The chemical structure and the crystalline structures of Bombyx mori silk fibroin

The chemical structure and the crystalline structures of Bombyx mori silk fibroin

BIOCHIMIE, 1979, 61, 205-214. The chemical structure and the crystalline structures of Bombyx mori silk fibroin. B e r n a r d LOTZ * and F r a n c o...

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BIOCHIMIE, 1979, 61, 205-214.

The chemical structure and the crystalline structures of Bombyx mori silk fibroin. B e r n a r d LOTZ * and F r a n c o i s COLONNA CESARI **

* C.N.R.S. et U.L.P., Centre de Recherches sur les Macromol~cules, 6, rue Boussingault, 67083 Strasbourg (France). ** Laboratoire de Biophysique, Centre du 1~" Cycle, UniversilE de N a n c y I, 54037 N a n c y (France).

R6sum6.

Summary.

Nous p a s s o n s en revue q u e l q u e s r 6 s u l t ~ s r6cents publi6s a u cours des dix derui~res a n n 6 e s sur Ies structures chirnique et cristalline de la sole de Bornblrx rnori. N o u s n o u s int~ressons principalernent & la portion cristallisable de la fibroine & sa constitution chimique et & s a conformation rnol6culaire m 6tudi6es au n i v e a u de la rnaille 616rnentaire m dans ses deux modifications cristallines : le feuillet pliss6 ~ et la structure du type Sole I. Les aspects structuraux sont fond6s sur u n e discussion des d o n n 6 e s de diffraction des r a y o n s X et de diffraction 61ectronique cfinsi que des cma1yses d'6nerqie conforrnationnelle d'un module polypeptidique d e l a f i b r o i n e : (Ala-G1y)~.

S o m e recent data (i.e. published in the krst ten years) on the chemical a n d crystalline structures of B. rnori silk are reviewed. The m a i n ernphasis is put on the crystallizable portion of silk iibroin, including its chemical constitution and its molecular conformation (at the crystalloqraphic unit-cell level) in the two crystalline modifications : the ~ pleated sheet a n d the silk I structures. The structural aspects are b a s e d on a discussion of X-rc~/ and electron diffraction data, and on coniorrnational e n e r g y a n a l y s e s of a model (Ala-Gly)n polypeptide of silk tlbroin.

L -- Introduction.

The u p r i s e of n e w techniques, or i m p r o v m e n t of existing ones has y i e l d e d in the last y e a r s a s t e a d y flow of ne~¢ results a n d m o r e d e t a i l e d analyses on silk a n d e s p e c i a l l y on silk fibroin. A revised sequence has in p a r t i c u l a r been p u t forw a r d , a n d the c r y s t a l l i n e p o l y m o r p h i s m h a s been m o r e fully app.reciated than in the p a s t : e x p e r i m e n t a l c o n d i t i o n s g i v i n g rise to the a m o r p h o u s , or one or the o t h e r of the t w o c r y s t a l l i n e m o d i f i cations of fibroin have been w e l l established. F i n a l l y , a f a i r degree of u n d e r s t a n d i n g of the s t r u c t u r e has been r e a c h e d , an.d a r e a s o n a b l e p r o p o s a l for the Silk I m o d i f i c a t i o n of fibroin has been a d v a n c e d .

I n v e s t i g a t i o n s on the c h e m i s t r y a n d structure of silk p r o t e i n have a long h i s t o r i c a l b a c k g r o u n d : at the t u r n of the c e n t u r y , a fair p r o p o r t i o n of the a m i n o a c i d s of the fibroin avas kn,o'wu [l] a n d silk f b e r s 'were s u b j e c t e d to X-ray d i f f r a c t i o n as e a r l y as 19'13 [2]. A p r e cise u n d e r s t a n d i n g of silk fibroin structure, b a s e d on d e t a i l e d p r o p o s a l s for its sequence, and its c r y s t a l l i n e .~ m o d i f i c a t i o n , d a t e s ho~cever o n l y from the e a r l y or m i d 1950's, w i t h the w o r k s of Lucas, S h a w a n d Smith [3] a n d Marsh, P a u l i n g a n d C o r c y [4]. A d e t a i l e d review on these aspects, a n d m a n y m o r e r e l a t i n g to silk p r o d u c t i o n in n a t u r e has been publish e d som~ ten y e a r s ago b y L u c a s and R u d a l l [5] and f u r t h e r i n f o r m a t i o n on the s t r u c t u r e of silks can be f o u n d in the excellent b o o k of F r a s e r a n d MacRae [6].

The p u r p o s e of this p a p e r is to review some of these m o r e r e c e n t results, and t h e r e f o r e to update a n d c o m p l e m e n t the r e v i e w of Lucas a n d Rudall. The v i e w p o i n t a d o p t e d h e r e is v e r y s p e c i f i c h o w ever, since B. mort silk fibroin only is c o n s i d e r e d .

B. L o t z a n d F. C o l o n n a Cesori.

206

Also, some m a t e r i a l of Lucas a n d Rudall's p a p e r is, u n a v o i d a b l y , used here. I n any event, the reader is referred to their review to get a sense of the pleasure f o u n d in investigating the properties of silk proteins.

II.-

The

chemical

composition

of

silk

fibroin. 1) AMINO ACID COMPOSITION. Investigations on the chemical composition have been p e r f o r m e d on either native fibroin, or fibroin treated w i t h various degradation or enzym a t i c agents. The crysta,lline fraction of the protein is usually o b t a i n e d as a precipitate w h e n p a n c r e a t i c enzymes act u p o n an aqueous solution of fibroin. These fractions are called Cr a n d TI,, for C h y m o t r y p s i n and T r y p s i n precipitates, a n d Cs a n d T~ for those parts of the p r o t e i n that rem a i n in solution, respectively. Knowledge of the whole fibroin, the C o or Tp, a n d C~ or T~ compositions (and sequences) helps differentiate the crystallizable p a r t of the p r o t e i n from the more soluble, and p r e s u m a b l y , more a m o r p h o u s ones. The p r e s e n t l y available data on the a m i n o acid compositions of whole fibroin, Cp fraction and, for c o m p a r i s o n purposes, C~ fraction a n d sericin,

are s u m m a r i z e d in table I. F r a c t i o n C~, w h i c h a m o u n t s to about 40 per cent of the fibroin molecule, is m a i n l y composed of o c t a - a n d tetrapeptides e n d i n g w i t h t y r o s i n e or p h e n y l a l a n i n e (in c o n f o r m i t y w i t h the mode of cleavage of c h y m o t r y p s i n ) , a n d in w h i c h the Gly-X a l t e r n a t i o n characteristic of the fibroin sequence is preserved. Other peptide fragments of the C~ fraction however, w h i c h comprise acid, basic, or b u l k y neutral side chains, do not display this a l t e r n a t i o n of Gly residues. One can therefore visualize [5] the fibroin molecule as a block c o p o l y p e p t i d e in w h i c h C~ fragments alternate with octa and tetrapeptides and these more soluble f r a g m e n t s : the block structure results from changes both in the sequence of the residues, and the n a t u r e of side chains. 2) SEQUENCE oF FRACTION.

