Intramolecular Electrostatic Interactions Research Articles

Structural and guanosine triphosphate/diphosphate requirements for transit peptide recognition by the cytosolic domain of the chloroplast outer envelope receptor, Toc34.

Toc34 is a transmembrane protein located in the outer envelope membrane of chloroplasts and involved in transit peptide recognition. The cytosolic region of Toc34 reveals 34% alpha-helical and 26% beta-strand structure and is stabilized by intramolecular electrostatic interaction. Toc34 binds both chloroplast preproteins and isolated transit peptides in a guanosine triphosphate- (GTP-) dependent mechanism. In this study we demonstrate that the soluble, cytosolic domain of Toc34 (Toc34deltaTM) functions as receptor in vitro and is capable to compete with the import of the preprotein of the small subunit (preSSU) of ribulose-1,5-bisphosphate carboxylase-oxygenase into chloroplasts in a GTP-dependent manner. We have developed a biosensor assay to study the interaction of Toc34deltaTM with purified preproteins and transit peptides. The results are compared with the interactions of both a full-size preprotein and the transit peptide of preSSU with the translocon of the outer envelope of chloroplasts (Toc complex) in situ. Several mutants of the transit peptide of preSSU were evaluated to identify amino acid segments that are specifically recognized by Toc34. We present a model of how Toc34 may recognize the transit peptide and discuss how this interaction may facilitate interaction and translocation of preproteins via the Toc complex in vivo.

The pKa's of 2‘-Hydroxyl Group in Nucleosides and Nucleotides

This thesis is based on nine research publications (I – IX) on structure and reactivity of RNA vis-a-vis DNA. The DNA and RNA are made of flexible pentose sugar units, polyelectrolytic phosphodiester backbone, and heterocyclic nucleobases. DNA stores our genetic code, whereas RNA is involved both in protein biosynthesis and catalysis. Various ligand-binding and recognition properties of DNA/RNA are mediated through inter- and intra-molecular H-bonding and stacking interactions, beside hydration, van der Waal and London dispersion forces. In this work the pH dependant chemical shift, pKa values of 2'-OH group as well as those the nucleobases in different sequence context, alkaline hydrolysis of the internucleotidic phosphodiester bonds and analysis of NOESY footprints along with NMR constrained molecular dynamics simulation were used as tools to explore and understand the physico-chemical behavior of various nucleic acid sequences, and the forces involved in their self-assembly process. Papers I – II showed that the ionization of 2'-OH group is nucleobase-dependant. Paper III showed that the chemical characters of internucleotidic phosphate are non-identical in RNA compared to that of DNA. Papers IV – VI show that variable intramolecular electrostatic interactions between electronically coupled nearest neighbor nucleobases in a ssRNA can modulate their respective pseudoaromatic character, and result in creation of a unique set of aglycons with unique properties depending on propensity and geometry of nearest neighbor interaction. Paper VII showed that the cross-modulation of the pseudoaromatic character of nucleobases by the nearest neighbor is sequence-dependant in nature in oligonucleotides. Paper VIII showed that the purine-rich hexameric ssDNA and ssRNA retain the right-handed helical structure (B-type in ssDNA and A-type in ssRNA) in the single-stranded form even in absence of intermolecular hydrogen bonding. The directionality of stacking geometry however differs in ssDNA compared to ssRNA. In ssDNA the relatively electron-rich imidazole stacks above the electron-deficient pyrimidine in the 5' to 3' direction, in contradistinction, the pyrimidine stacks above the imidazole in the 5' to 3' direction in ssRNA. Paper IX showed that the pKa values of the nucleobases in monomeric nucleotides can be used to show that a RNA-RNA duplex is more stable than a DNA-DNA duplex. The dissection of the relative strength of base-pairing and stacking showed that the relative contribution of former compared to that of the latter in an RNA-RNA over the corresponding DNA-DNA duplexes decreases with the increasing content of A-T/U base pairs in a sequence.

