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Mechanism of DNA cleavage catalyzed by Mung Bean Nuclease
Inorganica Chimica Acta 357 (2004) 2579–2592 www.elsevier.com/locate/ica
Mechanism of DNA cleavage catalyzed by Mung Bean Nuclease q Clarissa Silva Pires de Castro
a,*
, Jurandir Rodrigues SouzaDe b, Carlos Bloch Jr.
a
a
b
Laborat orio de Espectrometria de Massa, Embrapa Recursos Geneticos e Biotecnologia, P.O. Box 02372, Brası´lia, DF 70.770-900, Brazil Laborat orio de Quımica Analıtica e Ambiental, Instituto de Quımica, Universidade de Brasılia, P.O. Box 04394, Brası´lia, DF 70.919-970, Brazil Received 1 September 2003; accepted 7 February 2004 Available online 20 March 2004
Abstract The interaction of zinc with different forms of DNA (k phage DNA, ss-oligo, ds-oligo) and Mung Bean Nuclease was studied by voltammetric techniques in order to investigate the mechanism of DNA cleavage catalyzed by a zinc metalloenzyme. Stoichiometry, dissociation constant, zinc binding sites and functions were determined for these systems. Two zinc ions were found to be involved in stabilization of a 19 mer ds-oligodeoxyribonucleotide, which was synthesized by the phosphoramidite method and used as a DNA model in the studies. Three zinc ions (Zn1, Zn2, and Zn3), which have different roles in ds-oligo cleavage, were identified in the active site of Mung Bean Nuclease. A concerted SN 2 mechanism, which assigns a catalytic function to Zn2 and structural functions to Zn1 and Zn3, was proposed. The hydrolysis of phosphodiester bonds proceeds with inversion of configuration at the phosphorus center, forming a pentacoordinate transition state, which is stabilized by an arginine. Zn2 supplies the nucleophile, which is oriented by an aspartic acid, and activates the ds-oligo by its coordination to the phosphate free oxygen of the phosphodiester bond. Zn1 and Zn3 ions, besides stabilizing the tertiary structure of Mung Bean Nuclease, bind to the leaving group, blocking the cleavage reverse reaction. Ó 2004 Elsevier B.V. All rights reserved. Keywords: Voltammetry; DNA; Cleavage; Zinc; Mung Bean Nuclease
1. Introduction Mung Bean Nuclease [1] is a zinc metalloenzyme that catalyzes the hydrolysis of single-stranded DNA and RNA endonucleolytically to yield 50 -phosphoryl terminated products. While this nuclease prefers ssDNA over dsDNA by 30,000-fold, at very high concentrations, such as 14 U mg1 of DNA, this enzyme degrades double-stranded DNA preferentially from both ends [2]. Mung Bean Nuclease has been used for transcript mapping studies [3], flushing staggered ends and for the separation of cDNA strands after synthesis with reverse transcriptase and DNA polymerase [4]. The purification and properties of Mung Bean Nuclease have been reviewed [5]. However, little is known about the mechanism of DNA cleavage catalyzed by this enzyme. A q Supplementary data associated with this article can be found, in the online version, at doi:10.1016/j.ica.2004.02.004. * Corresponding author. Tel: +55-61-448-4671; fax: +55-61-3403658. E-mail address: [email protected] (C.S. Pires de Castro).
0020-1693/$ - see front matter Ó 2004 Elsevier B.V. All rights reserved. doi:10.1016/j.ica.2004.02.004
mechanistic study of Mung Bean Nuclease should cover the interaction of zinc with DNA and Mung Bean Nuclease, and also the catalytic mechanism of DNA cleavage. Zinc-ion binding to DNA has been studied by several techniques including UV–Vis spectroscopy [6] and equilibrium dialysis [7]. However, these techniques present considerable experimental difficulties or limitations. The utilization of UV–Vis spectroscopy is difficult in general because many metal complexes show small changes in molar absorptivity on binding to DNA [8]. Dialysis experiments reach equilibrium only in solutions of high ionic strength and at this condition the small monovalent cations, which are commonly used, compete with divalent ions for binding sites, making it difficult to measure the divalent ion binding at low concentration. Metal substitutions have proven to be a powerful tool in studying zinc metalloenzymes, by replacing the spectroscopically silent Zn(II) with paramagnetic metals, for example Co(II), Mn(II), Ni(II), Cu(II), or Cd(II). The resulting metalloderivatives can be investigated by many spectroscopic methods, such as electron
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spin/paramagnetic resonance (ES/PR), nuclear magnetic resonance (NMR), electronic absorption spectroscopy, circular dichroism (CD), magnetocircular dichroism (MCD), and perturbed angular correlation of c-rays (PAC) [9]. However, these metal exchanges have shown that the replacement of catalytic zinc with other metal ions can affect the enzyme activity profoundly. The electrochemical methods have been reported to have several advantages in determining the quantitative parameters of metal-macromolecule (DNA, proteins) complexes by studying the voltammetry of the metal ion in the absence and presence of the macromolecule and noting shifts in standard potential caused by the interaction [10–23]. These advantages include determination of qualitative and quantitative data (stoichiometry, dissociation constants, metal binding sites in DNA or protein molecule, mechanism and metal functions in the physiological reactions) of metal ion–DNA and metal ion–protein complexes near physiological conditions. A first step in understanding the catalytic mechanism of DNA cleavage by Mung Bean Nuclease is the determination of whether the enzymic reaction proceeds by direct attack of water on the phosphodiester bridge or whether a double-displacement mechanism is operative, whereby a covalent nucleotidylated-enzyme intermediate is formed and subsequently hydrolyzed. A stereochemical experiment permits distinction between these two possibilities [24–27]. Methods, whereby this question can be addressed for nucleases, have been developed in 1983 and rely on the use of dinucleoside phosphate analogs stereospecifically labelled with sulfur [28,29] or 18 O isotope [30–32]. Mung Bean Nuclease (Phaseolus aureus) has been found to cleave the Sp diastereoisomer of 50 -O-thymidyl 30 -O-(20 -deoxyadenosyl) phosphorothioate, (Sp )-d[As(S)T], in 18 O-labelled water with inversion of configuration at phosphorous to give (Sp )-thymidine 50 -[16 O,18 O]phosphorothioate [33,34]. A second step in understanding the catalytic mechanism of DNA cleavage by Mung Bean Nuclease is to know the precise role of zinc in the hydrolytic mechanism. Zinc ions can play a structural role or one of a number of catalytic roles: activation of a coordinated water molecule, recognition of a substrate, stabilization of the leaving group, among others. Experimental evaluation of the catalytic effects of zinc in Mung Bean Nuclease is problematic, since the zinc ions are intimately involved in substrate binding. In this work, several voltammetric techniques were used to investigate the mechanism of DNA cleavage catalyzed by Mung Bean Nuclease. Initially, the interaction of zinc with a natural DNA (DNA of the k bacteriophage virus) and with four synthetic models of DNA (single- and double-stranded oligodeoxyribonucleotides) was studied by differential pulse polarography (DPP), cyclic voltammetry (CV), and anodic stripping voltammetry (ASV). The second part of the work was
dedicated to the study of the interaction of Zn2þ with Mung Bean Nuclease by ASV and CV. Our main interest was focused on the cleavage of DNA catalyzed by this class of enzymes, which is an important biological process since through the DNA fragments produced, it is possible to both manipulate and map genes and identify some specific viruses and parasite groups. Zinc is an important regulatory element in the cleavage of DNA, but details of its chemical interaction with DNA and nucleases and its potential role in the ligand binding process are not well characterized. The importance of this work stems from the fact that it combines knowledge about the chemistry of metal ions with an understanding of biomolecules to perceive how complex living systems function. The growth of this new field, named bioinorganic chemistry, can be seen in a special issue of Proceedings of the National Academic of Sciences USA [35], which reports its evolution since the late 1950s with the discovery of iron in the blood and of cooper and zinc as essential elements for many physiological reactions until the beginning of the 21st century with the investigation of the linkages between inorganic elements and the information obtainable from genome sequences.
2. Experimental 2.1. Chemicals k phage DNA was purchased from Sigma Chemical Co. It was isolated from Escherichia coli Host Strain W3110 and has a 3.2 107 g mol1 molecular mass. The single-stranded oligodeoxyribonucleotides ARC5IIC2, 30 AOX1, and PR1AECO were purchased from Gibco and have 14 (MM ¼ 4.47 103 g mol1 ), 21 (MM ¼ 6.63 103 g mol1 ), and 31 (MM ¼ 1.04 104 g mol1 ) mer, respectively. The complementary strands of the double-stranded oligodeoxyribonucleotide were synthesized by the phosphoramidite method [36] using reagents purchased from Perkin–Elmer and Merck. Each strand has 19 mer, which corresponds to 5.88 103 g mol1 . Mung Bean Nuclease was purchased from Promega and Boehringer–Mannheim. It was isolated from P. aureus and has a 3.9 104 g mol1 molecular mass. All other chemicals were of reagent grade and all solutions were prepared with triple-distilled water from a quartz still (Quartex). 2.2. Apparatus Ultraviolet spectroscopic measurements were performed using U-2001 UV–Vis double beam spectrometer (Hitachi) at 260 and 280 nm. Differential pulse polarographic (DPP) and anodic stripping voltammetric (ASV) measurements were car-
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ried out on a 646 Metrohm Voltammetric Analyzer Processor connected to a 647 Metrohm electrochemical cell composed of a dropping mercury electrode or hanging mercury electrode (working electrodes), a Ag/ AgCl (3.0 M KCl) electrode (reference electrode) and a platinum electrode (auxiliary electrode). All DPP measurements were performed in the potential range 0.18 V (initial potential, Ei ) to )1.15 V (final potential, Ef ) at the following settings: surface area of the mercury drop 0.4 mm2 , pulse amplitude 50 mV, and the scan rate v ¼ 10 mV s1 . All ASV measurements were performed in the potential range )1.15 V (initial potential, Ei ) to 0.18 V (final potential, Ef ) at the following settings: accumulation potential Ed ¼ 1:15 V, accumulation time td ¼ 90 s, equilibration time te ¼ 20 s, surface area of the mercury drop 0.4 mm2 , pulse amplitude 50 mV and the scan rate v ¼ 10 mV s1 . Cyclic voltammetric (CV) measurements for k phage DNA and the single-stranded oligos ARC5IIC2, 30 AOX1, and PR1AECO were performed using a PAR 173 Potentiostat/Galvanostat or a PAR 174 polarographic system connected to a PAR 175 Universal Programmer and a Houston X–Y recorder at the following settings: initial potential Ei ¼ 0:2 V, switching potential Ew ¼ 1:6 V, and scan rate range 2 mV s1 6 v 6 100 mV s1 . A three-electrode system with a hanging mercury electrode (Metrohm) as working electrode, a Ag/AgCl (3.0 M KCl) electrode as reference electrode, and a platinum wire as the auxiliary electrode was used. Cyclic voltammetric (CV) measurements for doublestranded oligo and Mung Bean Nuclease were performed using a PAR 174 polarographic system connected to a PAR 175 Universal Programmer and a Houston X–Y recorder at the following settings: initial potential Ei ¼ 0:4 V, switching potential Ew ¼ 1:4 V, and scan rate range 2 mV s1 6 v 6 20 mV s1 . A threeelectrode system with a hanging mercury electrode (Metrohm) as working electrode, a saturated calomel electrode as reference electrode, and a platinum wire as the auxiliary electrode was used. Complementary strands of the double-stranded oligodeoxyribonucleotide were synthesized using the DNA/ RNA synthesizer model 392 (Applied Biosystems) and annealed using the MJ research PTC-100 Thermal cycler. MALDI-MS measurements were performed using the Voyager-DE STR Biospectrometry Workstation (Applied Biosystems) at the following settings: operation on linear mode, accelerating voltage 25,000 V, N2 laser, pressure at the ion source 1.11 107 torr, and pressure at detector 8.9 109 torr. 3-Hydroxypicolinic acid in ammonium citrate was used as matrix. 2.3. Procedure Prior to voltammetric measurements, k phage DNA, the single- and double-stranded oligos, and Mung Bean