RESIDUES

IN

THE

Much w o r k has been devoted to elucidate the sequence of a m i n o acid i n the C~, fraction, in view of its relevance to the crystalline structure of B o m b y x m o r t fibroin. Lucas, Shaw and Smith [3] showed that in the sequence of 59 a m i n o a c i d s w h i c h make up the Cp fragments, Gly residues alternate strictly with other residues, except for one Ala-Ala link, w h i c h is revealed by the pre-

TABLE 2.

A m i n o a c i d compositions of whole [ibroin, C o and C s fractions and sericin [rom B. mort silk (in percentage o[ total aminoacids). Whole fibroin

Cp Iraetion

Cs fraction

29 3 1,3 0.5 0.2 1.0 44.5 0.2

32.89 0.56 O. 18 0 0.43 48.0 0.06 o. 13 0 0 2 0 0.13 0 14.97 0 36 0 1.40 0.64

22.16 3.87 1.29 0 2.58 36.85 0.5

(a) (d)

Alanine Aspartic acid Arginine Cystine (half) Glutamic acid Glycine Histidtne Isoleucine Leucine Lysine Methionine Phenylalanine Proline Serine Threonine Thryptophaa Tyrosine ¥Mine (a~ (b! (c, (d)

0.7 0.5 0.3 0.1 0 6 0.3 12.1 0.9 0.2 5.2 2.2

(b)

In}

1.80 1.29 0 77 0 1.54 1.03 6.96 2 32 0 10.8 5,67

Sericin

{c) (d)

5.2 14.6 2.8 0 3 7 9 13 5 I .0 0.6 0.8 4 3 0.1 0.5 0.5 33.1 8.3 0.3 3.1 3 1

Lucas el al [3] ; Lucas, from Lucas and Rudall [51. Strydom et al [7]. Kirimura, from Lucas and Rudall [5]. For more data, see the aminoacid compoaitions collected 1)3" Fo::rnicr [36],

BIOCHIMIE, 1979, 61, n ° 2.

CRYSTALLINE

Chemical a n d crystalline s t r u c t u r e s of B. m o r t fibroin. sence of this d i p e p t i d e in small p r o p o r t i o n s in the p a r t i a l h y d r o l y s a t e . F u r t h e r m o r e , the 3-2-1 p r o p o r t i o n of Gly-Ala-Ser r e s i d u e s (cf. t a b l e I) reflects i n d e e d the p r e s e n c e of l o n g h e x a p e p t i d e sequences and Lucas el al. p r o p o s e d for Cp fraction t h e f o l l o w i n g sequence : Gly-Ala-Gly-kla-Gly-[ S e r - G l y 4 A l a - G l y ) , ] s-S er-GlyA la-A/a-Gly-Tyr w i t h n u s u a l l y equal to two. As noted r e c e n t l y b y S t r y d o m el al. [7] this sequence has been consid e r e d as f i r m l y established, w h i l e Lucas et al. c l e a r l y stated t h a t it is only p r o b a b l e w i t h the p o s i t i o n of the Ala-Ala link n e a r the e a r b o x y l e n d given o n l y as a t e n t a t i v e suggestion. I n d e e d , in t h e i r r e i n v e s t i g a t i o n of the sequence of silk fibroin p e p t i d e C~,, using a u t o m a t e d sequencers now a v a i l a b l e , S t r y d o m el al. f o u n d the Ala-Ala l i n k to be r a t h e r in p o s i t i o n 8-9 from the amino end of the p r o t e i n , thus l e a d i n g to the sequence : Gly-Ata-Gly-~la-Gly.Ser-Gly-Ala-A la-Gly- [Ser-Gly-, (Ala-Gly) n] s T y r w h e r e n is u s u a l l y 2. Due to the p r o g r e s s i v e d a m p i n g of r e s o l u t i o n of the m e t h o d h o w e v e r , the s e q u e n c i n g of a m i n o a c i d s w a s not p u r s u e d b e y o n d r e s i d u e 9. In a n y case, these results, together w i t h those of Lucas el al., c o n f i r m that strict a l t e r n a t i o n of glycine w i t h a l a n i n e and s e r i n e is mostly r e s p e c t e d in the c r y s t a l l i n e f r a c t i o n of fibroin. Moreover, the existence of only one Ala-Ala link i m p l i e s that the g l y c i n e s in the ,Cp fraction are ¢ out of phase >> on the t w o sides of t h e link. This feature of the sequence m a y h o w e v e r not n e c e s s a r i l y have consequences at the s t r u c t u r a l level, as ~vill be s h o w n later. Sequence analysis of silk fibroin has at p r e s e n t r e v e a l e d the p a r t of the iuolecule r e l e v a n t to the c r y s t a l l i n e structure. The complete sequence h o w ever is not yet knoven, in c o n t r a s t to that of the t r o p o c o l l a g e n molecule, d e s p i t e i m p r o v e m e n t s in a u t o m a t i c p r o t e i n sequencing. On the o t h e r h a n d , the c o m p l e t e p i c t u r e of v e r y long streches of B. mort fLbroin w i l l be soon y i e l d e d b y the elegant r a p i d DNA s e q u e n c i n g of the c o r r e s p o n d i n g fibroin gene or the c o m p l e m e n t a r y DNA of fibroin mRNA s u b j e c t e d to r e v e r s e t r a n s c r i p t a s e activity. So far, r e s t r i c t i o n e n d o n u c l e a s e digests of fibroin gene, either a n a l y z e d a f t e r c l o n i n g [8] or b y h y b r i d i z a t i o n [9] c o n f i r m the r e m a r k a b l e uniform i t y of the c o d i n g r e g i o n insensitive to a large n u m b e r of r e s t r i c t i o n enzymes a n d the p r e v i o u s i n d i r e c t c o d o n a s s i g n m e n t for the r e p e a t i n g unit [1~}]. These results also suggest that the fibroin core - - gene a n d p r o t e i n - - is a large homo-

BIOCHIMIE, 1979, 61, n ° 2.