Molecular structure of bis(pyridiniumvalerate) hydrogen perchlorate studied by X-ray diffraction, FTIR spectroscopy, PM3 and SAM1 calculations

In the crystal structure of bis(pyridiniumvalerate) hydrogen perchlorate, determined by X-ray diffraction, a pair of pyridiniumvalerate molecules form a linear cation bridged by a very strong hydrogen bond of length 2.458(9)Å. The positively charged N atoms of the cation interact electrostatically with the carboxylate groups from neighbouring molecules and also with the disordered perchlorate anions. The FTIR spectrum of the compound shows an intense broad (continuum) absorption below 2000cm−1, typical of short-strong hydrogen bonds, and a single νCO band at 1706cm−1. The PM3 and SAM1 calculations predict a non-linear structure of the isolated cation due to intramolecular electrostatic interactions of the N+ atoms with COO− groups. The effect of the number of CH2 groups on the conformation and geometry of the COO group in dimeric cation of pyridine betaines is discussed.

Intramolecular Coulomb repulsion and anisotropies of the repulsive Coulomb barrier in multiply charged anions

Photoelectron spectra of the three isomers of the benzene dicarboxylate dianion (o-, m-, and p-BDC2−) were measured in the gas phase at five photon energies. Detachment features from the carboxylate groups and the π electrons of the ring were clearly observed and distinguished. The electron binding energies were found to increase from the very small value of ∼0.2 eV in o-BDC2− to about 1.0 eV in p-BDC2−, due to the reduced Coulomb repulsion as the two excess charges become farther apart. We found that the repulsive Coulomb barrier (RCB) for detaching electrons from the carboxylates decreases from o-BDC2− to p-BDC2−. However, the RCB for detaching the ring π electrons was found to be significantly higher and remain constant for the three isomers. This distinct anisotropy in the RCB involving different detachment channels is related to the different intramolecular Coulomb repulsions experienced by electrons localized on the carboxylates and the ring. Theoretical calculations were performed to obtain the equilibrium structures of both the dianions and the monoanions and to gain insight into the intramolecular electrostatic interactions. The two carboxylates in m- and p-BDC2− were shown to be in-plane with the ring whereas the strong Coulomb repulsion in o-BDC2− forces the carboxylate groups out of the plane of the ring. The theoretical results clearly show the localized nature of the excess charges on the carboxylates and help us understand the intramolecular Coulomb repulsions within the three dianions.

Probing Bacterial Electrosteric Interactions Using Atomic Force Microscopy

Atomic force microscopy (AFM) was used to probe the effects of pH, ionic strength, and the presence of bacterial surface polymers on interaction forces between individual, negatively charged bacteria and silicon nitride. Bacterial surface polymers dominated interactions between bacteria and AFM silicon nitride tips. The measured forces were represented well by an electrosteric repulsion model accounting for repulsion between the tip and bacterial polymers but were much larger in magnitude and extended over longer distances (100’s of nanometers) than predicted by DLVO theory. The equilibrium length (Lo) of the polymers was allowed to vary with solution chemistry to account for intramolecular electrostatic interactions between individual polymer units. The effects of the variables pH and ionic strength on bacterial interaction forces were investigated independently. Pseudomonas putida KT2442 was studied

Theoretical Study of the Role of Boron−Nitrogen Dative Bonds in the Physiological Action of Boronated Compounds

Some boronated molecules have shown surprising physiological action; however, the mode of action of these compounds is not understood. Our hypothesis is that the boron moiety is attracted to Lewis base sites on an enzyme and the resulting interaction causes an inhibition of the physiological pathway. To study this problem, quantum mechanical calculations of boron−nitrogen bond dissociation energies for 12 molecules have been calculated and compared with physiological activities including anti-hyperlipidemic and anti-neoplastic behavior. Results of linear correlation analysis between bond dissociation energy and physiological action have shown evidence that our hypothesis has merit. Possible locations of enzyme inhibition by boronated compounds are inferred. In addition, structural and energetic features of boronated molecules, including intramolecular electrostatic interactions and Lewis acidity, are discussed.

