2 calculation of the relative stability of poly(γ-hydroxy-l -proline)

CNDO/2 calculation of the relative stability of poly(yohydroxy-L-proline) Masaru Ohsaku,* Tetsuo Kawamura and Hiromu Murata Department (~["Chemistry, Faculty of Science, Hiroshima University, Higashisenda-machi, Hiroshima 730, Japan

and Akira Imamura Department (~[ Chemistry, Shiga University of Medical Science, Setatsukinowa-cho, Otsu, Shiga 520-21, Japan (Received 9 March 1981)

The CNDO/2 method using the tight-binding approximation Jor polymers was applied to poly(7-hydroxy-gprolines) (PHP). 7he calculations were carried outJor PHPs which have the same backbone structure as those ~?] poly(L-proline I) (Pro-l) and poly(L-proline II) (Pro-ll). The results obtained show the preferred orientation (?[the OH group at the ),-position, which is in agreement with the experimental results. The calculations were also carried outJor the Bjorm (PHP-B). The conjormational stability between the A form (PHP-A) and PHP-B was explained by using the calculated results in connection with the previous experimental and theoretical treatments. From the analysis ~)["the total energy, the dominant stabilizing factors fi)r the two fi)rms are discussed. Keywords: Polypeptide; CNDO/2 calculation: peptide stabilizing factor: polyhydroxyproline;polyprolinc

Introduction Poly(L-proline) exists in two conformations, poly(Lproline I) (Pro-I) and poly(L-proline II) (Pro-II) in the solid state and in solution ~-5, With poly(y-hydroxy-Lproline) PHP), trans and cis forms are also present 6. Sasisekharan has reported the trans form of PHP-A, and recently the trans form of P H P - B has been revealed by theoretical and experimental work v'8. Extensive work has also been carried out with the cis form (form C; P H P C)9,10. There are two possibilities for attachment of the O H group at the 7-position of the pyrrolidine ring in PHP. Moreover there are two or more possibilities for orientation of the H atom of the O H group in relation to the other H atom at the 7-position. In the present work, only the cis and trans conformations are taken into consideration. It is of interest to determine for PHP: (a) which is the more energetically stable, the trans (form A) or the cis (form C) form, (b) which is the most favourable orientation of the H atom of the O H group in relation to the other 7-position proton of poly(L-proline), (c) is it possible to explain how the H atom of the O H group intersects with the other H atom at the 7-position, (d) which is more stable energetically, the P H P - A or the P H P - B form, (e) what factors are responsible for the abovementioned results. Another feature of the molecular and electronic structure of Pro and P H P is the absence of hydrogen * To whom all correspondence should be addressed. 0141 8130/82/010037~06503.00 ©1982 Butterworth & Co. (Publishers) Ltd

bonds in Pro. However in PHP, there is one hydrogen bond in the intrasegment and/or in the intersegment. An understanding of the hydrogen bonding in the system is therefore of interest. In order to clarify and explain these objectives, the CNDO/2 calculations11 using the tight-binding approximation ~2 for polymers were applied to PHP. The total energy obtained was partitioned with the use of the appropriate equations. By using the results of the partitioned energy, the conformational stability of the P H P molecule was discussed.

Method of calculation Numerical calculations were performed by the procedure described previously t 3.14. Geometries of PHP-A1 to A4 and PHP-C1 to C4 were taken to be the same as for Pro-I and Pro-II 15, except for the 7-hydroxyl group. Here, the geometry is as follows: r ( C - O ) = 1.46 A 6, r(O H ) = 1.01 A 16, and (p(COH)= 105.937 ~17. F o r m B geometries were determined from the literature v. Atoms are numbered as shown in Figure 1. Side views of P H P - A 4 and PHP-C4, and plan views of P H P - A and P H P - B are shown in Figures 2 and 3, respectively. The unit segment used to calculate data in Tables 1 3 is the same as in Ref. 14. The unit segment used to calculate data for Tables 4 8 is shown in Figure 1.

Results and discussion There are four acceptable conformations: i.e. there are two positions for the O atom and two for the H atom.