207

geneously r e p e t i t i v e b l o c k w i t h little e v i d e n c e for sequence d i v e r g e n c e . 3)

SYNTHETIC MODELS OF

Bomby m o r t

FIBROIN.

Significant r u n s of the c h e m i c a l s t r u c t u r e of B. mort fibroin are b a s i c a l l y an a l t e r n a t i o n of achiral glycine residues with two thirds alanine a n d one t h i r d serine. The r e p e t i t i v e p a r t of the s t r u c t u r e is thus w e l l r e p r e s e n t e d b y the polyhexapeptide : (Ala-Gly-Ala-Gly-Ser-Gly),. This m o d e l can h o w e v e r be f u r t h e r s i m p l i f i e d w h e n d i s r e g a r d i n g t h e difference b e t w e e n a l a n i n e CH 3 a n d s e r i n e CH20H side-chains. W i t h this a p p r o x i m a t i o n , the sequence of B. mort fibroin can thus be equated w i t h a strict a l t e r n a t i o n of Gly a n d Ala residues, i.e. w i t h the p e r i o d i c copol y p e p t i d e (Ala-Gly),. This s i m p l i c i t y has m a d e B. mort silk fibroin a v e r y a t t r a c t i v e m o d e l for m e t h o d s of p e p t i d e chem i s t r y a i m e d at p r o d u c i n g p e r i o d i c c o p o l y p e p tides, e s p e c i a l l y since its sequence i n c l u d e s (as for collagen) a g l y c i n e residue. I n d e e d , the esters first used to a c t i v a t e the p e r i o d i c m o n o m e r gave rise to some r a c e m i z a t i o n of the c a r b o x y l i c e n d r e s i d u e in the c o n d e n s a t i o n step. Use of g l y c i n e t e r m i n a t e d m o n o m e r s c i r c u m v e n t s this d r a w b a c k and yields stereochemic~lly satisfactory models of silk ~ibroin ( a n d of collagen as well). N u m e r o u s syntheses of poly(Ala-Gly) and of the p o l y h e x a p e p t i d e (Ala-Gly-Ala-Gly-Ser-Gly)j~ have been r e p o r t e d . These p o l y m e r s w e r e p r o d u c e d s p e c i f i c a l l y as silk models, or as p a r t of l a r g e r p r o g r a m s i n v o l v i n g investigation of r e s i d u e sequence a n d c o m p o s i t i o n on the s t r u c t u r e of p o l y p e p t i d e s (for reviews, see Goren [111 and Johnson [12]). The usefulness of such p o l y p e p t i d e s for c r y s t a l s t r u c t u r e d e t e r m i n a t i o n is evident, since k n o w ledge of the exact a m i n o a c i d c o m p o s i t i o n is a prerequisite for a c c u r a t e analysis of diffraction data, or for u n d e r t a k i n g c o n f o r m a t i o n a l e n e r g y calculations on the o b s e r v e d s t r u c t u r e s : these aspects ~vill be d e v e l o p p e d f u r t h e r in the next t w o sections d e a l i n g w i t h the c r y s t a l l i n e s t r u c t u r e of silk fibroin. On t h e o t h e r hand, the m o l e c u l a r w e i g h t and m o l e c u l a r w e i g h t d i s t r i b u t i o n are less w e l l controlled. W h i l e this is no d r a w b a c k in t e r m s of the c r y s t a l l i n e slructure (i.e. at the unit-cell level of o r g a n i z a t i o n ) , it helps differentiate features of the c r y s t a l l i n e superstructure (lamellar organization, etc...) that are due to the p o l y m e r i c n a t u r e of silk fibroin, f r o m l h o s e l i n k e d to long-range a m i n o

208

B. L o t z a n d F. C o l o n n a Cesari.

a c i d r e p e t i t i o n s . In t h i s respect, m a n y of the data available from w o r k s p u b l i s h e d before 1958 s h o u l d be r e a p p r a i s e d in the ]igh.t of m o r e r e c e n t c o n c e p t s on the c r y s t a l l i n e s t r u c t u r e of p o l y m e r s [13].

I I I . - - T h e c r y s t a l l i n e s t r u c t u r e s o f B. mort silk fibroin. 1) D'IMORPHISM OF SILK F R I B R O I N ACCOUNT.

: AN HISTORICAL

As most h o m o p o l y p e p t i d e s a n d some fibrous p r o t e i n s , B. m o r t fibroin m a y exist u n d e r two different c r y s t a l l i n e modifications, i n v o l v i n g two w i dely .different c h a i n c o n f o r m a t i o n s . Tqae s t r u c t u r e of silk fibroin existing in the spun filament w a s the subject of e a r l y X-ray i n v e s t i g a t i o n s ; it has been s h o w n by Marsh et al ~4~ to be a sheet structure, e a r l i e r d e s c r i b e d as a ~f5structure. This structure is called ,f3 silk fihroin, a t e r m i n o l o g y in c o m m o n use for o t h e r silks w i t h the same t y p e of sheet s t r u c t u r e as w e l l [6]. The c r y s t a l l i n e d i m o r p h i s r n of silk fibroin w a s first i n v e s t i g a t e d in c o n s i d e r a b l e detail b y Shimizu [14]. The n e w c r y s t a l l i n e m o d i f c a t i o n , w h i c h he called tt form, w a s later, a n d i n d e p e n d e n t l y , r e d i s c o v e r e d b y K r a t k y et al. [15], 'who n a m e d it (< Silk I>>. A m b r o s e et al. [16] called it ¢ w a t e r soluble silk >>. T h e t e r m ¢ c~ sil'k >> is still m u c h in use in the j a p a n e s e literature. It is h o w e v e r ntisl e a d i n g at it m a y create a confusion w i t h the ~t helix of P a u l i n g a n d Corey, e s p e c i a l l y since it w a s at one t i m e p r o p o s e d ( i n c o r r e c t l y ) that this form of fibroin m i g h t be b a s e d on the a h e l i x [17]. We w i l l use in the f o l l o w i n g the t e r m i n o l o g y of K r a t k y et al. i.e. Silk I. Since h o w e v e r the c r y s t a l line m o d i f i c a t i o n of (Ala-Gly)~ i s o m o r p h o u s to Silk I is o b t a i n e d u n d e r e x p e r i m e n t a l .conditions w h i c h , w i t h p o l y g l y c i n e , l e a d to porlyglycine II, it is n a m e d poly(Ala-Gly) II, or, in short, AG II [18]. As just m e n t i o n n e d , the s y n t h e t i c m o d e l p o l y p e p t i d e s of fibroin also d i s p l a y a c r y s t a l l i n e dim o r p h i s m , a n d the two forms are i s o m o r p h o u s w i t h the c o r r e s p o n d i n g ones of the p r o t e i n . Chain c o n f o r m a t i o n s d e s c r i b e d in the f o l l o w i n g a p p l y to both p o l y m e r s , a n d slight differences, u s u a l l y of i n t e r s h e e t spacings due to differences in the b u l k i n e s s of the s i d e - c h a i n s w i l l not be f u r t h e r c o m m e n t e d on. The .detailed .analysis w i l l be m a d e for .(Ala-Gly),,, s i n c e it p e r m i t s a q u a n t i t a t i v e anal y s i s of g e o m e t r i c a l p a r a m e t e r s and d i f f r a c t i o n data. BIOCHIMIE, 1979, 61, n ° 2.

