1-Aminocyclopropane-1-carboxylate (ACC) deaminases from Methylobacterium radiotolerans and Methylobacterium nodulans with higher specificity for ACC

Authors

  • Dmitry N. Fedorov,

    1. G.K. Skryabin Institute of Biochemistry and Physiology of Microorganisms RAS, Pushchino, Moscow region, Russia
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  • Galina A. Ekimova,

    1. G.K. Skryabin Institute of Biochemistry and Physiology of Microorganisms RAS, Pushchino, Moscow region, Russia
    2. Pushchino State Institute of Natural Sciences, Pushchino, Moscow region, Russia
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  • Nina V. Doronina,

    1. G.K. Skryabin Institute of Biochemistry and Physiology of Microorganisms RAS, Pushchino, Moscow region, Russia
    2. Pushchino State Institute of Natural Sciences, Pushchino, Moscow region, Russia
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  • Yuri A. Trotsenko

    Corresponding author
    1. Pushchino State Institute of Natural Sciences, Pushchino, Moscow region, Russia
    • G.K. Skryabin Institute of Biochemistry and Physiology of Microorganisms RAS, Pushchino, Moscow region, Russia
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Correspondence: Yuri A. Trotsenko, IBPM RAS, Prospekt Nauki, 5, Pushchino, Moscow region, Russia, 142290. Tel.: +7 495 9257448; fax: + 7 495 9563370; e-mail: trotsenko@ibpm.pushchino.ru

Abstract

The 1-aminocyclopropane-1-carboxylate (ACC) deaminases (EC 3.4.99.7), the key enzymes of degradation of the precursor of the phytohormone ethylene, have not been well studied despite their great importance for plant–bacterial interactions. Using blast, the open reading frames encoding ACC deaminases were found in the genomes of epiphytic methylotroph Methylobacterium radiotolerans JCM2831 and nodule-forming endosymbiont Methylobacterium nodulans ORS2060. These genes were named acdS and cloned; recombinant proteins were expressed and purified from Escherichia coli. The enzyme from M. nodulans displayed the highest substrate specificity among all of the characterized ACC deaminases (Km 0.80 ± 0.04 mM), whereas the enzyme from M. radiotolerans had Km 1.8 ± 0.3 mM. The kcat values were 111.8 ± 0.2 and 65.8 ± 2.8 min−1 for the enzymes of M. nodulans and M. radiotolerans, respectively. Both enzymes are homotetramers with a molecular mass of 144 kDa, as was demonstrated by size exclusion chromatography and native PAGE. The purified enzymes displayed the maximum activity at 45–50 °C and pH 8.0. Thus, the priority data have been obtained, extending the knowledge of biochemical properties of bacterial ACC deaminases.

Introduction

1-Aminocyclopropane-1-carboxylic acid (ACC) is an intermediate of the biosynthesis of ethylene, one of the basic plant hormones regulating many important processes such as senescence and fruit ripening (Adams & Yang, 1979). In plant tissues, ACC is formed from S-adenosylmethionine in the ACC synthase (EC 4.4.1.14) reaction and decomposed to ethylene, CO2 and HCN with the involvement of ACC oxidase (EC 1.14.17.4; Dong et al., 1992). On the other hand, a different enzyme of ACC degradation has been found in plant tissues and diverse microorganisms including different strains of Pseudomonas, rhizobacterium Enterobacter cloacae, and the yeast Hansenula (Cyberlindera) saturnus. This pyridoxal 5-phosphate-dependent enzyme, ACC deaminase, catalyzes ACC decomposition to 2-ketobutyrate and ammonium (Honma & Shimomura, 1978; Minami et al., 1998; Hontzeas et al., 2004; McDonnel et al., 2009). The study of bacterial ACC deaminases is of great importance because the inoculation of plants with bacteria possessing ACC deaminases always results in plant growth stimulation and enhanced resistance to different types of stresses including draught, excessive water, salt and heavy metals, and phytopathogens, due to the reduced level of ethylene production (Glick et al., 2007).