Synthesis and 13C NMR chemical shift assignments of 2,2'-bipyridine-4,4'-dicarboxylates of bile acid methyl esters

Novel 2,2'-bipyridine-4,4'-dicarboxylates 3a-3d of four bile acid methyl esters have been synthesized from 2,2'-bipyridine-4,4'-dicarboxylic acid 1 and the corresponding bile acid methyl esters (methyl lithocholate 2a, methyl chenodeoxycholate 2b, methyl deoxycholate 2c, and methyl cholate 2d). In addition to the desired products, 3α -(2,6-dichlorophenylcarboxy) bile acid methyl esters 4a-4d were obtained. The structures of 3a-4d have been ascertained by 1 D 1 H and 13 C NMR, 2 D PFG 1 H, 13 C HMQC, and MALDI TOF MS. Molecular weights and 13 C NMR chemical shifts of 3a-4d have been presented. The geometry of 3a has been optimized semi- empirically at the PM3 level and it has been observed that the minimum energy structure of 3a is a open type conformation due to lack of attractive intramolecular electrostatic interactions between the heads of the molecule which would have favoured the formation of cleft type structure. The synthesized bipyridine-bile acid conjugates are interesting structures from the molecular recognition point of view because they could have potential to form complexes with some transition metal ions, for example with silver, cadmium, and ruthenium.

On the unfolding of ?-lytic protease and the role of the pro region

Molecular dynamics simulations of alpha-lytic protease (alphaLP) alone and complexed with its pro region (PRO) are performed to understand the origin of its high unfolding (and folding) barrier when it is alone and how the pro region lowers this barrier. At room temperature, alphaLP exhibits lower dynamic fluctuations than alpha-chymotrypsin. Simulation of PRO alone led to reorientation of its N terminal helix and collapse to a more compact state. A model for the uncleaved proenzyme was built and found to be stable in the time scale of the simulations. Energetic analysis suggests that the origin of strain in the uncleaved proenzyme compared with the cleaved complex is in the intramolecular backbone electrostatic interactions of the cleaved strand. In high temperature simulations, the interaction of the long beta hairpin of the enzyme with the C terminal beta sheet of PRO is among the most stable in the complex and a likely "nucleation site" for folding. In the course of unfolding, the C terminal tail of PRO is sometimes observed to intervene between the long hairpin and the aspartate loop of the enzyme, perhaps thereby lowering the energy barrier for separation of the two hairpins. Tighter interactions at the interface between the enzyme and its pro region are also occasionally observed, providing an additional mechanism for unfolding catalysis. Simulations of a mutant enzyme where the buried ion pair residues R102 and D142 were replaced by W and L, respectively, did not display any distinguishable behavior compared with the wild type.

Hydrogen bonding effects on coordinated sulfoxides and relative role of intra- and inter-molecular interactions determining the dmso orientation in [RR′NHOH][fac-RuCl3(dmso)3] compounds: a crystallographic and molecular mechanics study

Compounds with hydroxyl ammonium cations, [RR′NHOH][fac-RuCl3(dmso–S)3], with R=R′=H (1), R=Me, R′=H (2) and R=R′=Et (3), have been prepared and structurally characterized by X-ray analyses. The three compounds display chain-like structures, formed by hydrogen bonding between the hydroxyl ammonium cations and the chlorine and oxygen atoms of the ruthenium anion. H-bonding involving the dmso oxygen atoms causes a lengthening of the S–O bonds. The comparison of the solid state structures with results of Molecular Mechanics calculations show that the arrangement of the fac-dmso–S ligands is not determined by H-bonding or packing effects, but from intramolecular steric and electrostatic interactions. These give rise to hindered rotation about the Ru–S bonds.

Photodetachment of Gaseous Multiply Charged Anions, Copper Phthalocyanine Tetrasulfonate Tetraanion: Tuning Molecular Electronic Energy Levels by Charging and Negative Electron Binding

We report photodetachment photoelectron spectroscopy (PES) of gaseous copper phthalocyanine (CuPc) tetrasulfonate quadruply charged anions, [CuPc(SO3)4]4-, and its monoprotonated and -sodiumated triply charged anions, [CuPc(SO3)4H]3- and [CuPc(SO3)4Na]3-. The [CuPc(SO3)4]4- tetraanion was found to possess a negative electron binding energy of −0.9 eV, whereas the trianions have binding energies of 1.0 and 1.2 eV for the sodiumated and protonated species, respectively. The PES spectral features of the three multiply charged anions were observed to be similar to that of the parent CuPc neutral molecule, except that the anions have lower binding energies due to the presence of the negative charges (−SO3-). The data thus suggested a stepwise tuning of the molecular electronic energy levels of the CuPc molecule through charging, wherein the molecular orbital energies of the parent molecule were systematically pushed up by the negative charges. We further carried out semiempirical calculations, which provided insight into the nature of the localized charges on the peripheral −SO3- groups and the intramolecular electrostatic interactions in the multiply charged anions and confirmed the interpretation of the stepwise tuning of molecular energy levels by charging. Photon energy-dependent studies revealed the effects of the repulsive Coulomb barriers on the photodetachment PES spectra of the multiply charged anions. The barrier heights were estimated to be about 3.5 and 2.5 eV for the tetra- and trianions, respectively. We also observed excited states for the multiply charged anions and resonant tunneling through the repulsive Coulomb barriers via the excited states.