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

37

C N D O / 2 calculations on P H P : M. Ohsaku et al. Stability (if P H P - A 4 and P H P - C 4 Unlike Pro 5, the cis form of PH P has only recently been

08

9H~C82/ ,oH/

,/3/C4HI5

)\

HII

\ /

Ht3

06

HI2

Figure 1 Schematic structures and numbered atoms of poly(;,hydroxy-L-proline) cJ~

0J c

jo

\ --~

/

c__~c/

~c~o PHP-A4

PHP-C4

Figure 2 Side view of PHP-A4 and PHP-C4 Assuming the same geometry for Pro-I and Pro-II ~5 except for the O H group position, C N D O / 2 calculations ~~ can then be carried out. Results are shown in Tables 1 and 2. The O H groups in PHP-A3 and PHP-A4 are found to have the same orientation as found by Sasisekharan 6b, the most stable form being the P H P - A 4 form. This agrees with X-ray analysis 6, although the H atom of the O H group is insensitive to X-ray techniques. To find the H atom direction, it is noted that the trans conformation (PHP-A1) of H 1 2 - O 6 - C 5 - H l l is nearly identical in energy to the cis form (PHP-A2). However, in PHP-A3 and PHP-A4, the cis (PHP-A4) form is more stable than the trans (PHP-A3). The direction of the O H group can thus be determined "by calculations on a single polymer chain. Calculations for cis forms (PHP-C1 to C4) gave analogous results.

38

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

reported 9"1°, although the reported structure may not be completely ordered cis. Here, we compare PHP-A4 and PHP-C4. In Table 3 we show total energies for cases 2 & 2 and 5 & 8, where the first figure indicates the number of neighbouring segments involved in calculating the core resonance integral and the second figure is the number participating in the electrostatic term. Form A exhibits the most stable intrasegment terms, while form C has the most stable intersegment terms. This is also observed in Pro-I and Pro-II 15 indicating that the electronic structure of P H P resembles that of Pro. Calculations involving five segment units (2 & 2) show PHP-A4 to be more stable than PHP-C4. However, for examples 5 & 8, P H P - C 4 is more stable than PHP-A4. Thus the conformational stability of PHP-A4 and PHPC4 is governed not only by the three skeletal rotational angles, ~), £0 and ~, but also by the number of segments involved. The same is also seen in Pro-I and Pro-II 1~ Therefore, whether P H P exists in the trans or cis form can be decided by the number of segments as well as by the skeletal molecular geometry. The cis form of P H P has been shown to exist in a specific salt solution ~°. Under these conditions, the interactions between the polymer and salt molecule or solvent molecule are small. In other solvents, however, the interaction between polymer molecule and solvent molecule can be large, and the more extended form of PHP-A is then preferable. In the reverse case, the polymer might gain stabilization energy between the polymer chains or between the different polymer segments. For these conditions, the cis form may be preferable. Comparison o f P H P - A

and P H P - B

The usual form in solution is form B 7'~. Using a semiempirical potential function, calculations indicated that form B is more stable than the form A. We here compare the forms of PHP-A4 and PHP-B, using data from Table 4. From total energy values, form B is more stable than form A. This agrees with the semiempirical calculations 7'~. From the partitioned energy, the results obtained are as follows (the procedure of energy partitioning was according to equations 1-4 of Ref. 14): Total intrasegment energy, form B < form A4. Total intersegment energy, form B < f o r m A4. Of the total intrasegment terms, the one centre term is lower in energy in form A4 than in form B. However, the total two centre term is smaller in form B than in form A4.

0

0

%

0 PHP-A

Figure 3 Plan view of PHP-A and PHP-B

PHP-B

CNDO/2 Table

1

Total

energy

(eV) of PHP-AI,

PHP-A2,

PHP-A3

Total Total

int rasegment

Total

one centre

Total

two

centre

Total intersegment Total two centre

and

calculations on PHP:

M . O h s a k u et al.

