Analysis of DNA complexes with small solutes by CE with LIF detection

In this article, we describe the analysis of aptamers for Hg²⁺ ions through CE with LIF (CE‐LIF) detection using 2% poly(ethylene oxide) solutions containing OliGreen (fluorophore). In the presence of an EOF, DNA strands migrating against the EOF were detected at the cathode end. Four DNA strands – T₃₃, T₅C₂₈, T₅C₅T₂₃, and T₁₅C₅T₁₃ – could not be separated through CE‐LIF in the absence of Hg²⁺. At 0.3 mM Hg²⁺, however, all four were partially separated within 20 min, with SDs of the migration times all being less than 2.5%. From the CE, fluorescence, and ellipticity data, we concluded that the conformations of these four DNA strands all changed from random‐coil to folded structures as a result of T–Hg²⁺–T bonding. In addition, we found that this CE approach provided different electropherograms patterns for T₇, T₁₅, and T₃₃ in the absence and presence of Hg²⁺, indicating various interactions of the DNA strands with Hg²⁺. Using this simple, high‐resolution CE approach, we also demonstrated that adenosine triphosphate has a stronger interaction with the adenosine triphosphate aptamer than with either the platelet‐derived growth factor aptamer or T₃₃. This CE approach holds great potential for screening aptamers for small solutes, studying the catalytic activity of DNAzymes, and evaluating the biological functions of microRNA.     

The Relationship between DNA Sequences and Oligonucleotide‐Templated Silver Nanoclusters and Their Fluorescence Properties

A novel approach was developed to study the relationship between DNA sequences and DNA‐templated silver nanoclusters (DNA‐Ag NCs) in detail by using an ordinary DNA strand as an example. Three kinds of Ag NCs are formed by using the DNA strand as a scaffold. By dividing the DNA template into several parts according to their different affinities to Ag⁺, it was found that the fluorescence properties of DNA‐Ag NCs are related to not only the sequences but also to the position of different parts in the template, which provides a more efficient approach to obtain DNA‐Ag NCs with required photoluminescence properties and may ultimately contribute to the targeted synthesis of DNA‐Ag NCs.     

Water-soluble homo-oligonucleotide stabilized fluorescent silver nanoclusters as fluorescent probes for mercury ion

Water–soluble fluorescent silver nanoclusters (Ag NCs) were prepared with the assistance of commercially available polyinosinic acid (PI) or polycytidylic acid (PC). The fluorescence of the Ag NCs is effectively quenched by trace mercury(II) ions, which can be applied for their detection. The response of the Ag NCs prepared with PI to Hg(II) ion is linear in the Hg(II) concentration range from 0.05 to 1.0 μM (R²?=?0.9873), and from 0.5 to 10 μM of Hg(II) (R²?=?0.9971) for Ag NCs prepared with PC. The detection limits are 3.0 nM and 9.0 nM (at an S/N of 3), respectively. The method is simple, sensitive and fairly selective.

Using electrospray ionization mass spectrometry to explore the interactions among polythymine oligonucleotides, ethidium bromide, and mercury ions

We have used electrospray ionization mass spectrometry (ESI-MS) and fluorescence and circular dichroism (CD) spectroscopy to explore the binding of ethidium bromide (EthBr) to non-self-complementary polythymine (polyT) strands in the absence and presence of Hg²⁺ ions. In the gas phase, ESI-MS revealed that Hg²⁺ ions have greater affinity, through T-Hg²⁺-T coordination, toward polyT strands than do other metal ions. These findings are consistent with our fluorescence and CD results obtained in solution; they revealed that more T₃₃-EthBr-Hg²⁺ complexes existed upon increasing the concentrations of Hg²⁺ ions (from 0 to 50 μM). Surprisingly, the ESI-MS data indicated that the Hg²⁺ concentration dependence of the interaction between T₃₃ and EthBr is biphasic. Our ESI-MS data revealed that the T₃₃-EthBr-Hg²⁺ complexes formed with various stoichiometries depending on their relative concentrations of the components and the length of the DNA strand. When the concentrations of T₃₃/EthBr/Hg²⁺ were 5/5/2. 5 μM and 5/10/7. 5 μM, 1:1:1 and 1:1:2 T₃₃-EthBr-Hg²⁺ complexes were predominantly formed, respectively. Thus, Hg²⁺-induced DNA conformational changes clearly affect the interactions between DNA and EthBr.     