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Nuclease were exhaustively dialyzed against 0.01 M EDTA at 10 °C in order to remove zinc and other metals. The resulting products were submitted to an additional dialysis step against Quartex water to remove all the EDTA and other salts. The concentration of k phage DNA and the double-stranded oligodeoxyribonucleotide was determined by UV measurements at 260 nm through the expression 1:0A260 nm DS DNA which corresponds to 50 lg mL1 [37]. The concentration of the single-stranded oligodeoxyribonucleotides was determined by UV measurements at 260 nm through the expression 1:0A260 nm SS DNA which corresponds to 33 lg mL1 [37]. The purity (freedom from bound protein) of all DNA samples was assessed from the ratio of the absorbances at 260 and 280 nm [37]. The concentration of Mung Bean Nuclease was determined by UV measurements at 280 nm through the Beer Law [37]. The molar absorption coefficient was determined by using the Edelhoch Method [38]. In order to avoid measurement interference due to DNA, oligos, Mung Bean Nuclease, and zinc adsorption on the working surfaces of the electrode system, electrodes were submitted to periodic cleaning with 20% HNO3 (v/v) followed by a generous wash with tripledistilled water. Experiments were performed at three temperatures (22, 10, and 5 °C) and preceded by a gentle N2 bubbling to prevent oxygen diffusion into the electrochemical cell (10 min for the supporting electrolyte – 0.1 M KNO3 and 3 min after each DNA/oligo or nuclease addition). The amperometric titration of zinc with k phage DNA by using differential pulse polarography and cyclic voltammetry was accomplished through additions of 5 or 10 lL of this virion DNA to the electrochemical cell containing 1.0 mL of 1.5 108 M Zn2þ in 20 mL of 0.1 M KNO3 or 1.5 mL of 1.5 108 M Zn2þ in 20 mL of 0.1 M KNO3 , respectively. The oxidation–reduction process of zinc was studied in the presence and absence of k phage DNA by using cyclic voltammetry through I (oxidation current of zinc) versus v1=2 (square root of scan rate) curves. The oxidation current of zinc was measured in the scan rate range 2 mV s1 6 v 6 50 mV s1 with and without the addition of 40 lL of 1.50 108 M k phage DNA to the electrochemical cell containing 1.5 mL of 1.50 108 M Zn2þ in 20 mL of 0.1 M KNO3 . The amperometric titration of zinc with the singlestranded oligos (ARC5IIC2, 30 AOX1, and PR1AECO) by using cyclic voltammetry was accomplished through additions of 100 lL of each oligo to the electrochemical cell containing 30 or 130 lL of 1.53 102 M Zn2þ in 25 mL of 0.1 M KNO3 . The oxidation–reduction process of zinc was studied in the presence and absence of the single-stranded oligos (ARC5IIC2, 3ÕAOX1, and PR1AECO) by using cyclic voltammetry through I (oxidation current of zinc) versus v1=2 (square root of
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scan rate) curves. The oxidation current of zinc was measured in the scan rate range 2 mV s1 6 v 6 100 mV s1 with and without the addition of 30 lL of 9.96 106 M ARC5IIC2 ss-oligo, 100 lL of 5.10 106 M 30 AOX1 ss-oligo or 500 lL of 1.13 105 M PR1AECO ss-oligo to the electrochemical cell containing 1.83 105 or 7.91 105 M Zn2þ in 25 mL of 0.1 M KNO3 . Complementary strands of the double-stranded oligodeoxyribonucleotide were synthesized by the solidphase phosphoramidite method [36] that relies on the coupling reaction between a 50 -hydroxyl group of a support-bound deoxynucleoside and an alkyl (methyl or 2-cyanoethyl) 50 -DMtr-(N-acylated)-deoxynucleoside 0 3 -O-(N,N-diisopropylamino)phosphite. The basic steps involved in one cycle of nucleotide addition using this method are: detritylation (removal of dimethoxytrityl groups) by trichloroacetic acid in methylene chloride; activation of phosphoramidite by tetrazole in acetonitrile solution; addition of activated phosphoramidite to the growing chain; blocking of chains which are not reacted during coupling reaction (capping); and oxidation of the intermediate phosphite to the phosphotriester by iodine and water. The cycle was repeated 18 times in order to obtain each 19 mer oligodeoxyribonucleotide. Deprotection and release from the support was done with concentrated aqueous ammonia at 57 °C for 12 h. MALDI-TOF/MS experiments were performed using 3.70 106 M oligo 1 and 4.25 106 M oligo 2. Both solutions were mixed with 3.59 109 M 3-hydroxypicolinic acid in 2.21 109 M ammonium citrate (8:1). About 1.0 lL of the matrix–analyte mixture was applied onto the sample plate and allowed to dry at room temperature. Annealing of complementary strands of the ds-oligo was done by mixing 7.03 107 M oligo 1 and 5.65 107 M oligo 2 in 0.01 M, pH 7.4, Tris–HCl buffer. The thermal cycler was programmed to incubate the resulting product at 95 °C for 3 min and 58 °C (theoretical Tm value) for 5 min, and then reduce the temperature to 23.5 °C at the end of the cycle. The amperometric titration of zinc with doublestranded oligo by using anodic stripping voltammetry and cyclic voltammetry was accomplished through additions of 2 or 5 lL of this oligo to the electrochemical cell containing 6.01 108 M Zn2þ in 20 mL of 0.1 M KNO3 or 6.07 109 M Zn2þ in 10 mL of 0.1 M KNO3 , respectively. The oxidation–reduction process of zinc was studied in the presence and absence of the ds-oligo by using cyclic voltammetry through I (oxidation current of zinc) versus v1=2 (square root of scan rate) curves. The oxidation current of zinc was measured in the scan rate range 2 mV s1 6 v 6 20 mV s1 with and without the addition of 10 lL of 8.13 107 M ds-oligo to the electrochemical cell containing 6.07 109 M Zn2þ in 10 mL of 0.1 M KNO3 .
The amperometric titration of zinc with Mung Bean Nuclease by using anodic stripping voltammetry and cyclic voltammetry was accomplished through additions of 5 or 10 lL of this enzyme to the electrochemical cell containing 1.71 108 M Zn2þ in 20 mL of 0.1 M KNO3 or 1.74 108 M Zn2þ in 20 mL of 0.1 M KNO3 , respectively.
3. Results and discussion 3.1. Zn2þ –DNA interactions 3.1.1. Zn2þ –k phage DNA interaction k phage is a bacterial virus composed by a protein capsid divided into an icosahedrally symmetric head that contains a DNA genome and a flexible helical tail that plays a role in attaching to the specific host bacterium (E. coli) and injecting DNA. The k genome is a linear double-stranded DNA molecule having almost 50,000 base pairs (bp) with 12 bp single-stranded complementary 50 -ends (sticky ends). It is a common substrate for restriction endonucleases and for generating DNA size markers fragments. Binding of zinc to k phage DNA was investigated by differential pulse voltammetry and cyclic voltammetry [14,17]. These methods rely on the direct monitoring of reduction and oxidation current of zinc in the absence and presence of this virion DNA. The formation of a stable complex between Zn2þ and the k phage DNA was verified by the decrease of the reduction (DPP) (see supplementary material, Figure 1S) and oxidation (CV) (Fig. 1) currents of zinc during incremental additions of this virion DNA. Titration graphs of zinc with k phage DNA were obtained in concentrations ranging from 3.57 1012 to 3.92 1011 M and 6.97 1012 to 5.56 1011 M. These data were used to calculate the stoichiometry and the dissociation constant of the complex. A stoichiometry rate of 23 Zn2þ ions (DPP) or 22 Zn2þ ions (CV), which have the function of stabilizing the double helix of the DNA by means of its interactions with the phosphate groups [14], per one k phage DNA molecule was determined for the reaction. The dissociation constant (Kd ) of Zn2þ –k phage DNA complex was calculated using the following equation [39,40]: i2p ¼
Kd ði2 i2p Þ þ i2p0 ½DNA; ½DNA p0
ð1Þ
where i2p0 is the reduction current of zinc in the absence of k phage DNA, i2p the reduction current of zinc in the presence of k phage DNA, and [DNA] the concentration of added k phage DNA in solution (M). Curves i2p versus ði2p0 i2p Þ=½DNA (Figs. 2 and 3) were plotted for Zn2þ -k phage DNA complex and two straight lines were obtained. From the slopes, the dis-
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Fig. 3. The plot i2p vs. ði2p0 i2p Þ=½DNA used to calculate the dissociation constant of Zn2þ –k phage DNA complex (CV measurements). R is the correlation coefficient; SD is the standard deviation; and P is the probability. Fig. 1. Cyclic voltammograms of 1.5 mL of 1.5 108 M Zn2þ in 20 mL of 0.1 M KNO3 with different concentrations of k phage DNA. (1) Zn2þ , no k phage DNA; (2) Zn2þ + 2.8 1011 M k phage DNA; (3) Zn2þ + 4.2 1011 M k phage DNA; (4) Zn2þ + 5.6 1011 M k phage DNA. Ei ¼ 0:2 V, Ew ¼ 1:6V , scan rate ¼ 10 mV s1 , working electrode: HMDE, reference electrode: Ag/AgCl (3 M KCl).
Fig. 4. Variation of peak current of 1.5 mL of 1.5 108 M Zn2þ in 20 mL of 0.1 M KNO3 with square root of the scan rate in absence (s) and presence () of 2.8 1011 M k phage DNA. Ei ¼ 0:2 V, Ew ¼ 1:6 V, scan rate range 2 mV s1 6 v 6 50 mV s1 , working electrode: HMDE, reference electrode: Ag/AgCl (3 M KCl). Fig. 2. The plot i2p vs. ði2p0 i2p Þ=½DNA used to calculate the dissociation constant of Zn2þ –k phage DNA complex (DPP measurements). R is the correlation coefficient; SD is the standard deviation; and P is the probability.
sociation constants were determined to be 3.44 1011 M (DPP) and 6.69 1011 M (CV). Curves I (oxidation current) versus v1=2 (square root of scan rate) show that the oxidation–reduction process of zinc is no longer controlled by diffusion in the presence of k phage DNA (Fig. 4). This phenomenon can be explained by the adsorption of k phage DNA onto mercury surface which mediates the charge transfer of bulk Zn2þ ions [14].
3.1.2. Zn2þ –ARCIIC2, Zn2þ –30 AOX1, and Zn2þ – PR1AECO interactions An oligodeoxyribonucleotide is a simple or doublestranded chain consisting of a number of deoxynucleoside units linked together by phosphodiester bridges. These macromolecules are used to identify and detect sequences of specific genes and locate specific mutations in genes of well-known sequence and in those generated by mutagenesis of cloned genes [36]. ARC5IIC2 (MM ¼ 4,472 g mol1 ) is a single-stranded oligodeoxyribonucleotide 14 mer, whose sequence (ACACCCAACGGAGA) corresponds to part of the coding region of an arcelin gene, a protein of the lectin family,
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found in seeds of wild bean. 30 AOX1 (MM ¼ 6,730 g mol1 ) is a single-stranded oligodeoxyribonucleotide 21 mer, whose sequence (GCAAATGGCATTCTGACATCC) corresponds to the 30 portion of the coding region of Pichia pastoris alcohol oxidase. PR1AECO (MM ¼ 10,038 g mol1 ) is a single-stranded oligodeoxyribonucleotide 31 mer, whose sequence (AAGAATTCGCIAAYCGTGYAAYCCIGCICAA) corresponds to a promoter region of the same gene of the ARC5IIC2 oligo. The interaction of zinc with ARC5IIC2, 30 AOX1, and PR1AECO was investigated by means of cyclic voltammetry [13,17] in order to determine optimal experimental parameters (DNA size, base sequence) for the synthesis of a model of double-stranded DNA (oligo). It was found that all the three oligos interact with zinc ions in the same way as a double-stranded DNA, causing a decrease in the reduction/oxidation current of this metal (Fig. 5; see supplementary material, Figures S2 and S3). A peak was also observed around )1.3 V in the cyclic voltammograms of the three oligos (Fig. 5; see supplementary materials, Figures S2 and S3), which can be attributed to adenine and cytosine reduction [41]. This peak is characteristic of a single-stranded DNA because in this case adenine and cytosine are free to reduce at mercury electrode and in the case of a doublestranded DNA, these bases are linked with thymine and guanine by hydrogen bonds, which blocks their reduction. Curves I (oxidation current) versus v1=2 (square
root of scan rate) show that the oxidation–reduction process of zinc is no longer controlled by diffusion in the presence of each single-stranded oligo (Figs. 6–8), as in the case of k phage DNA. With these experiments, we concluded that: both single and double-stranded DNAs interact with zinc, by the same mechanism. The size and base sequence of DNA do not interfere in the signals of this interaction, although the smaller ones produced better results. Based on these conclusions, two complementary strands of a 19 mer DNA were synthesized, consisting of 60% of GC residues and 40% of AT resi-
Fig. 6. Variation of peak current of 30 lL of 1.53 102 M Zn2þ in 25 mL of 0.1 M KNO3 with square root of the scan rate in absence (d) and presence () of 1.19 108 M ARC5IIC2 single-stranded oligo. Ei ¼ 0:2 V, Ew ¼ 1:6 V, scan rate range 2 mV s1 6 v 6 100 mV s1 , working electrode: HMDE, reference electrode: Ag/AgCl (3 M KCl).