2) TI~IE:~ STRUCTURE OP B. m o r t SILK FIBROIN. The c r y s t a l l i n e s t r u c t u r e p r e s e n t in B. m o r i silk t h r e a d has been a n a l y z e d b y m a n y authors [2119] 'who came to the c o r r e c t p i c t u r e of n e a r l y ext e n d e d p o l y p e p t i d e c h a i n s a r r a n g e d in h y d r o g e n b o n d e d sheet structures. The d e t a i l e d analysis, due to Marsh, P a u l i n g and Corey [4], has b e c o m e a classic of t e x t b o o k s on the s t r u c t u r e of prot e i n s : o n l y its m a i n outlines are r e c a l l e d here. As s h o w n in figure 1, the p o l y p e p t i d e chain is almost extended. Due to the 2~ s c r e w axis of t h e b a c k b o n e , successive a l a n i n e r e s i d u e s are l o c a t e d on one side of the .chain, and g l y c i n e residues Mike on the o t h e r side. H y d r o g e n b o n d i n g is m a d e b e t w e e n a n t i p a r M l e l c h a i n s o r i e n t e d in such a m a n n e r that M] alanines and aH glycines are on different sides of the sheets ; the sheets p~ck w i t h t h e i r a l a n i n e faces in contact, a n d t h e i r g l y c i n e faces also. T h e m o n o c l i n i c unit-cell has p a r a m e ters : a = 4.71 +_ 0.01 A, b = 6.90 ___ 0.05 3, a n d c = 8.96 to 9.20 ~ [6]. The two f o r m e r p a r a m e t e r s are almost i n v a r i a n t a n d c h a r a c t e r i z e i n t e r c h a i n a n d fiber r e p e a t d i s t a n c e s in the h y d r o g e n b o n d e d sheets, r e s p e c t i v e l y . The l a t t e r c o r r e s p o n d s to int e r s h e e t distances. It i n c r e a s e s s t e a d i l y (thus reflecting i n c r e a s i n g average b u l k i n e s s of the sidechains) f r o m (Ala-Gly) n to the p o l y h e x a p e p t i d e , the C,p f r a c t i o n a n d w h o l e p r o t e i n . The c p a r a m e ter is a c t u a l l y t h e sum of t w o different i n t e r s h e e t spacings, the l a r g e r a n d the s m a l l e r of w h i c h corr e s p o n d to a l a n i n e - a l a n i n e (or serine) a n d glycin.e_ gly.cine i n t e r a c t i o n s between n e i g h b o u r i n g sheets, r e s p e c t i v e l y (fig. 2). W h i l e deternfination of the overall c d i s t a n c e is s t r a i g h t f o r w a r d from the obs e r v e d X-ray spacings, the parlition of c into %~.,. a n d Ca1a r e q u i r e s an analysis of the relative intensities of the 00 1 reflections. These intensities are i n d e e d v e r y sensitive to the p o s i t i o n of the m i d d l e sheet in the unit-cell. F o r t h e i r analysis, Marsh et al. used C~l,. : 3.5 A, i.e. a value close to that a c c e p t e d for the i n t e r s h e e t d i s t a n c e in the f3 form of p o l y g l y c i n e ( p o l y g l y c i n e I or PG I). The cab~ d i s t a n c e (5.7 A) is thus m u c h l a r g e r t h a n that obs e r v e d in ~ poly-L-alanine, w h i c h w a s e x p l a i n e d b y the p r e s e n c e of b u l k i e r side-chains. L a t e r w o r k has s h o w n that w h i l e the s t r u c t u r e of Marsh et al is essentially correct, t h e i r values of egly a n d C~l~ need be a m e n d e d . Although the c o r r e c t i o n s are small on an absolute scale, t h e i r a n a l y s i s has h e l p e d u n d e r s t a n d the details of the m o l e c u l a r i n t e r a c t i o n s in the ~ s t r u c t u r e of silk fibroin. These m o r e r e c e n t results w i l l be a n a l y zed in m o r e detail. As i n d i c a t e d , the ~ s t r u c t u r e of (Ala-Gly)~, is isom o r p h o u s to that of silk fibroin. A carefu'l a n a l y -

C h e m i c a l a n d c r y s t a l l i n e s t r u c t u r e s o f B. m o r i f i b r o i n . sis of the diffraction data [6, 22] s h o w e d that in poly(Ala-Gly), the cgly distance is close to 3.8 A. The c~l~ distance is only 5.17 £, i.e. l o w e r than the i n t e r s h e e t distance o b s e r v e d in iB p o l y a l a n i n e (5.27 h). Similarly, an i n c r e a s e of Cg~yin the structure of silk fibroin f r o m 3.'5 X to 3.87 ,=~ and a c o r r e s p o n d i n g decrease of c ~ yields a better fit b e t w e e n calculated and o b s e r v e d intensities [6,