Pink-pigmented methylotrophs from the genus Methylobacterium are common inhabitants of most plant species. Methylotrophs utilize methanol produced by plants and also stimulate plant growth and development due to biosynthesis of phytohormones (auxins, cytokinins) and nitrogen fixation (Ivanova et al., 2000, 2001; Sy et al., 2001; Fedorov et al., 2011). Some strains of Methylobacterium fujisawaense and Methylobacterium ozyzae were also shown to possess ACC deaminase activities, and the respective genes were sequenced (Madhaiyan et al., 2004). However, at the moment only two enzymes from Pseudomonas strains (Hontzeas et al., 2004) and yeasts (Minami et al., 1998) have been properly characterized and there is no information at all on the biochemical properties of ACC deaminases from methylotrophs. Representatives of the genus Methylobacterium display two different types of symbiosis with plants: epiphytic symbiosis and nodule-forming symbiosis (the endophyte Methylobacterium nodulans). ACC deaminases of the bacteria occupying the same ecological niches as methylotrophs have not been studied. Hence, the role of ACC deaminases in the plant-Methylobacterium relationship is unclear and requires comprehensive study. Herein, we report, for the first time, the cloning, expression and characterization of 1-aminocyclopropane-1-carboxylate deaminases from the epiphytic symbiont Methylobacterium radiotolerans JCM 2831 and the nodule-forming endosymbiont M. nodulans ORS 2060.

Materials and methods

Bacterial strains, vectors and cultivation

Bacterial strains and plasmids are presented in Table 1. Methylobacterium radiotolerans JCM2831 and M. nodulans ORS2060 were grown in a minimal K medium with 0.5% methanol (Ivanova et al., 2001) at 28 °C on a rotary shaker (180 r.p.m.). The Escherichia coli Rosetta (DE3) strain listed in Table 1 was cultured in a Luria–Bertani (LB) medium with the appropriate antibiotics: 100 μg mL−1 ampicillin and 50 μg mL−1 chloramphenicol (Sambrook & Russell, 2001).

Table 1. Bacterial strains and plasmids
Strain or plasmidCharacteristics, genotypeReference or source
Methylobacterium radiotolerans Wild type strainJCM 2831 = VKM B-2067 = NCIMB 9133 = ATCC 14718
Methylobacterium nodulans Wild type strainORS 2060 = CNCMI 2342 = LMG 219667
Escherichia coli
Rosetta (DE3)F dcm ompT hsdSB(rB− mB−) gal λ(DE3) pRARE (CmR)Novagen
Plasmids
pHUEVector for expression of authentic proteins, AprCatanzariti et al. (2004)
p7A-37pHUE containing acdS gene from M. radiotoleransThis study
p7A-38pHUE containing acdS gene from M. nodulansThis study

General techniques

The isolation of chromosomal and plasmid DNA, cloning procedures, preparation and transformation of E. coli competent cells using calcium chloride were carried out according to the standard procedures (Sambrook & Russell, 2001). The PCR mixture contained 30 μL 1 × PCR buffer, 150 μM (each) deoxynucleotide triphosphates, 200 nM of the appropriate primers, 100 ng of genomic DNA, 3% (v/v) dimethylsulfoxide (Sigma) and 2 U Pfu-DNA-polymerase (Fermentas). The PCR conditions for all combinations of the primers were as follows: 3 min at 96 °C, followed by 30 cycles of 20 s at 94 °C, 20 s at 60 °C, and 4 min at 72 °C and a final extension of 5 min at 72 °C. All amplicons were gel-purified with a Wizard SV Gel and PCR Clean-up System (Promega).

Phylogenetic analysis

For identification of putative acdS, a blast search was performed in the Methylobacterium proteins with the amino acid sequence of Pseudomonas putida UW4 ACC deaminase (Q5PWZ8). Twenty-three amino acid sequences were selected for multiple sequence alignment with clustalw (Thompson et al., 1994). A phylogenetic tree based on the multiple sequence alignment was constructed using the UPGMA (unweighted-pair group method with average linkages) model and mega software (Tamura et al., 2007), and bootstrap values were used for reliability testing (1000 replicates).