Fig. 5. Cyclic voltammograms of 130 lL of 1.53 102 M Zn2þ in 25 mL of 0.1 M KNO3 with different concentrations of PR1AECO singlestranded oligo. (1) KNO3 , no Zn2þ and PR1AECO single-stranded oligo; (2) Zn2þ , no PR1AECO single-stranded oligo; (3) Zn2þ + 4.50 108 M PR1AECO single-stranded oligo; (4) Zn2þ + 8.97 108 M PR1AECO single-stranded oligo; (5) Zn2þ + 13.4 108 M PR1AECO single-stranded oligo; (6) Zn2þ + 17.8 108 M PR1AECO single-stranded oligo. Ei ¼ 0:2 V, Ew ¼ 1:6 V, scan rate ¼ 10 mV s1 , working electrode: HMDE, reference electrode: Ag/AgCl (3 M KCl).
Fig. 7. Variation of peak current of 30 lL of 1.53 102 M Zn2þ in 25 mL of 0.1 M KNO3 with square root of the scan rate in absence (d) and presence () of 2.03 108 M 3ÕAOX1 single-stranded oligo. Ei ¼ 0:2 V, Ew ¼ 1:6 V, scan rate range 2 mV s1 6 v 6 100 mV s1 , working electrode: HMDE, reference electrode: Ag/AgCl (3 M KCl).
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Fig. 8. Variation of peak current of 130 lL of 1.53 102 M Zn2þ in 25 mL of 0.1 M KNO3 with square root of the scan rate in absence (d) and presence () of 2.20 107 M PR1AECO single-stranded oligo. Ei ¼ 0:2V , Ew ¼ 1:6 V, scan rate range 2 mV s1 6 v 6 100 mV s1 , working electrode: HMDE, reference electrode: Ag/AgCl (3 M KCl).
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Fig. 10. MALDI-TOF/MS spectrum of 4.25 106 M oligo 2. Operation mode linear, accelerating voltage 25,000 V, N2 laser 2300 lJ cm2 , pressure at the ion source 1.11 107 torr, and pressure at detector 8.9 109 torr. 3-Hydroxypicolinic acid in ammonium citrate was used as matrix. A, adenine; C, cytosine; T, thymine; G, guanine.
3.1.3. Zn2þ –double stranded oligo interaction The melting behavior of the double-stranded oligo was monitored by measuring its UV absorption
(k ¼ 260 nm) as a function of temperature in order to verify if the methodology used for its complementary strands annealing was satisfactory [15]. A sigmoid melting curve (Fig. 11), which is composed by two steps, was observed for ds-oligo. Step 1 indicates that the dsoligo is denatured at 95 °C and step 2 indicates that it is annealed at room temperature. The melting temperature (Tm ) was found to be 54 °C and this result agrees with the theoretical value (58 °C) calculated through the expression: Tm (°C) ¼ [2 °C (number of AT base pairs) + 4 °C (number of GC base pairs)] [36]. Binding of zinc to the 19 mer double-stranded oligodeoxyribonucleotide was studied by anodic stripping voltammetry and cyclic voltammetry [15–17]. These methods rely on the direct monitoring of oxidation current of zinc in the absence and presence of this oligo. The formation of a stable complex between Zn2þ and the ds-oligodeoxyribonucleotide was verified by the
Fig. 9. MALDI-TOF/MS spectrum of 3.70 106 M oligo 1. Operation mode linear, accelerating voltage 25,000 V, N2 laser 2300 lJ cm2 , pressure at the ion source 1.11 107 torr, and pressure at detector 8.9 109 torr. 3-Hydroxypicolinic acid in ammonium citrate was used as matrix. A, adenine; C, cytosine; T, thymine; G, guanine.
Fig. 11. Melting curve obtained for double-stranded oligodeoxyribonucleotide. A, adenine; C, cytosine; T, thymine; G, guanine. 1, ds-oligo is denatured at 95 °C; 2, ds-oligo is annealed at room temperature.
dues (see supplementary material, Figure S4). The recovery rate of each step of the synthesis ranges from 97% to 100%, indicating the high efficiency of the phosphoramidite method. The purity of each strand (oligo) was assessed from the mass spectra obtained for each synthetic oligo (Figs. 9 and 10) [15], which show the appearance of only one peak. The experimental mass of these peaks (1 ¼ 5869.99 and 2 ¼ 5877.58) did not differ significantly to the theoretical values calculated for each oligo (1 ¼ 5867.71 Da and 2 ¼ 5876.71 Da). These results indicated that the two complementary strands of the 19 mer double-stranded oligo are pure and did not need an additional purification step.
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decrease of oxidation current of zinc during incremental additions of this oligo (Fig. 12; see supplementary material, Figure S5). Titration graphs of zinc with ds-oligo were obtained in concentrations ranging from
3.62 109 to 3.62 108 M and 4.06 1010 5.25 109 M. These data were used to calculate stoichiometry and the dissociation constant of complex. A stoichiometry rate of 2 Zn2þ ions per
to the the ds-
Fig. 12. Cyclic voltammograms of 6.07 109 M Zn2þ in 10 mL of 0.1 M KNO3 with different concentrations of double-stranded oligo. (1) Zn2þ , no double-stranded oligo; (2) Zn2þ + 4.06 1010 M double-stranded oligo; (3) Zn2þ + 8.12 1010 M double-stranded oligo; (4) Zn2þ + 12.2 1010 M double-stranded oligo; (5) Zn2þ + 16.2 1010 M double-stranded oligo; (6) Zn2þ + 20.3 1010 M double-stranded oligo; (7) Zn2þ + 24.3 1010 M double-stranded oligo; (8) Zn2þ + 28.3 1010 M double-stranded oligo; (9) Zn2þ + 32.4 1010 M double-stranded oligo; (10) Zn2þ + 36.4 1010 M double-stranded oligo; (11) Zn2þ + 40.4 1010 M double-stranded oligo; (12) Zn2þ + 44.5 1010 M double-stranded oligo; (13) Zn2þ + 48.5 1010 M double-stranded oligo; (14) Zn2þ + 52.5 1010 M double-stranded oligo. Ei ¼ 0:4 V, Ew ¼ 1:4 V, scan rate ¼ 20 mV s1 , working electrode: HMDE, reference electrode: saturated calomel electrode.
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oligo molecule was determined for the reaction by ASV and CV. Several lines of evidence suggest that these zinc ions interact with the two terminal phosphate groups (50 ), stabilizing the double helix of the oligo: (a) The concentration of zinc that had been used in the experiments was low (small Zn2þ :DNA-P rate), which favors the stabilization of double helix by Zn2þ ions; (b) The destabilization of the double helix is negligible when the concentration of the monovalent cation (Kþ ) is P 0.1 M and the concentration of Zn2þ is 6 104 M; (c) The absence of the peak around )1.3 V in the cyclic voltammograms obtained for the ds-oligo indicates that it is native. Consequently, Zn2þ ions cannot be linked by GC bridges because this phenomenon occurs only when DNA is denatured; (d) If zinc ions were linked by GC bridges, the obtained stoichiometry would be 10 Zn2þ ions per one ds-oligo molecule; (e) DNA regions that are rich in AT residues favor the interaction of zinc with phosphate groups [6]. The dissociation constant of Zn2þ -dsoligo complex was calculated to be 4.71 108 M (ASV) and 1.62 109 M (CV) using Eq. (1). These low Kd values are close and imply that zinc ions are probably interacting not only with the active site of the enzyme during DNA hydrolysis, but also with DNA. Curves I (oxidation current) versus v1=2 (square root of scan rate) show that the oxidation–reduction process of zinc is no longer controlled by diffusion in the presence of ds-oligo, as it had already been found for k phage DNA and the three single-stranded oligos (Fig. 13).
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monitoring of the oxidation current of zinc in the absence and presence of Mung Bean Nuclease (Figs. 14 and 15). Titration curves of zinc with the enzyme were obtained in concentrations ranging from 1.08 109 to 1.07 108 M and 1.16 108 to 1.04 107 M. The acquired data were used to calculate the stoichiometry and the dissociation constant of the complex. A stoichiometry rate of 3 Zn2þ ions per one Mung Bean Nuclease molecule was determined for the reaction by ASV and CV. This result is in agreement with the crystallographic data obtained for P1 nuclease [42]. P1 nuclease consists of 269 amino acid residues and three zinc ions per subunit. The zinc cluster in P1 nuclease is located at the bottom of the substrate binding cleft and consists of a relatively inaccessible binuclear site containing Zn1 and from each other, and a more Zn3 at a distance of 3.2 A reexposed single site containing Zn2, which is 5.8 A moved from Zn1 and 4.7 A from Zn3. Two histidine ring nitrogens (His60Nd and His116Ne ), two aspartate side chain oxygens (Asp45Od1 and Asp120Od1 ), and one
3.2. Zn2þ –Mung Bean Nuclease interaction Binding of zinc to Mung Bean Nuclease was investigated by anodic stripping voltammetry and cyclic voltammetry [18,19,22]. These methods rely on the direct
Fig. 13. Variation of peak current of 6.07 109 M Zn2þ in 10 mL of 0.1 M KNO3 with square root of the scan rate in absence () and presence (s) of 8.12 1010 M double-stranded oligo. Ei ¼ 0:4 V, Ew ¼ 1:4 V, scan rate range ¼ 2 mV s1 6 v 6 20 mV s1 , working electrode: HMDE, reference electrode: saturated calomel electrode.
Fig. 14. Anodic stripping voltammograms of 1.71 108 M Zn2þ in 20 mL of 0.1 M KNO3 with different concentrations of Mung Bean Nuclease. (1) Zn2þ , no Mung Bean Nuclease; (2) Zn2þ + 1.08 109 M Mung Bean Nuclease; (3) Zn2þ + 2.15 109 M Mung Bean Nuclease; (4) Zn2þ + 3.23 109 M Mung Bean Nuclease; (5) Zn2þ + 4.30 109 M Mung Bean Nuclease; (6) Zn2þ + 5.38 109 M Mung Bean Nuclease; (7) Zn2þ + 6.45 109 M Mung Bean Nuclease; (8) Zn2þ + 7.53 109 M Mung Bean Nuclease; (9) Zn2þ + 8.60 109 M Mung Bean Nuclease. Ed ¼ 1:15 V, td ¼ 90 s, Ei ¼ 1:15 V, Ef ¼ 0:180 V, pulse amplitude ¼ 50 mV, scan rate ¼ 10 mV s1 , working electrode: HMDE, reference electrode: Ag/AgCl (3 M KCl).
