Nucleobases Adenine Research Articles

Lysine linkage in abasic site-binding ligand-thiazole orange conjugates for improved binding affinity to orphan nucleobases in DNA/RNA hybrids.

Introduction of lysine linkage in the conjugate between abasic site-binding ligands and thiazole orange significantly improved the binding affinity for target orphan adenine or uracil nucleobase in DNA/RNA hybrids.

Mechanisms and energetics for N-glycosidic bond cleavage of protonated adenine nucleosides: N3 protonation induces base rotation and enhances N-glycosidic bond stability.

Our previous gas-phase infrared multiple photon dissociation action spectroscopy study of protonated 2'-deoxyadenosine and adenosine, [dAdo+H](+) and [Ado+H](+), found that both N3 and N1 protonated conformers are populated with the N3 protonated ground-state conformers predominant in the experiments. Therefore, N-glycosidic bond dissociation mechanisms of N3 and N1 protonated [dAdo+H](+) and [Ado+H](+) and the associated quantitative thermochemical values are investigated here using both experimental and theoretical approaches. Threshold collision-induced dissociation (TCID) of [dAdo+H](+) and [Ado+H](+) with Xe is studied using guided ion beam tandem mass spectrometry techniques. For both systems, N-glycosidic bond cleavage reactions are observed as the major dissociation pathways resulting in production of protonated adenine or elimination of neutral adenine. Electronic structure calculations are performed at the B3LYP/6-311+G(d,p) level of theory to probe the potential energy surfaces (PESs) for N-glycosidic bond cleavage of [dAdo+H](+) and [Ado+H](+). Relative energetics of the reactants, transition states, intermediates and products along the PESs for N-glycosidic bond cleavage are determined at the B3LYP/6-311+G(2d,2p), B3LYP-GD3BJ/6-311+G(2d,2p), and MP2(full)/6-311+G(2d,2p) levels of theory. The predicted N-glycosidic bond dissociation mechanisms for the N3 and N1 protonated species differ. Base rotation of the adenine residue enables formation of a strong N3H(+)O5' hydrogen-bonding interaction that stabilizes the N3 protonated species and its glycosidic bond. Comparison between experiment and theory indicates that the N3 protonated species determine the threshold energies, as excellent agreement between the measured and B3LYP computed activation energies (AEs) and reaction enthalpies (ΔHrxns) for N-glycosidic bond cleavage of the N3 protonated species is found.

A Study of π-π Stacking Interactions and Aromaticity in Polycyclic Aromatic Hydrocarbon/Nucleobase Complexes.

We analysed the interactions and aromaticity electron-density delocalisation observed in π-π complexes between the phenalenyl radical and acenaphthylene, and the DNA and RNA nucleobases (adenine, guanine, cytosine, thymine and uracil). Interaction energies are obtained at the M06-2X/6-311++G(2df,p) computational level for gas phase and PCM-water conditions. For both the phenalenyl radical and acenaphthylene, the complexes formed with guanine are the most stable ones. Atoms in molecules and natural bond orbital results reveal weak π-π interactions between both interacting moieties, characterized by bond critical points between C⋅⋅⋅C and C⋅⋅⋅N atoms. Nucleus independent chemical shifts (NICS) indicate the retention of the aromatic character of the monomers in the outer region of the complex. The fluctuation indexes reveal a loss of electron delocalisation upon complexation for all cases except guanine complexes. Nevertheless, the interface region shows large negative NICS values, which is not associated with an increase of the aromaticity or electron-density delocalisation, but with magnetic couplings of both molecules, leading to an unrealistic description of the aromatic behaviour in that region.

Photoelectron spectroscopy of hexachloroplatinate-nucleobase complexes: Nucleobase excited state decay observed via delayed electron emission.