Cloning of the acdS genes in the expression vector

The open reading frame (ORF) of the acdS gene (NCBI locus tag: Mrad2831_1521) encoding ACC deaminase was amplified by PCR using the JCM2831 strain genomic DNA as a template (chromosome sequence GenBank accession number: CP001001) and the following primers: forward 5′-ATCTCCGCGGTGGTATGCTGGACAAATTCGAGC-3′ and reverse 5′-ATCAAGCTTCAGCCGTTGCGGAACGTGTAGC-3′, containing SacII and HindIII sites, respectively. The ORF of the acdS (NCBI locus tag: Mnod_5479) gene from M. nodulans genomic DNA (chromosome sequence GenBank accession number: CP001349) was amplified in the same manner using forward primer 5′- AAGGATCCGTGCTGGAGAAATTCGAACG-3′ and reverse primer 5′- AACAAGCTTCAGCCGTTGCGGAAGGTGTAG-3′, containing the BamHI and HindIII sites, respectively. The resultant 1.2-kb DNA fragments were digested with SacII and HindIII for strain JCM2831 and with BamHI and HindIII for strain ORS2060 and cloned in the pHUE vector cleaved at corresponding sites, yielding plasmids p7A-37 and p7A-38, respectively (Table 1).

Purification of recombinant ACC deaminases

For overproduction of AcdS proteins fused with the N-terminal ubiquitin and hexahistidine affinity tag, the cells of E. coli Rosetta (DE3, p7A-37 or p7A-38) were grown at 28 °C until the culture reached an optical density (OD) at 600 nm (OD600) 0.5–0.6 in 2 L of an LB medium containing ampicillin (100 μg mL−1) and chloramphenicol (50 μg mL−1). Protein synthesis was induced by the addition of 0.2 mM isopropyl-1-thio-β-d-galactopyranoside (IPTG), and the growth was continued overnight at 28 °C. The His6-Ub-AcdS proteins from E. coli cells were purified according to the Qiagen protocols with minor changes (Henco, 1992). The cells were precipitated by centrifugation at 7000 g for 15 min at 4 °C, washed in 20 mM Tris–HCl (pH, 8.0) containing 0.5 M NaCl and 10 mM imidazole and then resuspended and sonicated in 30 mL of the same buffer with the addition of lysozyme (10 mg mL−1). The cell lysate was centrifuged at 10 000 g for 20 min at 4 °C, and the supernatant was tested for AcdS-activity. Then the supernatant was applied onto a column with 1 mL of Ni2+-nitrilotriacetate agarose (Qiagen). After intensive washing with 20 mM Tris–HCl (pH 8.0) containing 0.5 M NaCl and 60 mM imidazole, the bound His6-Ub-AcdS was eluted with 20 mM Tris–HCl (pH 8.0) containing 0.5 M NaCl and 200 mM imidazole.

The protein spectra of the collected fractions were analyzed by SDS-PAGE (Laemmli, 1970). The fractions containing His6-Ub-AcdS were combined and Usp2-cc protease was added according to the recommendations of Catanzariti et al. (2004). The preparations were dialyzed overnight against 50 mM Tris–HCl (pH 8.0) and enzymes were purified using a column with Ni2+-NTA agarose equilibrated with the same buffer (Catanzariti et al., 2004). Protein concentrations were determined by direct optical measurement (ε280 29780 M−1 cm−1 for M. nodulans enzyme and 32340 M−1 cm−1 for M. radiotolerans enzyme), calculated using the Peptide Property Calculator (http://www.basic.northwestern.edu/biotools/proteincalc.html) or by the Lowry method using bovine serum albumin (BSA) as a standard (Lowry et al., 1951).

Enzyme assays

The 1-aminocyclopropane-1-carboxylate deaminase activity was measured using different assays.

Measurement of the enzyme activity by 2-ketobutyrate formation

The enzyme activity was monitored by spectrophotometric measurement of NADH oxidation in the coupled reaction with rabbit lactate dehydrogenase (Sigma; Hontzeas et al., 2004). The reaction was performed at 30 °C in 1 mL of 50 mM Tris–HCl (pH 8.0), 0.3 mM NADH, 5 U rabbit muscle lactate dehydrogenase, 0.1–10 mM 1-aminocyclopropane-1-carboxylate, and 100 nM of purified AcdS. The reaction was started by adding the substrate. NADH oxidation was performed at 340 nm using the molar absorption coefficient of 6220 M−1 cm−1. The plot of the reaction rate vs. the substrate concentration was fitted using the Michaelis–Menten equation in sigmaplot 10.0 (Systat Software).