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Fig. 15. Cyclic voltammograms of 1.5 mL of 2.50 106 M Zn2þ in 20 mL of 0.1 M KNO3 with different concentrations of Mung Bean Nuclease. (1) Zn2þ , no Mung Bean Nuclease; (2) Zn2þ + 1.16 108 M Mung Bean Nuclease; (3) Zn2þ + 3.48 108 M Mung Bean Nuclease; (4) Zn2þ + 1.04 107 M Mung Bean Nuclease. T ¼ 22 °C, Ei ¼ 0:4 V, Ew ¼ 1:4 V, scan rate ¼ 5 mV s1 , working electrode: HMDE, reference electrode: saturated calomel electrode.
bridging water molecule serve as ligands for Zn1. Asp120 is also a ligand of Zn3 by its Od2 atom. Zn3 is further coordinated by His6Nd , the bridging water molecule and the main chain N and O of Trp1. The binuclear Zn site has an important function in the stabilization of the folding of P1 by tightly linking together three regions that are far apart in the amino acid sequence. The coordination of Zn2 in catalytic active sites is quite well established [43], sharing the common feature of three amino acids ligands (His126Ne , His149Ne , and Asp153Od1 ) – with two of them separated by a short spacer and the third further away in the primary sequence – and two water ligands. This suggests that Zn2 is directly involved in catalysis. The dissociation constants (Kd ) of the Zn2þ –Mung Bean Nuclease complex at 22, 10, and 5 °C were calculated to be 2.50 109 (ASV – 22 °C), 2.53 108 (CV – 22 °C), 3.24 108 (CV – 10 °C), and 5.18 108 (CV – 5 °C) M using Eq. (1). These low Kd values are close and imply that Zn2þ ions are indispensable for catalytic function and structural stability of nucleases,
which participate in the hydrolysis of genetic material (DNA and RNA) of all species. The binding sites of zinc in the Mung Bean Nuclease molecule were investigated by using cyclic voltammetry [22]. Two shifts in standard potential of zinc were noticed by studying the voltammetry of this metal ion in the absence and presence of the nuclease at 22 °C (Fig. 15). These results imply that two different kinds of zinc complexes are being formed during additions of Mung Bean Nuclease to the electrochemical cell. Similar cyclic voltammetric experiments were carried out at 10 and 5 °C, and the same voltammetric behavior was observed for zinc in the absence and presence of Mung Bean Nuclease. Based on X-ray crystallographic studies that have been done with P1 nuclease [42], it can be proposed that these complexes are the chemical species formed by the interactions of Zn2–Mung Bean Nuclease and Zn1,Zn3–Mung Bean Nuclease. Therefore, the existence of two kinds of zinc binding sites in the Mung Bean molecule can be attributed to a mononuclear exposed binding site of zinc with catalytic functions and to an inaccessible binuclear binding site of zinc with structural functions (Fig. 16). Three zinc ions, coordinated by different ligands, compose these two binding sites. Therefore, three different methods (Dong and Zhang [39,40], Saroff and Mark [44], and Scatchard plot [45]) were employed here to determine and analyze the individual dissociation constants of the three Zn2þ – Mung Bean Nuclease complexes. Table 1 shows Kd1 , Kd2 , and Kd3 values calculated for the interaction between each zinc ion and Mung Bean Nuclease by using the three methods. These results, supported by crystallographic data obtained for P1 nuclease, lead us to think that: (a) Kd1 represents the dissociation constant of the complex Zn2–Mung Bean Nuclease; (b) Kd2 and Kd3 represent the dissociation constants of Zn1–Mung Bean Nuclease and Zn3–Mung Bean Nuclease complexes, respectively. Indeed, due to its higher residual values, Kd1 fits the crystallographic model that implies the existence of a lower affinity ion, with higher mobility in the
Fig. 16. Schematic of the co-catalytic zinc site proposed for Mung Bean Nuclease. H, histidine; D, aspartic acid; W, tryptophan.
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Table 1 Kd values calculated for the interaction between each zinc ion and Mung Bean Nuclease by using Dong and Zhang, Saroff and Mark, and Scatchard Plot methods Method
Kd1 (nM)
Kd2 (nM)
Kd3 (nM)
KT (mean) (nM)
Technique
T (°C)
Dong and Zhanga Dong and Zhang Saroff and Markb Saroff and Mark Scatchard Plotc Scatchard Plot Dong and Zhang Saroff and Mark Scatchard Plot Dong and Zhang Saroff and Mark Scatchard Plot
2.31 29.7 0.148 4.00 0.0581 2.56 36.7 1.55 1.61 57.6 0.401 1.43
2.10 23.1 0.0756 2.00 0.00522 0.246 22.5 0.777 0.152 39.9 0.194 0.133
0.111 3.97 0.000112 0.0141 0.00191 0.129 2.15 0.00338 0.0797 2.89 0.000736 0.0699
2.50 25.3 0.0746 2.00 0.0217 0.978 32.4 0.777 0.614 51.8 0.199 0.541
ASV CV ASV CV ASV CV CV CV CV CV CV CV
22 22 22 22 22 22 10 10 10 5 5 5
a 2 ip ¼ kd =½MBði2p0 i2p Þ þ i2p0 ½MB, where Kd is the dissociation constant of the complex Zn2þ –Mung Bean Nuclease, i2p0 is the oxidation current of zinc in the absence of Mung Bean Nuclease, i2p is the oxidation current of zinc in the presence of Mung Bean Nuclease, [MB] the concentration of added Mung Bean Nuclease in solution. b m ¼ ðC0 Cm Þ=P ¼ Ka Cm n1 þ Ka Cm , where Ka is the association constant of the complex Zn2þ –Mung Bean Nuclease, C0 is the concentration of initial zinc, Cm is the concentration of free zinc in the equivalence point, P is the concentration of Mung Bean Nuclease in the equivalence point, n is the number of zinc binding sites, and m is the stoichiometry determined by voltammetric techniques. c m=½Zn2þ vs. m, where m is the average number of sites occupied by zinc per Mung Bean Nuclease molecule. nM ¼ 109 M.
enzyme active site in order to exert catalytic functions during the nucleic acid hydrolysis. Whilst Zn1 and Zn3 may have structural functions, since they show higher affinities to the Nuclease, hence their lower Kd values are demonstrated (Table 1). 3.3. Mechanism of DNA cleavage catalyzed by Mung Bean Nuclease The detailed mechanism of DNA cleavage by enzymes is of significant current interest. One of the most important questions in this respect is the catalytic and structural roles of metal ions such as Zn2þ . While it is clear that divalent ions play a major role in DNA hydrolysis, it is uncertain as to what function such cations have in hydrolysis and why two or three are needed in some cases and only one in others. A probable mechanism [46,47], with respect to the stereochemical course and zinc functions, for DNA (19 mer double-stranded oligodeoxyribonucleotide) cleavage catalyzed by Mung Bean Nuclease, under similar physiological conditions, is proposed here by using all the experimental results previously presented and the literature data [33,34,42,48–52]. Mung Bean Nuclease cleaves the double-stranded oligo molecule, which is stabilized by two Zn2þ ions, preferentially from both ends (regions that are rich in AT residues) under conditions of soft denaturation (high concentrations of the enzyme) and it produces three fragments, according to the reaction illustrated in Fig. 17 [48]. 3.3.1. Stereochemical course The stereochemical course of any chemical reaction is determined by the structure of the transition state of
that reaction, or in multistep reactions by the structures of transition states and intermediates. Associative and dissociative mechanisms of nucleophilic substitution at phosphorous in phosphates have been proposed based on detailed studies of non-enzymatic reactions [49]. The dissociative mechanism is a SN 1 mechanism, in which the phosphate undergoing substitution expels the leaving group in the rate limiting step, producing a planar electrophilic metaphosphate as an intermediate, which captures the nucleophile in a second step. Three associative mechanisms that differ with respect to the occurrence and decomposition of pentacovalent trigonal bipyramidal intermediates have been proposed. The first associative mechanism is a concerted SN 2, in which the nucleophile attacks from the side opposite the leaving group and displaces it in a single step. Substitution of this mechanism proceeds with inversion of configuration at a chiral phosphorous center. The two other associative mechanisms differ from the foregoing in that they involve intermediates and they differ in the manner in which the intermediates are produced and decomposed. In the second associative mechanism, the nucleophile approaches from the side opposite the leaving group, forming a bond to the phosphorous atom. The resulting pentacovalent trigonal bipyramidal intermediate, which has the displacing nucleophile and the leaving group in the apical positions and the other three substituents in the equatorial plane, decomposes and forms the products by the departure of R1 OH group from its apical position. The stereochemical course dictated by this mechanism involves inversion of configuration at chiral phosphorous. In the third associative mechanism, the leaving group is in the equatorial plane while the nucleophile is in an apical position of the first intermediate.
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Fig. 17. Cleavage of the 19 mer double-stranded oligodeoxyribonucleotide catalyzed by Mung Bean Nuclease. P, phosphate; A, adenine; C, cytosine; T, thymine; G, guanine.
The expulsion of the leaving group must be preceded by a pseudorotatory rearrangement to a second intermediate in which the two apical groups of the first intermediate become equatorial and two equatorial groups become apical. R1 OH then departs from its apical position in the second intermediate. The overall stereochemical course dictated by this mechanism involves retention of configuration at chiral phosphorous. Hamblin et al. [33,34] studied the stereochemical course of DNA cleavage catalyzed by Mung Bean Nuclease using a deoxydinucleoside phosphorothioate analog stereospecifically labelled with 18 O isotope. They demonstrated that the hydrolysis of phosphodiester bonds proceeds with inversion of configuration at phosphorous and presumably via a direct ‘‘in-line’’ attack of water opposite the 30 OH-R leaving group, rather than via the intermediacy of a covalent nucleotidyl-enzyme intermediate. Similarly, we can propose a concerted SN2 mechanism for the double-stranded oligodeoxyribonucleotide cleavage catalyzed by Mung Bean Nuclease (see supplementary material, Figure S6). 3.3.2. Zinc functions Based on crystallographic studies, three different mechanisms were proposed to explain zinc functions in
the DNA cleavage catalyzed by P1 Nuclease. All the mechanisms involve the nucleophilic attack of one water molecule, which is activated by one zinc atom, and the stabilization of a pentacoordinate transition state by an arginine-48. But, they assign different functions to the three zinc atoms and to the water molecules of P1 nuclease crystalline structure. In the first mechanism [42,50], Zn2 activates the water molecule, and the DNA and Zn1 and Zn3 stabilize the leaving group. In the second mechanism [51], Zn1 and Zn3 activate the water molecule, and Zn2 activates the DNA and stabilizes the leaving group. In the third mechanism [52], Zn1 and Zn3 activate the DNA and stabilize the leaving group and Zn2 activates the water molecule. Analyzing our Kd values (Table 1), which show that Zn1 and Zn3 have higher affinities to Mung Bean Nuclease (lower Kd values) and Zn2 has higher mobility in the enzyme active site (higher Kd value), we conclude that the first mechanism is the most appropriate to explain the functions of zinc atoms in the ds-oligo cleavage catalyzed by Mung Bean Nuclease. The proposed mechanism (Fig. 18) assigns a catalytic function to Zn2 and structural functions to Zn1 and Zn3. Zn2 activates the ds-oligo by means of its coordination to the free oxygen from the phosphate of the phosphodiester bond
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(the O3 water molecule of Zn2 is substituted). Its O2 water molecule is activated by ionization, forming the hydroxide ion (nucleophile) that attacks in line the phosphorous center, forming a pentacoordinate transition state (generally stabilized by an arginine). This attack proceeds with inversion of configuration at phosphorous and it is generally assisted by an aspartic acid (Zn2 ligand), which guides the nucleophile. Zn1 or Zn3 links to the leaving group avoiding that it reacts with the transition state and promotes the reverse reaction. The similarity between Kd1 (Zn2–Mung Bean Nuclease complex) and Kd (Zn2þ -oligo complex) values enables us to enrich the proposed hypothetical model, in the following way: as the substrate (oligo) approaches the active site of the Mung Bean Nuclease, a displacement of the Zn2 (catalytic zinc) in direction to the phosphodiester bond happens during the formation of the pentacoordinate transition state. This displacement shows that Zn2 is being shared by Mung Bean Nuclease and the oligo, promoting an ‘‘yo-yo’’ effect. Zn2 is displaced in the direction to the phosphodiester bond, exerts its function in the reaction as a catalyst, and then comes back to the active site of Mung Bean Nuclease. We can still point out that Zn1 and Zn3 are more strongly linked to Mung Bean Nuclease molecule (lower Kd values) and as a consequence the possibility of their displacement in the direction to the phosphodiester bond to act as catalyst is low. Another fact that corroborates this proposition is the steric impediment, since
Fig. 18. Schematic of the transition state formed by the cleavage of the 19 mer double-stranded oligodeoxyribonucleotide catalyzed by Mung Bean Nuclease. P, phosphate; A, adenine; T, thymine; G, guanine; H, histidine; D, aspartic acid; W, tryptophan.
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these zinc atoms are probably placed in an inaccessible region of Mung Bean Nuclease molecule, as seen for nuclease P1.
4. Supplementary material Supplementary figures indicated in text are available from the corresponding author.
Acknowledgements The authors express their gratitude to Professors A.C. Barbosa and L. Morhy for providing certain facilities, to Dr. Daniel Rigden for his help in revising the English text, and to CNPq, CAPES, and FAPDF for financial support.
