N H 2> C 0-N H -C H 2-C 00H(2) G lycy l a lan ine  (G L Y -A L A ):H -C H (N H 2)-C 0-N H -C H  (C H 3 > C 0 0 H(3) A lan y l a lan in e  (A L A -A  L A ) :CH3-CH (N H 2)-C0-N H -C H  (C H jV CO OH(4) G lycyl g lycine (G L Y -G L Y ) :H -C H (N H 2>C O -N H -C H 2-C C X mC 2 0 0 2  lA C S578Table 1. Geometry o f the peptide unit in the peptidePuspitapallah Chaudhuri and Sylvio CanutoW e u s e  h ig h - le v e l  a b  in i t io  q u a n tu m  m e c h a n ic a l  m e th o d s  to  m o d e l a ll th e  fo u r  m o le c u le s  m e n tio n e d  ab ove . 'Fhe b a s ic  in te re s t o f  th e  p re se n t s tu d y  is to  an a ly z e  th e  e ffe c t o f  h ig h e r -o rd e r  e le c tro n  co rre la tio n  on  th e  b in d in g  en e rg y . H o w e v e r  ro ta tio n a l p ro p e r tie s  a re  a lso  c o n sid e red .2 . M e th o d  o f  c a lc u la tio nF u lly  u n c o n s tra in e d  g e o m e try  o p tim iz a tio n s  a re  p e rfo rm ed  fo r A L A -G L Y , G L Y -A L A , A L A -A L A , G L Y -G L Y , A lan in e , G ly c in e  an d  w a te r  u s in g  H a rtre e -F o c k  (H F ) an d  seco n d - o rd e r  M o lle r-P le ss e t th e o ry  (M P 2 ) u s in g  g ra d ie n t te c h n iq u e s[7] an d  th e  6 - 3 IG *  b a s is  se t. A f te r  o b ta in in g  th e  o p tim ized  g e o m e try  a t th e  M P 2  lev e l, s in g le -p o in t c a lc u la tio n s  a re  p e r fo rm e d  u s in g  m a n y -b o d y  p c x tu rb a tio n /c o u p le d -c lu s te r  th e o r ie s  (M B P T /C C ) [8 ] w ith  th e  sam e  6 - 3 IG *  b a s is  set. T h e se  in c lu d e  th e  m o re  so p h is tic a te d  c o u p le d -c lu s te r  m o d e ls  su c h  as  C e S D  [8 ] a n d  C C S D (T ) [9]. T h u s  a t th e  h ig h e s t le v e l ,  g e o m e t r y  o p t im iz a t io n  o f  th e  s e v e n  m o le c u le s  m e n tio n e d  a b o v e  a re  p e rfo rm e d  a t th e  M P 2 /6 -3 IG *  level an d  s in g le -p o in t c a lc u la tio n s  a re  fu r th e r  m ad e  up  to  th e  C C S D (T )/ 6 - 3 IG *  lev e l. C o m p a riso n  b e tw een  th e se  re su lts  a llo w s  a sy s te m a tic  a n a ly s is  o f  th e  e le c tro n  c o rre la tio n  e ffec ts  on  th e  b in d in g  e n e rg ie s . T h e  b in d in g  e n e rg ie s  fo r  a ll th e  fo u r p e p tid e s  a re  c a lc u la te d  w ith  a ll th e  a b o v e  th e o re tic a l m o d e ls , w ith  and  w ith o u t th e  z e ro -p o in t e n e rg y  co rrec tio n . T h u s  w e can  a lso  see  th e  e ffe c t o f  z e ro -p o in t e n e rg y  o n  th e  b in d in g  en e rg ie s .T o  m a k e  su re  th a t all o p tim iz e d  g e o m e trie s  a rc  tru e  m in im u m  th e  g e o m e try  o p tim iz a tio n s  a re  fo llo w ed  b y  a c a lc u la tio n  o f  th e  h ess ian . I 'h e s e  h e ss ia n s  a re  th en  ust:d to  c a lc u la te d  th e  h a rm o n ic  v ib ra tio n a l f req u en c ie s  a re  th e re fro m  th e  z e ro -e n e rg y  v ib ra tio n . A ll th e  c a lc u la tio n s  a re  p e rfo rm ed  u s in g  th e  G A U S S IA N /9 8  p ro g ram  [10].3 . R e s u lts  a n d  d is c u s s io n sT he  p e p tid e  b o n d  s tru c tu r e  :It is w e ll k n o w n  [ I ]  th a t b o th  g ly c in e  an d  a lan in e  can  h av e  sev e ra l s tru c tu ra l c o n fo rm a tio n s  d e