22]. The noticeable d i f f e r e n c e in spacings b e t w e e n

Cgly and the c o r r e s p o n d i n g i n t e r s h e e t distance in

209

PG I is of course striking. It has been r e c e n t l y exp l a i n e d t h r o u g h a) the e l u c i d a t i o n of the s t r u c t u r e of p o l y g l y c i n e I, and b) c o n f o r m a t i o n a l energy analysis of the ~ sheet structures of p o l y g l y c i n e , p o l y a l a n i n e , and (Ala-Gly) n. a) The s t r u c t u r e of p o l y g l y c i n e I, w h i c h was thought to be a f a m i l i a r a n t i p a r a l l e l pleated shect is in fact of a different, but related type, d e s c r i b e d by P a u l i n g and Corey as an a n t i p a r a l l e l r i p p l e d sheet [23]. The latter derives from the f o r m e r by

Fi~. 1. - - A£omie mode~s of (Ala-Oly)n, a m,o&el of B. mort silk. On ~he r i g h t : ne)arly extended eh~M,n con.formation obs,erved in the st~rueture ; on tl~e l ef~ : th'e two possible chain confovma~tions suggested for the AG II, and Silk I structures. In both casos, the chains are seen along the hyda,ogen bond direction., and the chain axis is vevt'ical.

c.3

B'

,k3

"~"

~ A

'

k.)

~- - /

('-]

~

it._)

~

t a k i n g the m i r r o r image of e v e r y other chain in a p l a n e parallel to the sheet. The r i p p l e d sheet s t r u c t u r e is c e n t r o s y m m e t r i c , w h i c h w o u l d be inconsistent w i t h the p r e s e n c e of optically active residues (unless e v e r y other c h a i n in the sheet w e r e m a d e of L residues, and of D residues, resp e c t i v e l y ) but is fully p e r m i t t e d for the achiral p o l y g l y c i n e [24].

~'~--~"

i'~

)

FIG. 2. - - The g struetore of B. mori silk suggested by Marsh et al [4]. While tile general features of the structure are correct, the intersheet distances indicated are in error (see texL).

BIOCHIMIE, 1979, 61, n ° 2.

The r i p p l e d and pleated sheet s t r u c t u r e s of p o l y g l y c i n e are not e x p e c t e d to h a v e s i m i l a r cell g e o m e t r i e s and p a r a m e t e r s , i n d e e d , e n e r g y calculations on the two structures E25] s h o w that the p a c k i n g of r i p p l e d sheets is m o r e c o m p a c t .(hence the structure m o r e stable) than that of pleated sheets. F o r rippler sheets the c a l c u l a t e d c~)y is 3.35 .~ (observed value 3.38 .~) w h i l e for pleated sheets it is 3.55 £ (table II, columns 1 and 2).

210

B. L o t z and F. Coionna Cesari. TABLE II.

Stable structures o[ ,~ sheet structures of polyglycine, (Ala-Gly), and polyalanine, 1

2

3

4

5

Poly~lycine

(1) c

Rippled sheet

Pleated sheet

760

600

--

c61y CAIa

3.35 (2) --

E (Kcal/mol. residue)

- - 12.01

7

(Aia-Gly)n Polyalanine

B. (X-rays}m°ri silk Conf energy

3 35 --

5.10 (3)

69.90 8.72 3.70 5.02

- - 11.01

- - 14.78

-- 15.32

--

6

73.30 --

X-rays

72.70 8.96 (4) 3.83 5.13

-8.96 3.79 5.17

-9.20 3.87 5.33

~ 15.24

--

--

(I) a is, in chain axis projection, the angle between the a axis of the unit-cell and the orientation of the C ~ atom relative to, the chain, axi.s. (2) Observed value : 3~38 A. (3) Observed value : 5.2~7 A. (4) Taken cqua,1 to the experimental value (ecrlumn 6).

As (Ala-Gly). a n d silk have optically active residues i n every c h a i n of the structure, they must adopt the pleated sheet structure. T h e i r C~l~. dist a n c e should therefore be compared, not to the Cg~. of PG I w h i c h relates to a different structure, but to that of the (hy~pothetical) pleated sheet structure of p o l y g l y c i n e : part of the increase in cg~y is thus explained.

the calculated Ca1a value is slightly smaller in (Ala-Gly)n t h a n i n the h o m o p o l y m e r . As the potentials used u n d e r e s t i m a t e slightly the intersheet distances, the m e a s u r e d c value of poly(Ala-Gly) was t a k e n as fixed i n a final calculation. The p a r t i t i o n into Cg~y and c,~, determined by X-ray a n d calculated by energy analysis agree w i t h i n e x p e r i m e n t a l e r r o r (Table II, col u m n s 5 a n d 6). The i m p o r t a n t increase of c~., and even the small decrease of c,1 . i n (Ala-Gly) n (when c o m p a r e d to the c o r r e s p o n d i n g homopolymers) are therefore fully a c c o u n t e d for.

b) F u r t h e r i n s i g h t into the m o l e c u l a r interactions c a n be gained w h e n c o m p a r i n g the ~ pleated s t r u c t u r e s of p o t y a l a n i n e , (Ala-Gly)= a n d polyglycine .(the latter is not actually observed), as deter. m i n e d b y c o n f o r m a t i o n a l energy c a l c u l a t i o n s [26]. The i m p o r t a n t variable appears to be the azimuthal o r i e n t a t i o n of the c h a i n on its axis. As s h o w n i n table II (columns 2 a n d 3), these o r i e n t a t i o n s differ m a r k e d l y i n the pleated sheets of polyglycine a n d p o l y a l a n i n e (a = 60 a n d 73°3, respectively). F u r t h e r , the range of v a r i a t i o n of a is fairly l i m i t e d i n .~ p o l y a l a n i n e due no the onset of strong intersheet i n t e r a c t i o n s i v a n tier Waals contacts b e t w e e n m e t h y l groups) w h e n a --~ 70 °.

I n silk fibroin, a s i m i l a r situation c e r t a i n l y exists, w h i c h lends strong s u p p o r t to the more recent p a r t i t i o n (table II, .column 7) p r o p o s e d by F r a s e r a n d MacRae (3.87 a n d 5,33 ~) [6]. A notable i m p l i c a t i o n of the fairly short 5.33 X distance is that, c o n t r a r y to previous belief, a m i n o acids w i t h large side-chains (such as tyrosine, etc...) are most p r o b a b l y not i n c o r p o r a t e d i n the s t r u c t u r e but r a t h e r located outside the c r y s t a l l i n e regions.