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[37] G.D. Fasman, Handbook of Biochemistry and Molecular Biology, third ed., CRC Press, Cleveland, OH, 1975. [38] C.N. Pace, F. Vadjos, L. Fee, G. Grimsley, T. Gray, Protein Sci. 4 (1995) 2411. [39] J. Niu, G. Cheng, S. Dong, Electrochim. Acta 39 (1994) 2455. [40] S. Dong, D. Zhang, Acta Chim. Sin. 46 (1988) 335. [41] E. Palecek, B.D. Frary, Arch. Biochem. Biophys. 115 (1966) 431. [42] A. Volbeda, A. Lahm, F. Sakiyama, D. Suck, EMBO J. 10 (1991) 1607. [43] B.L. Vallee, D.S. Auld, Proc. Natl. Acad. Sci. USA 87 (1990) 220. [44] H.A. Saroff, H.J. Mark, J. Am. Chem. Soc. 75 (1953) 1420. [45] K.E. Van Holde, W.C. Johnson, P.S. Ho, Principles of Physical Biochemistry, Prentice-Hall, Englewood Cliffs, NJ, 1998. [46] C.S.P. Castro, Ph.D. Thesis, Universidade de Brasilia, 2001. [47] C.S.P Castro, J.R. Souza, C. Bloch Jr., in: 2001 Joint International Meeting: The 200th Meeting of Electrochemical Society and The 52nd Meeting of the International Society of Electrochemistry, San Francisco, EUA, 2001, p. 1129. [48] W. Kroeker, S. Spurgeon, Promega Notes 2 (1985). [49] P.A. Frey, Tetrahedron 38 (1982) 1541. [50] J.E. Coleman, Annu. Rev. Biochem. 61 (1992) 897. [51] C. Romier, R. Dominguez, A. Lahm, O. Dahl, D. Suck, Proteins 32 (1998) 414. [52] J.A. Gerlt, in: S.M. Linn, R.S. Lloyd, R.J. Roberts (Eds.), Nucleases, second ed., Mechanistic Principles of Enzyme-Catalyzed Cleavage of Phosphodiester Bonds, Cold Spring Harbor Laboratory Press, New York, 1993, pp. 1–34.
Mechanism of DNA cleavage catalyzed by Mung Bean Nuclease q Clarissa Silva Pires de Castro
a,*
, Jurandir Rodrigues SouzaDe b, Carlos Bloch Jr.
a
a
b
Laborat orio de Espectrometria de Massa, Embrapa Recursos Geneticos e Biotecnologia, P.O. Box 02372, Brası´lia, DF 70.770-900, Brazil Laborat orio de Quımica Analıtica e Ambiental, Instituto de Quımica, Universidade de Brasılia, P.O. Box 04394, Brası´lia, DF 70.919-970, Brazil Received 1 September 2003; accepted 7 February 2004 Available online 20 March 2004
Abstract The interaction of zinc with different forms of DNA (k phage DNA, ss-oligo, ds-oligo) and Mung Bean Nuclease was studied by voltammetric techniques in order to investigate the mechanism of DNA cleavage catalyzed by a zinc metalloenzyme. Stoichiometry, dissociation constant, zinc binding sites and functions were determined for these systems. Two zinc ions were found to be involved in stabilization of a 19 mer ds-oligodeoxyribonucleotide, which was synthesized by the phosphoramidite method and used as a DNA model in the studies. Three zinc ions (Zn1, Zn2, and Zn3), which have different roles in ds-oligo cleavage, were identified in the active site of Mung Bean Nuclease. A concerted SN 2 mechanism, which assigns a catalytic function to Zn2 and structural functions to Zn1 and Zn3, was proposed. The hydrolysis of phosphodiester bonds proceeds with inversion of configuration at the phosphorus center, forming a pentacoordinate transition state, which is stabilized by an arginine. Zn2 supplies the nucleophile, which is oriented by an aspartic acid, and activates the ds-oligo by its coordination to the phosphate free oxygen of the phosphodiester bond. Zn1 and Zn3 ions, besides stabilizing the tertiary structure of Mung Bean Nuclease, bind to the leaving group, blocking the cleavage reverse reaction. Ó 2004 Elsevier B.V. All rights reserved. Keywords: Voltammetry; DNA; Cleavage; Zinc; Mung Bean Nuclease
1. Introduction Mung Bean Nuclease [1] is a zinc metalloenzyme that catalyzes the hydrolysis of single-stranded DNA and RNA endonucleolytically to yield 50 -phosphoryl terminated products. While this nuclease prefers ssDNA over dsDNA by 30,000-fold, at very high concentrations, such as 14 U mg1 of DNA, this enzyme degrades double-stranded DNA preferentially from both ends [2]. Mung Bean Nuclease has been used for transcript mapping studies [3], flushing staggered ends and for the separation of cDNA strands after synthesis with reverse transcriptase and DNA polymerase [4]. The purification and properties of Mung Bean Nuclease have been reviewed [5]. However, little is known about the mechanism of DNA cleavage catalyzed by this enzyme. A q Supplementary data associated with this article can be found, in the online version, at doi:10.1016/j.ica.2004.02.004. * Corresponding author. Tel: +55-61-448-4671; fax: +55-61-3403658. E-mail address: [email protected] (C.S. Pires de Castro).
0020-1693/$ - see front matter Ó 2004 Elsevier B.V. All rights reserved. doi:10.1016/j.ica.2004.02.004
mechanistic study of Mung Bean Nuclease should cover the interaction of zinc with DNA and Mung Bean Nuclease, and also the catalytic mechanism of DNA cleavage. Zinc-ion binding to DNA has been studied by several techniques including UV–Vis spectroscopy [6] and equilibrium dialysis [7]. However, these techniques present considerable experimental difficulties or limitations. The utilization of UV–Vis spectroscopy is difficult in general because many metal complexes show small changes in molar absorptivity on binding to DNA [8]. Dialysis experiments reach equilibrium only in solutions of high ionic strength and at this condition the small monovalent cations, which are commonly used, compete with divalent ions for binding sites, making it difficult to measure the divalent ion binding at low concentration. Metal substitutions have proven to be a powerful tool in studying zinc metalloenzymes, by replacing the spectroscopically silent Zn(II) with paramagnetic metals, for example Co(II), Mn(II), Ni(II), Cu(II), or Cd(II). The resulting metalloderivatives can be investigated by many spectroscopic methods, such as electron
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spin/paramagnetic resonance (ES/PR), nuclear magnetic resonance (NMR), electronic absorption spectroscopy, circular dichroism (CD), magnetocircular dichroism (MCD), and perturbed angular correlation of c-rays (PAC) [9]. However, these metal exchanges have shown that the replacement of catalytic zinc with other metal ions can affect the enzyme activity profoundly. The electrochemical methods have been reported to have several advantages in determining the quantitative parameters of metal-macromolecule (DNA, proteins) complexes by studying the voltammetry of the metal ion in the absence and presence of the macromolecule and noting shifts in standard potential caused by the interaction [10–23]. These advantages include determination of qualitative and quantitative data (stoichiometry, dissociation constants, metal binding sites in DNA or protein molecule, mechanism and metal functions in the physiological reactions) of metal ion–DNA and metal ion–protein complexes near physiological conditions. A first step in understanding the catalytic mechanism of DNA cleavage by Mung Bean Nuclease is the determination of whether the enzymic reaction proceeds by direct attack of water on the phosphodiester bridge or whether a double-displacement mechanism is operative, whereby a covalent nucleotidylated-enzyme intermediate is formed and subsequently hydrolyzed. A stereochemical experiment permits distinction between these two possibilities [24–27]. Methods, whereby this question can be addressed for nucleases, have been developed in 1983 and rely on the use of dinucleoside phosphate analogs stereospecifically labelled with sulfur [28,29] or 18 O isotope [30–32]. Mung Bean Nuclease (Phaseolus aureus) has been found to cleave the Sp diastereoisomer of 50 -O-thymidyl 30 -O-(20 -deoxyadenosyl) phosphorothioate, (Sp )-d[As(S)T], in 18 O-labelled water with inversion of configuration at phosphorous to give (Sp )-thymidine 50 -[16 O,18 O]phosphorothioate [33,34]. A second step in understanding the catalytic mechanism of DNA cleavage by Mung Bean Nuclease is to know the precise role of zinc in the hydrolytic mechanism. Zinc ions can play a structural role or one of a number of catalytic roles: activation of a coordinated water molecule, recognition of a substrate, stabilization of the leaving group, among others. Experimental evaluation of the catalytic effects of zinc in Mung Bean Nuclease is problematic, since the zinc ions are intimately involved in substrate binding. In this work, several voltammetric techniques were used to investigate the mechanism of DNA cleavage catalyzed by Mung Bean Nuclease. Initially, the interaction of zinc with a natural DNA (DNA of the k bacteriophage virus) and with four synthetic models of DNA (single- and double-stranded oligodeoxyribonucleotides) was studied by differential pulse polarography (DPP), cyclic voltammetry (CV), and anodic stripping voltammetry (ASV). The second part of the work was
dedicated to the study of the interaction of Zn2þ with Mung Bean Nuclease by ASV and CV. Our main interest was focused on the cleavage of DNA catalyzed by this class of enzymes, which is an important biological process since through the DNA fragments produced, it is possible to both manipulate and map genes and identify some specific viruses and parasite groups. Zinc is an important regulatory element in the cleavage of DNA, but details of its chemical interaction with DNA and nucleases and its potential role in the ligand binding process are not well characterized. The importance of this work stems from the fact that it combines knowledge about the chemistry of metal ions with an understanding of biomolecules to perceive how complex living systems function. The growth of this new field, named bioinorganic chemistry, can be seen in a special issue of Proceedings of the National Academic of Sciences USA [35], which reports its evolution since the late 1950s with the discovery of iron in the blood and of cooper and zinc as essential elements for many physiological reactions until the beginning of the 21st century with the investigation of the linkages between inorganic elements and the information obtainable from genome sequences.