p e n d in g  o n  th e  in te rna l ro ta tio n a l d eg ree s  o f  freed o m . T he  p re sen t o p tim ized  s truc tu re  o f  g ly c in e  c o rre sp o n d s  c lo se ly  to  th e  s tru c tu re  IV n  o f  C sdz^r [ 1 1 ], w h e re a s  th a t o f  a la n in e  c o rre sp o n d s  to  th e  s tru c tu re  11b  [ 1 2 ].T h e  F ig u re  l a  il lu s tra te s  th e  fo u r  p e p tid e  m o le c u le s  co n s id e re d  in th is  p ap e r. T h e  b o n d  len g th s  an d  a n g le s  o f  th e  p ep tid e  un it, C " -C O -N H -C " , in a lan y lg ly c in e  (A L A -G L Y ) as o b ta in ed  by  th e  tw o  m e th o d s  a re  sh o w n  in F ig u re  l b  an d  in T ab le  1 w h e re  th e y  a re  c o m p a re d  w ith  th e  e x p e rim e n ta l param ete rs  [1 3 -1 5 ].ALA-GLY. Bond lengths arc given in Angstrom and the bondrl r r^  degree.GeometryHF/6 -3IG^MP2/6-31G*Ref.fl31Ref(M)C-N 1.349 1,359 1.32 1.33.^c«-c 1.531 1 528 1.53 1 522N-C« 1-436 1.441 1 47 I 449N-H 0.995 1.014 1.00 0.96C-O 1 203 1 237 1 24 1 229< C«-C-N 116.09 116.26 114 116 6< c«-c-o 121.88 121.79 121 120.4< N-C-O 122.03 122.05 125 122.9< H-N-C« 117.35 117.26 114 118 4C«-N-C 121.28 120.55 123 121 9< H-N-C 121.37 122 29 123 119 8I u.In c o m p a r in g  o u r  re su lts  am o n g  th em se lv e s  mv] v e x p e rim e n ta l v a lu e s  o n e  sh o u ld  reca ll th a t  expcriiru};i m e a su re m e n ts  on  th e  s tru c tu re s  o f  p ep tid e s  a rc  done u> c o n d en sed  p h a se  th a t c o n ta in  b o th  b o n d e d  an d  non-t>oo'i in te rac tio n s . H o w ev e r, c o m p a r in g  w ith  th e  thu ;e  ex p e rim e n ta l re su lts , w e  n o te  an o v e ra ll go o d  agrcrfiu- b e tw een  th e o ry  an d  ex p e rim e n t. B oth  IIF  and  M P2 p/<Klih a lm o s t th e  sam e  v a lu e s  fo r  the  b o n d  an g les . Howevet il H F  b o n d  len g th s  a re  g e n e ra lly  sm a lle r  th an  th a t o f  MP2 i i C -N  b o n d  leng th  is a lw a y s  lo n g e r th an  th a t o f  expcrin)ciii a ll th eo re tic a l lev e ls  as h a s  a lre a d y  b een  observed  hetf[16].R o ta tio n a l sp e c tra  :T h e  ro ta tio n a l c o n s ta n ts  a re  v e ry  u s e fu l in the raui  ^a s tro n o m y  id en tif ica tio n  o f  m o lecu le s  in th e  interstellat T h e  d ip o le  m o m en t, on  th e  o th e r  h a n d , is im portan t as it re la ted  to  th e  in ten s ity  o f  th e  ro ta tio n a l lines. T h ese  rotatiun c o n s ta n ts  can  be  e v a lu a te d  d ire c tly  fro m  th e  m o m en ts» inertia . In  T ab le  2  w e  c o m p a re  th e  ro ta tio n a l constants ar d ip o le  m o m e n ts  o b ta in e d  b y  H F  a n d  M P 2  m eth o d s . We no th a t /I >  B =  C  in a ll cases , in d ic a tin g  th a t all thti m o lecu les  can  b e  rep re sen ted  by  a  n ea r-p ro la te  approximatK in a r ig id  m o d e l.T he b in d in g  e n e rg y  :T a b le  3 sh o w s th e  c a lc u la te d  b in d in g  e n e rg ie s  (B L ) obtains b y  th e se  tw o  m e th o d s  a lo n g  w ith  th e  ze ro -p o in t energ co rre c tio n s  to  it. B E  a re  c a lc u la te d  as a  d if fe re n c e  betwee th e  su m  o f  th e  e q u il ib r iu m  en e rg y  o f  th e  final chann< (p e p tid e  m o le c u le  w a te r)  a n d  th a t o f  th e  ind iv