The calculated stable structure of (Ala-Gly)~ is, not u n e x p e c t e d l y , a c o m p r o m i s e b e t w e e n those of poIyglycine a n d p o l y a l a n i n e : w h i l e i n t e r a c t i o n s on the glycine side w o u l d tend to favour low a's, the value actually calculated c o r r e s p o n d s to the lower limit p e r m i s s i b l e on the a l a n i n e side, i.e. about 70" (tabte II, c o l u n m 4). This value differs significanHy from the favorable one in polyglycine, w h i c h results i n a cgly m u c h larger t h a n that of the pleated sheet and, a f o r t i o r i , of the r i p p l e d sheet structure p r e s e n t in PG I. At the same time,

The agreement b e t w e e n observed distances and those calculated for an ideal structure also suggests a v i r t u a l absence of irregularities, such as possible c h a i n i n v e r s i o n s w h i c h w o u l d b r i n g the glycine residues of one c h a i n in the mostly alan i n e side of the sheet. This type of disorder had been envisaged as a possible e x p l a n a t i o n to the larger egly distance [27] and c o n f o r m a l i o n a l energy analysis indicates it to be sterically feasable. While this hypothesis needs not be i n v o k e d for (Ala.Gly) n it is h o w e v e r relevant to the whole pro-

BIOCHIMIE, 1979, 61, u ° 2.

Chemical and crystalline structures of B. m o r t fibroin. tein, or the Cp fraction. As already m e n t i o n n e d , the N t e r m i n a l octapeptide of the C o fraction is out of phase w i t h the rest of the molecule. If it is i n c o r p o r a t e d in a ~ structure, the molecular stem b e a r i n g this sequence will have four of its alanines (or serines) on one side of the sheet, and the r e m a i n d e r on the other side, giving rise to a local defect w h i c h could affect intersheet distances. Only if the structure 'were composed of m o l e c u l a r stems no longer t h a n eight residues in the c h a i n axis d i r e c t i o n (i.e. ,~ 28 ~) could this defect be i n c o r p o r a t e d i n the less ordered part of the (presu.ma.bly .lamellar) structure. The present results c o n s i d e r only the more regular parts of the crystalline structure of B. nmri fibroin. Its .chemical c o n s t i t u t i o n suggests h o w e v e r a composite structure w i t h less crystalline, or a m o r p h o u s material. Periodicities larger than those of the unit-cell just c o n s i d e r e d have i n d e e d been r e p o r t e d for silk fibroin. P e r i o d i c i t i e s of a'bout 21 X have been associated w i t h the disturbances created by seryl residues at regular intervals in the structure [6] ; larger periodicities prob a b l y reflect the existence of a different level of organization, such as l a m e l l a r structures w i t h c h a i n fol.ding, well 'known in the field of synthetic p o l y m e r s [133. W h i l e the cross ~ structure of Chrysopa [lava silk has been i n t e r p r e t e d on this basis I28], only little work has been done along s i m i l a r lines in the case of B. mort fibroin. 3) T H E STRUCTURE OF SILK I. Tile m o l e c u l a r c o n f o r m a t i o n a n d crystal structure of the second crystal m o d i f i c a t i o n of silk fibroin is by far less well established than the I~ form. Silk I is o b t a i n e d w h e n the silk gland c o n t e n t is let to dry w i t h o u t m e c h a n i c a l disturbance. It has also been obtained from silk or Cp fraction dissolved i n aqueous l i t h i u m b r o m i d e , l i t h i u m sulfoeyanide, or c u p r i e t h y l e n e d i a m i n e solutions. Presence of alkohols i n the solution h o w e v e r induces the ;~ form. T e m p e r a t u r e also has an influence : the silk I a n d ,B forms are o b t a i n e d from aqueous solutions of silk dried at t e m p e r a t u r e s below a n d above ,,~ 40°C, respectively [29]. W h e n sheared, or disturbed, or first frozen, these same solutions give rise to the i~ form, even for T < 40°C, p r e s u m a b l y t h r o u g h f o r m a t i o n of seeds with ~ structure in stressed parts of the solution. The sensitivity of Silk I to m e c h a n i c a l s h e a r i n g or r o l l i n g and the ease with w h i c h the 8 structure is o b t a i n e d u n d e r these conditions, has made s t r u c t u r a l investigations difficult, as only u n o r i e n -

BIOCHIMIE,

1979, 61, n ° 2.

211

ted, or poorly o r i e n t e d Silk I m i x e d w i t h the form could be o b t a i n e d : n e i t h e r the structure, n o r even the cell geometry had been established. Progress was made t h r o u g h a better u n d e r s t a n ding of p o l y m e r morphology, gained from studies on synthetic polymers. Indeed, Konishi et al. [30] observed that the precipitate o b t a i n e d w h e n the Ca f r a c t i o n is crystallized from dilute L i B r / w a t e r solutions is made of lamellar single crystals. An electron d i f f r a c t i o n p a t t e r n from a sheaf-like assembly of such crystals ,led them to propose an o r t h o r h o m b i c cell p r o j e c t i o n with p a r a m e t e r s a ---- 4.49 a n d b = 7.20 A ; an X-ray diffraction p a t t e r n t a k e n parallel to the p l a n e of a mat of such crystals gives essentially a fiber pattern, but w i t h i n h e r e n t l y love o r i e n t a t i o n ; a c p a r a m e t e r of 9.08 X was p r o p o s e d on the basis of an observed reflection at 2.27 A, assumed to be on the mer i d i a n of the fourth layer line [31]. (Ala-Gly)n gives also, w h e n dialyzed from an aqueous LiBr solution, the same crystal modification [18J. The p r e c i p i t a t e is again made of lamellar single crystals whose diffraction p a t t e r n indicates an o r t h o r h o m b i e celt p r o j e c t i o n w i t h a : 4.72 h, a n d b : 14.4 A (fig. 3). In diffraction patterns o b t a i n e d from tilted specimens, hkl reflections w e r e i n d e x e d as h k 1 and hk 3 with a fiber period of 9.6 h [32]. C o m b i n a t i o n of the best established pieces of i n f o r m a t i o n from these two studies is needed to a p p r o a c h the correct cell geometry. The cell projection, as established for (Alagly) n, has definitely an a p a r a m e t e r of 4.72 £, and not 4.49 A, thus suggesting a sheet structure. On the other h a n d the n o n - e q u a t o r i a l reflections are located on the first, second and fourth layer lines. The e p a r a m e t e r of 9.08 A appears h o w e v e r r a t h e r short ; if the 2.27 .~ reflection were slightly offm e r i d o n a l (i.e. i n d e x e d as (}14 instead of 004, a possibility w h i c h c a n n o t be discarded on the ba. sis of available evidence), the fiber repeat w o u l d be close to 9.4 A, w h i c h enables a better overall i n d e x i n g of the pattern. The latter value w i l l be assumed in the following. A m o d e l of c h a i n c o n f o r m a t i o n compatible w i t h the above cell geometry and w h i c h fulfils the stereochemical rules of peptide c o n f o r m a t i o n has been p r o p o s e d [32]. The c h a i n has an overall c r a n k s h a f t geometry (fig. 1) in w h i c h the structural repeat u n i t is a dipeptide, as the c h e m i c a l repeat unit. The c o n f o r m a t i o n of the a l a n i n e a n d glycine residues are w i d e l y different and close to those of the ~ s t r u c t u r e a n d a helix, respectively. Since c o n f o r m a t i o n s characteristic of left (L) and right (R)-handed ~ helices c a n be envisaged for