Conformational analysis of 5-piperidinevaleric acid, 5-(N-methylpiperidine)valerate and their hydrogen halides by MO calculations, X-ray diffraction and FTIR spectroscopy

The most stable conformers of 5-(piperidine)valeric acid (1), 5-(N-methylpiperidine)valerate (2) and their hydrogen halides (3 and 4) were analyzed by the semiempirical PM3 method and selected compounds by the B3LYP/6-31G(d,p) method. As some of the investigated compounds are charged and the others can be neutral, some have acidic proton, others do not. They are capable of forming ionic bonds (via Coulombic attraction between the oppositely charged groups) or of forming the various types of hydrogen bonded conformers. As a result these compounds are ideally suited to study the importance of electrostatic interactions and hydrogen bonding on the relative stabilities of conformers. In the case of compounds containing N-methylpiperidine unit, for a particular conformer, the intramolecular attractive electrostatic interactions between the charged group play key roles in their relative stability in the gas phase. The electrostatic interaction of the X− ion with the positively charged nitrogen atom decreases their proton-acceptor properties and COOH⋯X− hydrogen bonds are present in all hydrogen halides (3). 5-Piperidine valeric acid with HF forms a molecular complex, while with HCl, HBr and HI an ion pair, according to the B3LYP calculations. The PM3 calculations predict a molecular complex also with HCl. The crystal structure of 5-(piperidine)valeric acid hydrogen bromide (4HBr), space group of crystals P21/n with a=6.204(1), b=32.777(7), c=6.416(1)Å, β=106.21(3)°, Z=4 and R=0.0685 was characterised by X-ray crystallography methods. Br− ion forms two types of hydrogen bonds: Br⋯N(1), 3.247(14)Å, and O(1) ⋯Br, 3.118(11)Å. Moreover, C–H⋯Br short contacts, which can be recognized as weak hydrogen bonds, exist in the crystal. The FTIR spectrum of 1 in the solid state shows an intense broad absorption in the 1600–400cm−1 region typical for a very short NHO hydrogen bonds. In solution the hydrogen bond seems to be longer. The bands of νCO at 1708cm−1 and νasCOO− at 1615cm−1 in CD3CN solution show that OH⋯N⇌O−⋯HN+ equilibrium exists. Ab initio calculations predict molecular structures of three most stable conformers of 1 in the gas phase.

Physicochemical properties of arterial elastin and its associated glycoproteins.

Microfibrillar glycoproteins are a significant component of vascular elastic tissue, but little is known about their contribution to vascular physiology and pathology. We have investigated some physicochemical properties of the glycoproteins that may be pertinent to these roles. Because of the difficulty in isolating intact glycoproteins in a form and quantity suitable for physicochemical examination, we based our analysis on a comparison of the properties of porcine thoracic aorta and pulmonary artery extracted with GuHCl and collagenase (preparation GC) and after further treatment with dithioerythritol to remove glycoproteins (preparation GC/DTE). Amino acid analysis showed that GC/DTE had the amino acid composition of pure elastin while GC contained a higher proportion of polar amino acids, particularly in the aortic preparation. GC stained with alcian blue, particularly in the intimal region, but GC/DTE did not. GC had a higher water content and a slower viscoelastic response and the circumferential elastic modulus was approximately 50% lower (whether expressed in terms of sample weight or elastin content). Clearly, therefore, the microfibrils do not stiffen the network and may prevent the alignment of elastin fibers in the circumferential direction. Their effect on hydration may arise either because they impose mechanical constraints on the geometry of the network or because they modify the inter- and intramolecular hydrophobic or electrostatic interactions that influence the tissue organization and hydration. Molecular probe measurements of the intrafibrillar pore structure using radiolabeled and fluorescent probes showed that removal of the microfibrils caused a slight decrease in the extrafibrillar water space and a larger decrease in the intrafibrillar water space. Sucrose, a small probe molecule, was able to penetrate most of the intrafibrillar water space when microfibrils were present but was virtually excluded when they were not. Potentiometric titration and radiotracer assays of ion binding both showed that the microfibrils contribute a considerable negative charge (-9 mumoles/g wet tissue in the aortic preparation and -16 mumoles/g wet weight in the pulmonary artery) and increase calcium binding by approximately 30%.