Colorimetric measurement

The reaction was performed at 30 °C in 0.5 mL of 50 mM Tris–HCl (pH 8.0), 0.02 mM pyridoxal phosphate, 20 mM 1-aminocyclopropane-1-carboxylate, and 100 μg purified AcdS (Honma & Shimomura, 1978). The reaction was started by adding the substrate, followed by incubation for 15 min. The reaction was stopped by adding 1 mL of 0.56 M HCl, followed by centrifugation for 5 min at 16 000 g. A 0.4-mL aliquot of 0.56 M HCl and 150 μL of 0.2% 2,4-dinitrophenylhydrazine in 2 M HCl were mixed with 0.5 mL of the supernatant, and the mixture incubated for 30 min at 30 °C. The reaction mixture was neutralized by adding 1 mL of 2 M NaOH, and optical density at 540 nm was measured. The standard 2-ketobutyrate solutions were used for calibration.

Measurement of NH3 formation

The enzyme activity was monitored spectrophotometrically through the measurement of NADH oxidation in the coupled reaction with glutamate dehydrogenase (Serva). The reaction was performed at 30 °C in 1 mL of 50 mM Tris–HCl (pH 8.0), 0.3 mM NADH, 5 U glutamate dehydrogenase, 1 mM 2-ketoglutarate, 1 mM ACC, and 100 nM purified AcdS. The reaction was performed as described for 2-ketobutyrate formation.

Determination of molecular masses of the enzymes

The molecular masses of the holoenzymes were estimated by size exclusion chromatography on a Sephacryl S-200 column (1.5 × 60 cm; Pharmacia) equilibrated with 20 mM Tris–HCl, pH 7.5, and 150 mM KCl (flow rate 0.2 mL min−1). Ferritin (450 kDa), catalase (240 kDa), γ-globulin (158 kDa), BSA (68 kDa), and ovalbumin (45 kDa) were used as molecular mass standards. Electrophoresis of the purified AcdS and crude protein extracts was carried out in 4–30% gradient polyacrylamide gels according to the recommendations of the Pharmacia. High molecular weight calibration kit proteins (Pharmacia) were used as standards. For ACC deaminase activity staining, the gels were incubated overnight at 37 °C in the reaction buffer containing 50 mM potassium phosphate (pH 8.0), 2 M ACC, 0.2 mM pyridoxal phosphate (PLP), 0.05 mg mL−1 phenazine methosulfate and 0.1 mg mL−1 nitroblue tetrazolium.

Results and discussion

Although some of the Methylobacterium strains are known to possess the ACC deaminase activity, not a single methylobacterial enzyme had been characterized and no acdS genes have been searched for in the published genomes of different methylotrophs. The search for ACC deaminase genes in the GenBank database using blast showed the presence of ORFs encoding the homologs of ACC deaminases from P. putida in the genomes of M. radiotolerans JCM2831, M. nodulans ORS2060, Methylobacterium sp. 4–46, and Methylibium petroleiphilum. The analysis of amino acid residues in the active centers of predicted AcdS proteins according to Todorovic & Glick (2008) showed that methylotrophic proteins possessed the same glutamic acid and leucine residues, corresponding to Glu295 and Leu322 in the molecule of AcdS from P. putida UW4 (Fig. 1). The rather high level of amino acid identity (up to 70%) between predicted proteins and the P. putida protein also demonstrates that methylotrophic enzymes may be ACC deaminases.

Figure 1.

Multiple alignment of active center amino acid sequences of the characterized and putative ACC deaminases and d-cysteine desulfhydrases. The asterisk indicates serine 358 of the tomato d-cysteine desulfhydrase and glutamate 295 of the Pseudomonas putida ACC deaminase. The arrow indicates the position of threonine 386 of the tomato d-cysteine desulfhydrase and leucine 322 of the P. putida ACC deaminase. Solanum, tomato Solanum lycopersicum (ACC95419); Arabidop, Arabidopsis thaliana (NP_175275); Escher, Escherichia coli K-12 (AP_002534); AM1, Methylobacterium extorquens AM1 (YP_002963420); CM4, M. extorquens CM4 (YP_002421404); DM4, M. extorquens DM4 (YP_003068648); PA1, M. extorquens PA1 (YP_001639823); BJ001, Methylobacterium populi BJ001 (YP_001925011); Pseudom, P. putida UW4 (Q5PWZ8); JCM2831, Methylobacterium radiotolerans JCM2831 (YP_001754199); 4–46, Methylobacterium sp. 4–46 (YP_001767276); Mnod, Methylobacterium nodulans ORS2060 (YP_002500626); Methylib, Methylibium petroleiphilum PM1 (YP_001022786).