2. Experimental 2.1. Chemicals k phage DNA was purchased from Sigma Chemical Co. It was isolated from Escherichia coli Host Strain W3110 and has a 3.2 107 g mol1 molecular mass. The single-stranded oligodeoxyribonucleotides ARC5IIC2, 30 AOX1, and PR1AECO were purchased from Gibco and have 14 (MM ¼ 4.47 103 g mol1 ), 21 (MM ¼ 6.63 103 g mol1 ), and 31 (MM ¼ 1.04 104 g mol1 ) mer, respectively. The complementary strands of the double-stranded oligodeoxyribonucleotide were synthesized by the phosphoramidite method [36] using reagents purchased from Perkin–Elmer and Merck. Each strand has 19 mer, which corresponds to 5.88 103 g mol1 . Mung Bean Nuclease was purchased from Promega and Boehringer–Mannheim. It was isolated from P. aureus and has a 3.9 104 g mol1 molecular mass. All other chemicals were of reagent grade and all solutions were prepared with triple-distilled water from a quartz still (Quartex). 2.2. Apparatus Ultraviolet spectroscopic measurements were performed using U-2001 UV–Vis double beam spectrometer (Hitachi) at 260 and 280 nm. Differential pulse polarographic (DPP) and anodic stripping voltammetric (ASV) measurements were car-
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ried out on a 646 Metrohm Voltammetric Analyzer Processor connected to a 647 Metrohm electrochemical cell composed of a dropping mercury electrode or hanging mercury electrode (working electrodes), a Ag/ AgCl (3.0 M KCl) electrode (reference electrode) and a platinum electrode (auxiliary electrode). All DPP measurements were performed in the potential range 0.18 V (initial potential, Ei ) to )1.15 V (final potential, Ef ) at the following settings: surface area of the mercury drop 0.4 mm2 , pulse amplitude 50 mV, and the scan rate v ¼ 10 mV s1 . All ASV measurements were performed in the potential range )1.15 V (initial potential, Ei ) to 0.18 V (final potential, Ef ) at the following settings: accumulation potential Ed ¼ 1:15 V, accumulation time td ¼ 90 s, equilibration time te ¼ 20 s, surface area of the mercury drop 0.4 mm2 , pulse amplitude 50 mV and the scan rate v ¼ 10 mV s1 . Cyclic voltammetric (CV) measurements for k phage DNA and the single-stranded oligos ARC5IIC2, 30 AOX1, and PR1AECO were performed using a PAR 173 Potentiostat/Galvanostat or a PAR 174 polarographic system connected to a PAR 175 Universal Programmer and a Houston X–Y recorder at the following settings: initial potential Ei ¼ 0:2 V, switching potential Ew ¼ 1:6 V, and scan rate range 2 mV s1 6 v 6 100 mV s1 . A three-electrode system with a hanging mercury electrode (Metrohm) as working electrode, a Ag/AgCl (3.0 M KCl) electrode as reference electrode, and a platinum wire as the auxiliary electrode was used. Cyclic voltammetric (CV) measurements for doublestranded oligo and Mung Bean Nuclease were performed using a PAR 174 polarographic system connected to a PAR 175 Universal Programmer and a Houston X–Y recorder at the following settings: initial potential Ei ¼ 0:4 V, switching potential Ew ¼ 1:4 V, and scan rate range 2 mV s1 6 v 6 20 mV s1 . A threeelectrode system with a hanging mercury electrode (Metrohm) as working electrode, a saturated calomel electrode as reference electrode, and a platinum wire as the auxiliary electrode was used. Complementary strands of the double-stranded oligodeoxyribonucleotide were synthesized using the DNA/ RNA synthesizer model 392 (Applied Biosystems) and annealed using the MJ research PTC-100 Thermal cycler. MALDI-MS measurements were performed using the Voyager-DE STR Biospectrometry Workstation (Applied Biosystems) at the following settings: operation on linear mode, accelerating voltage 25,000 V, N2 laser, pressure at the ion source 1.11 107 torr, and pressure at detector 8.9 109 torr. 3-Hydroxypicolinic acid in ammonium citrate was used as matrix. 2.3. Procedure Prior to voltammetric measurements, k phage DNA, the single- and double-stranded oligos, and Mung Bean
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Nuclease were exhaustively dialyzed against 0.01 M EDTA at 10 °C in order to remove zinc and other metals. The resulting products were submitted to an additional dialysis step against Quartex water to remove all the EDTA and other salts. The concentration of k phage DNA and the double-stranded oligodeoxyribonucleotide was determined by UV measurements at 260 nm through the expression 1:0A260 nm DS DNA which corresponds to 50 lg mL1 [37]. The concentration of the single-stranded oligodeoxyribonucleotides was determined by UV measurements at 260 nm through the expression 1:0A260 nm SS DNA which corresponds to 33 lg mL1 [37]. The purity (freedom from bound protein) of all DNA samples was assessed from the ratio of the absorbances at 260 and 280 nm [37]. The concentration of Mung Bean Nuclease was determined by UV measurements at 280 nm through the Beer Law [37]. The molar absorption coefficient was determined by using the Edelhoch Method [38]. In order to avoid measurement interference due to DNA, oligos, Mung Bean Nuclease, and zinc adsorption on the working surfaces of the electrode system, electrodes were submitted to periodic cleaning with 20% HNO3 (v/v) followed by a generous wash with tripledistilled water. Experiments were performed at three temperatures (22, 10, and 5 °C) and preceded by a gentle N2 bubbling to prevent oxygen diffusion into the electrochemical cell (10 min for the supporting electrolyte – 0.1 M KNO3 and 3 min after each DNA/oligo or nuclease addition). The amperometric titration of zinc with k phage DNA by using differential pulse polarography and cyclic voltammetry was accomplished through additions of 5 or 10 lL of this virion DNA to the electrochemical cell containing 1.0 mL of 1.5 108 M Zn2þ in 20 mL of 0.1 M KNO3 or 1.5 mL of 1.5 108 M Zn2þ in 20 mL of 0.1 M KNO3 , respectively. The oxidation–reduction process of zinc was studied in the presence and absence of k phage DNA by using cyclic voltammetry through I (oxidation current of zinc) versus v1=2 (square root of scan rate) curves. The oxidation current of zinc was measured in the scan rate range 2 mV s1 6 v 6 50 mV s1 with and without the addition of 40 lL of 1.50 108 M k phage DNA to the electrochemical cell containing 1.5 mL of 1.50 108 M Zn2þ in 20 mL of 0.1 M KNO3 . The amperometric titration of zinc with the singlestranded oligos (ARC5IIC2, 30 AOX1, and PR1AECO) by using cyclic voltammetry was accomplished through additions of 100 lL of each oligo to the electrochemical cell containing 30 or 130 lL of 1.53 102 M Zn2þ in 25 mL of 0.1 M KNO3 . The oxidation–reduction process of zinc was studied in the presence and absence of the single-stranded oligos (ARC5IIC2, 3ÕAOX1, and PR1AECO) by using cyclic voltammetry through I (oxidation current of zinc) versus v1=2 (square root of
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scan rate) curves. The oxidation current of zinc was measured in the scan rate range 2 mV s1 6 v 6 100 mV s1 with and without the addition of 30 lL of 9.96 106 M ARC5IIC2 ss-oligo, 100 lL of 5.10 106 M 30 AOX1 ss-oligo or 500 lL of 1.13 105 M PR1AECO ss-oligo to the electrochemical cell containing 1.83 105 or 7.91 105 M Zn2þ in 25 mL of 0.1 M KNO3 . Complementary strands of the double-stranded oligodeoxyribonucleotide were synthesized by the solidphase phosphoramidite method [36] that relies on the coupling reaction between a 50 -hydroxyl group of a support-bound deoxynucleoside and an alkyl (methyl or 2-cyanoethyl) 50 -DMtr-(N-acylated)-deoxynucleoside 0 3 -O-(N,N-diisopropylamino)phosphite. The basic steps involved in one cycle of nucleotide addition using this method are: detritylation (removal of dimethoxytrityl groups) by trichloroacetic acid in methylene chloride; activation of phosphoramidite by tetrazole in acetonitrile solution; addition of activated phosphoramidite to the growing chain; blocking of chains which are not reacted during coupling reaction (capping); and oxidation of the intermediate phosphite to the phosphotriester by iodine and water. The cycle was repeated 18 times in order to obtain each 19 mer oligodeoxyribonucleotide. Deprotection and release from the support was done with concentrated aqueous ammonia at 57 °C for 12 h. MALDI-TOF/MS experiments were performed using 3.70 106 M oligo 1 and 4.25 106 M oligo 2. Both solutions were mixed with 3.59 109 M 3-hydroxypicolinic acid in 2.21 109 M ammonium citrate (8:1). About 1.0 lL of the matrix–analyte mixture was applied onto the sample plate and allowed to dry at room temperature. Annealing of complementary strands of the ds-oligo was done by mixing 7.03 107 M oligo 1 and 5.65 107 M oligo 2 in 0.01 M, pH 7.4, Tris–HCl buffer. The thermal cycler was programmed to incubate the resulting product at 95 °C for 3 min and 58 °C (theoretical Tm value) for 5 min, and then reduce the temperature to 23.5 °C at the end of the cycle. The amperometric titration of zinc with doublestranded oligo by using anodic stripping voltammetry and cyclic voltammetry was accomplished through additions of 2 or 5 lL of this oligo to the electrochemical cell containing 6.01 108 M Zn2þ in 20 mL of 0.1 M KNO3 or 6.07 109 M Zn2þ in 10 mL of 0.1 M KNO3 , respectively. The oxidation–reduction process of zinc was studied in the presence and absence of the ds-oligo by using cyclic voltammetry through I (oxidation current of zinc) versus v1=2 (square root of scan rate) curves. The oxidation current of zinc was measured in the scan rate range 2 mV s1 6 v 6 20 mV s1 with and without the addition of 10 lL of 8.13 107 M ds-oligo to the electrochemical cell containing 6.07 109 M Zn2þ in 10 mL of 0.1 M KNO3 .
The amperometric titration of zinc with Mung Bean Nuclease by using anodic stripping voltammetry and cyclic voltammetry was accomplished through additions of 5 or 10 lL of this enzyme to the electrochemical cell containing 1.71 108 M Zn2þ in 20 mL of 0.1 M KNO3 or 1.74 108 M Zn2þ in 20 mL of 0.1 M KNO3 , respectively.
3. Results and discussion 3.1. Zn2þ –DNA interactions 3.1.1. Zn2þ –k phage DNA interaction k phage is a bacterial virus composed by a protein capsid divided into an icosahedrally symmetric head that contains a DNA genome and a flexible helical tail that plays a role in attaching to the specific host bacterium (E. coli) and injecting DNA. The k genome is a linear double-stranded DNA molecule having almost 50,000 base pairs (bp) with 12 bp single-stranded complementary 50 -ends (sticky ends). It is a common substrate for restriction endonucleases and for generating DNA size markers fragments. Binding of zinc to k phage DNA was investigated by differential pulse voltammetry and cyclic voltammetry [14,17]. These methods rely on the direct monitoring of reduction and oxidation current of zinc in the absence and presence of this virion DNA. The formation of a stable complex between Zn2þ and the k phage DNA was verified by the decrease of the reduction (DPP) (see supplementary material, Figure 1S) and oxidation (CV) (Fig. 1) currents of zinc during incremental additions of this virion DNA. Titration graphs of zinc with k phage DNA were obtained in concentrations ranging from 3.57 1012 to 3.92 1011 M and 6.97 1012 to 5.56 1011 M. These data were used to calculate the stoichiometry and the dissociation constant of the complex. A stoichiometry rate of 23 Zn2þ ions (DPP) or 22 Zn2þ ions (CV), which have the function of stabilizing the double helix of the DNA by means of its interactions with the phosphate groups [14], per one k phage DNA molecule was determined for the reaction. The dissociation constant (Kd ) of Zn2þ –k phage DNA complex was calculated using the following equation [39,40]: i2p ¼
Kd ði2 i2p Þ þ i2p0 ½DNA; ½DNA p0
ð1Þ
where i2p0 is the reduction current of zinc in the absence of k phage DNA, i2p the reduction current of zinc in the presence of k phage DNA, and [DNA] the concentration of added k phage DNA in solution (M). Curves i2p versus ði2p0 i2p Þ=½DNA (Figs. 2 and 3) were plotted for Zn2þ -k phage DNA complex and two straight lines were obtained. From the slopes, the dis-
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Fig. 3. The plot i2p vs. ði2p0 i2p Þ=½DNA used to calculate the dissociation constant of Zn2þ –k phage DNA complex (CV measurements). R is the correlation coefficient; SD is the standard deviation; and P is the probability. Fig. 1. Cyclic voltammograms of 1.5 mL of 1.5 108 M Zn2þ in 20 mL of 0.1 M KNO3 with different concentrations of k phage DNA. (1) Zn2þ , no k phage DNA; (2) Zn2þ + 2.8 1011 M k phage DNA; (3) Zn2þ + 4.2 1011 M k phage DNA; (4) Zn2þ + 5.6 1011 M k phage DNA. Ei ¼ 0:2 V, Ew ¼ 1:6V , scan rate ¼ 10 mV s1 , working electrode: HMDE, reference electrode: Ag/AgCl (3 M KCl).
Fig. 4. Variation of peak current of 1.5 mL of 1.5 108 M Zn2þ in 20 mL of 0.1 M KNO3 with square root of the scan rate in absence (s) and presence () of 2.8 1011 M k phage DNA. Ei ¼ 0:2 V, Ew ¼ 1:6 V, scan rate range 2 mV s1 6 v 6 50 mV s1 , working electrode: HMDE, reference electrode: Ag/AgCl (3 M KCl). Fig. 2. The plot i2p vs. ði2p0 i2p Þ=½DNA used to calculate the dissociation constant of Zn2þ –k phage DNA complex (DPP measurements). R is the correlation coefficient; SD is the standard deviation; and P is the probability.
sociation constants were determined to be 3.44 1011 M (DPP) and 6.69 1011 M (CV). Curves I (oxidation current) versus v1=2 (square root of scan rate) show that the oxidation–reduction process of zinc is no longer controlled by diffusion in the presence of k phage DNA (Fig. 4). This phenomenon can be explained by the adsorption of k phage DNA onto mercury surface which mediates the charge transfer of bulk Zn2þ ions [14].
3.1.2. Zn2þ –ARCIIC2, Zn2þ –30 AOX1, and Zn2þ – PR1AECO interactions An oligodeoxyribonucleotide is a simple or doublestranded chain consisting of a number of deoxynucleoside units linked together by phosphodiester bridges. These macromolecules are used to identify and detect sequences of specific genes and locate specific mutations in genes of well-known sequence and in those generated by mutagenesis of cloned genes [36]. ARC5IIC2 (MM ¼ 4,472 g mol1 ) is a single-stranded oligodeoxyribonucleotide 14 mer, whose sequence (ACACCCAACGGAGA) corresponds to part of the coding region of an arcelin gene, a protein of the lectin family,
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found in seeds of wild bean. 30 AOX1 (MM ¼ 6,730 g mol1 ) is a single-stranded oligodeoxyribonucleotide 21 mer, whose sequence (GCAAATGGCATTCTGACATCC) corresponds to the 30 portion of the coding region of Pichia pastoris alcohol oxidase. PR1AECO (MM ¼ 10,038 g mol1 ) is a single-stranded oligodeoxyribonucleotide 31 mer, whose sequence (AAGAATTCGCIAAYCGTGYAAYCCIGCICAA) corresponds to a promoter region of the same gene of the ARC5IIC2 oligo. The interaction of zinc with ARC5IIC2, 30 AOX1, and PR1AECO was investigated by means of cyclic voltammetry [13,17] in order to determine optimal experimental parameters (DNA size, base sequence) for the synthesis of a model of double-stranded DNA (oligo). It was found that all the three oligos interact with zinc ions in the same way as a double-stranded DNA, causing a decrease in the reduction/oxidation current of this metal (Fig. 5; see supplementary material, Figures S2 and S3). A peak was also observed around )1.3 V in the cyclic voltammograms of the three oligos (Fig. 5; see supplementary materials, Figures S2 and S3), which can be attributed to adenine and cytosine reduction [41]. This peak is characteristic of a single-stranded DNA because in this case adenine and cytosine are free to reduce at mercury electrode and in the case of a doublestranded DNA, these bases are linked with thymine and guanine by hydrogen bonds, which blocks their reduction. Curves I (oxidation current) versus v1=2 (square
root of scan rate) show that the oxidation–reduction process of zinc is no longer controlled by diffusion in the presence of each single-stranded oligo (Figs. 6–8), as in the case of k phage DNA. With these experiments, we concluded that: both single and double-stranded DNAs interact with zinc, by the same mechanism. The size and base sequence of DNA do not interfere in the signals of this interaction, although the smaller ones produced better results. Based on these conclusions, two complementary strands of a 19 mer DNA were synthesized, consisting of 60% of GC residues and 40% of AT resi-
Fig. 6. Variation of peak current of 30 lL of 1.53 102 M Zn2þ in 25 mL of 0.1 M KNO3 with square root of the scan rate in absence (d) and presence () of 1.19 108 M ARC5IIC2 single-stranded oligo. Ei ¼ 0:2 V, Ew ¼ 1:6 V, scan rate range 2 mV s1 6 v 6 100 mV s1 , working electrode: HMDE, reference electrode: Ag/AgCl (3 M KCl).