Fluorescent Silver Nanoclusters as Effective Probes for Highly Selective Detection of Mercury(II) at Parts‐per‐Billion Levels

Facile preparation of water‐soluble and fluorescent Ag nanoclusters (NCs) stabilized by glutathione at room temperature is described. Although the glutathione layer was introduced to prevent the silver nanoparticles from decomposition and increase their water solubility, this simple surface optimization resulted in surprisingly high efficiency of selective Hg²⁺ sensing, where the limit of detection (LOD) was as low as 10^?10 M (0.02 ppb, 0.1 nM ). This result revealed a simple and practical strategy for Hg²⁺ detection using fluorescent Ag NCs as sensor probe, with the lowest detecting limits reported to date.     

Cytidine-stabilized gold nanocluster as a fluorescence turn-on and turn-off probe for dual functional detection of Ag and Hg

In this study, we have developed a label-free, dual functional detection strategy for highly selective and sensitive determination of aqueous Ag⁺ and Hg²⁺ by using cytidine stabilized Au NCs and AuAg NCs as fluorescent turn-on and turn off probes, respectively. The Au NCs and AuAg NCs showed a remarkably rapid response and high selectivity for Ag⁺ and Hg²⁺ over other metal ions, and relevant detection limit of Ag⁺ and Hg²⁺ is ca. 10 nM and 30 nM, respectively. Importantly, the fluorescence enhanced Au NCs by doping Ag⁺ can be conveniently reusable for the detection of Hg²⁺ based on the corresponding fluorescence quenching. The sensing mechanism was based on the high-affinity metallophilic Hg²⁺–Ag⁺ interaction, which effectively quenched the fluorescence of AuAg NCs. Furthermore, these fluorescent nanoprobes could be readily applied to Ag⁺ and Hg²⁺ detection in environmental water samples, indicating their possibility to be utilized as a convenient, dual functional, rapid response, and label-free fluorescence sensor for related environmental and health monitoring.     

Lighting‐Up of the Dye Malachite Green with Mercury(II)–DNA and Its Application for Fluorescence Turn‐Off Detection of Cysteine and Glutathione

This work describes a novel strategy for the highly sensitive and selective detection of cysteine (Cys) and glutathione (GSH) based on the Hg²⁺–AGRO100–malachite green (MG) complex system. The dye MG, which has a very low quantum yield in aqueous solution by itself, can bind with the thymine‐rich DNA AGRO100 in the presence of Hg²⁺ ions to generate a striking fluorescence intensity enhancement of 1000‐fold. As sulfur‐containing amino acids, Cys and GSH effectively sequester Hg²⁺ ions from the Hg²⁺–AGRO100–MG complex structure to switch the ‘lit‐up’ chemosensor to the ‘off’ state (about a 50‐fold fluorescence intensity decrease), thus providing a facile, but effective, method to probe for Cys/GSH. The fluorescence titration, UV absorption, CD, and Raman spectra provide some insight into the structural and chemical basis for the enhancement effect. The formation of the Hg²⁺–AGRO100–MG complex significantly affects the electronic structure and conformation of the MG molecule by leading to an extended π system, which is the likely origin of the observed striking fluorescence intensity enhancement. Notably, the proposed sensing platform exhibits exquisite selectivity and sensitivity toward Cys/GSH with limits of detection of 5 nM for Cys and 10 nM for GSH, respectively. Furthermore, the straightforward assay design avoids labeling of the probe, uses only commercially available materials, and still displays comparable sensitivity and excellent selectivity.     

Metal-Triggered DNA Folding by Different Mechanisms

Metal-mediated base pairs by the interaction between metal ions and artificial bases in oligonucleotides has been widely used in DNA nanotechnology and biosensing technique. Using isothermal titration calorimetry, circular dichroism spectroscopy and fluorescence spectroscopy, the folding process of T-C-rich oligonucleotides (TCO) induced by Hg²⁺ and Ag⁺ with the synthetic sequence d(T₆C₆T₆C₆T₆C₆T₆) was studied and analyzed. Although thermodynamic data predict that TCO should initially fold into a relatively stable hairpin through two possible pathways of conformational transitions whether Hg²⁺ or Ag⁺ were added at first, the mechanisms and final products between the two are entirely different from isothermal titration calorimetry outcomes. When Hg²⁺ were added first, the haipin was formed through T-Hg-T structure with further stabilization by C-Ag-C after Ag⁺ addition. However, it is proposed that an unusual metal-base pair for Ag⁺ binding is generated instead classical C-Ag-C when Ag⁺ was injected first. Moreover, further confirmation of this unconventional metal-base pair T-Ag-C was verified by circular dichroism and fluorescence spectroscopy.     