The blast analysis also revealed the distribution of the acdS and dcyD genes encoding d-cysteine desulfhydrase (the protein closely related to ACC deaminases) in the genus Methylobacterium. For example, Methylobacterium extorquens and Methylobacterium populi strains possess dcyD instead of acdS genes. The active center residues of d-cysteine desulfhydrase were analyzed to avoid the ambiguity concerning the similarity between proteins AcdS and DcyD. As shown in Fig. 1, methylobacterial DcyD contains the same Ser358 and Tre386 as the protein of d-cysteine desulfhydrase from tomato (Todorovic & Glick, 2008).

Despite some evidence of the acdS horizontal transfer between bacteria (Hontzeas et al., 2005), the general view of the phylogenetic tree of ACC deaminases correlates well with the taxonomic positions of bacteria (Fig. 2). Thus, methylobacterial proteins have their closest relatives in the genomes of diverse Alphaproteobacteria, which form a separate cluster on the tree, while another cluster consists of the sequences of proteins from Betaproteobacteria including the facultative methylotroph M. petroleiphilum, Gammaproteobacteria, as well as the only well characterized bacterial ACC deaminase from P. putida (Fig. 2).

Figure 2.

Phylogenetic tree constructed from the amino acid sequences of various putative and characterized bacterial 1-aminocyclopropane-1-carboxylate deaminases. The characterized enzymes are in bold and the amino acid accession numbers are in brackets.

The two acdS genes from M. radiotolerans and M. nodulans were chosen for the cloning and expression in E. coli because they are phylogenetically distinct from the Pseudomonas enzyme. The genes were cloned in the pHUE vector, and the recombinant proteins were purified using the conventional IMAC. Further proteolysis allowed us to obtain proteins without any affinity tags. The purified AcdS proteins were visualized by denaturing SDS-PAGE and Coomassie staining (Fig. 3). The molecular masses of protein monomers were around 36 kDa, in agreement with the theoretical calculation. Native PAGE revealed that active AcdS proteins had molecular masses of about 117 kDa (Supporting Information, Fig. S1); however, the size exclusion chromatography showed the molecular mass of holoenzymes to be 144 kDa, that is corresponding to a homotetrameric structure. These findings are in agreement with the data obtained for the enzyme from P. putida: its molecular mass was determined as corresponding to a trimer, but the crystals of the protein contained tetrameric molecules (Karthikeyan et al., 2004).

Figure 3.

SDS-PAGE of the purified 1-aminocyclopropane-1-carboxylate deaminase of Methylobacterium radiotolerans JCM2831 (a) and Methylobacterium nodulans ORS2060 (b). Lane 1, purified AcdS; lane 2, the reaction mixture of AcdS and protease Usp2-cc; lane 3, the processed purified AcdS; lane 4, low molecular mass marker proteins.

The specific activities of purified AcdS enzymes were 0.44 and 0.74 μmol min−1 mg−1 for M. radiotolerans and M. nodulans, respectively, in the reaction with ACC (in 50 mM Tris–HCl, pH 7.4, at 30 °C) and were absent with d- or l-cysteine (even at high protein concentrations of 1 mg mL−1). Thus, it has been shown that the acdS genes in Methylobacterium strains are actually ACC deaminases. NH3 and 2-ketobutyrate were formed from ACC in stoichiometric quantities due to the equal reaction rates as measured by different methods. The enzyme had an absorbance peak at 420 nm and was strongly inhibited by 2 mM of phenylhydrazine, hydroxylamine and semicarbazide. This means that methylobacterial enzymes are PLP-dependent, like all previously described homologs (Honma & Shimomura, 1978; Minami et al., 1998; Hontzeas et al., 2004).

In addition, the pH optimum of the enzymes was 8.0 as measured in Tris–HCl buffer, which is the common feature of ACC deaminases. Although the temperature optimum of the P. putida enzyme was 37 °C, the optima of methylobacterial enzymes were shifted to the higher temperatures: 45–50 °C (Table 2).

