J. Mol. Biol. (1983) 166, 631-640
Characterization of the Proteinase Inhibitor IIA from Bull Seminal Plasma by 1H Nuclear Magnetic Resonance Stability, Amide Proton Exchange and Mobility of Aromatic Residues PETR STROPt AND K t ' a T Wt~THRI('H
lnstitut fiir Molekularbiologie und Biophysik Eidgendssische Technische Hochschule ETH-H6nggerberg, CH-8093 Ziirich, Switzerland (Received 23 November 1982) The isoinhibitor IIA from bull seminal plasma was investigated in aqueous solution by 1H nuclear magnetic resonance (n.m.r.). The analysis of the IH n.m.r. data was based on individual resonance assignments, which are described in the following paper. Large conformation-dependent chemical shifts for aliphatic amino acid side-chains, numerous slowly exchanging amide protons and unusual pH titrations of two aromatic residues show that this protein forms a compact, globular conformation. This form of the protein is stable between pH 4 and 12 at 25~ and between 5 and 50~ at pH 4"9. At temperatures above 50~ there is evidencefor an equilibrium between several different conformations, with the rate of exchange between the different species being in the intermediate range on the n.m.r, time-scale. Preliminary data are presented for the individual exchange rates of 18 backbone amide protons. Among the four aromatic rings, Phel0, Phe38 and Tyrl6 undergo rapid 180~ flips over the entire temperature range, whereas for Tyr32 a temperature-dependent transition from low-frequency to high-frequency flipping motions was observed.
1. Introduction Protein proteinase inhibitors are ubiquitous both in the tissue and in secretions of organs from m a m m a l i a n species (for reviews see, e.g. Tschesche, 1974; Laskowski & K a t o , 1980; Fink & Fritz, 1976: Schiessler et al., 1976a). A m o n g the secretory inhibitors those found in the seminal p l a s m a have recently a t t r a c t e d considerable interest. Evidence has been presented t h a t regulation of proteinase a c t i v i t y in sperm and sperm p l a s m a b y inhibitors is an i m p o r t a n t factor in the protection of sexual tissues against i n f l a m m a t o r y processes (Fritz et al., 1978), and possible roles of proteinase inhibitors in the fertilization of the o v u m (MeRorie & Williams, 1974; Schiessler et al., 1976b) and their practical use for a n t i - e n z y m a t i c contraception h a v e been discussed (Tschesche, 1974). t Present address: Institute of Organic Chemistry and Biochemistry C.S.A.V., 16610 Prague 6, C.S.S.R. 631 0022-2836/83/160631-10 $03.00/0
9 1983 Academic Press Inc. (London) Ltd.
632
P. ~TROP AND K. Wt)THRICH
The p r i m a r y structures of several seminal proteinase inhibitors have been determined (Tschesche et al., 1976; Meloun & (~echovs 1979; (~echovs & Meloun, 1979; K a t o et al., 1976), b u t except for ini~rences from d a t a obtained with homologous secretory inhibitors of the K a z a l t y p e (Weber et al., 1981 ; DeMarco et al., 1979,1982 ; P a p a m o k o s el al., 1982 ; F u j i n a g a et al., 1982 : Ogino et al., 1982), relatively little is known a b o u t the spatial structures. We have s t a r t e d a nuclear magnetic resonance investigation of the bull seminal inhibitor B U S I I I A t . The present p a p e r describes how the stability of the globular conformation with respect to p H and t e m p e r a t u r e , and the internal mobility of B U S I I I A , were characterized b y n.m.r. These d a t a are closely linked with the contents of the following p a p e r (~trop et al., 1983), which describes the assignment of the t H n.m.r, spectrum of B U S I I I A with the use of two-dimensional n.m.r. On the one hand, the observations reported here provided the basis for selecting the conditions for the two-dimensional n.m.r, experiments. On the other hand, the present account makes use of the individual resonance assignments for B U S I I I A (~trop et al., 1983).
