Gene, 80 (1989) 39-48 Elsevier GENE 03069
Cloning of the hiotin synthetase gene from Bacillus sphaericus and expression in Escherichia coli and Bacilli (Recombinant DNA; complementation;
plasmid vector; gene cluster; sequence comparison)
I. Ohsawa”, D. Speck b, T. Kisoua, K. Hayakawa *, M. Zinsius b, R. Gloeckler b, Y. Lemoine b and K. Kamogawaa a Biological Science Institute,R & D Center, Nippon Zeon Co., Ltd., Kawasaki-Ku, Kawasaki (Japan 210) andb Transgene S.A., II Rue de Malsheim, 67082 Strasbourg Ckdex (France) Tel. 88222490 Received by A.J. Podhajska: 14 September 1988 Revised: 22 November 1988 Accepted: 17 January 1989
Biotin synthetase (BS) catalyses the biotransformation of dethiobiotin (DTB) to biotin. Here we report the cloning, characterization and expression of the gene encoding B S of Bacillus sphaericus. A recombinant plasmid pSBO1, containing an 8.2-kb DNA fragment from B. sphaericus, was isolated by phenotypic complementation of an Escherichia coli bioB strain. Nucleotide sequence analysis of this fragment and N-terminal sequence determination of the recombinant protein product revealed that the bioB gene of B. sphaericus consists of a 996-bp open reading frame which is closely associated with at least one other gene. E. coli cells transformed with a bioB expression vector performed efficient bioconversion of DTB to biotin under defined culture conditions. Biotin production from transformed Bacillus subtilis and B. sphaericus recombinant strains was also demonstrated. Comparison of the amino acid sequences of BS from E. coli and B. sphaericus revealed extensive similarity.
Although the biological pathway for the conversion of pimelyl-CoA to DTB is clearly documented, the last step of biotin biosynthesis remains Correspondenceto: Dr. I. Ohsawa, Biological Science Institute, R&D Center,NipponZeon Co.,Ltd., 1-2-l Yako, Kawasaki-Ku, Kawasaki (Japan 210) Tel. 0442763744; Fax 0442763720. Abbreviations: aa, amino acid(s); ACM, actithiazic acid; Ap, ampicillin; bp, base pair(s); BS, biotin synthetase(s); CA, see MATERIALS AND METHODS, section c; cm, colony-forming unit(s); DM3, DM4, see MATERIALS AND METHODS, section b; DTB, dethiobiotin; GP, see MATERIALS AND
0378-l 119/89/$03 50 0
to be elucidated (Izumi et al., 1980). Two major unsolved problems are connected with this specific transformation. Both the precise nature of the sulfur donor and the mechanism of the sulfur introduction process which leads to the formation of two C-S METHODS, section b; IAA, 3-b-indoleacrylic acid; kb, kilobase(s) or 1000 bp; Km, kanamycin; nt, nucleotide(s); ORF, open reading frame; PAGE, polyacrylamide gel electrophoresis; PC, see MATERIALS AND METHODS, section e; PolIk, Klenow (large) fragment of E. coli DNA polymerase I; RBS, ribosome-binding site; SDS, sodium dodecyl sulfate; Tc, tetracycline; TVA, 5-(2-thienylkvaleric acid; wt, wild type; [ 1,designates plasmid-carrier state.
bonds, are unknown. It has been shown that functionalization of the DTB carbon(s) at position 2 and/or 5 either by desaturation or hydroxylation mechanisms is unlikely to occur (Frappier et al., 1979; 1982), and stereochemical analysis indicated that the conjuration of the carbon at position 2 of DTB is retained during the cyclization reaction. It has been concluded by analogy with the isopenicillin N synthesis that the formation of biotin could be linked to a carbon radical reaction (Parry, 1983). In E. co&, a single genetic locus (the bioB gene) is associated with this metabolic function (Rolfe and Eisenberg, 1968). The BS polypeptide is encoded by the first cistron of the right arm of a divergent operon, bioABFCD (Cleary and Campbell, 1972; Guha et al., 1971; Szybalski and Szybalski, 1982). The complete sequence of this gene has recently been reported, predicting the 38.7-kDa size for the corresponding protein (Hirono et al., 1986). In comparison with E. coli, B. sphae~~us IF03525 produces a greater amount of biotin and, furthermore, the immediate precursor of biotin, DTB, is secreted from this strain at even higher concentrations (Izumi et al., 1981). It has already been demonstrated that the levels of DTB and biotin could be enhanced by selecting ACM and TVA-resistant mutants of this bacterium (Yamada et al., 1983). The last step of biotin biosynthesis is thus interesting from various points of view. We undertook the cloning of the bioB gene from B. sphaericus with the aim of studying the BS enzymatic reaction after amplification of this gene in different bacteria.