We report low-temperature photoelectron spectra of isolated gas-phase complexes of the hexachloroplatinate dianion bound to the nucleobases uracil, thymine, cytosine, and adenine. The spectra display well-resolved, distinct peaks that are consistent with complexes where the hexachloroplatinate dianion is largely intact. Adiabatic electron detachment energies for the hexachloroplatinate-nucleobase complexes are measured as 2.26-2.36 eV. The magnitudes of the repulsive Coulomb barriers (RCBs) of the complexes are all ∼1.7 eV, values that are lower than the RCB of the uncomplexed PtCl6 (2-) dianion as a result of charge solvation by the nucleobases. In addition to the resolved spectral features, broad featureless bands indicative of delayed electron detachment are observed in the 193 nm photoelectron spectra of the four clusters. The 266 nm spectra of the PtCl6 (2-) ⋅ thymine and PtCl6 (2-) ⋅ adenine complexes also display very prominent delayed electron emission bands. These results mirror recent results on the related Pt(CN)4 (2-) ⋅ nucleobase complexes [A. Sen et al., J. Phys. Chem. B 119, 11626 (2015)]. The observation of delayed electron emission bands in the PtCl6 (2-) ⋅ nucleobase spectra obtained in this work, as for the previously studied Pt(CN)4 (2-) ⋅ nucleobase complexes, is attributed to one-photon excitation of nucleobase-centred excited states that can effectively couple to the electron detachment continuum, producing strong electron detachment. Moreover, the selective, strong excitation of the delayed emission bands in the 266 nm spectra is linked to fundamental differences in the individual nucleobase photophysics at this excitation energy. This strongly supports our previous suggestion that the dianion within these clusters can be viewed as a "dynamic tag" which has the propensity to emit electrons when the attached nucleobase decays over a time scale long enough to allow autodetachment.

DFT Investigation of the Mechanism of Action of Organoiridium(III) Complexes As Anticancer Agents.

The potential use of synthetic metal complexes able to catalyze chemical transformations in living organisms is currently attracting a great deal of attention. Recently, organometallic ruthenium and iridium complexes have revealed an unexpected ability to modulate the redox status of cancer cells. In particular, half-sandwich organoiridium(III) cyclopentadienyl complexes of general formula [(η(5)-Cp(x))Ir(III)(X(∧)Y)Z](0/+), where Cp(x) = Cp*, Cp(xph) (tetramethyl-(phenyl)cyclopentadienyl) or Cp(xbiph) (tetramethyl(biphenyl)-cyclopentadienyl), X(∧)Y = bidentate ligand with nitrogen, oxygen, and/or carbon donor atoms, and Z = Cl, H2O, or pyridine (py) have shown promising antiproliferative activity toward cancer cells, higher potency than cisplatin, and a different mechanism of action due to the increase of the oxidative stress in cells. As such, complexes can belong to the class of DNA interacting compounds and attack on DNA can represent a secondary mechanism of action. We have explored here by means of density functional calculations (M06-L) and with the support of experimental observations for both [(η(5)-Cp(xbiph))Ir-(phpy) (Cl)], 1-Cl, and [(η(5)-Cp(xbiph))Ir-(phpy) (py)], 1-py, complexes the mechanistic aspects of the hydrolysis reaction, H2O2 ROS production by assisted hydride transfer from NADH to molecular oxygen, interaction with purine nucleobases adenine and guanine as well as gluthatione, that is highly abundant in cells, alongside the reaction mechanism for the oxidation of the formed sulfur-coordinated thiolate to the corresponding sulfenato complex. The comparison between kinetic and thermodynamic parameters calculated for all the involved processes shows that, according to the hypothesis based on experimental findings, the interaction with the tripeptide glutathione causes deactivation of 1-Cl, whereas 1-py, in both its aquated and nonaquated form, can induce cell apoptosis in a dual manner: DNA damage and H2O2 ROS production to increase oxidative stress.

Synthetic G-Quartets as Versatile Nanotools for the Luminescent Detection of G-Quadruplexes.

Recent years have witnessed a tremendous increase in the biotechnological applications of nucleic acid-based nanotools. Beyond their biological relevance, nucleobases have indeed found new scopes of applications in bionanotechnology, which are expanding nowadays at an accelerated pace. Among the four canonical nucleobases (adenine, guanine, cytosine and thymine), guanine is certainly the most useful and used base, thanks to its versatile H-bond donating/accepting properties that make it suitable for being involved in various assemblies ranging from base-pairs to base-quartets. Here, we would like to report on an innovative guanine-based molecular tool named Tb. Pyro-DOTASQ: this metal complex has a sophisticated chemical structure that allows formation of an intramolecular G-quartet upon interaction with alternative secondary structures known as G-quadruplexes. This target-promoted molecular switch triggers a luminescence response that would permit the use of Tb. Pyro-DOTASQ to search and detect quadruplex-forming DNA and RNA sequences: its unique design indeed allows it i) to create specific interaction with quadruplexes, ii) to provide an easily readable luminescent output to monitor this association and iii) to be readily immobilized on graphene surface, thus making Tb. Pyro-DOTASQ a high-value molecular device. Results obtained in the course of in-depth biophysical analyses raise questions about the actual supramolecular structure of Tb. Pyro-DOTASQ: these results thus shed a bright light on the care that must be exercised when using intricate molecular architectures to construct elaborated supramolecular metal complexes.

