2 calculations of the relative stability of the goniomers in poly(dl -alanine)

CNDO/2 calculations of the relative stability of the goniomers in poly(DL-alanine) Masaru Ohsaku* and Hiromu Murata Department oJ Chemistry, Faculty of Science, Hiroshima University, Higashisenda-machi, Hiroshima 730, Japan

and Akira lmamura Department of Chemistry, Shi.qa University of Medical Science, Setatsukinowa-cho, Otsu, Shi.qa 520-21, Japan (Received 21 April 1981; revised 24 July 1981)

Goniomers of single-stranded poly(OL-alanine) rcoL helices were treated by the semiempirical CNDO/2 MO procedure. The ~ and c~oc forms were also calculated. From the calculated total energies and partitioned eneryies we discuss the conformational stability of ,qoniomers q/poly(DL-alanines). The conJormational stability of the 7 and ~ jorms is also compared. Keywords: Polypeptides; poly(DL-alanine);peptide stability; CNDO/2 MO goniomer

Introduction

Method of calculation

Poly(L-alanine) has several stable conformations, for example,/3 sheet and eR helical structures 1-3. For these conformational isomers, statistical treatment using semiempirical potential functions has been performed extensively. Statistical calculations have been extended to //-structure, e-helix, single-stranded and double-stranded helices 4-7. The CNDO/2 treatment s has also been applied 9 to the e-helical form. Molecular structures of poly(g-alanines) have also been studied by analysis of their vibrational spectra 10. For these species, conformational analyses were performed using the solvent effect, by n.m.r, spectroscopy 11'~2. Moreover, structural studies of ~oe helices have been focused on gramicidin and poly(y-benzyl DL-glutamate) (PBD-LG) using a variety of procedures ~3-~9. From these investigations, Heitz et al. 16 ~s have concluded that PBD-LG assumes a variety of conformations depending on the solvent, and these conformations are interchangeable. In order to investigate this phenomenon, it is useful to take up a similar model, such as poly (DLalanine). However, electronic analysis has not yet been applied to the ZDC forms of this species. Moreover, the interactions which govern the geometrical stability have not been adjusted completely in previous works 4 ~. It is of interest to discover which interaction plays an important stabilizing role in various forms of poly(DL-alanine). In this paper we carry out CNDO/2 calculations s for poly(DL-alanine) goniomers, using the tight-binding approximation 2°, in order to obtain information on their conformational stability. From the results obtained, we analyse the intra- and inter-segment interactions in poly(DL-alanines) in more detail than previous statistical works 4-7.

Numerical calculations were performed according to the procedure described in previous papers 9'21. Geometries used are those reported 2'3 except r(C, H), r(C~ H) and r(N H), and these were adequately assumed: r(C, H) = 109 A, r(C~-H)= 107 A, r(N H)= 1.00 A. Schematic structures and atom and segment numberings of poly(DLalanine) are shown in Figure 1. Notations used for conformational isomers, dihedral angles 7, and helical parameters of the goniomers and e-helices are summarized in Table 1. Dihedral angles of poly(DLalanine) have been reported by several groups of researchers. In the present work, we have performed calculations on the conformations reported by Ramachandran et al. 5, Scheraga et al. 6, and by Lotz et al. 7. These are named in the present article as 7ZDLR,ZrDLS,and rCDCb respectively.

* To whom all correspondence should be addressed.

0141 8130/82/020103 04503.00 © 1982 Butterworth & Co (Publishers) Ltd

4 6-8 R ' .H 5

HI2

%,

OZO

I

/ C 3 ~ / N , = ~ / k ~.C.~ ~ ~'C

Hz

Oto

D /Cig.. / -

Ri4

u

HI5

%/

L /C-...<.. I ~ N / L

H

.

0

*o R

%

%c /

II

0

I

% H

1

H

H .