Physicochemical properties of arterial elastin and its associated glycoproteins

Microfibrillar glycoproteins are a significant component of vascular elastic tissue, but little is known about their contribution to vascular physiology and pathology. We have investigated some physicochemical properties of the glycoproteins that may be pertinent to these roles. Because of the difficulty in isolating intact glycoproteins in a form and quantity suitable for physicochemical examination, we based our analysis on a comparison of the properties of porcine thoracic aorta and pulmonary artery extracted with GuHCl and collagenase (preparation GC) and after further treatment with dithioerythritol to remove glycoproteins (preparation GC/DTE). Amino acid analysis showed that GC/DTE had the amino acid composition of pure elastin while GC contained a higher proportion of polar amino acids, particularly in the aortic preparation. GC stained with alcian blue, particularly in the intimal region, but GC/DTE did not. GC had a higher water content and a slower viscoelastic response and the circumferential elastic modulus was approximately 50% lower (whether expressed in terms of sample weight or elastin content). Clearly, therefore, the microfibrils do not stiffen the network and may prevent the alignment of elastin fibers in the circumferential direction. Their effect on hydration may arise either because they impose mechanical constraints on the geometry of the network or because they modify the inter- and intramolecular hydrophobic or electrostatic interactions that influence the tissue organization and hydration. Molecular probe measurements of the intrafibrillar pore structure using radiolabeled and fluorescent probes showed that removal of the microfibrils caused a slight decrease in the extrafibrillar water space and a larger decrease in the intrafibrillar water space. Sucrose, a small probe molecule, was able to penetrate most of the intrafibrillar water space when microfibrils were present but was virtually excluded when they were not. Potentiometric titration and radiotracer assays of ion binding both showed that the microfibrils contribute a considerable negative charge (−9 μmoles/g wet tissue in the aortic preparation and −16 μmoles/g wet weight in the pulmonary artery) and increase calcium binding by approximately 30%. © 1999 John Wiley & Sons, Inc. Biopoly 49: 255–265, 1999

The locally denatured state of glutathione S-transferase A1-1: transition state analysis of ligand-dependent formation of the C-terminal helix.

On the basis of available x-ray structures, A-class glutathione S-transferases (GSTs) contain at their C-termini a short alpha-helix that provides a 'lid' over the active site in the presence of the reaction products, glutathione-conjugates. However, in the ligand-free enzyme this helix is disordered and crystallographically invisible. An aromatic cluster including Phe-10, Phe-220, and the catalytic Tyr-9 within the C-terminal strand control the order of this helix. Here, preliminary x-ray crystallographic analyses of the wild type and F220Y rGSTA1-1 in the presence of GSH are described. Also, a transition state analysis is presented for ligand-dependent formation of the helix, based on variable temperature stopped-flow fluorescence. Together, the results suggest that the ligand-dependent ordering of the C-terminal strand occurs with a transition state that is highly desolvated, but with few intramolecular hydrogen bonds or electrostatic interactions. However, substitutions at Phe-220 modulate the activation parameters through interactions with the side chain of Tyr-9.

On the conformational preferences of nylons-n: Analysis of the intramolecular interactions in even nylons-n

The relative stability between the fully-extended and quasi-extended conformations characteristic of the a and y forms of nylons, respectively, has been investigated for both even and odd nylons-n using ab initio quantum mechanical calculations. For nylon-2 the fully-extended is the most favored conformation and its stability clearly increases with the number of residues. On the other hand, for nylons-4 and -6 the quasi-extended conformation is slightly favored with respect to the fully-extended one, although the relative energy between the two conformations decreases with the number of residues. Thus, the fully-extended conformation is predicted as the most stable conformation in compounds with a larger number of residues for nylons-4 and -6. On the other hand, the quasi-extended conformation is the most favored for odd nylons-n and even nylons-n with n > 6. The results have been explained in terms of the intramolecular electrostatic interactions that appear in nylons-2, -4 and -6 between the N-H and C=O groups of a residue.