Fig. 5. Cyclic voltammograms of 130 lL of 1.53 102 M Zn2þ in 25 mL of 0.1 M KNO3 with different concentrations of PR1AECO singlestranded oligo. (1) KNO3 , no Zn2þ and PR1AECO single-stranded oligo; (2) Zn2þ , no PR1AECO single-stranded oligo; (3) Zn2þ + 4.50 108 M PR1AECO single-stranded oligo; (4) Zn2þ + 8.97 108 M PR1AECO single-stranded oligo; (5) Zn2þ + 13.4 108 M PR1AECO single-stranded oligo; (6) Zn2þ + 17.8 108 M PR1AECO single-stranded oligo. Ei ¼ 0:2 V, Ew ¼ 1:6 V, scan rate ¼ 10 mV s1 , working electrode: HMDE, reference electrode: Ag/AgCl (3 M KCl).
Fig. 7. Variation of peak current of 30 lL of 1.53 102 M Zn2þ in 25 mL of 0.1 M KNO3 with square root of the scan rate in absence (d) and presence () of 2.03 108 M 3ÕAOX1 single-stranded oligo. Ei ¼ 0:2 V, Ew ¼ 1:6 V, scan rate range 2 mV s1 6 v 6 100 mV s1 , working electrode: HMDE, reference electrode: Ag/AgCl (3 M KCl).
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Fig. 8. Variation of peak current of 130 lL of 1.53 102 M Zn2þ in 25 mL of 0.1 M KNO3 with square root of the scan rate in absence (d) and presence () of 2.20 107 M PR1AECO single-stranded oligo. Ei ¼ 0:2V , Ew ¼ 1:6 V, scan rate range 2 mV s1 6 v 6 100 mV s1 , working electrode: HMDE, reference electrode: Ag/AgCl (3 M KCl).
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Fig. 10. MALDI-TOF/MS spectrum of 4.25 106 M oligo 2. Operation mode linear, accelerating voltage 25,000 V, N2 laser 2300 lJ cm2 , pressure at the ion source 1.11 107 torr, and pressure at detector 8.9 109 torr. 3-Hydroxypicolinic acid in ammonium citrate was used as matrix. A, adenine; C, cytosine; T, thymine; G, guanine.
3.1.3. Zn2þ –double stranded oligo interaction The melting behavior of the double-stranded oligo was monitored by measuring its UV absorption
(k ¼ 260 nm) as a function of temperature in order to verify if the methodology used for its complementary strands annealing was satisfactory [15]. A sigmoid melting curve (Fig. 11), which is composed by two steps, was observed for ds-oligo. Step 1 indicates that the dsoligo is denatured at 95 °C and step 2 indicates that it is annealed at room temperature. The melting temperature (Tm ) was found to be 54 °C and this result agrees with the theoretical value (58 °C) calculated through the expression: Tm (°C) ¼ [2 °C (number of AT base pairs) + 4 °C (number of GC base pairs)] [36]. Binding of zinc to the 19 mer double-stranded oligodeoxyribonucleotide was studied by anodic stripping voltammetry and cyclic voltammetry [15–17]. These methods rely on the direct monitoring of oxidation current of zinc in the absence and presence of this oligo. The formation of a stable complex between Zn2þ and the ds-oligodeoxyribonucleotide was verified by the
Fig. 9. MALDI-TOF/MS spectrum of 3.70 106 M oligo 1. Operation mode linear, accelerating voltage 25,000 V, N2 laser 2300 lJ cm2 , pressure at the ion source 1.11 107 torr, and pressure at detector 8.9 109 torr. 3-Hydroxypicolinic acid in ammonium citrate was used as matrix. A, adenine; C, cytosine; T, thymine; G, guanine.
Fig. 11. Melting curve obtained for double-stranded oligodeoxyribonucleotide. A, adenine; C, cytosine; T, thymine; G, guanine. 1, ds-oligo is denatured at 95 °C; 2, ds-oligo is annealed at room temperature.
dues (see supplementary material, Figure S4). The recovery rate of each step of the synthesis ranges from 97% to 100%, indicating the high efficiency of the phosphoramidite method. The purity of each strand (oligo) was assessed from the mass spectra obtained for each synthetic oligo (Figs. 9 and 10) [15], which show the appearance of only one peak. The experimental mass of these peaks (1 ¼ 5869.99 and 2 ¼ 5877.58) did not differ significantly to the theoretical values calculated for each oligo (1 ¼ 5867.71 Da and 2 ¼ 5876.71 Da). These results indicated that the two complementary strands of the 19 mer double-stranded oligo are pure and did not need an additional purification step.
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decrease of oxidation current of zinc during incremental additions of this oligo (Fig. 12; see supplementary material, Figure S5). Titration graphs of zinc with ds-oligo were obtained in concentrations ranging from
3.62 109 to 3.62 108 M and 4.06 1010 5.25 109 M. These data were used to calculate stoichiometry and the dissociation constant of complex. A stoichiometry rate of 2 Zn2þ ions per
to the the ds-
Fig. 12. Cyclic voltammograms of 6.07 109 M Zn2þ in 10 mL of 0.1 M KNO3 with different concentrations of double-stranded oligo. (1) Zn2þ , no double-stranded oligo; (2) Zn2þ + 4.06 1010 M double-stranded oligo; (3) Zn2þ + 8.12 1010 M double-stranded oligo; (4) Zn2þ + 12.2 1010 M double-stranded oligo; (5) Zn2þ + 16.2 1010 M double-stranded oligo; (6) Zn2þ + 20.3 1010 M double-stranded oligo; (7) Zn2þ + 24.3 1010 M double-stranded oligo; (8) Zn2þ + 28.3 1010 M double-stranded oligo; (9) Zn2þ + 32.4 1010 M double-stranded oligo; (10) Zn2þ + 36.4 1010 M double-stranded oligo; (11) Zn2þ + 40.4 1010 M double-stranded oligo; (12) Zn2þ + 44.5 1010 M double-stranded oligo; (13) Zn2þ + 48.5 1010 M double-stranded oligo; (14) Zn2þ + 52.5 1010 M double-stranded oligo. Ei ¼ 0:4 V, Ew ¼ 1:4 V, scan rate ¼ 20 mV s1 , working electrode: HMDE, reference electrode: saturated calomel electrode.
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oligo molecule was determined for the reaction by ASV and CV. Several lines of evidence suggest that these zinc ions interact with the two terminal phosphate groups (50 ), stabilizing the double helix of the oligo: (a) The concentration of zinc that had been used in the experiments was low (small Zn2þ :DNA-P rate), which favors the stabilization of double helix by Zn2þ ions; (b) The destabilization of the double helix is negligible when the concentration of the monovalent cation (Kþ ) is P 0.1 M and the concentration of Zn2þ is 6 104 M; (c) The absence of the peak around )1.3 V in the cyclic voltammograms obtained for the ds-oligo indicates that it is native. Consequently, Zn2þ ions cannot be linked by GC bridges because this phenomenon occurs only when DNA is denatured; (d) If zinc ions were linked by GC bridges, the obtained stoichiometry would be 10 Zn2þ ions per one ds-oligo molecule; (e) DNA regions that are rich in AT residues favor the interaction of zinc with phosphate groups [6]. The dissociation constant of Zn2þ -dsoligo complex was calculated to be 4.71 108 M (ASV) and 1.62 109 M (CV) using Eq. (1). These low Kd values are close and imply that zinc ions are probably interacting not only with the active site of the enzyme during DNA hydrolysis, but also with DNA. Curves I (oxidation current) versus v1=2 (square root of scan rate) show that the oxidation–reduction process of zinc is no longer controlled by diffusion in the presence of ds-oligo, as it had already been found for k phage DNA and the three single-stranded oligos (Fig. 13).
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monitoring of the oxidation current of zinc in the absence and presence of Mung Bean Nuclease (Figs. 14 and 15). Titration curves of zinc with the enzyme were obtained in concentrations ranging from 1.08 109 to 1.07 108 M and 1.16 108 to 1.04 107 M. The acquired data were used to calculate the stoichiometry and the dissociation constant of the complex. A stoichiometry rate of 3 Zn2þ ions per one Mung Bean Nuclease molecule was determined for the reaction by ASV and CV. This result is in agreement with the crystallographic data obtained for P1 nuclease [42]. P1 nuclease consists of 269 amino acid residues and three zinc ions per subunit. The zinc cluster in P1 nuclease is located at the bottom of the substrate binding cleft and consists of a relatively inaccessible binuclear site containing Zn1 and from each other, and a more Zn3 at a distance of 3.2 A reexposed single site containing Zn2, which is 5.8 A moved from Zn1 and 4.7 A from Zn3. Two histidine ring nitrogens (His60Nd and His116Ne ), two aspartate side chain oxygens (Asp45Od1 and Asp120Od1 ), and one
3.2. Zn2þ –Mung Bean Nuclease interaction Binding of zinc to Mung Bean Nuclease was investigated by anodic stripping voltammetry and cyclic voltammetry [18,19,22]. These methods rely on the direct
Fig. 13. Variation of peak current of 6.07 109 M Zn2þ in 10 mL of 0.1 M KNO3 with square root of the scan rate in absence () and presence (s) of 8.12 1010 M double-stranded oligo. Ei ¼ 0:4 V, Ew ¼ 1:4 V, scan rate range ¼ 2 mV s1 6 v 6 20 mV s1 , working electrode: HMDE, reference electrode: saturated calomel electrode.
Fig. 14. Anodic stripping voltammograms of 1.71 108 M Zn2þ in 20 mL of 0.1 M KNO3 with different concentrations of Mung Bean Nuclease. (1) Zn2þ , no Mung Bean Nuclease; (2) Zn2þ + 1.08 109 M Mung Bean Nuclease; (3) Zn2þ + 2.15 109 M Mung Bean Nuclease; (4) Zn2þ + 3.23 109 M Mung Bean Nuclease; (5) Zn2þ + 4.30 109 M Mung Bean Nuclease; (6) Zn2þ + 5.38 109 M Mung Bean Nuclease; (7) Zn2þ + 6.45 109 M Mung Bean Nuclease; (8) Zn2þ + 7.53 109 M Mung Bean Nuclease; (9) Zn2þ + 8.60 109 M Mung Bean Nuclease. Ed ¼ 1:15 V, td ¼ 90 s, Ei ¼ 1:15 V, Ef ¼ 0:180 V, pulse amplitude ¼ 50 mV, scan rate ¼ 10 mV s1 , working electrode: HMDE, reference electrode: Ag/AgCl (3 M KCl).