PHP-A4

PHP-A 1 5 & 5h

PHP-A2 5 & 5b

PHP-A3 5 & 5b

PHP-A4 5 & 5b

- 2438.67

- 2438.67

- 2438.59

- 2438.69

- 2410.29

- 2410.45

- 2410.34

- 2410.44

- 2028.90

- 2029.01

- 2028.95

- 2029.01

- 381.40

- 381.44

- 381.39

- 381.44

- 28.26 - 14.11 - 0.02

- 28.25 - 14.10 - 0.02

- 28.22

- 28.38 - 14.17 - 0.02

0 1 'L 0 2

-

14.09 - 0.02

H\

H 0

/ 0c'v

O~H

/

\H

Oc

H

/

Ocd" \ H

Oc

O--H

HI 0

" F o r s i m p l i c i t y , 0 1 ( s e g m e n t s ) r e f e r s to t h e c e n t r a l a n d t h e first n e a r e s t n e i g h b o u r s e g m e n t s , 0 - 2 , . . . , r e f e r s to t h e c e n t r a l a n d t h e s e c o n d . . . . . n e a r e s t n e i g h b o u r s e g m e n t s . I n t h e p r e s e n t w o r k , 0 - 1 ( N = 3) t o 0 - 8 ( N = 15) s e g m e n t s w e r e t a k e n i n t o c o n s i d e r a t i o n . E n e r g y t e r m : a b s o l u t e v a l u e s less t h a n 0.0l e V a r e n o t c a t a l o g u e d . E n e r g i e s w e r e c a l c u l a t e d f r o m e q u a t i o n s ( 1 ~ ( 4 ) o f Ref. 14 ~' T h e first f i g u r e is t h e n u m b e r o f s e g m e n t s o f t h e c o r e r e s o n a n c e i n t e g r a l a n d t h e s e c o n d t h e n u m b e r o f t h e e l e c t r o s t a t i c t e r m

Table

2

Total

energy

(eV) of PHP-C1,

PHP-C2,

PHP-C3 PHP-C1 5 & 5b

Total Total

intrasegment

and

PHP-C4 PHP-C2 5 & 5b

PHP-C3 5 & 5b

PHP-C4 5 & 5b

- 2438.69

- 2438.68

- 2438.60

- 2438.70

- 2409.94

- 2410.11

- 2410.00

- 2410.10

Total

one

centre

- 2028.93

- 2029.03

- 2029.00

- 2029.03

Total

two

centre

- 381.01

- 381.08

- 381.00

- 381.07

- 28.75

- 28.57

- 28.60

- 28.60

- 14.30 - 0.02

- 14.21 - 0.02

- 14.22 - 0.02

- 14.23 - 0.03

0-3

- 0.03

- 0.03

- 0.03

- 0.03

0-4

- 0.02

- 0.02

- 0.02

- 0.02

Total

intersegment

Total

two

centre

0- 1° 0-2

..b A s in Table 1

H

B0.. /

H

cd" \

/0 H

Table

3

Total

energy

(eV) of PHP-A4

Total Total

intrasegment

and

\

H

/

/

804".c,\

O-H

0

04;0(

O-H

H

H

PHP-C4 PHP-A4 2 & 2b

PHP-C4 2 & 2b

PHP-A4 5 & 8b

PHP-C4 5 & 8b

- 2438.65

- 2438.64

- 2438.70

- 2438.74

- 2410.46

- 2410.14

- 2410.44

- 2410.08

Total

one

centre

- 2029.00

- 2029.03

- 2029.01

- 2029.04

Total

two

centre

- 381.47

- 381.11

- 381.43

- 381.04

- 28.19

- 28.50

- 28.26

- 28.66

- 14.09

- 14.25

- 14.10 - 0.02

- 14.23 - 0.03

Total

intersegment

Total

two

centre

0 1" 0-2 0-3

-0.03

0-4

- 0.02

0-5

-0.01

.,b A s in Table 1

int.