2. Materials and Methods Isoinhibitor BUSI IIA was purified by following the procedures of (~echovs et al. (1979). For the n.m.r, experiments solutions (approx. 0-003 M to 0"006 M) of the protein in 2H20 were prepared. The p2H of the samples was adjusted by the addition of minute amounts of NaO2H or 2HCI. p2H values correspond to the pH meter readings, without correction for isotope effects (Kalinichenko, 1976; Bundi & Wfithrich, 1979a). IH n.m.r, spectra were recorded at 360 MHz on a Bruker HX360 spectrometer and at 500 MHz on a Bruker WM500 spectrometer. Standard procedures were used to obtain conventional, 1-dimensional IH n.m.r, spectra under different experimental conditions. For the amide proton exchange studies the protein was dissolved in 2H20 that had been acidified by the addition of 2HCl. The first n.m.r, recording was started 1"7 min after the protein had been dissolved, and 310 transients were accumulated during approx. 3 min. For the measurements of the exchange rates the time of this recording was taken to be 3 min after BUSI IIA had been brought into solution (Fig. 3). Similarly, using a fresh sample for each experiment, measurements were obtained for different, longer exchange times (Fig. 3), whereby between 400 and 800 transients were accumulated for each recording. The exchange rates in Table 1 were determined by measuring the timedependent decrease of the resonance peak heights, whereby the amide proton peak heights were calibrated relative to those of non-labile hydrogen atoms in the same spectrum. Approximate rate constants resulted from linear least-squares fits of semilogarithmic plots of the resonance peak heights versus time (Richarz et al., 1979).
3. Results The 1H n.m.r, spectra contain clear indications t h a t B U S I I I A forms a globular structure, with a sizeable proportion of the amino acid residues involved in regular secondary structure. O u t s t a n d i n g 1H n.m.r, features t h a t can be related with a globular protein conformation are: several high-field shifted m e t h y l resonances (Fig. 1), the chemical shifts and p2H titrations of the a r o m a t i c sidechains (Figs 1 and 2) and the a p p e a r a n c e of n u m e r o u s peaks corresponding to t Abbreviations used: BUSI IIA, protease inhibitor IIA from bull seminal plasma: n.m.r, nuclear magnetic resonance: p.p.m., parts per million.
STABILITY OF BULL SEMINAL INHIBITOR IIA
633
amide protons that are only slowly exchanged in 2H20 solution of the protein (Fig. 3). (a) Stability of the globtdar conformation of B U S I I I A Observation of changes with temperature and pH in the circular dichroism spectrum (recorded on a Jasco J 5 0 0 A spectropolarimeter) was an efficient technique for delineation of the experimental conditions in which denaturation of BUSI IIA sets in. The observations by circular dichroism were then followed up by 1H n.m.r, studies. The temperature stability at p2H 4"9 can be assessed from the data in Figure 1. Features of a globular protein were observed over the entire temperature range fi:om 10~ to 770(.` (Fig. 1). Similar observations were made at different pH values in the range from 4"0 to 7"0, and in this range the protein solution could be heated to 85~ for one hour without causing irreversible changes of conformation. A closer look at the spectra in Figure 1 shows that there are spectral changes with temperature over the entire range studied. In the high-field region the three methyl resonances of Val42 and Leu51 between 0"0 and 0"7 p.p.m, move to lower field at higher temperature. The largest temperature shifts prevail for the two lines at highest field. Between 10~ and 45~ a doublet fine structure is clearly recognized for the three high-field methyl groups. At 55~ (Fig. 1) additional fine structure appears, which indicates conformational heterogeneity for these methyl groups. At 70~ and even more at 