Table 2. Comparison of the characterized 1-aminocyclopropane-1-carboxylate deaminases
CharacteristicsMethylobacterium nodulans ORS2060Methylobacterium radiotolerans JCM2831Pseudomonas putida UW4 Cyberlindera saturnus
Km, mM0.80 ± 0.041.8 ± 0.33.4 ± 0.22.6
kcat, min−1111.8 ± 0.265.8 ± 2.8146 ± 5 
kcat/Km139.836.543.9 
pH optimum8.08.08.09.0
Temperature optimum, °C504537 
Oligomeric structure, molecular mass kDaHomotetramer, 144Homotetramer, 144Homotetramer, 168Monomer, 69
CofactorPyridoxal phosphatePyridoxal phosphatePyridoxal phosphatePyridoxal phosphate
ReferenceThis workThis workHontzeas et al. (2004)Honma & Shimomura (1978)

The kinetic characteristics of enzymatic conversion of ACC were then studied in the coupled assay with lactate dehydrogenase. All possible controls were carried out, including reaction without ACC deaminase, reaction with boiled ACC deaminase, reaction without substrate or lactate dehydrogenase; in all cases activity was not detected and was restored only by addition of the lacking component. The Michaelis–Menten kinetics of the dependence of both enzyme activities on ACC concentration is shown in Fig. 4. The Km value for ACC deaminase from M. radiotolerans was 1.8 mM, which is quite similar to the values calculated for ACC deaminases from Pseudomonas and other microorganisms (1.5–17.4 mM), despite being one of the lowest values reported (Table 2). Intriguingly, the Km value for the enzyme from M. nodulans was twice a low as the lowest value reported for other enzymes, indicating that this enzyme possessed the highest substrate specificity of all characterized ACC deaminases. Due to their low Km values, both methylobacterial enzymes displayed high catalytic efficiency (Table 2).

Figure 4.

Dependence of the enzyme activity on ACC concentration for 1-aminocyclopropane-1-carboxylate deaminase from Methylobacterium nodulans (1) and Methylobacterium radiotolerans (2). The dots are experimental data and the line is the approximation of the Michaelis–Menten equation.

As seen in the phylogenetic tree, the presence of ACC deaminases in bacteria correlates well with their ability to form associations with plants (Fig. 2). However, only the enzymes from bacteria of the genus Pseudomonas that promote plant growth through the action in the rhizosphere are well characterized. Many Methylobacterium species are considered to be epiphytic symbionts, with the exception of M. nodulans, which is a true nodule-forming and nitrogen-fixing symbiont. Although there is a lack of biochemical data on rhizobial ACC deaminases, there is a lot of genetic evidence of the importance of this enzyme for nodule-forming symbiosis. For example, the acdS mutants of Rhizobium leguminosarum bv. viceae and Mesorhizobium loti demonstrated lower abilities to form nodules compared with the wild-type strains (Ma et al., 2003; Uchiumi et al., 2004). Moreover, transformation of the ACC deaminase-lacking Sinorhizobium meliloti strain resulted in enhanced root nodule formation (Ma et al., 2004). In the present work we have demonstrated that the first characterized enzyme from M. nodulans possesses the highest catalytic efficiency and substrate specificity of all the known ACC deaminases. This may be due to the close relationship between bacteria and plants, which allows the bacteria to consume ACC directly from plant tissues more effectively than rhizobacteria.

The importance of ACC deaminase from rhizosphere bacteria was demonstrated in the experiments with the acdS-gene deficient strain of P. putida, which, in contrast to the wild type strain, cannot facilitate the growth of canola during salt stress (Cheng et al., 2007). The mutant in the ACC deaminase gene has not been obtained in epiphytic bacteria such as M. radiotolerans. Hence, these experiments are of great importance, as the mechanism of methylobacteria–plant interaction has not yet been shown for phyllosphere bacteria. Moreover, various Methylobacterium species found in plant tissues are able to directly take up different plant metabolites including ACC, which may lead to plant growth stimulation.

In conclusion, we have identified and characterized two novel ACC deaminases with the highest substrate specificity to ACC of all known enzymes. The presence of these enzymes in methylobacteria is indicative of their close relationship with plants. Further experiments with the mutant strains are required to elucidate the precise role of methylobacterial ACC deaminases in phytosymbiosis. In addition, the high substrate specificity of the enzymes will help find the clues for construction of modified ACC deaminases with improved catalytic efficiency.

Acknowledgements

The work was supported by the grant of the Russian Foundation for Basic Research (RFBR 10-04-00808-a).

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