idual annnCorrelation effects on peptide molecules 579laMf 2 rotational constants (A. B and C) in the umts ot GH/ and dipole momants <□) in debye of the four peptide molecules, alanylglycine.Ul)wVlalanine, alanylalaninc and glycylglycincAlanylglycine(GLY<(jLY)Olycylalaninc-ALA)Alanylalaninc(Al A-ALA)Cilycylglycinc tCiLYAil Y)HF m p : in3.2463  0 5771 0 52<?l 2/^1883 1872 0 5706 0 5261 3 17383.0393 0 6404 0 5709 2.8092MP7 IIF MP2 HF MP23.0)27 J.2159 2 2022 5.2066 4.98850 6389 1.5622 0 5569 0 6722 0 66910 5655 4 4<)I4 |.86330 4887 0 6015 0.59723.011 I 3 0930 2 8595 3.0847ajJ com ponents in th e  in itia l ch an n e l. T ab le  3 show s that Mih electron c o rre la tio n  e ffe c ts  an d  ze ro -p o in t v ib ra tiona llajtiv i < alculaied binding energies (k.cal/rnol) for the peptide molecules : 111', the basis set 6-3IG'*' at the IIF and MP2 level BL and /PC' denote nc bidiiing energy and the correction due to the difference in /cro vibrational energies on the binding energy.Molfuiie BF.(HF) Vul \M -\-Al A.1 Y1.34 1 471 79 I 02After ZPC' BH(MP2) After /PC3 05 5 623.7i 6112 <A 5 463 823 954 58  ^ 18 4 17, 6 34and  G L V -A L A , d ecrease  fo r A L A -A L A  an d  h av e  a m in o r e ffec t ff>r A LA -G LY '. I f  one  co n sid e rs  th e  h ig h es t level o fI'ahle 4. Calculated binding energies using MP2 geometries for the peptide bonds, with 6-3IG* basis set in ditt'erent methods. ZPC is the calculated MP2 /.cro-point energy correction::cctiotts (Z P C ) in c rease  th e  13F T he  e lec tro n  co rre la tio n  itea ob ta ined  in se c o n d -o rd e r  M P2 g iv es a su bstan tia l miiibution to  B E . A m o n g  th e  fo u r m o lecu le s  th e  effec t is niximurn in c a se  o f  G L Y -G L Y  w h ere  B E  increases by 3,15 cal diol and m in im u m  in A L A -A L A  w h e re  the increase  is ’‘il\ 0.64 k ca l/n io l. Z P C  are  fo u n d  to  be m o re  im p o rtan t fo r 4 V (i | Y a t th e H F  level b u t fo r A L A -A L A  at the co rre la ted  level. C o n s id e r in g  th e  M P 2  resu lts , the  m o st b o u n d  Atom IS G l.Y -G L Y  w ith  a B E  o f  6 .34  kca l/m o l. C o m p o site  ^sterns such  A L A -G l.Y  an d  G L Y -A L A  are  in te m e d ia te  •' tween the A L A -A l.A  an d  G L Y -G L Y  system s. A t th is stage > appropriate to  in c lu d e  h ig h e r  level co rre la tio n  co rrections, has, s in g le -p o in t fu ll fo u r th -o rd e r  M P 4  an d  C C S D (T ) alculations a re  p e rfo rm e d  fo r all m o lecu le s  in th e ir  M P2 .^‘ometries. T h e  re su lts  a re  sh o w n  in l a b l c  4. T h ere  are  ^^ nie in te r e s t in g  a s p e c t s  r e la te d  to  th e  h ig h e r - o r d e r  <^rrelation co n trib u tio n s. F irst, all ca lcu la ted  B E are  decreased  I ilie C C S D (T ) lev e l c o m p a re d  to  th e  p rev io u s  M P 2  resu lts , oinparison b e tw een  th e  re su lts  o b ta in ed  a t th e  M P 4(S D Q ) M P4(D Q ) sh o w s th a t s in g le  ex c ita tio n s  at the  fou rth  rder decrease th e  B E  b u t co m p a riso n  b e tw een  M P 4 (S D Q ) C e S D  s h o w s  th a t  h ig h - o r d e r  s in g le  a n d  d o u b le  ’^ ^itaiions in c rea se  B E  fo r  a ll sy s tem s . A d d itio n a lly , th e  ^^^ribution o f  tr ip le  ex c ita tio n s  in  to u rth -o rd e r, as