77~ the two highest field lines are broadened, so th at no fine structure is resolved. These spectral features are indicative of a situation where the 1H n.m.r, signals of two or several different conformers are averaged, with the rate of exchange at 70o(' and 77~ in the intermediate range on the n.m.r, time-scale (W(ithrich, 1976). The aromatic region shows, in addition to temperature-dependent changes that can be attributed to the rate processes that are also seen at the high-field end of the spectrum, spectral variations related to the dynamics of the aromatic rings, as will be discussed below. Information on the pH stability of BUSI IIA is contained in the titration curves of Figure 2. Between pH 4 and 12 there is no indication of a pH-dependent change of conformation. Below pH 4"0 the resonance lines of the two histidines shift towards the random-coil positions (Wiithrich, 1976: Bundi & Wiithrich, 1979a), which they reach at pH values near 2"0. The tyrosine resonances in the globular protein are near the random-coil chemical shifts, and therefore they experience only minor shifts when the protein is denatured. The acid denaturation of BUSI IIA between pH 4 and pH 2 was also manifested in other regions of the IH n.m.r, spectrum. (b) IH n.m.r, of the aromatic rings The assignments of the aromatic resonances between 6-7 and 7"4 p.p.m, are indicated in Figure 1. These assignments result from the combination of the data in Figures 1 and 2 with the sequential assignments described in the following paper (Strop el al., 1983). For Phel0, Phe38 and T y r l 6 symmetric AB2Xz and A2X 2 spin systems, respectively, were identified at all temperatures between 10~ and 70~ which indicates t hat these rings undergo rapid 180~ flips about the
634
P. ~TROP
AND K. WOTHRICH
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Fro. 2. Plots of chemical shire versus p2H for the aromatic ~H n.m.r, lines of Tyrl6, His24 and His53 in BUSI IIA. The experimental points were obtained fi'om 360MHz IH n.m.r, spectra recorded in a 0-005 ~n solution of the protein in 2H20 at 25~ The p2H was varied by the addition of minute amounts of 2HCI and NaO2H. The following acidity constants were obtained from non-linear leastsquares fits to one-proton titration curves: Tyrl6, pK, 25~-- 10-5+_0'2: His53, pK~TM = 6"4+_0"2; His20 and Tyr32 (not shown) do not tit,-ate between pH4"0 and 12-0. except that His24 C4H shows a small downfield shift in the p2H range near pK~• of Tyu?16. C ~ - - C ~ b o n d ( W i i t h r i c h , 1976). T h i s c o n c l u s i o n was f u r t h e r c o r r o b o r a t e d b y t h e o b s e r v a t i o n t h a t for these t h r e e rings t h e r e are o n l y s m a l l c h e m i c a l - s h i f t v a r i a t i o n s w i t h t e m p e r a t u r e . T h e o n l y such shift t h a t is r e a d i l y recognized in F i g u r e 1 causes t h e C3, 5 H r e s o n a n c e of T y r 1 6 a n d t h e C 2 , 6 H a n d C4H r e s o n a n c e s of P h e 3 8 , which are s e p a r a t e d a t 24~ a n d lower t e m p e r a t u r e s , to be s u p e r i m p o s e d in t h e t e m p e r a t u r e r a n g e f r o m 45~ to 77~ A t 45~ o n l y one t w o - p r o t o n line was o b s e r v e d for T y r 3 2 , w h i c h was a s s i g n e d to the C2, 6 H p r o t o n s (Strop et a l . , 1983). A t lower t e m p e r a t u r e s , this r e s o n a n c e b r o a d e n s m a r k e d l y , w h e r e a s a t 70~ it is a s h a r p line w i t h i n t e n s i t y c o r r e s p o n d i n g
Fro. I. Temperature dependence between 24~ and 77~ of the high-field shifted methyl resonances between 0 and 0"8 p.p.m, and the aromatic resonances between 6-8 and 7-4 p.p.m, in the 500 MHz *H n.m.r, spectrum of a 0'003 M solution of BUSI IIA in 2H20, pZH 4"9. The resonance assignments at 45~ are from ~trop el al. (1983). In all 5 spectra the HC4 resonance of His53 is identified by an asterisk.