bioB141 sacA321) was obtained from the Bacillus Genetic Stock Center, the Ohio State University, Columbus, OH. Plasmids pBR322 (Bolivar et al., 1977), pUC9 (Vieira and Messing, 1982) and pDR720 (Russell and Bennett, 1982) were used for cloning, subcloning and ~onst~ction of the expression vector for E. coli, respectively. Plasmid PUB 110 (Gryczan et al., 1978) was the expression vector for Bacilli.
(b) Transformations Tr~sfo~ation of B. subbed was achieved by the protoplast method (Chang and Cohen, 1979). B. sphaericus cells were transformed essentially according to the protocol initially described by McDonald and Burke (1984). Namely, lysozyme was replaced by N-acetyl muramidase SG (Seikagaku Kogyo, Co.) to make protoplasts of cells. The tr~sfo~~ts were then selected on DM4 regeneration medium containing 15Opg Km/ml. Medium DM4, in contrast to DM3, contains 0.33 M succinic acid disodium salt and glycerol instead of succinic acid monosodium salt and glucose, respectively. Finally, the selected transformants were transferred onto GP medium supplemented with 5 pg Km/ml. GP medium contains per liter: 20 g ~ycerol/30 g proteose peptoneJ5 g Casamino acids (vitamin-free Difco)/l g KzHP0,/0.5 gKC1/0.5 gMgS0,*7Hz0/ 0.01 g FeSO, - 7H,0/0.01 g MnSO, .4-6H,0/20 pg thiamine * HCl pH 7.0. (c) Selection of biuBcomplemented transformations E. coli bioB complements
MATERIALS AND METHODS
(a) Bacterial strains and plasmids The ACM and TVA-resistant mutant, T-178-367, of B. sphaeric~ IF03525 was obtained by the method of Yamada et al. (1983) and used for isolation of chromosomal DNA. B. sphaericus NCIB9370, E. coli DHl (Ham&an, 1983) and MC169 (Zehnbauer and Markovitz, 1980) were used as the recipient strains for recombinant plasmids. E. coli Cl62 (bioB his), a gift from Y. Izumi, Kyoto University, Kyoto (Japan), was used in the complementation tests. B. subtilis IA92 (argA2 aroG932
colonies were selected on CA agar supplemented with 50 pg Ap/rnl. CA agar contains 20 g glycerol/l0 g Casamino acids (Difco, vitamin-free)/2 g K,HPO,/l g KH,PO,/ 0.5 g MgSO, - 7H,0/0.01 g FeSO, - 7H,0/0.01 g MnSO, - 4-6H,O/O. 1 mg thiamine - HCl/ 15 g agarose in 1 liter of tap water pH 7.0. Without biotin, E. co& Cl62 is unable to grow on this medium. (d) Sequencing of DNA Sequencing was performed using the dideoxy chain-termination method of Sanger et al. (1977). Fragments of DNA ~ont~n~g the bioB gene were subcloned in both orientations into derivatives of
bacte~oph~e M13mp7 (Messing, 1983) and the sequence was entirely determined on both strands, by successive primers designed according to the sequence already determined.
M~nheim, PolIk, deoxy- and didzoxy-nt were obtained from Pharmacia and Amersham. D,L-DTB and biotin were from Sigma.