Development of silver/gold nanocages onto indium tin oxide glass as a reagentless plasmonic mercury sensor

We demonstrate the utilization of silver/gold nanocages (Ag/Au NCs) deposited onto transparent indium tin oxide (ITO) film glass as the basis of a reagentless, simple and inexpensive mercury probe. The localized surface plasmon resonance (LSPR) peak wavelength was located at ∼800 nm. By utilizing the redox reaction between Hg²⁺ ions and Ag atoms that existed in Ag/Au NCs, the LSPR peak of Ag/Au NCs was blue-shifted. Thus, we develop an optical sensing probe for the detection of Hg²⁺ ions. The LSPR peak changes were lineally proportional to the concentration of Hg²⁺ ions over the range from 10 ppb to 0.5 ppm. The detection limit was ∼5 ppb. This plasmonic probe shows good selectivity and high sensitivity. The proposed optical probe is successfully applied to the sensing of Hg²⁺ in real samples.     

A Terbium Metal–Organic Framework for Highly Selective and Sensitive Luminescence Sensing of Hg2+ Ions in Aqueous Solution

A series of isomorphic lanthanide metal–organic frameworks (MOFs) Ln(TATAB)?(DMF)₄(H₂O)(MeOH)_0.5 (LnTATAB, Ln=Eu, Tb, Sm, Dy, Gd; H₃TATAB=4,4′,4′′‐s‐triazine‐1,3,5‐triyltri‐p‐aminobenzoic acid) have been solvothermally synthesized and structurally characterized. Among these MOFs, TbTATAB exhibits good water stability and a high fluorescence quantum yield. Because mercury ions (Hg²⁺) have a high affinity to nitrogen atoms, and the space between multiple nitrogen atoms from triazine and imino groups is suitable for interacting with Hg²⁺ ions, TbTATAB shows highly selective and sensitive detection of Hg²⁺ in aqueous solution with a detection limit of 4.4 nm . Furthermore, it was successfully applied to detect Hg²⁺ ions in natural water samples.     

Polymer‐based fluorescence sensors incorporating chiral binaphthyl and benzo[2,1,3]thiadiazole moieties for Hg2+ detection

Three chiral polymers P‐1 , P‐2 , and P‐3 could be obtained by the polymerization of (R)‐6,6′‐dibutyl‐3,3′‐diiodo‐2, 2′‐binaphthol (R‐M‐1) , (R)‐6,6′‐dibutyl‐3,3′‐diiodo‐2,2′‐bisoctoxy‐1,1′‐binaphthyl ( R‐M‐2 ), and (R)‐6,6′‐dibutyl‐3,3′‐diiodo‐2,2′‐bis (diethylaminoethoxy)‐1,1′‐binaphthyl ( R‐M‐3 ) with 4,7‐diethynyl‐benzo[2,1,3]‐thiadiazole ( M‐1) via Pd‐catalyzed Sonogashira reaction, respectively. P‐1 , P‐2 , and P‐3 can show pale red, blue–green, and orange fluorescence. The responsive optical properties of these polymers on various metal ions were investigated by fluorescence spectra. Compared with other cations, such as Co²⁺, Ni²⁺, Ag⁺, Cd²⁺, Cu²⁺, and Zn²⁺, Hg²⁺ can exhibit the most pronounced fluorescence response of these polymers. P‐1 and P‐2 show obvious fluorescence quenching effect upon addition of Hg²⁺, on the contrary, P‐3 shows fluorescence enhancement. Three polymer‐based fluorescent sensors also show excellent fluorescence response for Hg²⁺ detection without interference from other metal ions. The results indicate that these kinds of tunable chiral polybinaphthyls can be used as fluorescence sensors for Hg²⁺ detection. © 2010 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 48: 997–1006, 2010     