R

'#~

%

0

H

Lt C

I N

L

Rd ""H

R

H

% C~... /

II

0

Figure 1 Schematic structure and atom and numberings of poly(DL-alanine): R, methyl group

segment

Int. J. Biol. Macromol., 1982, Vol 4, March

103

C N D O calculations on poly(DL-alanine): M a s u r u Ohsaku et al. Table

1

Torsional angles

Conformatiions/ st ruct u r e s

( ) a n d helical p a r a m e t e r s of s o m e s t r u c t u r e s of poly(D L-alanine)

"~ D

qoD

g*D

~oL

qoL

g*L

n

h

7~[)LR

1 ~0.00

140./)1/

-- 130.00

181).00

-- 106.00

122.00

1.515

115.38

7rDkS

-- 180.00

141.00

- 127.00

180.00

111.00

125.00

1.625

113.76

/TI)I L

180.00

126.8

105.00

180.00

- 132.00

141.00

1.69

114.28

:%

177.82

-59.17

47.36

177.73

-59.47

47.58

2.79

198.6

~Dt

178.46

--50.10

--50.38

176.4/)

--59.94

47.36

2.89

201.82

Table 2

T o t a l e n e r g y (eV) of poly{D L-alanines) ~DLR

Total

7~I)LS

~I)[.l.

:2R

3(DL

3008.41

3008.14

3008.02

- 3008.76

3008.56

Total intrasegment

- 2973.06

- 2973.90

2974.09

2971.42

- 2972.47

Total one centre

- 2484.55

- 2484.86

- 2484.95

- 2484.07

- 2484.28

Total two centre

488.51

489.04

489.14

- 487.35

488.19

Total intersegment

- 35.35

34.25

- 33.94

- 37.33

- 36.09

0 1" T o t a l

- 16.80

- 16.77

16.75

- 16.94

16.84

Resonance

- 18.94

- 18.92

- 18.91

- 19.09

- 19.00

Exchange

- 3.46

- 3.45

- 3.45

- 3.48

- 3.45

5.60

5.60

5.61

5.63

5.6 I

0.01

1.66

- 1.15

1.75

-

Electrostatic 0 2 Total Resonance Exchange Electrostatic 0

3 Total

-

Resonance Exchange Electrostatic

.066

-.023

-/).27

0.16

0.01

0.37

0.18

- 0.16

- 0.04

- 0.03

- 0.04

- 0.03

0.03

1t.02

- 0.03

0.02

0.62

0.16

- 0.09

- 0.08

- 0./12

- 0.01

0.05

- 0.06

- 0.06

0 4 Total

-0.21

-0.12

-0.05

Resonance

- 0.21

- 0.10

- 0.04

Exchange

- 0.03

- 0.01

Electrostatic E n e r g y terms:

0.02

- 0.02

• absolute valuesar¢ <0.01 cV.(Energy, secequations 1 4ofRef.

1.16

21 for m o r e details)

For simplicity, 0 I (segments) means the central and the first nearest neighbour segments, 0 2, 0 3. . . . refers to the central and the second, third ..... nearest neighbours. In the present article, up to 0 4 segments were taken into consideration

Results and discussion 7T,DL.'/()rDIs The calculated total energy and the partitioned energy ( p r o c e d u r e o f e n e r g y p a r t i t i o n i n g is s h o w n in Ref. 211 a r e s h o w n in Table 2. F r o m t h e c a l c u l a t e d t o t a l e n e r g i e s , t h e conformational s t a b i l i t y a m o n g t h e t h r e e ~rDL f o r m s is a s follows: ~I)L+R ~ 7~l)lS ~ 71"DIL O. 2 7 O. 1 2

here the differences per segment are given m eV. The energy difference between the three forms may not be as much, since the CNDO/2 procedure sometimes o v e r e s t i m a t e s t h e e n e r g y d i f f e r e n c e . T h i s i m p l i e s t h a t in

104

I n t . J. B i o l . M a c r o m o l . ,

1 9 8 2 , V o l 4, M a r c h

s o l u t i o n t h e p r e s e n t s p e c i e s e x i s t s in a v a r i e t y o f f o r m s . T h i s a g r e e s w e l l w i t h t h e r e s u l t s o f L o t z et al. 7. F r o m t h e s e results, we can see that the parent molecule, PBG-LG or gramicidine, has a variety of conformations in solutionl6 18, a l t h o u g h in t h e p r e s e n t c a l c u l a t i o n s t h e solvent molecules were not taken into consideration. W e n o w d i s c u s s t h e e n e r g y d i f f e r e n c e in m o r e d e t a i l . The total intrasegment and the intersegment energies are as follows: Total intrasegment energy: TCDLL< T~DLS< TEDLR