J. Biol.

Macromol.,

1982,

Vol

4, February

39

C N D O / 2 calculations on PHP: M. Ohsaku et al. Table 4

Total energy (eV) of PHP-A4 and PHP-B

Total Total intrasegment Total one centre Total two centre Resonance Exchange Electrostatic Total intersegment 0 1 Total" Resonance Exchange Electrostatic 0 2 Total Resonance Exchange Electrostatic

PHP-A4 5 & 5/'

PHP-B 5 & 5p'

- 2438.69 2404.80 -2/)29.00 -375.80 391.05 82.70 97.94 33.89 - 16.93 - 18.99 3.51 5.57 -0.0l

- 2440.02 2405.73 2027.74 377.99 391.35 - 82.29 95.64 - 34.29 16.75 - 18.7,~ 3.4~ 5.52 0.39 0.38 - 0.05 0.04

0.01

,,.b As in Table I

Table 5

The difference in two centre interaction energy (eV) in the central segment between form B and form A4" NI

Resonance term b C2 C4 C5 06 08 H9 H12 HI4 HI5 Exchange term C2 06 H12 H15 Electrostatic term C2 C4 C5 06 08 H9 HI1 H12 H13 H14 H15 Total

C2

C3

C4

C5

06

C7

HII

Total 0.30

2.46 -

0.26 1.83 0.21

-0.58 -0.45 2.50 0.85

-0.23 - 0.37

0.20

- 0.23 -

1.54

-0.14 0.23 0.24

-0.22 0.34 2.30 1.33 0.50 0.34 --1.17

-0.73 0.23 0.27 0.32 0.21 0.23 2.36 2.19

"Digits show the energy difference: (form A4) - (form B). Energy term: absolute values < 0.20 eV are not catalogued. See equation !3) of Ref. 14 for details b Atom numbering is shown in Figure 1 U s i n g d a t a f r o m Table 5 this will be d i s c u s s e d in detail. T h e p o s i t i v e v a l u e s s h o w t h a t f o r m B is m o r e stable t h a n f o r m A4, w h i l e for the n e g a t i v e v a l u e s the reverse is true. T h e r e s o n a n c e t e r m stabilizes f o r m B m o r e t h a n f o r m A4, b u t the e x c h a n g e t e r m stabilizes f o r m A4 m o r e t h a n f o r m B. B r o a d l y s p e a k i n g , t h e s e t w o t e r m s c a n c e l o n e a n o t h e r w h i l e the e l e c t r o s t a t i c t e r m r e m a i n s . T h e largest e l e m e n t in the electrostatic t e r m is (H15,C3). T h i s e l e m e n t plays an i m p o r t a n t role in s t a b i l i z i n g f o r m B in the i n t r a s e g m e n t t w o c e n t r e term.

40

Int. J. Biol. M a c r o m o l . , 1982, Vol 4, F e b r u a r y

T h e difference in the i n t e r s e g m e n t t e r m a p p e a r e d in the 0 1 a n d the 0 - 2 segments. T h e s h o r t c o n t a c t s b e l o w 2.4 A b e t w e e n the c e n t r a l a n d the first nearest n e i g h b o u r and b e t w e e n the c e n t r a l a n d the s e c o n d nearest n e i g h b o u r s e g m e n t s are s h o w n in Table 6. T h e r e are t w o short c o n t a c t s b e t w e e n the 0-1 s e g m e n t s a n d n o s h o r t c o n t a c t s b e t w e e n the 0~2 s e g m e n t s in the A4 form. F o r f o r m B, t h e r e are a fair n u m b e r of s h o r t c o n t a c t s b e t w e e n the 0 l s e g m e n t s a n d b e t w e e n the 0~2 s e g m e n t s as s h o w n in Table 6. L a r g e e l e m e n t s in the 0-1 s e g m e n t s a n d in the 0 2