Crystal structure of a NIR‐Emitting DNA‐Stabilized Ag16 Nanocluster

DNA has been used as a scaffold to stabilize small, atomically monodisperse silver nanoclusters, which have attracted attention due to their intriguing photophysical properties. Herein, we describe the X‐ray crystal structure of a DNA‐encapsulated, near‐infrared emitting Ag₁₆ nanocluster (DNA–Ag₁₆NC). The asymmetric unit of the crystal contains two DNA–Ag₁₆NCs and the crystal packing between the DNA–Ag₁₆NCs is promoted by several interactions, such as two silver‐mediated base pairs between 3′‐terminal adenines, two phosphate–Ca²⁺–phosphate interactions, and π‐stacking between two neighboring thymines. Each Ag₁₆NC is confined by two DNA decamers that take on a horse‐shoe‐like conformation and is almost fully shielded from the solvent environment. This structural insight will aid in the determination of the structure/photophysical property relationship for this class of emitters and opens up new research opportunities in fluorescence imaging and sensing using noble‐metal clusters.     

Aptamer-modified AuRe Nanoalloy Probe for Trace Hg2+ Using Resonance Scattering as Detection Technique

The AuRe nanoalloy particles in molar ratio of 9:1 were prepared by sodium borohydride procedure, and modified by single strand DNA (ssDNA) to prepare an aptamer AuRe nanoprobe (AuRessDNA) for Hg²⁺. In the pH 7.0 Na₂HPO₄‐NaH₂PO₄ buffer solution and in the presence of NaCl, Hg²⁺ interacted with AuRessDNA to form double‐stranded T‐Hg²⁺‐T mismatched and release AuRe nanoparticles that aggregate to large AuRe nanoparticles clusters causing the resonance scattering (RS) peak red shifting and the RS intensity enhanced linearly. On those grounds, 0.067–33.3 nmol·L^?1 Hg²⁺ can be detected rapidly by the aptamer‐modified AuRe nanoparticles RS assay, with a detection limit of 0.04 nmol·L^?1 Hg²⁺. If the aggregated AuRe particles were removed by membrane filtration, the excess AuRessDNA in the filtration solution exhibits catalytic effect on the new Te particle reaction between Na₂TeO₄ and SnCl₂. As the concentration of Hg²⁺ increased, the AuRessDNA nanoparticles in the filtrate solution decreased, the RS intensity at 734 nm decreased linearly. The Hg²⁺ concentration (c) in the range of 0.00133–0.267 nmol·L^?1 was linear to the decreased RS intensity (ΔI_734nm), with a regression equation of ΔI= ?786.4c?4.4, a correlation coefficient of 0.9975, and a detection limit of 0.9 pmol·L^?1 Hg²⁺. This method was applied to the detection of Hg²⁺ in water samples, with satisfactory results.     

Label-free colorimetric sensor for mercury(II) and DNA on the basis of mercury(II) switched-on the oxidase-mimicking activity of silver nanoclusters

In this paper, a novel colorimetric biosensor for Hg²⁺ and DNA molecules is presented based on Hg²⁺ stimulated oxidase-like activity of bovine serum albumin protected silver clusters (BSA-Ag NCs). Under mild conditions, Hg²⁺ activated BSA-Ag NCs to show high catalytic activity toward the oxidation of 3,3′,5, 5′-tetramethylbenzidine (TMB) using ambient dissolved oxygen as an oxidant. The oxidase-like activity of BSA-Ag NCs was “switched-on” selectively in the presence of Hg²⁺, which permitted a novel and facile colorimetric sensor for Hg²⁺. As low as 25 nmol L⁻¹ Hg²⁺ could be detected with a linear range from 80 nmol L⁻¹ to 50 mmol L⁻¹. In addition, the sensing strategy was also employed to detect DNA molecules. Hg²⁺ is known to bind very strongly and specifically with two DNA thymine bases (T) to form thymine–Hg²⁺–thymine (T–Hg²⁺–T) base pairs. The hairpin-structure was disrupted and Hg²⁺ ions were released after hybridization with the DNA target. By coupling the Hg²⁺ switched-on the oxidase-mimicking activity of BSA-Ag NCs, we developed a novel label-free strategy for facile and fast colorimetric detection of DNA molecules. More important, target DNA can be detected as low as 10 nmol L⁻¹ with a linear range from 30 to 225 nmol L⁻¹. Compared with other methods, this method presents several advantages such as the independence of hydrogen peroxide, high sensitivity and good selectivity, avoiding any modification or immobilization of DNA, which holds a great potential of metal NCs for clinical application in biosensing and biotechnology.     