(e) Growth conditions and bioassay of biotin
RESULTSAND DISCUSSION E. cofi tr~sfo~~ts
were incubate at 37°C for one to three days in peptone-Casamino acids (PC) medium which contained 20 g glycerol/50 g proteose peptone/ g Casamino acids/l g K,HPO,/O.S g KCl/OS g MgSO, * 7H,0/0.01 g FeSO, * 7H,O/ 0.01 g MnSO, - 4-6H,O in 1 liter of tap water pH 7.0, supplemented with appropriate antibiotics. B. s~hae~c~ recombin~t strains were incubated at 37°C for two to three days in GP medium and B. subtilis were in GP medium without Casamino acids. For all strains, D,L-DTB (50-100 pg/ml) was added to the medium as biotin precursor. After incubation, centrifuged culture medium was applied to bioassay (paper disc-plate method) with Lactobaei~~~ ~~u~~~~ (Want and Skeggs, 1944). (f) Extraction of proteins for SDS-PAGE and subsequent amino acid sequencing
After cultivation of the E. coli or B. subtilis strains in appropriate medium, bacterial cells were collected by c~t~fugation, washed in 50 mM Tris * HCl pH 7.5 and then resuspended in the same buffer (i/lo culture volume). For B. subtilis extracts, lysozyme at 2 mg/ml was added, and the mixture incubated 15 min at 37°C; cells were then disrupted by sonitication and cellular debris removed by centrifugation at 15 000 rev./n&i for 30 min at 4°C in a microfuge (Sigma Chemical, Co.). Proteins from soluble and pellet fractions were then separated by SDS-PAGE according to Laemmli (1970). After staining, the gel corresponding to the pellet fraction was electroblotted on polybrene-coated glass-fiber sheets (Vandekerckhove et al., 1985) and samples were then analyzed by automated Edman degradation using an Applied Biosystem 470 gas-phase microsequencer. (g) Enzymes and chemicals
Restriction endonucleases and T4 DNA ligase were purchased from Takara Shuzo and Boehringer-
(a) Cloning of the B~cii~~s sphericus
B. sphuericus T-178-367 chromosomal DNA was extracted and partially digested with Mb01 before insertion into the BumHI site of pBR322. With this ligation mixture, E. cofi DH 1 was transformed to Ap resistance at a frequency of 104cfu/~g of DNA. Recombinant plasmid DNA was isolated from approx. 2000 independent Tc-sensitive clones, and introduced into E. coli Cl62 bioB, resulting in the recovery of two biotin prototrophic transformants on CA agar supplemented with 50 ,ug Ap/ml. One of these, pSBO1, contained an 8.2-kb DNA insert. To localize the bioB-coding region, pSBO1 was partially digested with EcoRI and self-ligated to generate pSB03, of which the HindIII fragments were subsequently subcloned into the Hind111 site of pUC9, giving pSB103 (Fig. 1). Phenotypic complementation of the biotin auxotrophy of E. coli Cl62 was observed upon transformation of these cells with pSB103. Further experiments (not shown) proved that the 1.5-kb ~buI-~i~dII1 fragment from the pSB103 insert still carried the bioB gene and was present in the B. sphaericus genomic DNA. (b) Nucleotide sequence of the Bacillus sphuericus T-178-367 bioB gene
Sequence analysis of the ~boI-~~~dIII fragment (Fig. 2) revealed an ORF extending from a GUG start codon (position 1) to an UAA stop codon (position 997). In Gram-positive bacteria, almost 12% of the initiation sites use GUG to initiate protein synthesis (Hager and Rabinowitz, 1985). This 996nt sequence has a coding capacity for a 332-aa protein of 37 kDa. A putative RBS with a partial similarity to the 3’ end of the B. sub& 16s rRNA (McLaughlin et al., 1981) is located at 3 nt upstream from the GUG start codon. N-terminal sequence analysis of BS recombinant proteins synthesized in E. coli and B. sub&s confirmed this
sequence at the 3’ end of the DNA is characteristic of a transcription terminator. No dflerence was found in the sequence of bioB gene from the wt B. sphaericus IF03525 This fact proved that the elevated level of biotin and the vitamers associated with the T-178-367 strain is not due to a mutation in the bioB structural gene. (c) Construction of an Escherichia coli bioB expression vector and evaluation of biotin production in transformed cells
Fig. 1. Structures of the plasmid pSBO1 and its derivatives. The hatched segments are the DNA fragments derived from B. ~~~~e~~ and the lightly shaded regions correspond to the pl~mid pun. Plasmid pSBOl was partially digested withEcoR1 and self-ligated to produce the deleted piasmid pSBO3. The Hind111 fragment of pSB03 was then subcloned into the Hind111 site ofpUC?J to construct pSB103 which complemented the bioB defect when introduced into E. coli Cl 62. The detailed restriction map of the 1.5-kb MM-HindIII fragment of pSB103 is also shown. Restriction sites are: B, BarnHI; E, EcoRI; H, HindIII; P, &I; s, SalI.