B. L o t z and F. Colonna Cesari.

212

the g l y c i n e r e s i d u e , t w o c h a i n c o n f o r m a t i o n s (I a n d II) s h o u l d be c o n s i d e r e d , b a s e d on ~ala-aRgly a n d !~ala-aLgly. As s h o w n in f i g u r e t, c h a i n s I a n d II h a v e v e r y s i m i l a r shapes, but o p p o s i t e ( c h e m i c a l )

c h a i n senses. T h e p o s i t i o n of c a r b o x y l a n d N H g r o u p s is s u c h t h a t h y d r o g e n b o n d i n g is o n l y possible b e t w e e n p a r a l l e l c h a i n s of t h e s a m e type, t h u s g i v i n g r i s e to sheets m a d e of c h a i n s I, or of

FIG. 3 . Chain folded, lamellar single crystal of (Ala-Gly),, in the AG II modification, arid corresponding electron diffraction pattern. The chains have their axis normal to tl~e plane of the paper and hydrogen-bond direction is parallel to the longest dimension of the cryscal [32].

Fro. 4. - - Two views of a sheet of AG II built ~vith alternating chains of type I and type II (see figure 1). This structure corresponds to Mod~el 1 in table III. Note that alternating chains arc antiparallel.

BtOCHIM1E, 1979, 61, n ~ 2.

Chemical and crystalline structures of B. m o r t fibroin. chains II only. Chains I and H c a n also alternate r e g u l a r l y in the sheet : h y d r o g e n - b o n d s are thus m a d e b e t w e e n (chemically) a n t i p a r a l l e l chains, w h i c h is a f a m i l i a r situation in ~ structures. In the p r e s e n t case h o w e v e r , the c o n f o r m a t i o n s of t h e a l t e r n a t i n g a n t i p a r a l l e l c h a i n s are different, w h i c h r e p r e s e n t s an unusual case (in t h e field of p o l y m e r s ) of <> [33]. The r e s u l t i n g sheet is s h o w n in figure 4. F o r all t h r e e types of sheet s t r u c t u r e s h o w e v e r , h y d r o gen-bon.ds are o r i e n t e d r o u g h l y at right angle to the c h a i n axis, in a g r e e m e n t ~vith p o l a r i z e d inf r a r e d e v i d e n c e on p a r t l y o r i e n t e d Silk I [34]. P a c k i n g of the sheets in the unit-call is m o r e difficult to foresee in v i e w of the c o m p l i c a t e d g e o m e t r y of the sheets. T h e i n t e r s h e e t i n t e r a c t i o n s in any case must r e p r e s e n t only a small f r a c t i o n of the o v e r a l l p a c k i n g energy. T h e w e a k n e s s and p o v e r t y of hkl reflections suggests a fair degree of disorder. A s t r u c t u r a l d i s o r d e r by w h i c h c h a i n s are d i s p l a c e d by ± c / 3 along the c h a i n axis h a d been e n v i s a g e d [32] but is c o n t r a d i c t e d by the re. sults on mats of single crystals. A s t r u c t u r a l diso r d e r of this type w a s nevertheless also consider e d in later studies, and a p p e a r s to be a r e a l i s t i c assumption. An extensive c o n f o r m a t i o n a l e n e r g y analysis on the possible c h a i n geometries, sheet structures and sheet p a c k i n g s c o n s i d e r e d above has been p e r f o r m e d [35]. Since m a n y m o l e c u l a r p a r a m e t e r s (internal r o t a t i o n angles) and p a c k i n g v a r i a b l e s (relative positions of the chains, the sheets, etc...) need be c o n s i d e r e d , a p l a n a r p e p t i d e g e o m e t r y

213

was assumed. Besides the usual, f a v o u r a b l e energy c r i t e r i o n , the c a l c u l a t e d i n t e r s h e e t distance w a s also taken as a useful test for assessing the v a l i d i t y of the structures : c a l c u l a t e d distances should c o m p a r e "with the o b s e r v e d 7.20 ,~ distance, or be slightly l o w e r (.since the potentials used t e n d to u n d e r e s t i m a t e the inter-sheet distances, cf. table II). A n u m b e r of p a c k i n g s and orientations of the sheets h a v e been c o n s i d e r e d : in particular, v a r i o u s r e l a t i v e p o s i t i o n s of successive sheets along the c h a i n axis h a v e been e x a m i n e d to test the l i k e l i h o o d of s t r u c t u r a l d i s o r d e r ; aJso, the relative o r i e n t a t i o n s of successive sheets c a n be s y n c l i n e or a n t i c l i n e if c h a i n s of like c o n f o r m a t i o n in these sheets are p a r a l l e l or a n t i p a r a l l e l , respectively. By the l o w e n e r g y and r e a s o n a b l e i n t e r s h e e t distance c r i t e r i a no s t r u c t u r e w i t h s i d e - c h a i n s att a c h e d to the r e s i d u e in u c o n f o r m a t i o n is acceptable. It is clear t h e r e f o r e that ~hese v a r i o u s struct u r e s are only p e r m i s s i b l e for a ,(Gly-X) n sequence. S e v e r a l s t r u c t u r e s w i t h the a l a n i n e r e s i d u e in ~1 c o n f o r m a t i o n a p p e a r h o w e v e r reasonable, and t h e i r i m p o r t a n t p a r a m e t e r s are s u m m a r i z e d in table III. A s t r u c t u r e m a d e of sheets wi~h p a r a l l e l c h a i n s in w h i c h r e s i d u e c o n f o r m a t i o n s are t3ala-aLgly appears to be the most stable ; it m a y p e r m i t a positional d i s o r d e r of sheets, as t w o m i n i m a of d c are calculated, s e p a r a t e d by ,~ ± c / 2 , w h i c h w o u l d a c c o u n t for the o b s e r v e d w e a k n e s s of reflections on o d d l a y e r lines. H o w e v e r a s t r u c t u r e w i t h sheets i n v o l v i n g a l t e r n a t i n g c h a i n geome-

TABLE III.