Incorporating Rare‐Earth Terbium(III) Ions into Cs2AgInCl6:Bi Nanocrystals toward Tunable Photoluminescence

The incorporation of impurity ions or doping is a promising method for controlling the electronic and optical properties and the structural stability of halide perovskite nanocrystals (NCs). Herein, we establish relationships between rare‐earth ions doping and intrinsic emission of lead‐free double perovskite Cs₂AgInCl₆ NCs to impart and tune the optical performances in the visible light region. Tb³⁺ ions were incorporated into Cs₂AgInCl₆ NCs and occupied In³⁺ sites as verified by both crystallographic analyses and first‐principles calculations. Trace amounts of Bi doping endowed the characteristic emission (⁵D₄→⁷F_6‐3) of Tb³⁺ ions with a new excitation peak at 368 nm rather than the single characteristic excitation at 290 nm of Tb³⁺. By controlling Tb³⁺ ions concentration, the emission colors of Bi‐doped Cs₂Ag(In_1?xTb_x)Cl₆ NCs could be continuously tuned from green to orange, through the efficient energy‐transfer channel from self‐trapped excitons to Tb³⁺ ions. Our study provides the salient features of the material design of lead‐free perovskite NCs and to expand their luminescence applications.     

Carbazole‐based conjugated polymer covalently coated Fe3O4 nanoparticle as efficient and reversible Hg2+ optical probe

A type of fluorescent–magnetic dual‐function nanocomposite, Fe₃O₄@SiO₂@P‐2, was successfully obtained by Cu⁺‐catalyzed click reaction between acetylene (C?C? H)‐substituted carbazole‐based conjugated polymer ( P‐2) and azide‐terminated silica‐coated magnetic iron oxide nanoparticles (Fe₃O₄@SiO₂–N₃). Optical and magnetization analyses indicate that Fe₃O₄@SiO₂@P‐2 exhibits stable fluorescence and rapid magnetic response. The fluorescence of Fe₃O₄@SiO₂@P‐2 was quenched significantly in the presence of I^? and gave a detection limit (DL) of ～8.85 × 10^?7 M. Given the high binding constant and matching ratio between Hg²⁺ and I^?, the fluorescence of Fe₃O₄@SiO₂@P‐2/I^? complex recovered efficiently with the addition of Hg²⁺. A DL of ～4.17 × 10^?7 M was obtained by this probing system. Recycling of Fe₃O₄@SiO₂@P‐2 probe was readily achieved by simple magnetic separation. Results indicate that Fe₃O₄@SiO₂@P‐2 can be used as an “on–off–on” fluorescent switchable and recyclable Hg²⁺ probe. © 2013 Wiley Periodicals, Inc. J. Polym. Sci., Part A: Polym. Chem. 2013, 51, 3636–3645     

Colloidal Synthesis and Charge‐Carrier Dynamics of Cs2AgSb1−yBiyX6 (X: Br,Cl; 0 ≤y ≤1) Double Perovskite Nanocrystals

A series of lead‐free double perovskite nanocrystals (NCs) Cs₂AgSb_1?yBi_yX₆ (X: Br, Cl; 0≤y≤1) is synthesized. In particular, the Cs₂AgSbBr₆ NCs is a new double perovskite material that has not been reported for the bulk form. Mixed Ag–Sb/Bi NCs exhibit enhanced stability in colloidal solution compared to Ag–Bi or Ag–Sb NCs. Femtosecond transient absorption studies indicate the presence of two prominent fast trapping processes in the charge‐carrier relaxation. The two fast trapping processes are dominated by intrinsic self‐trapping (ca. 1–2 ps) arising from giant exciton–phonon coupling and surface‐defect trapping (ca. 50–100 ps). Slow hot‐carrier relaxation is observed at high pump fluence, and the possible mechanisms for the slow hot‐carrier relaxation are also discussed.     