Crystal structure of the Varkud satellite ribozyme.

Varkud Satellite (VS) ribozyme mediates rolling circle replication of a plasmid found in the Neurospora mitochondria. We report crystal structures of this ribozyme at 3.1Å resolution, revealing an intertwined dimer formed by an exchange of substrate helices. Within each protomer, an arrangement of three-way helical junctions organizes seven helices into a global fold that creates a docking site for the substrate helix of the other protomer, resulting in the formation of two active sites in trans. This mode of RNA-RNA association resembles the process of domain swapping in proteins and has implications for RNA regulation and evolution. Within each active site, adenine and guanine nucleobases abut the scissile phosphate, poised to serve direct roles in catalysis. Similarities to the active sites of the hairpin and hammerhead ribozymes highlight the functional significance of active site features, underscore the ability of RNA to access functional architectures from distant regions of sequence space, and suggest convergent evolution.

Water-mediated recognition of t1-adenosine anchors Argonaute2 to microRNA targets.

MicroRNAs (miRNAs) direct post-transcriptional regulation of human genes by guiding Argonaute proteins to complementary sites in messenger RNAs (mRNAs) targeted for repression. An enigmatic feature of many conserved mammalian miRNA target sites is that an adenosine (A) nucleotide opposite miRNA nucleotide-1 confers enhanced target repression independently of base pairing potential to the miRNA. In this study, we show that human Argonaute2 (Ago2) possesses a solvated surface pocket that specifically binds adenine nucleobases in the 1 position (t1) of target RNAs. t1A nucleotides are recognized indirectly through a hydrogen-bonding network of water molecules that preferentially interacts with the N6 amine on adenine. t1A nucleotides are not utilized during the initial binding of Ago2 to its target, but instead function by increasing the dwell time on target RNA. We also show that N6 adenosine methylation blocks t1A recognition, revealing a possible mechanism for modulation of miRNA target site potency.

Branching of poly(ADP-ribose): Synthesis of the Core Motif.

The synthesis of the core motif of branched poly(adenosine diphosphate ribose) (poly(ADPr)) is described, and structural analysis reasserted the proposed stereochemistry for branching. For the synthesis, a ribose trisaccharide was first constructed with only α-O-glycosidic linkages. Finally, the adenine nucleobase was introduced via a Vorbrüggen-type glycosylation reaction. The orthogonality of the selected protecting groups was demonstrated, allowing for the construction of branched poly(ADPr) oligomers in the near future.

Synthesis and X-ray crystal structure of the dirhenium complex Re2(i-C3H7COO)4Cl2 and its interactions with the DNA purine nucleobases

The dirhenium complex Re2(i-C3H7COO)4Cl2 was synthesized and characterized by X-ray crystallography, 1H NMR and electronic spectroscopies, and electrospray ionization-mass spectrometry. The reactions of Re2(i-C3H7COO)4Cl2 with the substituted DNA purine nucleobases guanine (9-methylguanine and 9-ethylguanine) and adenine (9-methyladenine and 9-ethyladenine) were investigated by proton nuclear magnetic resonance and electronic spectroscopies as well as electrospray ionization-mass spectrometry. The data corroborate binding of two 9-methylguanine (or 9-ethylguanine) and 9-methyladenine (or 9-ethyladenine) bases per dirhenium unit in a bidentate fashion, in equatorial positions, via sites N7/O6 and N1/N6, respectively, with concomitant substitution of two carboxylate groups to form a single isomer of cis-Re2(i-C3H7COO)2(nucleobase)2Cl2. The binding of the bases to the dirhenium core disrupts important nucleobase interactions and may have important biological implications with respect to the anticancer activity of dirhenium complexes.