C N D O / 2 calculations on P H P : M. Ohsaku et al. segments of the intersegment two centre term in the A4 and B forms are s u m m a r i z e d in Tables 7 a n d 8, respectively. Here the elements are shown as the difference: (form A 4 ? ( f o r m B). As shown in Table 7, form A4 is stabilized m o r e than form B by the 0- 1 interaction term. Here the exchange a n d the electrostatic terms a l m o s t c o m p e n s a t e each other. Therefore, it follows that form A4 is stabilized by the r e s o n a n c e term. T h e element (°C7, ~N1) is the d o m i n a n t element in the energy difference by the 0-1 interaction. W i t h the 0 2 interaction terms, as shown in Table 8, form B is stabilized m o r e than form A4. In this case the exchange and electrostatic terms cancel each other. Therefore, the resonance term is the d o m i n a n t term which governs the energy difference of the (>2 interaction between form A4 and form B, and the d o m i n a n t elements are (008, 2H9) a n d (°O8, 2H12). These elements will be discussed in the following section. C o m p a r i n g Table 6 to 8, we can easily recognize that the short c o n t a c t pairs are closely related to the interaction energy between the 0- 1 and 0 2 segments. Hydro qen bondin9 As shown in the preceding section the P H P - A 4 form c a n n o t form i n t r a m o l e c u l a r h y d r o g e n bonds. However, in the case of P H P - B , there are two possibilities for h y d r o g e n bonding: ( o 0 8 . . . 2H9) a n d ( ° O 8 " - ' 2 H 1 2 ) . In the case o f ( ° O 8 ... 2H9) the distance involved ~ is t o o great for s t r o n g h y d r o g e n bonding. This h y d r o g e n b o n d i n g ( ° 0 8 , 2H~2) stabilizes form B ~ 0 . 4 eV more t h a n form A4 per bond. Therefore form B is ~ 0 . 8 eV m o r e stable than form A4. W h e n we s u b t r a c t e d the stabilization energy from the total energy of form B, the energy difference between form A4 a n d form B becomes v e r y small.

In collagen P H P is present as the three interacting m o l e c u l a r chains in a unit cell °. In the present work, however, we have dealt only with single p o l y m e r chains. W h e n e v e r considering only one p o l y m e r chain, it was found that the n a t u r e of P H P molecule can be d r a w n enough. T r e a t m e n t of m o r e t h a n one p o l y m e r chain will be dealt with in a future paper. W a t e r molecules m a y also play an i m p o r t a n t role in stabilizing form A. W o r k on this was published which explained the b e h a v i o u r of P H P residues in a collagenrelated p e p t i d e 19. In the present article, the role of water molecules is not considered. This point will be dealt with in a future paper.

Conclusions C N D O / 2 calculations of P H P reveal the possible o r i e n t a t i o n of the O H g r o u p at the 7-position of the c a r b o n atom. T h e existence of the cis form is indicated from the calculations. The c o n f o r m a t i o n a l stability of P H P d e p e n d s on the three internal r o t a t i o n angles (co, q~, ~) and also on the n u m b e r s of segments treated in the p o l y m e r concerned, especially between forms A a n d C. The c o n f o r m a t i o n a l stability of form A a n d B can be d e t e r m i n e d by the t o t a l intersegment energy. T h a t is, the difference in total energy of forms A and B which a p p e a r e d largely in the (>1, and in the (>2 intersegment terms. The h y d r o g e n b o n d i n g between the 0- 2 segments m a y play an Table 8 The difference in the two centre interaction energy (eV) in the 0,2 segments between form B and form A4" 2C5

Table 6

Short contacts between the 0,1 segments and between the 0 2 segments below 2.4 A in the PHP-A4 and PHP-B

0 1 segments PHP-A4 (008... IN1} (°H15...tH10)

O 2 segments P H P-A4 Nothing _ Table 7

2.27 2.21

PHP-B (008... tN1) (°H15... lC2) (°H15...'H9) (°HI5...1H10) PH P-B (008...2H9) (°08...XH12)

2.26 2.24 1.84 2.36 2.23 1.87

Resonance term b'" 008 Exchange term 008 Electrostatic term o06 °C7 008 Total

206

2H9

2H12

(t.03 0.05

Total 0.38

0.37 0.05 0.03 - (1.05 0.03 - 0.10 0.13

0.07 -0.14

0.04

0.38

° Digitsshowtheenergydifference:(formA4)-(formBj.Energy terms: absolute values < 0.03 eV are not catalogued. See equation {4}of Ref. 14 for details h As in Table 5 ~ As in Table 7