Fluorescence detection of mercury(II) and lead(II) ions using aptamer/reporter conjugates

We have developed a fluorescence technique for the detection of Hg²⁺ and Pb²⁺ ions using polythymine (T₃₃)/benzothiazolium-4-quinolinium dimer derivative (TOTO-3) and polyguanine (G₃₃)/terbium ions (Tb³⁺) conjugates, respectively. Hg²⁺ ions induce T₃₃ to form folded structures, leading to increased fluorescence of the T₃₃/TOTO-3 conjugates. Because Pb²⁺ ions compete with Tb³⁺ ions to form complexes with G₃₃, the extent of formation of the G₃₃-Tb³⁺ complexes decreases upon increasing the Pb²⁺ concentration, leading to decreased fluorescence at 545 nm when excited at 290 nm. To minimize interference from Hg²⁺ ions during the detection of Pb²⁺ ions, we conducted two-step fluorescence measurements; prior to addition of the G₃₃/Tb³⁺ probe, we recorded the fluorescence of a mixture of the T₃₃/TOTO-3 conjugates and Hg²⁺ ions. The fluorescence signal obtained was linear with respect to the Hg²⁺ concentration over the range 25.0-500 nM (R² = 0.99); for Pb²⁺ ions, it was linear over the range 3.0-50 nM (R² = 0.98). The limits of detection (at a signal-to-noise ratio of 3) for Hg²⁺ and Pb²⁺ ions were 10.0 and 1.0 nM, respectively. Relative to other techniques for the detection of Hg²⁺ and Pb²⁺ ions in soil and water samples, our present approach is simpler, faster, and more cost-effective.     

Selective Detection of Hg2+ Ions with Boron Dipyrromethene‐Based Fluorescent Probes Appended with a Bis(1,2,3‐triazole)amino Receptor

By using a copper‐promoted alkyne–azide cycloaddition reaction, two boron dipyrromethene (BODIPY) derivatives bearing a bis(1,2,3‐triazole)amino receptor at the meso position were prepared and characterized. For the analogue with two terminal triethylene glycol chains, the fluorescence emission at 509 nm responded selectively toward Hg²⁺ ions, which greatly increased the fluorescence quantum yield from 0.003 to 0.25 as a result of inhibition of the photoinduced electron transfer (PET) process. By introducing two additional rhodamine moieties at the termini, the resulting conjugate could also detect Hg²⁺ ions in a highly selective manner. Upon excitation at the BODIPY core, the fluorescence emission of rhodamine at 580 nm was observed and the intensity increased substantially upon addition of Hg²⁺ ions due to inhibition of the PET process followed by highly efficient fluorescence resonance energy transfer (FRET) from the BODIPY core to the rhodamine moieties. The Hg²⁺‐responsive fluorescence change of these two probes could be easily seen with the naked eye. The binding stoichiometry between the probes and Hg²⁺ ions in CH₃CN was determined to be 1:2 by Job′s plot analysis and ¹H NMR titration, and the binding constants were found to be (1.2±0.1)×10¹¹ m ^?2 and (1.3±0.3)×10¹⁰ m ^?2, respectively. The overall results suggest that these two BODIPY derivatives can serve as highly selective fluorescent probes for Hg²⁺ ions. The rhodamine derivative makes use of a combined PET‐FRET sensing mechanism which can greatly increase the sensitivity of detection.     

Colloidal Synthesis and Charge‐Carrier Dynamics of Cs2AgSb1−yBiyX6 (X: Br,Cl; 0 ≤y ≤1) Double Perovskite Nanocrystals

A series of lead‐free double perovskite nanocrystals (NCs) Cs₂AgSb_1?yBi_yX₆ (X: Br, Cl; 0≤y≤1) is synthesized. In particular, the Cs₂AgSbBr₆ NCs is a new double perovskite material that has not been reported for the bulk form. Mixed Ag–Sb/Bi NCs exhibit enhanced stability in colloidal solution compared to Ag–Bi or Ag–Sb NCs. Femtosecond transient absorption studies indicate the presence of two prominent fast trapping processes in the charge‐carrier relaxation. The two fast trapping processes are dominated by intrinsic self‐trapping (ca. 1–2 ps) arising from giant exciton–phonon coupling and surface‐defect trapping (ca. 50–100 ps). Slow hot‐carrier relaxation is observed at high pump fluence, and the possible mechanisms for the slow hot‐carrier relaxation are also discussed.