On the conformational preferences of nylons-n: Analysis of the intramolecular interactions in even nylons-n

The relative stability between the fully-extended and quasi-extended conformations characteristic of the α and β forms of nylons, respectively, has been investigated for both even and odd nylons-n using ab initio quantum mechanical calculations. For nylon-2 the fully-extended is the most favored conformation and its stability clearly increases with the number of residues. On the other hand, for nylons-4 and -6 the quasi-extended conformation is slightly favored with respect to the fully-extended one, although the relative energy between the two conformations decreases with the number of residues. Thus, the fully-extended conformation is predicted as the most stable conformation in compounds with a larger number of residues for nylons-4 and -6. On the other hand, the quasi-extended conformation is the most favored for odd nylons-n and even nylons-n with n > 6. The results have been explained in terms of the intramolecular electrostatic interactions that appear in nylons-2, -4 and -6 between the NH and CO groups of a residue.

Probing the Potential Barriers and Intramolecular Electrostatic Interactions in Free Doubly Charged Anions

Multiply charged anions, though ubiquitous in nature, have been difficult to produce and study in the gas phase. Photoelectron spectroscopy has been combined with an electrospray ion source to probe the repulsive Coulomb barriers, excess electron binding, and intramolecular electron-electron interactions in a series of dicarboxylate dianions, ${}^{\ensuremath{-}}{\mathrm{O}}_{2}\mathrm{C}({\mathrm{CH}}_{2}{)}_{n}{\mathrm{CO}}_{2}^{\ensuremath{-}}$ $(n\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}3--10)$. These experiments provide quantitative information about the repulsive Coulomb barriers and how the excess electron binding energy and the barrier height depend on the intramolecular Coulomb repulsion.

The pH effect in the diffusion coefficient of humic matter: influence in speciation studies using voltammetric techniques

The dynamic aggregation properties of humic matter and the influence of intramolecular electrostatic interaction lead to an increase of polydispersity at pH > 5 in two humic samples studied (“Purified Peat Humic Acid”, PPHA and “Laurentian Fulvic acid”, LFA). The smaller entities formed at pH increasing above 5 are responsible for the increase of the diffusion coefficient as “seen” by voltammetry. The voltammetric results show that the diffusion coefficient of the humic complex inmplex increases from 5 × 10 −12 m 2 s −1 (pH≤5) up to 2 × 10 −11 m 2 s −1 (pH=6) for Cd PPHA and from 6 × 10 −11 m 2 s −1 (pH < or =5) up to 1.2 × 10 −10 m 2 s −1 (pH=5.5) for Pb LFA . Systematic shifts in voltammetric results with changing ligand concentrations often attributed to adsorption of humic matter on the electrode and/or heterogeneity effects, may also be due to incorrect diffusion coefficient values used in speciation calculations. The aim of this paper is to show that the diffusion coefficient of metal-humic complexes is a function of pH. It is necessary to take this into account to obtain more accurate speciation data from voltammetric results and interpret the physicochemical background of the metal humic interaction.

Metal-Substituted Bacteriochlorophylls. 2. Changes in Redox Potentials and Electronic Transition Energies Are Dominated by Intramolecular Electrostatic Interactions

Changes in the electronic transition energies and redox potentials because of metal substitution in bacteriochlorophyll a justify the recently suggested correlation between electronegativity χM, co...

Modeling of previtamin D conformational equilibrium: effect of intramolecular electrostatic interactions

The effect of intramolecular electrostatic interactions on previtamin D conformational equilibrium has been studied by MMX force-field calculations using charge-charge and dipole-dipole approximations in parallel with the analysis of simple model compounds. The very fine balance between steric and electrostatic factors determining the conformational preference has been demonstrated and is discussed in terms of a classical charge-charge interactions. The results of this search are discussed with respect to available experimental data and give clues to the noticeable incidence of atomic point charges in previtamin D ground-state equilibrium. Comparison of the results with those of semi-empirical AM1 calculations reveals that conformational search results on previtamin D are highly dependent on the computational model used and indicate that care is required both in the selection of the computational method and in the interpretation of the results.