SEEDING THE PREGENETIC EARTH: METEORITIC ABUNDANCES OF NUCLEOBASES AND POTENTIAL REACTION PATHWAYS

Carbonaceous chondrites are a class of meteorite known for having a high content of water and organics. In this study, abundances of the nucleobases, i.e., the building blocks of RNA and DNA, found in carbonaceous chondrites are collated from a variety of published data and compared across various meteorite classes. An extensive review of abiotic chemical reactions producing nucleobases is then performed. These reactions are then reduced to a list of 15 individual reaction pathways that could potentially occur within meteorite parent bodies. The nucleobases guanine, adenine and uracil are found in carbonaceous chondrites in the amounts of 1$-$500 ppb. It is currently unknown which reaction is responsible for their synthesis within the meteorite parent bodies. One class of carbonaceous meteorites dominate the abundances of both amino acids and nucleobases$-$the so-called CM2 (e.g. Murchison meteorite). CR2 meteorites (e.g. Graves Nunataks) also dominate the abundances of amino acids, but are the least abundant in nucleobases. The abundances of total nucleobases in these two classes are $330 \pm250$ ppb and $16 \pm13$ ppb respectively. Guanine most often has the greatest abundances in carbonaceous chondrites with respect to the other nucleobases, but is 1$-$2 orders of magnitude less abundant in CM2 meteorites than glycine (the most abundant amino acid). Our survey of the reaction mechanisms for nucleobase formation suggests that Fischer-Tropsch synthesis (i.e. CO, H$_2$ and NH$_3$ gases reacting in the presence of a catalyst such as alumina or silica) is the most likely for conditions that characterize early states of planetesimals.

Differential nucleobase protection against 5-fluorouracil toxicity for squamous and columnar cells: implication for tissue function and oncogenesis.

SummaryPurpose The goal of these studies was to test if local excess of a normal nucleobase substrate prevents the toxicity of protracted 5FU exposure used in human cancer treatment. Methods Messenger RNA expression studies were performed of 5FU activating enzymes in human colon cancer cells lines (CaCo-2, HT-29), primary human gingival cells (HEGP), and normal esophageal and gastric clinical tissue samples. Excess nucleobase was then used in vitro to protect cells from 5FU toxicity. Results Pyrimidine salvage pathways predominate in squamous cells of the gingiva (HEGP) and esophageal tissue. Excess salvage nucleobase uracil but not adenine prevented 5FU toxicity in HEGP cells. Pyrimidine de novo synthesis predominates in columnar Caco-2, HT-29 and gastric tissue. Excess nucleobase adenine but not uracil prevented 5FU toxicity to Caco-2 and HT-29 cells. Conclusion The directed application of the normal nucleobase uracil to the squamous cells of the oral mucosa and palms and soles together with the delivery of the normal nucleobase adenine to the columnar cells of the GI tract may enable the safe delivery of higher 5FU dose intensity. These results also suggest a feature of tissue function where squamous cells grow largely by recycling overlying tissue cell components. Columnar cells use absorbed surface nutrients for de novo growth. A disruption of this tissue function can result in growth derived from an underlying nutrient source. That change would also cause the loss of the region of cell turnover at the tissue surface. Subsequent cell proliferation with limiting nutrient availability could promote oncogenesis in such initiated tissue.

Kinetics and Thermodynamics of the Reaction between the (•)OH Radical and Adenine: A Theoretical Investigation.

The accessibility of all possible reaction paths for the reaction between the nucleobase adenine and the (•)OH radical is investigated through quantum chemical calculations of barrier heights and rate constants at the ωB97X-D/6-311++G(2df,2pd) level with Eckart tunneling corrections. First the computational method is validated by considering the hydrogen abstraction from the heterocyclic N9 nitrogen in adenine as a test system. Geometries for all molecules in the reaction are optimized with four different DFT exchange-correlation functionals (B3LYP, BHandHLYP, M06-2X, and ωB97X-D), in combination with Pople and Dunning basis sets, all of which have been employed in similar investigations in the literature. Improved energies are obtained through single point calculations with CCSD(T) and the same basis sets, and reaction rate constants are calculated for all methods both without tunneling corrections and with the Wigner, Bell, and Eckart corrections. In comparison to CCSD(T)//BHandHLYP/aug-cc-pVTZ reference results, the ωB97X-D/6-311++G(2df,2pd) method combined with Eckart tunneling corrections provides a sensible compromise between accuracy and time. Using this method, all subreactions of the reaction between adenine and the (•)OH radical are investigated. The total rate constants for hydrogen abstraction and addition for adenine are predicted with this method to be 1.06 × 10(-12) and 1.10 × 10(-12) cm(3) molecules(-1) s(-1), respectively. Abstractions of H61 and H62 contribute the most, while only addition to the C8 carbon is found to be of any significance, in contrast to previous claims that addition is the dominant reaction pathway. The overall rate constant for the complete reaction is found to be 2.17 × 10(-12) cm(3) molecules(-1) s(-1), which agrees exceptionally well with experimental results.