P. ~ T R O P A N D K. W ~ T H R I C H
636
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STABILITY OF BULL SEMINAL I N H I B I T O R IIA
637
to four protons. This shows t h a t the ring-flips of Tyr32 a b o u t the CP--C ~ bond are restrained by the environment. While the chemical shifts of the C2, 6 protons are nonetheless averaged at t e m p e r a t u r e s a b o v e a p p r o x i m a t e l y 40~ the C3, 5H lines are a v e r a g e d only a t t e m p e r a t u r e s around 70~ (WLithrich, 1976), a t which the average chemical shifts for C2, 6H and C3, 5H at 70~ are nearly identical (Fig. 1). For T y r l 6 and His53 the pK~ values in B U S I I I A (see legend to Fig. 2) deviate by less t h a n 0-5 of a p H unit from the respective random-coil values (Bundi & Wfithrich, 1979a). On the other hand, His24 and Tyr32 do not t i t r a t e in the entire p H range in which the globular form of the protein is preserved. His24 C4H shows a small down-field titration at high p H values, which m u s t arise from throughspace interactions with one of the titrating groups in the protein (Bystrov et al., 1978; Bundi & Wfithrich, 1979b). (c) Amide proton exchange In the I H n.m.r, spectrum of a fl'eshly prepared 2H20 solution of B U S I I I A one observes resonance lines of a p p r o x i m a t e l y 30 amide protons between 7"0 and 10"0 p.p.m. (Fig. 3). In a preliminary s t u d y of the proton exchange, a p p r o x i m a t e rate constants at 25~ and p2H 4"1 were obtained tbr 13 protons (Fig. 3, Table 1). Similar e x p e r i m e n t s at 25~ and p2H 5"9 showed t h a t the order of the relative rates for the individual protons was preserved, even though the absolute exchange rates increased with increasing p2H (Richarz el al., 1979). I n Table 1 exchange rates are listed for those residues for which the resonances are sufficiently wellresolved to be followed in the spectra of Figure 3, and for which u n a m b i g u o u s resonance assignments were obtained from comparison of the one-dimensional with the two-dimensional I H n.m.r, spectra (Strop et al., 1983; see also footnote to Table 1). In addition, upper limits are indicated for five residues t h a t are n o t well-resolved in the one-dimensional spectra, but for which slow exchange was observed in a two-dimensional correlated spectrum recorded in 2H20 (Strop et al., 1983). Table 1 should include all the amide protons for which the exchange rates are smaller t h a n 1 x 10 -3 min - I a t p2H 4.1 and 25~
4. Discussion The I H n.m.r, spectra of B U S I I I A show t h a t this protein a d o p t s a globular conformation over a p H range from 4 to 12 at 25~ and over a t e m p e r a t u r e range fl.om 5~ to 50~ at p H 4.9. At t e m p e r a t u r e s a b o v e 50~ there a p p e a r s to be an equilibrium between multiple conformations with different chemical shifts for
Fro. 3. Region between 7'0 and 10'0 p.l).m, of tile 360 MHz 1H n.m.r, spectra of BUSI IIA at 25~ and p2H 4"1 in 2H20, which were recorded at diffelvnt times, tc~r after dissolving the protein in 2H20. Resonance positions for 5 amide protons, which oveHap with other lines, ane indicated in the top trace (see text). Otherwise tile amide proton lines am identified in the last spectrum in which they can be observed. The asterisk identifies an artifactual "spike", which was introduced by the instrument. Approximate exchange rates computed from these data and additional measurements at different exchange times are listed in Table 1. When comparing the different spectra in this Figure, note that different vertical scales were used in each case and that in each spectrum the intensities of the exchanging proton lines were calibrated relative to those of the non-labile protons.
638
P. ~ T R O P AND K. W t ~ T i l R I ( ' H TABLE 1
Chemical shifts, 8(NH ), and approximate exchange rates, k .... of 18 slowly exchanging amide protons obserced in ='H..,Osohttions of B U S I I I A at 25~ a~d p'-'H4"l Resonance assignment
8(XH)? (p.p.m.)
km ( 106 m in - t )
Phel0 Argl9 Asn22 H is24 Gly26 Ser27 GIu30 Tyr32 Asn34 Ala37 Phe38 Cys39 Lys40 Ala41 Va142 Asn50 Lys52 Cys57
7.75 8.46 9"]6 9-33 (9"63) 9"53 7.,q0 (9"63) 7"41 8.53 7'99 8.94 (8"86) (7-25) 8-32 (8.87) 9'05 8.21
2() 000 90 000 60 000 3000 <~1000 90~( 900 ~<1000 2000 500 40 l t~0 ~<1000 <~1090 90 ~ 11109 1(~00 1l) (}00