seen ' ^1P4(SDTQ), a n d  h ig h e r -o rd e r  as seen  in C C S D (T ), do  have a d e fin e d  sig n . T h ey  in c rea se  B E  fo r G L Y -G L YMFTHOD ALA-GLY (jLY-ALA ALA-ALA GLY-GLYMP2 3 05 3.71 2.64 4.17MF2  ^ ZPC 5 62 6 i 1 5 46 6.34MP3 2 96 3 52 2 59 3 92MP4(D) 2.67 3 28 2.35 3 62MP4(DQ) 2 64 3 18 2 48 3 36MP4(SI)Q) 2 34 2.94 1 91 3.15MP4(SD1\)) 2.22 3.01 1.95 3.32CeSD 2 51 3 08 2 37 3 25CC'SD(T) 2 51 3 21 2.03 3.72CCSI)(0  ^ ZPC 5 09 5.61 4 86 5.89ca lcu la tio n , C C S D ( I ). and  Z PC , a t th e  M P 2  level, w e find  tha t th e  best re su lt co n sid e red  h ere  g iv es B E  o f  4 .8 6  k ca l/ m ol, 5 .09 kcal/m ol, 5.61 kcal/m ol and  5 .89 kcal/m o l fo r A L A - A l-A . ALA GI y .  G LY -A LA  and G L Y -G l.Y , respectively.c \cIIoHNFigure lb- The structure of the peptide unit taken from ALA-GLY to be compared with the experiments in fable 1 fhe symbol C* stands for the standard notation CP used in the text and table.4. C o n c lu s io n sf h e  p re s e n t a b  in itio  c a lc u la tio n s  sh o w  th e  e ffe c ts  o f  e lec tro n  co rre la tio n  on  th e  b in d in g  en e rg y  o f  th e  p e p tid e  m o lecu le s  c o n s id e rin g  th e  fo u r  p o ss ib le  c o m b in a tio n  o f580 Puspitapallab Chaudhuri and Sylvia Canutoalanine and glycine to form dipeptides in gas phase. HF and MP2 methods are used to optimize geometries and to calculate the total energies and vibrational frequencies of the four molecules: ALA-GLY, GLY-ALA, ALA-ALA and GLY-GLY. The effect of electron correlation is found to be significant as it increases the binding energies nearly duplicating the HF value in all cases. Most of the correlation effect is obtained already in second-order but higher-order effects slightly decrease the binding energies (around 0.5 kcal/mol). The zero-point energy corrections are found to be crucial and they also increase the binding energy. Among the four molecules considered, GLY-GLY is found to have the highest binding energy (5.9 kcal/mol) while ALA-ALA has the lowest one (4.9 kcal/mol).R e fe re n ce s[1] A G  CsSz4r Prog in Biophys. and Mol. Biol 71 243 (1999)[2] W D Cornell, I R Gould and P A Kollman, J  Mol Struc (Theochem) 392 101 (1997)[3] IK  Roterman el al Biomol Struc Dynam 7 421 (1989)[4] 1 R Gould, W D Cornell and I H Hltlier J. Am. Chem. Soc i9250 (1994) ' ‘[5] T Head-Gordon et al J. Am. Chem. Soc. 113 5989 (1991)[6 ] H Bohm and S Brode J. Am. Chem. Soc. 113 7129 (I991)[7] H B Schlegel J. Comp. Chem. 3 214 (1982)[8 ] R J Barden y. Phys. Chem. 93 1997 (1989)[9] K Raghavchari Ann. Rev. Phys. Chem. 42 615 (1991)[10] M J Frisch el al Gaussian 98, Revision A. 7, Pittsburgh }’ ,i(1998)[11] A O  Cs4sz4r J. Am. Chem. Soc. 114 9568 (1992)[12] A G Csiais J. Phys. Chem. 100 3541 (1995)[13] R B Corey and L Pauling, Proc. Roy. Soc. (London) BI4 i ]o (1953)[14] E Bencdctti Peptides eds. M Goodman and J Meinenhorcr (Nc» York : Wiley) (1977)[15] R E  Marsh and J Donohue Adv. Protein Chem. 22 249 (1967.[16] J N Scarsdale el alJ .  Am. Chem. Soc 105 3438 (1983)This work has been partially supported by CNPq and FAITSl’ Drazil.

Correlation Effects on Peptide Molecules

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Correlation Effects on Peptide Molecules

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