A New Analogue of Locked Cyclohexane Nucleic Acids

We report on a new analogue of locked cyclohexane nucleic acids that contains an adenine nucleobase at an alternative position and which resembles homo-DNA. The crucial locked carbocyclic nucleo­side monomer was prepared with high enantioselectivity and was subsequently incorporated into a pair of modified oligonucleotides that were subjected to hybridization studies.

Atomic polarization justified Fukui indices and the affinity indicators in aromatic heterocycles and nucleobases

Atomic Fukui indices have been calculated by integration of the polarization justified Fukui functions over the atomic basins. Resulting indices have been explored in the definition of the atomic and group affinity indicator and softnesses on the ground of the formal analysis of the polarization effect. These indicators combine the effect of the atomic charge and atomic Fukui index. They are potentially applicable in testing a sensing effect on a molecule induced by an approaching point agent, nucleophilic (−) or electrophilic (+), at a distance in the order of v.d. Waals radii. Calculated atomic and group affinity and softness indicators have been proved to be consistent with the well established trends of reactivity for a control group of the five-atom-ring heterocycles (imidazole, oxazole, thiazole). The indices have been applied to the set of 5 nucleobases (adenine, guanine, cytosine, thymine, uracyl), whose diverse reactivity towards electrophiles has been recognized as a key factor determining the sensitivity of DNA to cytotoxic agents. The pairing effect of the nucleobases bases in the DNA chain and the experimental trends of the site reactivity of these molecules have been properly accounted for by the calculated indicators.

Measurements of single nucleotide electronic states as nanoelectronic fingerprints for identification of DNA nucleobases, their protonated and unprotonated states, isomers, and tautomers.

Several nanoelectronic techniques have been explored to distinguish the sequence of nucleic acids in DNA macromolecules. Identification of unique electronic signatures using nanopore conductance, tunneling spectroscopy, or other nanoelectronic techniques depends on electronic states of the DNA nucleotides. While several experimental and computational studies have focused on interaction of nucleobases with different substrates, the effect of nucleic acid biochemistry on its electronic properties has been largely unexplored. Here, we present correlated measurements of frontier molecular orbitals and higher-order electronic states for four DNA nucleobases (adenine, cytosine, thymine, and guanine), and first-principle quantum chemical density functional theoretical (DFT) computations. Using different pH conditions in our experiments, we show that small changes in the biochemical state of these nucleic acids strongly affect the intrinsic electronic structure, measured using scanning tunneling spectroscopy (STS). In our experimental measurements and computations, significant differences were observed between the position of frontier orbitals and higher-energy states between protonated and unprotonated nucleic acids, isomers, and different keto-enol tautomer's formed in these nucleotides, leading to their facile identification. Furthermore, we show unique "electronic fingerprints" for all nucleotides (A, G, T, C) using STS, with most distinct states identified at acidic pH. These results can have important implications for identification of nucleic acid sequences in DNA molecules using a high-throughput nanoelectronic identification technique.

Improved Performance of OLEDs on Cellulose/Epoxy Substrate Using Adenine as a Hole Injection Layer

Organic light-emitting diodes (OLED) fabricated from all “natural” materials will lead to renewable, sustainable, and potentially inexpensive organic optoelectronics. Achieving this goal will require reimagining all the various aspects of the OLED with natural-based renewable materials. Here, we replace the common substrate, electrode, and hole injection layer in the OLED structure with cellulose, gold, and the DNA nucleobase adenine. Gold films are used as semitransparent electrodes on plant-based cellulose substrates, providing flexible anodes that are highly conductive without annealing. A lift-off fabrication method (template stripping) employed UV curable epoxy to transfer patterned gold from silicon to cellulose. The gold has excellent adhesion to the epoxy (is not damaged when wiped), and the two serve as a smoothing layer for the cellulose substrate, resulting in very uniform OLED emission. DNA and DNA nucleobases are demonstrating to be versatile materials in natural electronics due to their wide...