Structural parameters o[ various models for AG I1 (and Silk I) structures. Model 2 • Model t

{anticline packing)

ah XItala • gly

~2gly. de (~) (1) 1/2 of b (A) (2) Esheet (Keal/mol. residue) Etotal (Kcal/mol. residue)

- - 104.6 112.2

- - 124.5 88.2 79.8 -49.8 49.7 - - 76.1 5.03 7.16 - - 10.24 -- 12.89

Anticline packing

--

94.2 126.2 60.8 54.5 0.10 7.17 -9.86

97.6 102.0 83.8 57.4 5.29 7.01 - - 10.67

--

--

--

--

12.66

--

Syneline packing

13.80

96.7 128.9 60.0 52.6 6.31 7.21 -9.79 12.07

Model I : Sheets made of ,alternating chains with different conformations (Model of figure 4) , anticline packing of successive sheets in .the unit-cell. Model 2 : S~eets made wit,h parallel eha,ins with eonforrn,ation:s (XLQ~y'~IAt~. (I) Characterizes the rel,ative position of successive sheets along the chain ax,is. (2) Calculated intersheet distance, to be compared w~th the observ,ed va,lue : 7.20 .~. BIOCH1MIE, 1979, 61, n ° 2.

15

214

B. Lotz and F. Colonna

tries c a n n o t be r u l e d out on the basis of these calculations. In fact, t h e v e r y s i m i l a r energies of the different m o d e l s suggests that t h e actual s t r u c t u r e m a y w e l l be a b l e n d of these v a r i o u s possibilities, thus also a c c o u n t i n g for the p a u c i t y of d i f f r a c t i o n d a t a : I n the absence of m o r e c o n c l u s i v e e v i d e n c e , in p a r t i c u l a r of an u n d i s p u t e d m e a s u r e of the c h a i n axis r e p e a t distance, f u r t h e r analysis of t h e p r e s e n t m o d e l appears h a r d l y justified. Efforts in o b t a i n i n g this m e a s u r e are n o w be4ng p u r s u e d by a t t e m p t i n g to crystallize e p i t a x i a l l y Silk I on o r i e n t e d substrates ; one can a l r e a d y notice that a small change of c w o u l d result in only m i n o r var i a t i o n s of the c o n f o r m a t i o n a l angles in the structure.

Conclusion. W h i l e the m a i n features of the c h e m i c a l and c r y s t a l l i n e s t r u c t u r e of B. m o r t fibroin w e r e well established, t h e last years h a v e a d d e d t h e i r share of n e w i n f o r m a t i o n and f u r t h e r insights into these aspects. P r o m i s i n g p r o s p e c t s can h o w e v e r still be foreseen for the e l u c i d a t i o n of the chemical s t r u c t u r e via s e q u e n c i n g of the n u c l e i c acids. Analysis of the c r y s t a l l i n e s t r u c t u r e of ~he ~ form on the o t h e r h a n d has n e a r l y r e a c h e d c o m p l e t i o n , since this s t r u c t u r e is n o w u n d e r s t o o d at the molec u l a r i n t e r a c t i o n s level. P a r t of the puzzle r e p r e sented by S i l k I m a y be c o n s i d e r e d as solved. W h i l e this s t r u c t u r e h a d eluded most of the classical m e a n s of investigation, it has b e c o m e clear that w e are .dealing w i t h a h i g h l y c o n t r a c t e d sheet s t r u c t u r e specific to an a l t e r n a t i n g sequence of the type : .(GIy-X)~. So far, the only X residues are Ala a n d Ser. Inves¢igation of o t h e r m o d e l s w i t h different X - a m i n o a c i d s m a y i n d i c a t e w h e t h e r longer, p o l a r or b u l k i e r side c h a i n s are also p e r m i s sible for this structure. F r o m a b i o l o g i c a l standc h a i n c o n f o r m a t i o n of Silk I plays any role in the silk gland, i.e. w h e t h e r o r g a n i z e d p o r t i o n s of t h e point, it w o u l d be of interest to .establish if the fibroin can exist as single sheets or tactoids in the lumen. F u r t h e r d.evelopments for s t r u c t u r a l inwestigations e x i s t avhen, l e a v i n g the m o l e c u l a r agency in the unit-cell, w h i c h w a s our m a i n c o n c e r n here, one c o n s i d e r s l a r g e r levels of o r g a n i z a t i o n : these m a y i n c l u d e liqu.id-crystalline structures p r o d u c e d by some siik gels or c o n c e n t r a t e d solutions, a n d l a m e l l a r c r y s t a l l i n e structures, as a l r e a d y

BIOCHIMIE, 1979, 61, n ° 2.

Cesari.

o b s e r v e d in a n u m b e r of p o l y p e p t i d e s and synthetic p o l y m e r s . Such structures h o w e v e r rely m o r e on the m a c r o m o l e c u l a r r a t h e r t h a n t h e specific p r o t e i n c h a r a c t e r of silk ; they also c l e a r l y deviate f r o m and forget the o r i g i n a l interest of silk, w h i c h r e m a i n s p r i m a r i l y an a l r e a d y spun, almost r e a d y to use filamenteous material. RIPFERENCES. 1. Fischer, E. ,~ ~kita, A. (19:01) Z. Physiol. Chem., 33, 177. 2. Nishikawa, M. • Ono, S. (1913) T o k y o Math. Phys. ~Soc. Rep., 7, 131. 3. Lacas, F., S~aw, J. T. B. ~ Smith, S. G. (1957) Biochem. J., 66, 4~68. 4. Marsh, R. E., Corey, R. B. ~ Pauling, L. (19'55) Biochim. Biophys. Acta, 16, 1. 5. La~ca.s, F. ,~ Ruda'll, K. ~..1968) In <