site of initiation to be functional in these bacteria (see sections c and d below). A second ORF was identified upstream from this sequence with a minimal coding capacity of 93 aa. In this case, the UAG stop codon partially overlaps with the GUG start codon of the longer ORF, a typical feature of bacterial operons (Kroger and Hobom, 1982; Norrnark etal., 1983). As expected, no classical promoter sequences (Moran et al., 1982) were found upstream from the GUG start codon, strongly suggesting that, in B. sphue~c~, BS is translated from a polycis~onic mRNA. The presence of a 17-bp inverted repeat
To regulate the production of BS, the bioE gene was placed under the control of the ttp promoter. The advantage of this system is that it can be induced in any E. coligenetic background, provided the strain is trpR + . The 2.1-kb Mae1 fragment of pSB103 was treated with Sl nuclease before ligation with SmaIdigested pDR720. The resulting plasmid was designated pSB301 (Fig. 3). The E. co& MC169[pSB301] strain was cultured in PC medium at 37’ C in the presence of the inducer, IAA. SDS-PAGE analysis of total protein showed the appearance of the expected 37-kDa band (Fig. 4). The culture conditions and the concentration and time of addition of IAA were then explored to reach the optimal bioconversion of DTB to biotin. A sharp peak was obtained reflecting the biotin level at diflerent IAA concentrations (Fig. 5A). This peak did not correlate with the level of BS as measured by SDS-PAGE, but more closely paralleled the cell density. After the incubation for 48 h, the 100 fig D,L-DTB per ml initially present were converted to 16 pg excreted biotin per ml. The quantity of secreted biotin very closely followed the increase of the cellular biomass (Fig. 5B). The expression of the B. sphaericus bioB gene in E. coli JM 103 was also driven from the coliphage T.5 promoter, pNz6 (Gentz and Bujard, 1985), under the control of the lac operator (data not shown). After SDS-PAGE of total cellular proteins, the 37-kDa band was electroblotted and the N-terminal sequence of BS was determined by automated Edman degradation (see MATERIALS AND METHODS, section f). The results indicated that the GUG start codon was functional in E. coli and that the recombinant BS still contained the N-terminal Met residue, suggesting an inefficient ~inopeptidase cleavage on this protein.
of the bioB gene and the deduced aa sequence. The putative RBS is doubly underlined. There is a second 281-nt ORF upstream from the GUG start codon. Facing arrows show the palindromic structures which may function as a transcriptional terminator. The nt are numbered starting from the GUG start codon of BS. The asterisks indicate the stop codons.
Fig.2. Nucleotide sequence
CGT~GCA~A~ACG~T~ GT~G~T~TATGATTATG~TGCT~GTGGC ArgLysHisTyrTyrGlyLysLysValLysLeuAsnMetIleMetAsnAlaLysSerGly
PheArgSerAlaArgAlaIleLysLeuValGlnIleGluLysGluAsnVa~~***** 6 TTCCGTTCCGCTAGAGCTATAAAACTTG'PGCAAATTGAAAAGGAGAATGTTTAGTGAAT * METAsn RBS
Fig. 3. Construction of bid hyperexpression vector. The 2. I-kb Mae1 fragment from pSB103 (see Fig. 1) was treated with Sl n&ease and ligated to SmaI-digested pDR720. Restriction sites are: H, HindHI; M, MoeI; Sm, &WI. The black arrow and the hatched box represent the tryptophan operator-promoter region (trp0P) and the bioB gene, respectively.