Sequential injection-adsorptive stripping voltammetric quantitation of purine nucleobases using an electrochemically activated carbositall electrode

The present paper describes an electroanalytical application of an activated carbositall electrode (ACSE) for the detection of purine nucleobases (adenine and guanine) and their derivatives by sequential injection-adsorptive stripping voltammetric approach (SI-AdSVA). It was found that ACSE characterized by significant electrocatalytic and adsorptive abilities toward investigated compounds over a wide pH range, good stability and reproducibility under the fixed hydrodynamic conditions. Utilizing on-line adsorption accumulation of an analyte during 120s, the limit of detection (S/N=3σ) was achieved down to 8ng/mL (50nM) and 10ng/mL (75nM) for guanine and adenine, respectively. It was demonstrated that the proposed SI-AdSVA method could be efficiently used for the routine analysis of real samples with satisfactory results.

Adenine suppresses IgE-mediated mast cell activation

Nucleobase adenine is produced by dividing human lymphoblasts mainly from polyamine synthesis and inhibits immunological functions of lymphocytes. We investigated the anti-allergic effect of adenine on IgE-mediated mast cell activation in vitro and passive cutaneous anaphylaxis (PCA) in mice. Intraperitoneal injection of adenine to IgE-sensitized mice attenuated IgE-mediated PCA reaction in a dose dependent manner, resulting in a median effective concentration of 4.21mg/kg. In mast cell cultures, only adenine among cytosine, adenine, adenosine, ADP and ATP dose-dependently suppressed FcɛRI (a high affinity receptor for IgE)-mediated degranulation with a median inhibitory concentration of 1.6mM. It also blocked the production of LTB4, an inflammatory lipid mediator, and inflammatory cytokines TNF-α and IL-4. In addition, adenine blocked thapsigargin-induced degranulation which is FcɛRI-independent but shares FcɛRI-dependent signaling events. Adenine inhibited the phosphorylation of signaling molecules important to FcɛRI-mediated allergic reactions such as Syk, PLCγ2, Gab2, Akt, and mitogen activated protein kinases ERK and JNK. From this result, we report for the first time that adenine inhibits PCA in mice and allergic reaction by inhibiting FcɛRI-mediated signaling events in mast cells. Therefore, adenine may be useful for the treatment of mast cell-mediated allergic diseases. Also, the upregulation of adenine production may provide another mechanism for suppressing mast cell activity especially at inflammatory sites.

DNA bases assembled on the Au(110)/electrolyte interface: a combined experimental and theoretical study.

Among the low-index single-crystal gold surfaces, the Au(110) surface is the most active toward molecular adsorption and the one with fewest electrochemical adsorption data reported. Cyclic voltammetry (CV), electrochemically controlled scanning tunneling microscopy (EC-STM), and density functional theory (DFT) calculations have been employed in the present study to address the adsorption of the four nucleobases adenine (A), cytosine (C), guanine (G), and thymine (T), on the Au(110)-electrode surface. Au(110) undergoes reconstruction to the (1 × 3) surface in electrochemical environment, accompanied by a pair of strong voltammetry peaks in the double-layer region in acid solutions. Adsorption of the DNA bases gives featureless voltammograms with lower double-layer capacitance, suggesting that all the bases are chemisorbed on the Au(110) surface. Further investigation of the surface structures of the adlayers of the four DNA bases by EC-STM disclosed lifting of the Au(110) reconstruction, specific molecular packing in dense monolayers, and pH dependence of the A and G adsorption. DFT computations based on a cluster model for the Au(110) surface were performed to investigate the adsorption energy and geometry of the DNA bases in different adsorbate orientations. The optimized geometry is further used to compute models for STM images which are compared with the recorded STM images. This has provided insight into the physical nature of the adsorption. The specific orientations of A, C, G, and T on Au(110) and the nature of the physical adsorbate/surface interaction based on the combination of the experimental and theoretical studies are proposed, and differences from nucleobase adsorption on Au(111)- and Au(100)-electrode surfaces are discussed.