t Numbers in parentheses indicate that the amide lm)ton line in question was overlapped with other resonances in the 1-dimensional spectrum. The positions of these resonanees are identified in the to]) trace of Fig. 3. For these 5 protons the resonances were well-separated in the 2-dimensional cortvlated IH n.m.r. (COSY) and the upper limits for k~ were estimated from the observation that these peaks were present in a 2-dimensional spectrum recorded dm'iag 24 h in a freshly prepared ~-H20 solution of BESI IIA at p H 4-9 and 25 C (Strop el eft., 1983). c e r t a i n r e s o n a n c e lines, w h e r e b y t h e r a t e s o f e x c h a n g e b e t w e e n t h e d i f f e r e n t c o n f o r m a t i o n s are in t h e i n t e r m e d i a t e r a n g e on t h e n . m . r , t i m e - s c a l e (W~ithrich, 1976). T h e r e s u l t s o f t h e p r e s e n t i n v e s t i g a t i o n p r o v i d e d t h e b a s i s for t h e s e l e c t i o n o f the experimental conditions at which a determination of the solution c o n f o r m a t i o n o f B U S I I I A b y t w o - d i m e n s i o n a l n . m . r , w a s s t a r t e d . T o be w i t h i n t h e s t a b i l i t y r a n g e in w h i c h a single, g l o b u l a r c o n f ( ) r m a t i o n is m a n i f e s t e d in t h e I H n . m . r . , it was d e c i d e d t o use p H 4"9 a n d to s t u d y t h e s o l u t i o n s a t t w o d i f f e r e n t t e m p e r a t u r e s , i.e. 18~ a n d 45~ ( S t r o p et al., 1983). Once the spatial arrangement of the polypeptide backbone has been d e t e r m i n e d in o t h e r e x p e r i m e n t s ( W f t h r i c h et al., 1982), t h e d a t a o f F i g u r e s 1 t o 3 a n d T a b l e 1 s h o u l d be o f c o n s i d e r a b l e i n t e r e s t for f u r t h e r i n v e s t i g a t i o n s o f t h e solution conformation of BUSI IIA. For example, from the pH titrations of the t y r o s i n e s , T y r l 6 m u s t be in a s o l v e n t - a c c e s s i b l e l o c a t i o n n e a r t h e surface, w h e r e a s T y r 3 2 is s h i e l d e d f r o m t h e s o l v e n t in t h e i n t e r i o r o f t h e m o l e c u l a r s t r u c t u r e . 9 I n d e p e n d e n t s u p p o r t for a l o c a t i o n o f T y r 3 2 in a t i g h t l y p a c k e d i n t e r i o r r e g i o n o f the protein comes from the restricted ring mobility. The pH titration indicates f u r t h e r %hat H i s 5 3 is a c c e s s i b l e t o t h e s o l v e n t , a n d its p r o p e r t i e s c o i n c i d e q u i t e
STABILITY OF BULL SEMINAL INHIBITOR IIA
639
closely with those of the homologous histidines in chicken ovomucoid (Ogino et al., 1982). F o r His24 the downfield titration of C4H at p H 10"5 indicates t h a t this p r o t o n is in close p r o x i m i t y to, or forms a hydrogen bond or a salt-bridge with, T y r l 6 or one of the lysine side-chains (Brown et al., 1976,1978; B y s t r o v el al., 1978; Bundi & Wiithrich, 1979b). However, the most intriguing observation is t h a t no intrinsic titration shift for His2~ was observed in the p H range in which the globular form of BUSI I I A is stable, and t h a t the chemical shifts indicate t h a t the unprotonated, uncharged form of the imidazole ring is present in the n a t i v e protein. The n.m.r, spectral properties of B U S I I I A appear to coincide in m a n y ways with those of the porcine pancreatic secretory trypsin inhibitor (DeMarco el al., 1979,1982). F o r example, the mobility of Tyr31 in the porcine inhibitor was found to be restricted, three methyl doublets were observed between 0 and 0"5 p.p.m., and numerous slowly exchanging amide protons occurred between 7 and I0 p.p.m. At present this comparison must remain rather superficial, since only a small n u m b e r of n.m.r, lines were assigned in the porcine inhibitor (DeMarco el al., 1982). Nonetheless the a p p a r e n t conformational similarities manifested in the n.m.r, spectra of the two inhibitors are quite interesting, since only 12 out of 56 locations contain identical amino acids in both proteins. Financial support by the Schweizerischer Nationalfonds (project 3.528.79) and by a special grant of the EidgenSssische Technische Hochschule, Ziirieh is gratefully acknowledged. We would like to thank Mrs E. Huber and Mrs E. H. Hunziker for the careful preparation of the manuscript and the illustrations and Dr D. (~echovs for providing the sample of BUSI IIA used in this study.