Total

intcrsegment

energy: T/TDLR~ ~DLS ~ ~DLL

C N D O calculations on poly(DL-alanine): Masuru Ohsaku et al. Table 3

Short contacts between the 0 3 and (>4 segments below 2.5 A in the nDLR, nDLS and nDLc forms

7'~DL R

7~DLS

[0 3 segments] (°H5---3010) (°HI2...3010) (°O20...3H15) [0 4 segments] (o020-. -'*H2)

2.29 1.74 2.14 1.96

[0 3 segments] (°H5-..3010) (°H12..-3010) (o020...3H 15) (>4 segments] (o020" "*H2)

2.47 2.15 2.48 2.17

T~I)LL

[0 3 segments] (°H12""3010) [0 4 segments] (0020"" "4H2)

Table 4

2.27 2.45

Large elements in the (>3 and 0~, segments in the 7rDLR

form Resonance term" [0 3 segments] (°H5, 3010) (°Nll, 3010) (°H 12, 3010) (°O20, 3H15) [%4 segments] (0020, 4H2) E change term ~ [0 3 segments] (°H 12, 3Ol0) [(>4 segments] b (o020, '~H2) a h d

these small differences greatly affect the total energies of the intersegment terms, especially in the (>3 segments. In Table 3, the short contacts of the atoms below 2.5 A between the 0-3 and O-4 segments of the nDLR, nDLS, and nDLLare summarized, and in Tables 4- 6, the large elements which appear in the O-3 and 0-4 segments are summarized. By comparison of Table 3 with Tables 4 6, we can easily recognize that short contact elements closely relate to the large contribution elements. Here the electrostatic elements almost cancel with each other. Moreover, the large energy difference a m o n g the three forms is considered to be due mainly to intersegment hydrogen bonding. Therefore, the small difference in dihedral angles a m o n g the three nDL forms is found to be closely related to the likelihood and the strength of t h e hydrogen bonding.

-0.05 0.09 -0.56 -0.09 -0.24

Electrostatic term ~ [(>3 segments] (°C9, 3C9) (°C9, 3010) (°O10, 3010) {°Nll, 3010) (°C19, 3010) (°020, 3C9)

(0020, 3010) -0.05

(0020, 3C19) (o020, ~O20) [(>4 segmentsl e

0.21 -0.32 0.27 0.24 -0.27 -0.27 0.35 -0.31 0.26

-0.02

Energy terms: absolute values less than 0.05 eV are not given Energy terms: absolute values less than 0.02 eV are not given Energy terms: absolute values less than 0.20 eV are not given Energy terms: not catalogued

~R and o~vL.forms For comparison with the nDL form, the :tR and :tDk forms were also calculated. Here the unit segment of the ~R form taken up was the same as that used in the case of the nDL form. In the c% and C~DLforms, the total energies obtained are smaller than for the riDE forms. The energy difference calculated between the n and ~ forms, however, m a y become smaller when we consider longer polymer ranges: this will be discussed later. This implies that the polymer considered here can be changed not only between goniomers but also between the n and ~ forms. This agrees with the statistical calculations 7. For the ~ Rand ~DL forms, large negative values appear in the % 2 segment, as shown

Table 5

Large elements in the O 3 and 0 4 segments in the nDLs

form Resonance term s [(>3 segments]