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Fig. 15. Cyclic voltammograms of 1.5 mL of 2.50 106 M Zn2þ in 20 mL of 0.1 M KNO3 with different concentrations of Mung Bean Nuclease. (1) Zn2þ , no Mung Bean Nuclease; (2) Zn2þ + 1.16 108 M Mung Bean Nuclease; (3) Zn2þ + 3.48 108 M Mung Bean Nuclease; (4) Zn2þ + 1.04 107 M Mung Bean Nuclease. T ¼ 22 °C, Ei ¼ 0:4 V, Ew ¼ 1:4 V, scan rate ¼ 5 mV s1 , working electrode: HMDE, reference electrode: saturated calomel electrode.
bridging water molecule serve as ligands for Zn1. Asp120 is also a ligand of Zn3 by its Od2 atom. Zn3 is further coordinated by His6Nd , the bridging water molecule and the main chain N and O of Trp1. The binuclear Zn site has an important function in the stabilization of the folding of P1 by tightly linking together three regions that are far apart in the amino acid sequence. The coordination of Zn2 in catalytic active sites is quite well established [43], sharing the common feature of three amino acids ligands (His126Ne , His149Ne , and Asp153Od1 ) – with two of them separated by a short spacer and the third further away in the primary sequence – and two water ligands. This suggests that Zn2 is directly involved in catalysis. The dissociation constants (Kd ) of the Zn2þ –Mung Bean Nuclease complex at 22, 10, and 5 °C were calculated to be 2.50 109 (ASV – 22 °C), 2.53 108 (CV – 22 °C), 3.24 108 (CV – 10 °C), and 5.18 108 (CV – 5 °C) M using Eq. (1). These low Kd values are close and imply that Zn2þ ions are indispensable for catalytic function and structural stability of nucleases,
which participate in the hydrolysis of genetic material (DNA and RNA) of all species. The binding sites of zinc in the Mung Bean Nuclease molecule were investigated by using cyclic voltammetry [22]. Two shifts in standard potential of zinc were noticed by studying the voltammetry of this metal ion in the absence and presence of the nuclease at 22 °C (Fig. 15). These results imply that two different kinds of zinc complexes are being formed during additions of Mung Bean Nuclease to the electrochemical cell. Similar cyclic voltammetric experiments were carried out at 10 and 5 °C, and the same voltammetric behavior was observed for zinc in the absence and presence of Mung Bean Nuclease. Based on X-ray crystallographic studies that have been done with P1 nuclease [42], it can be proposed that these complexes are the chemical species formed by the interactions of Zn2–Mung Bean Nuclease and Zn1,Zn3–Mung Bean Nuclease. Therefore, the existence of two kinds of zinc binding sites in the Mung Bean molecule can be attributed to a mononuclear exposed binding site of zinc with catalytic functions and to an inaccessible binuclear binding site of zinc with structural functions (Fig. 16). Three zinc ions, coordinated by different ligands, compose these two binding sites. Therefore, three different methods (Dong and Zhang [39,40], Saroff and Mark [44], and Scatchard plot [45]) were employed here to determine and analyze the individual dissociation constants of the three Zn2þ – Mung Bean Nuclease complexes. Table 1 shows Kd1 , Kd2 , and Kd3 values calculated for the interaction between each zinc ion and Mung Bean Nuclease by using the three methods. These results, supported by crystallographic data obtained for P1 nuclease, lead us to think that: (a) Kd1 represents the dissociation constant of the complex Zn2–Mung Bean Nuclease; (b) Kd2 and Kd3 represent the dissociation constants of Zn1–Mung Bean Nuclease and Zn3–Mung Bean Nuclease complexes, respectively. Indeed, due to its higher residual values, Kd1 fits the crystallographic model that implies the existence of a lower affinity ion, with higher mobility in the
Fig. 16. Schematic of the co-catalytic zinc site proposed for Mung Bean Nuclease. H, histidine; D, aspartic acid; W, tryptophan.
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Table 1 Kd values calculated for the interaction between each zinc ion and Mung Bean Nuclease by using Dong and Zhang, Saroff and Mark, and Scatchard Plot methods Method
Kd1 (nM)
Kd2 (nM)
Kd3 (nM)
KT (mean) (nM)
Technique
T (°C)
Dong and Zhanga Dong and Zhang Saroff and Markb Saroff and Mark Scatchard Plotc Scatchard Plot Dong and Zhang Saroff and Mark Scatchard Plot Dong and Zhang Saroff and Mark Scatchard Plot
2.31 29.7 0.148 4.00 0.0581 2.56 36.7 1.55 1.61 57.6 0.401 1.43
2.10 23.1 0.0756 2.00 0.00522 0.246 22.5 0.777 0.152 39.9 0.194 0.133
0.111 3.97 0.000112 0.0141 0.00191 0.129 2.15 0.00338 0.0797 2.89 0.000736 0.0699
2.50 25.3 0.0746 2.00 0.0217 0.978 32.4 0.777 0.614 51.8 0.199 0.541
ASV CV ASV CV ASV CV CV CV CV CV CV CV
22 22 22 22 22 22 10 10 10 5 5 5
a 2 ip ¼ kd =½MBði2p0 i2p Þ þ i2p0 ½MB, where Kd is the dissociation constant of the complex Zn2þ –Mung Bean Nuclease, i2p0 is the oxidation current of zinc in the absence of Mung Bean Nuclease, i2p is the oxidation current of zinc in the presence of Mung Bean Nuclease, [MB] the concentration of added Mung Bean Nuclease in solution. b m ¼ ðC0 Cm Þ=P ¼ Ka Cm n1 þ Ka Cm , where Ka is the association constant of the complex Zn2þ –Mung Bean Nuclease, C0 is the concentration of initial zinc, Cm is the concentration of free zinc in the equivalence point, P is the concentration of Mung Bean Nuclease in the equivalence point, n is the number of zinc binding sites, and m is the stoichiometry determined by voltammetric techniques. c m=½Zn2þ vs. m, where m is the average number of sites occupied by zinc per Mung Bean Nuclease molecule. nM ¼ 109 M.
enzyme active site in order to exert catalytic functions during the nucleic acid hydrolysis. Whilst Zn1 and Zn3 may have structural functions, since they show higher affinities to the Nuclease, hence their lower Kd values are demonstrated (Table 1). 3.3. Mechanism of DNA cleavage catalyzed by Mung Bean Nuclease The detailed mechanism of DNA cleavage by enzymes is of significant current interest. One of the most important questions in this respect is the catalytic and structural roles of metal ions such as Zn2þ . While it is clear that divalent ions play a major role in DNA hydrolysis, it is uncertain as to what function such cations have in hydrolysis and why two or three are needed in some cases and only one in others. A probable mechanism [46,47], with respect to the stereochemical course and zinc functions, for DNA (19 mer double-stranded oligodeoxyribonucleotide) cleavage catalyzed by Mung Bean Nuclease, under similar physiological conditions, is proposed here by using all the experimental results previously presented and the literature data [33,34,42,48–52]. Mung Bean Nuclease cleaves the double-stranded oligo molecule, which is stabilized by two Zn2þ ions, preferentially from both ends (regions that are rich in AT residues) under conditions of soft denaturation (high concentrations of the enzyme) and it produces three fragments, according to the reaction illustrated in Fig. 17 [48]. 3.3.1. Stereochemical course The stereochemical course of any chemical reaction is determined by the structure of the transition state of
that reaction, or in multistep reactions by the structures of transition states and intermediates. Associative and dissociative mechanisms of nucleophilic substitution at phosphorous in phosphates have been proposed based on detailed studies of non-enzymatic reactions [49]. The dissociative mechanism is a SN 1 mechanism, in which the phosphate undergoing substitution expels the leaving group in the rate limiting step, producing a planar electrophilic metaphosphate as an intermediate, which captures the nucleophile in a second step. Three associative mechanisms that differ with respect to the occurrence and decomposition of pentacovalent trigonal bipyramidal intermediates have been proposed. The first associative mechanism is a concerted SN 2, in which the nucleophile attacks from the side opposite the leaving group and displaces it in a single step. Substitution of this mechanism proceeds with inversion of configuration at a chiral phosphorous center. The two other associative mechanisms differ from the foregoing in that they involve intermediates and they differ in the manner in which the intermediates are produced and decomposed. In the second associative mechanism, the nucleophile approaches from the side opposite the leaving group, forming a bond to the phosphorous atom. The resulting pentacovalent trigonal bipyramidal intermediate, which has the displacing nucleophile and the leaving group in the apical positions and the other three substituents in the equatorial plane, decomposes and forms the products by the departure of R1 OH group from its apical position. The stereochemical course dictated by this mechanism involves inversion of configuration at chiral phosphorous. In the third associative mechanism, the leaving group is in the equatorial plane while the nucleophile is in an apical position of the first intermediate.
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Fig. 17. Cleavage of the 19 mer double-stranded oligodeoxyribonucleotide catalyzed by Mung Bean Nuclease. P, phosphate; A, adenine; C, cytosine; T, thymine; G, guanine.
The expulsion of the leaving group must be preceded by a pseudorotatory rearrangement to a second intermediate in which the two apical groups of the first intermediate become equatorial and two equatorial groups become apical. R1 OH then departs from its apical position in the second intermediate. The overall stereochemical course dictated by this mechanism involves retention of configuration at chiral phosphorous. Hamblin et al. [33,34] studied the stereochemical course of DNA cleavage catalyzed by Mung Bean Nuclease using a deoxydinucleoside phosphorothioate analog stereospecifically labelled with 18 O isotope. They demonstrated that the hydrolysis of phosphodiester bonds proceeds with inversion of configuration at phosphorous and presumably via a direct ‘‘in-line’’ attack of water opposite the 30 OH-R leaving group, rather than via the intermediacy of a covalent nucleotidyl-enzyme intermediate. Similarly, we can propose a concerted SN2 mechanism for the double-stranded oligodeoxyribonucleotide cleavage catalyzed by Mung Bean Nuclease (see supplementary material, Figure S6). 3.3.2. Zinc functions Based on crystallographic studies, three different mechanisms were proposed to explain zinc functions in
the DNA cleavage catalyzed by P1 Nuclease. All the mechanisms involve the nucleophilic attack of one water molecule, which is activated by one zinc atom, and the stabilization of a pentacoordinate transition state by an arginine-48. But, they assign different functions to the three zinc atoms and to the water molecules of P1 nuclease crystalline structure. In the first mechanism [42,50], Zn2 activates the water molecule, and the DNA and Zn1 and Zn3 stabilize the leaving group. In the second mechanism [51], Zn1 and Zn3 activate the water molecule, and Zn2 activates the DNA and stabilizes the leaving group. In the third mechanism [52], Zn1 and Zn3 activate the DNA and stabilize the leaving group and Zn2 activates the water molecule. Analyzing our Kd values (Table 1), which show that Zn1 and Zn3 have higher affinities to Mung Bean Nuclease (lower Kd values) and Zn2 has higher mobility in the enzyme active site (higher Kd value), we conclude that the first mechanism is the most appropriate to explain the functions of zinc atoms in the ds-oligo cleavage catalyzed by Mung Bean Nuclease. The proposed mechanism (Fig. 18) assigns a catalytic function to Zn2 and structural functions to Zn1 and Zn3. Zn2 activates the ds-oligo by means of its coordination to the free oxygen from the phosphate of the phosphodiester bond
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(the O3 water molecule of Zn2 is substituted). Its O2 water molecule is activated by ionization, forming the hydroxide ion (nucleophile) that attacks in line the phosphorous center, forming a pentacoordinate transition state (generally stabilized by an arginine). This attack proceeds with inversion of configuration at phosphorous and it is generally assisted by an aspartic acid (Zn2 ligand), which guides the nucleophile. Zn1 or Zn3 links to the leaving group avoiding that it reacts with the transition state and promotes the reverse reaction. The similarity between Kd1 (Zn2–Mung Bean Nuclease complex) and Kd (Zn2þ -oligo complex) values enables us to enrich the proposed hypothetical model, in the following way: as the substrate (oligo) approaches the active site of the Mung Bean Nuclease, a displacement of the Zn2 (catalytic zinc) in direction to the phosphodiester bond happens during the formation of the pentacoordinate transition state. This displacement shows that Zn2 is being shared by Mung Bean Nuclease and the oligo, promoting an ‘‘yo-yo’’ effect. Zn2 is displaced in the direction to the phosphodiester bond, exerts its function in the reaction as a catalyst, and then comes back to the active site of Mung Bean Nuclease. We can still point out that Zn1 and Zn3 are more strongly linked to Mung Bean Nuclease molecule (lower Kd values) and as a consequence the possibility of their displacement in the direction to the phosphodiester bond to act as catalyst is low. Another fact that corroborates this proposition is the steric impediment, since
Fig. 18. Schematic of the transition state formed by the cleavage of the 19 mer double-stranded oligodeoxyribonucleotide catalyzed by Mung Bean Nuclease. P, phosphate; A, adenine; T, thymine; G, guanine; H, histidine; D, aspartic acid; W, tryptophan.
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these zinc atoms are probably placed in an inaccessible region of Mung Bean Nuclease molecule, as seen for nuclease P1.
4. Supplementary material Supplementary figures indicated in text are available from the corresponding author.
Acknowledgements The authors express their gratitude to Professors A.C. Barbosa and L. Morhy for providing certain facilities, to Dr. Daniel Rigden for his help in revising the English text, and to CNPq, CAPES, and FAPDF for financial support.
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