REFERENCES Brown, L. R., DeMarco, A., Wagner, G. & Wiithrich, K. (1976). Eur. J. Biochem. 62, 103107. Brown, L. R., DeMarco, A:, Richarz, R., Wagner, G. & Wiithrich, K. (1978). Eur. J. Biochem. 88, 87-95. Bundi, A. & Wiithrich, K. (1979a). Biopolymers, 18, 285-298. Bundi, A. & Wiithrich, K. (1979b). Biopolymers, 18, 299-311. Bystrov, V. F., Arseniev, A. S. & Gavrilov, Yu. D. (1978). J. Magn. Reson. 30, 151-184. (~echovs D. & Meloun, B. (1979). Hoppe-Seyler's Z. Physiol. Chem. 360, 1497-1500. (~echovs D., Jons163 V., Sedl~kovs E. &Mach, O. (1979). Hoppe-Seyler's Z. Physiol. Chem. 360, 1753-1758. DeMarco, A., Menegatti, E. & Guarneri, M. (1979). Eur. J. Biochem. 102, 185-194. DeMarco, A., Menegatti, E. & Guarneri, M. (1982). Biochemistry, 21,222-229. Fink, E. & Fritz, H. (1976). Methods Enzymol. 45B, 834-847. Fritz, H., Schiessler, H., Geiger, R., Ohlsson, K. & Hochstrasser, K. (1978). Agents Actions, 8, 57-64. Fujinaga, M., Read, R. J., S-ielecki, A., Ardelt, W., Laskowski~ M. & James, M. N. G. (1982). Proc. Nat. Acad. Sr U.S.A. 79, 4868-4872. Kalinichenko, P. (1976). Stud. Biophys. 58, 235-240. Kato, I., Schrode, J., Wilson, K. A. & Laskowski, M. Jr (1976). Protides of Biological Fluids-23. Colloquium (Peeters, H., ed.), pp. 235-255, Pergamon Press, New York. Laskowski, M. Jr & Kato, I. (1980). Annu. Rev. Biochem. 49, 593-626. McRorie, R. A. & Williams, W. L. (1974). Annu. Rev. Biochem. 43, 777-803.
640
P. ~TROP AND K. W[~THRICH
Meloun, B. & ~echov~, D. (1979). Collect. Czechoslov. Chem. Commun. 44, 2710-2720. Ogino, T., Croll, D. H., Kato, I. & Markley, J. L. (1982). Biochemistry, 21, 3452-3460. Papamokos, E., Weber, E., Bode, W., Huber, R., Empie, M. W., Kato, I. & Laskowski, M. (1982). J. Mol. Biol. 158, 515-537. Riehalu, R., Sehr, P., Wagner, G. & Wiithrieh. K. (1979). J. Mol. Biol. 130, 19-30. Schiessler, H., Fink, E. & Fritz, H. (1976a). Methods Enzymol. 45B, 847-859. Schiessler, H., Arnold, M., Ohlsson, K. & Fritz. H. (1976b). Hoppe-Seyler's Z. Physiol. Chem. 357, 1251-1260. ~trop, P., Wider, G. & Wiithrich, K. (1983). 166, 641-667. Tschesche, H. (1974). Angew. Chem. (Internat. Edit.), 13, 10-28. Tschesche, H., Kupfer, S. & Klauser, R. (1976). Protides of Biologiccd Fhtids-23. Colloqui~lm (Peeters, H., ed.), pp. 255-266, Pergamon Press, New York. Weber, E., Papamokos, E., Bode, W.. Huber, R.. Kato, I. & Laskowski, M. J r (1981). J. Mol. Biol. 149, 109-123. Wiithrieh, K. (1976). NMR in Biological Research: Peptides and Proteins, North-Holland Publishing Company, Amsterdam. Wiithrich. K., Wider, G., Wagner, G. & Braun, W. (1982). J. Mol. Biol. 155, 311-319.
Edited by J. ('. Kendrew
Note added in proof: We have just been informed that ill addition to tile changes described in the following ])aper (Strop el al., 1983) tile amino acid sequence of BUSI IIA published by Meloun & ~echov~ (1979) must be modified in the following positions: His20 ~ Glu20, Asp22 ~ Asn22. Gln24 -* His24 and Asp34 ~ Asn34 (B. Meloun, submitted to Atlas of Protein Seq~ence and Structure, vol. 6 (Dayhoff, M. O. et al., eds), Nat. Biomed. Res. Found., Georgetown Univ. Med. (!enter, Washington D.C., U.S.A., 1983). The corrected sequence is used in the present paper.