F o r the total intrasegment term, both the one centre and the two centre terms are in the order, 7I'DLL%TrDLS<'R'DLR. that is, the nDLL form is stabilized more than the other forms by the one centre as well as the two centre terms. O n the other hand, for the total intersegment term, the three forms exhibit a large energy difference. However, there are no marked differences in energy a m o n g the three forms for the O-1 and the 0-2 terms. There is a fairly large energy difference a m o n g the O-3 terms; the O-4 terms also differ, although not by so much. The main part of the difference appears to be due to the resonance term. This is a very important finding. F r o m statistical conformational energy calculations 7, the total energies calculated are: - 8.95, - 6.44, and - 9.05 kcal/mol residue for the nDLR, /I"DLS, and /I:DLL forms, respectively. Therefore, the nDLLfOrm was calculated to be the most stable. However, by the C N D O / 2 procedure, this form is calculated to be the most unstable. This disagreement m a y be due to the particular properties of the C N D O / a p p r o x i m a t i o n . The relationship between the 7rDt.R and the nDLs forms obtained by the C N D O / 2 calculation corresponds very well to that obtained by the statistical calculation 7. Lotz et al. 7 placed ~DLR and nDLS in one category and they suggested that the relationship between the 7I'DLRand nDLLforms, or that between the nDLSand nDLLforms is that present in the goniomer. Differences between the dihedral angles of the nDLR and nDLSforms are not great, however,

(°H5, 3010) (°H12, 3010) (°O20, 3H15) [(>4 segments] (o020, 4H2) Exchange term b [0 3 segments] (°H12, 3010) [0 4 segments] (o020, 3H2)

-0.03 -0.12 -0.03 -0.11 -0.01

Electrostatic term" [0 3 segments] (°C9, 3010) (°O10, 3010) (°C19, 3010) (°020, 3C9) (o020, 3010) (o020, 3C19) (°020, 3020) [0 4 segments] a

-0.27 0.23 -0.24 - 0.24 0.31 -0.27 0.23

0.01

a Energy terms: absolute values less than 0.03 eV are not given h Energy terms: absolute values less than 0.01 eV are not given "J See footnote ,,.a of Table 4 Table 6

Large elements in the (>3 and 0 4 segments in the nDLL

form Resonance term" [(>3 segments] (°H12, 3010) [0-4 segments] {o020, 4H2) Exchange term s Nothing

-- 0.08 -- 0.04

Electrostatic term b [0 3 segments] (°C9, 3010) (°Ol0, 3010) 1°C19, 3010) (o020, 3C9) (o020, 3010) (0020, 3C19) (o020, 3020) [(>4 segments] c

-0.26 0.22 -0.25 -0.22 0.31 -0.25 0.22

" Energy terms: absolute values less than 0.02 eV are not given h.~ See footnote c.e of Table 4

Int. J. Biol. Macromol., 1982, Vol 4, March

105

CNDO

c a l c u l a t i o n s on p o l y ( D L - a l a n i n e ) : M a s u r u

O h s a k u et al.

in Table 2. These can be related to i n t e r s e g m e n t h y d r o g e n bonding. This has a l r e a d y been s h o w n by I m a m u r a et al. 9. In the two species, % a n d ~I~L, it can be seen that the i n t e r a c t i o n s between the central a n d distal segments d o not have m u c h effect on the t o t a l energy of the two forms. T h a t is, the 0 3 and 0 4 terms are - 0 . 0 4 and - 0 . 0 3 eV, and - 0 . 0 3 a n d - 0 . 0 2 eV, respectively, for the c~R and aPE forms. However, in the 7rDL species, fairly large negative values a p p e a r e d even in the 0 - 4 segments as s h o w n in the preceding p a r a g r a p h . These intimately relate to the differences in m o l e c u l a r structures of the ~ a n d 7t forms. Therefore, when we consider larger n u m b e r s of segments in the calculations, smaller energy differences can be expected between the ~ and 7r forms. In the present article, we have considered nine segments (see also f o o t n o t e " of Table 2.) An a n a l o g o u s t e n d e n c y is also e x p l a i n e d in the case of poly(L-proline) I and I122. This implies that in p o l y m e r s such as poly(alaninel, the energy difference between the ~ and ~r forms m a y be very small. As a result, this p o l y m e r in solution m a y exist in the form of several c o n f o r m a t i o n a l isomers.