(d) Expression of the bioB gene and biotin production in bacilli In pTG498 (Fig. 6), the bioB gene of B. sphaericus was inserted into the BamHI site, downstream from
the ‘HpaII promoter’ located around the HpaII site at 0.32 kb on PUB 110 (Zyprian and Matzura, 1986). In the same construction, the putative RBS from B. sp~ae~cus was replaced by a 21-bp synthetic RBS strictly complementary to the 16s rRNA of B. subtilis, giving pTG494 plasmid (Fig. 6). SDSPAGE of proteins extracted from B. subtilis lA92[pTG494], revealed the appearance of a new 37-kDa band. The expressed BS was represented more in the pellet fraction than in the soluble fraction of the crude extract (Fig. 7). N-terminal sequence analysis of BS (see MATERIALS AND METHODS, section f), indicated that the GUG start codon
Fig. 4. Analysis by SDS-PAGE of whole celI extracts from E. coli MC169 harboring the control vector pDR720 (lanes 1 and 2) and the bid expression vector pSB301 (lanes 3 and 4). Bacterial cultures were grown in the absence (lanes 1 and 3) or in the presence (lanes 2 and 4) of 10 /.6gIAA/ml. Samples were applied to the 1.5 ye (w/v) polyacrylamide gel. After 2 h electrophoresis at 40 mA, the gel was stained with 0.25% Coomassie blue in 9% acetic acid and 45% methanol buffer. Numbers on the left margin are M, standards. The arrow indicates the position of BS.
proved to be functional in B. subtilis. Similar results were obtained for BS produced in B. subtilis lA92[pTG498], strongly suggesting that the GUG corresponds to the natural start codon of BS in B, sphaericus.
As shown in Table I, a level of 15 pg biotin per ml was obtained in the culture supernatant of strain lA92[pTG494]. This level dropped to 2 pg per ml for the lA92[pTG498] strain In this case, the quantities of secreted biotin followed the level of expression of BS, as measured by SDS-PAGE (data not shown). Because of the very close similarity between the structures ofpTG494 and pTG498, the difference in the expression level of BS in the B. subtilis strain seems to be related to improved translation efficiency from an optimal RBS. In i3. [email protected]
~c~, a hun~edfold increase in the efficiency of the biotin synthesis from DTB was obtained (Table I) by amplifying the bioB gene in IF03525 strain. This result confirmed that the cellular content in BS was a major limiting step in the bioconversion.
TABLE I Amount of biotin excreted by recombinant strains Strains a
Biotin excretedc @g/ml)
B. subtilis IA92
pUBll0 pTG498 pTG494
0.01 2 15
B. sphaericus IF03525
B. sphaericus NCIB9370
E. coli MC169
a See MATERIALS AND METHODS, section a. b Plasmids PUB 110 and pDR720 are described in MATERIALS AND METHODS, section a. pTG494, pTG498 and pSB301 are described in RESULTS AND DISCUSSION, sections c and d. Plasmid pBHB5022 consists ofthe pUBl10 replicon bearing the bioB gene fused to the RBS ofthe B. licheniformis a-amylase gene. ’ For B. subfiZk and B. sphaericur strains, production of biotin from D,L-DTB (So-100 &ml) was monitored after 72 h incubation at 37°C in GP medium supplemented with 5 pg Km/ml. E. coli strains were cultivated for 48 h at 37°C in PC medium containing D,L-DTB (100 &ml). IAA was added at a final concentration of 10 pg/ml when the A was 0.5.
(e) Homology between Bacillus Escherichia coli biotin syothetase 0.11 0
Fig. 5. Induction of biotin biosynthesis. (Panel A) Effect of IAA concentration on the quantity of biotin secreted and on the total synthesis of BS. E. coli MC169[pSB301] was cultivated at 37°C in PC medium with 100 ng D,L-DTB/ml and 50 pg Ap/ml. At A 0.5, IAA was added to the medium and cultivation was continued for 30 h. Three hours after addition of IAA, cells were collected for protein analysis. Boiled cell extracts were applied on a 15% (w/v) polyacrylamide gel. After Coomassie blue staining, the gel was scanned with a Shimadzu CS-930 TLC apparatus. At the top of the figure, the absorbance of the cultures is presented (black dots), while at the bottom the amount of BS as a y0 of total proteins is indicated (blackened circles). The accumulated biotin is represented by open circles. (Panel B)Time course of the accumulation of biotin in the medium. Growth conditions as in panel A. 1Opg IAA/ml was added at A 0.5. The absorbance (black dots) and the accumulated biotin (open circles) are plotted.
The degree of sequence similarity between BS of B. sphaericus and E. coli was analyzed using a computer software from Intelligenetics (Mountain View, CA). The best alignment is shown in Fig. 8. The overall sequence homology is 32.5%, increasing to 55% when conservative replacements are considered. The position of Cys residues is wellconserved in the N-terminal and central parts of both polypeptides. Within these regions, two distinct sequences sharing more than 50% homology were identified. (f) Conclusions
(1) The efficient bioconversion of DTB into biotin has been demonstrated in E. coli and Bacillus species when the expression of BS from B. sphaericus was
Fig. 6. Schematic representation of the B. subtilisexpression vectors pTG494 and pTG498. The bioB gene, fused to its initial or optimal RBS was inserted into the EarnHI site of PUB 110, downstream from the ‘HpnII promoter’. The sequence of the 16s rRNA is shown to illustrate the degree of complementarity between the two RBS signals.