The difference in the two centre interaction energy {eV) in the 0,1 segments between form-B and form-A4" INl

Resonance term b'c °C7 °Hl5 Exchange term °C7 Electrostatic term ~O6 °C7 o08 Total

- 0.27

1C2 0.09 0.06

1C3

106

1C7

IH9

1Hl2

Total -0.21

- 0.07 0.03 --0.03

-- 0.04 0.06 0.13

--0.03

0.04 -- 0.04

0.03 -- 0.07 0.06 --0.18

"Digits show the energy difference:[form A4) - (form B). Energy terms: absolute values < 0.03 eV are not catalogued. See equation (4) of Ref. 14 for details i, As in TaMe 5 ' For example, (°C7, 1NI) refers to the interaction element between the C7 carbon atom in the central segment and the NI nitrogen atom in the first nearest neighbour segment

Int. J. Biol. M a c r o m o l . , 1982, Vol 4, F e b r u a r y

41

CNDO/2

calculations on PHP:

M. Ohsaku

et al.

i m p o r t a n t r o l e in g o v e r n i n g t h e c o n f o r m a t i o n a l s t a b i l i t y o f f o r m s A a n d B.

Acknowledgements This work was supported in part by a Grant-in-Aid for Scientific Research from the Ministry of Education, for which the authors express their gratitude. We are also grateful to the Information Processing Center of Hiroshima University, the Data Processing Center of Kyoto University, and the Computer Center of Institute for Molecular Science, for generous permission to use HITAC M-180H, F A C O M M-200, and H I T A C M-200H computers, respectively.

References 1 2

3 4

42

Traub,W. and Shmueli, U. Nature 1963, 198, 1165 Traub, W. and Shmueli, U. in 'Aspects of Protein Structure" (W. Traub and U. Shmueli, Ed.), Academic Press, New York, N.Y., 1963, pp. 81 92 Cowan, P. W. and McGavin, S. Nature 1955, 176, 501 Sasisekharan, V. Acta Crystallo,qr. 1959, 12, 879

Int. J. Biol. M a c r o m o l , , 1982, Vol 4, F e b r u a r y

5 6a 6b 7 8 9 10 I1 12 13 I4 15 16 17 18 19

Scheraga, H. A. (_'hem. Rer. 1971,71,195: Deber, C. M.. Madison. V. and Blout, E. R. Ace. Chem. Res. 1976, 9, 106 Donohue, J. and Trueblood, K. N. Aeta Crystallo~jr. 1952, 5, 419 Sasisekharan, V. Acta Crystallo{tr. 1959, 12, 903 Bansal, M., Brahmachari, S. K. and Sasisekharan, V. Maeromoleeules 1979, 12, 19 Brahmachari, S. K., Bansal, M., Ananthanarayanan, V. S. and Sasisekharan, V. Macromolecales 1979, 12. 23 Dechter, J. J., Clark, D. S. and Manderkern. L. Macromoh, cuh'~ 1978, 11, 274 Clark, D. S., Dechter, J. J. and Mandelkern. L. Macromolecuh'~ 1979, 12, 626 Pople, J. A. and Beveridge, D. L. in "Approximate Molecular Orbital Theory" 1970. McGraw-Hill, New York, N.Y. Slater, J. C. "Quantum Theory of Molecules and Solids'. 1965, McGraw-Hill, New York, N.Y. Imamura. A. and Fujita, H. J. Chem. Phys. 1974, 61, 115 Ohsaku, M. and Imamura. A. Macromolecules 1978, !1,970 Ohsaku, M. and Imamura, A. Int. J. Biol. Maeromol. 1980, 2, 347 Schneider, S. and Kern, C. W. J. Am. Chem. Soc. 1979. 101, 4081 Aziz, Nour El Din Abdel and Rogowski, F. Z. Natarti~rsch. !B) 1966, 21,996 Ohsaku, M., Murata, H. and Imamura, A. Int. J. Biol. Mmromol. 1980, 2, 381 Hospital, M., Courseille, C., Leroy, F. and Roques, B. P. Biopolymers 1979, 18, 1141