Conclusions F r o m the present investigation, we can d e d u c e the following: (i) energy differences a m o n g the g o n i o m e r s of p o l y (DLalanine) in the ~DL forms can be a t t r i b u t e d to the w e a k n e s s / s t r e n g t h of the intersegment h y d r o g e n b o n d i n g in the 0- 3 a n d 0 - 4 segments. T h e r e s o n a n c e t e r m plays the d o m i n a n t role in the interactions, but the exchange and the electrostatic terms do not. This is one of the m a i n findings in the present w o r k and the result of p a r t i t i o n i n g the t o t a l energy reveals which a t o m s or a t o m pairs stabilize the forms. (ii) for the energy difference between the ~w":%L form a n d the ZrDL forms, the larger the n u m b e r of segments considered, the less energy difference between t h e m can be expected. In the present article, only a single p o l y m e r chain was considered. C a l c u l a t i o n s which deal with two or m o r e p o l y m e r chains a n d include solvent molecules will be discussed in a future work, t a k i n g into a c c o u n t the results of the present work.

106

Int. J. Biol. M a c r o m o l . , 1982, Vol 4, M a r c h

Acknowledgements This w o r k was s u p p o r t e d in p a r t by a G r a n t - i n - A i d for Scientific Research from the M i n i s t r y of E d u c a t i o n , for which the a u t h o r s express their gratitude. W e are also grateful to the I n f o r m a t i o n Processing Center of H i r o s h i m a University, the D a t a Processing Center of K y o t o University, a n d the C o m p u t e r Center of Institute for M o l e c u l a r Science, for generous p e r m i s s i o n to use Hitac M-180H, F a c o m M-200, and Hitac M-200H c o m p u t e r s , respectively.

References l 2 3 4 5 6 7 8 9 10 11 12

Brown, L. and Trotter, 1. F. Trans. Faraday Soc. 1956, 52, 537 Arnott, S. and Wanacott, A. J. J. Mol. Biol. 1966, 21,371 Arnott, S. and Dover, S. D. J. Mol. Biol. 1967, 30, 209 Brant, D. A. and Flory, P. J. J. Am. Chem. Soc. 1965, 87, 2791 Ramachandran, G. N. and Chandrasekaran, R. Indian J. Biochem. Biophys. 1972, 9, 1 Hesselink, F. T. and Scheraga, H. A. Macromolecules 1972, 5, 455 Colonna-Cesari, F., Premilat, S., Heitz, F., Spach, G. and Lotz, B. Mac:'omolecules 1977, 10, 1284 Pople, J. A. and Beveridge, D. L. in 'Approximate Molecular Orbital Theory', McGraw-Hill, New York, N.Y., 1970 Imamura, A. and Fujita, H. J. Chem. Phys. 1974, 61, 115 Rabolt, J. F., Moore, W. H. and Krimm, S. Macromolecules 1977, 10, 1065 Suzuki, Y., Inoue, Y. and Chfij6, R. Biopolymers 1977, 16, 2521 Asakura, T., Ando, I. and Nishioka, A. Makromol. Chem. 1977.

178, 1111 13 14 15 16 17 18 I9 20 21 22

Urry, D. W., Goodall, M. C., Glickson, J. D. and Mayers, D. F. Proc. Natl. Acad. Sci. USA 1971, 68, 1907 Veatch, W. R., Fossel, E. T. and Blout, E. R. Biochemistry 1974, 13, 5249 Lotz, B., Colonna-Cesari, F., Heitz, F. and Spach, G. J. Mol. Biol. 1976, 106, 915 Heitz, F. and Spach, G. Macromolecules 1977, 10, 520 Hell,z,F., Cary, P. D. and Crane-Robinson, C. Macromolecule~s 1977, 10, 526 Heitz, F. Macromolecules 1977, 10, 1289 Shoji, A., Kawai, T. and Nishioka, A. Macromolecules 1977, 10, 1292 For example, Slater, J. C. in 'Quantum Theory of Molecules and Solids', McGraw-Hill, New York, N.Y., 1965 Ohsaku, M. and Imamura, A. Macromolecules 1978, 11,970 Ohsaku, M., Murata, H. and Imamura, A. Int. J. Biol. Macromol. 1980, 2, 381