Fig. 7. SDS-PAGE of cellular protein from B. subtilk lA92[pTG494]. Protein was extracted as described in MATERIALS AND METHODS, section f. Samples were subjected to electrophoresis on a 12% (w/v) polyacrylamide gel for 5 h at 25 mA. The gel was then stained with O.I% Coomassie blue in 7.5% acetic acid and 5% methanol buffer. (A) Pellet fractions. (9) Soluble fractions. Lanes: 1, cell extract from lA92[pUBllO]; 2, cell extract from lA92[pTG494]; M, M, markers. The arrow indicates the position of BS.
amplified. N~erous parameters will influence the final yield of this bio~~sformation, for example: DTB cell permeation, catalytic activity of a recombinant protein, cellular concentration of the sulfur donor and the physiological state of the cells. (2) Results obtained in E. coli showed that, under very specific conditions, it was possible to detect extracellular accusation of biotin tightly coupled to cell growth. The decrease in biotin synthesis at higher inducer doses might be linked to protein precipitation when a critical concentration of BS is reached inside the cells. Another factor of importance could be the physiological state of the bacteria, which might diminish their ability to perform the catalytic reaction, possibly in linkage with a strong station in the sulfur donor substrate. (3) The synthesis and catalytic activity of the recombinant BS in B. subtih have been clearly improved by the substitution of the original RBS with an optimal one. Similar examples have been described (Band and Henner, 1984). (4) By sequencing of DNA, it has been demonstrated that the bioB gene of B. sphaericus is linked to at least one other gene. The leftward flanking region was recently cloned and proved to encode other bio genes organized in a typical operon structure (R. Gloeckler, I. Ohsawa, D. Speck, C. Ledoux, S. Bernard, M. Zinsius, D. Villeval, T. Kisou, K. Kamogawa and Y. Lemoine, results to be published elsewhere). In contrast to E. co&, the bioB gene of B. sphaericus corresponds to the last cistron distal to the promoter region. The distal position of bioB as
47 IO BNWLQLADRV
50 AIRKHYYGKK II...
MARRPRWTL SQVTELFEKP 19 9
VKLRHIMN 1. . .
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VRRQHFDPRQ VQVSTLLS 49 39 100 EILAGAKRAF ..[ .,..I QVLESARKAK
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* I LEAERLMEVE 79
I..I *I* **I* AAWKNPHERD MPYLEQMVQG 119 99 109
*GLLKERQ AQQLK~G~D II I I I II I *II*1
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Vertical bars and dots between Fig. 8. Alignment of the aa sequence of gene products (refer to Fig. 2). (a) B. .Fphaericm; (b)E.CC&bioB. the aligned protein sequences indicate identical and conserved aa, respectively. Dashes indicate gaps introduced to maximize simihrrity between both sequences. Cys residues are shaded and the boxed regions indicate stretches of more than 50% homology. The aa are numbered from the first Met residue.
well as the possibility of infrequent translational initiation, might explain the low level of BS and consequent accumulation of DTB observed in B. s~~~e~c~ (Izumi et al., 1981). Experiments on amplification of this gene in this bacterium totally confirmed this hypothesis. (5) The high level of B S produced in recombinant strains may permit the development of an in vitro system to study the catalytic mechanism. The ability to perform the synthetase reaction with partially or
completely purified components would allow further characterization of the sulfur donor.
We thank Dr. Y. Izumi for providing E. coli C162. We acknowledge the help of D. Villeval, D. Carvallo, D. Roeckim and Y. Cordier in DNA sequencing,
protein N-terminal determination and oligodeoxyribonucleotide synthesis, respectively. We are grateful to Drs. E. Chambon and N. Poujol for their expert secretarial assistance and to Dr. M. Courtney for critical reading of the manuscript. We thank Dr. J.-P. Lecocq for helpful discussions and Dr. A. Yosioka for his interest in this work.
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