Simultaneous extraction of order parameters and orientational distribution fuctions from 31[superscript]P NMR spectra of magnetically partially oriented phospholipid bilayers

Order parameter profiles extracted from the NMR spectra of model membranes are a valuable source of information about their structure and molecular motions. To al1alyze powder spectra the de-Pake-ing (numerical deconvolution) ~echnique can be used, but it assumes a random (spherical) dist.ribution of orientations in the sample. Multilamellar vesicles are known to deform and orient in the strong magnetic fields of NMR magnets, producing non-spherical orientation distributions. A recently developed technique for simultaneously extracting the anisotropies of the system as well as the orientation distributions is applied to the analysis of partially magnetically oriented 31p NMR spectra of phospholipids. A mixture of synthetic lipids, POPE and POPG, is analyzed to measure distortion of multilamellar vesicles in a magnetic field. In the analysis three models describing the shape of the distorted vesicles are examined. Ellipsoids of rotation with a semiaxis ratio of about 1.14 are found to provide a good approximation of the shape of the distorted vesicles. This is in reasonable agreement with published experimental work. All three models yield clearly non-spherical orientational distributions, as well as a precise measure of the anisotropy of the chemical shift. Noise in the experimental data prevented the analysis from concluding which of the three models is the best approximation. A discretization scheme for finding stability in the algorithm is outlined

The electronic spectra and the determination of the excited state geometry of 3A" propynal /|nby Chhiu-Tsu Lin. -- 260 St. Catharines, Ont. : [s. n.],

Impurity free eluission spectra of HCCCHO and DCCCHO have been rephotographed using the electronic-energy-exchange method with benzene as a carrier gas. The near ultraviolet spectra of ReeCHO and DCCCHO were photographed in a sorption under conditions of high resolution with absorption path lengths up to 100 meters. The emission and absorption spectra of Propynal resulting from 3 n 1 t 1\ - A excitation has been reanalyzed in som.e detail. Botrl of the eH out-of-plane wagging modes were found to have negative anharmonicity. A barrier height of 56.8/0.0 cm- 1 and a nonplanar oft , , equilibrium angle of 17 3 /30 are calculated for the V 10/ lJ 11 modes. The in-plane and out-of-plane v1. brational modes in the 3A." and 1a~. ' elec ronic states of Propynal were subjected to a normal coordinate treatment in the approximat :on of tIle Urey-Bradley force field. From the relative oscillator strengths of the trans1·t1·0ns connect i ng t he v ibrat1•0n1ess lA' , state and t,he V1· bron1·C 3· if levels of the A state, the differences in equilibrium configuration were evaluated from an approximate Franck-Condon analysis based on the ground state normal coordinates. As this treatment gave 512 possible geometrical structures for the upper state, it 4 was necessary to resort to a comparison of the observed and calculated moments of inertia along with chemical intuition to isolate the structure. A test of the correctness of the calculated structure change and the vibrational assignment was raade by evaluating the intensities of the inplane and out-oi-plane fundarnental, sequence, and cross sequellce transitions y the exact Franck-Condon method.

The satellite band patterns in the near ultraviolet absorption spectra of isotopic compounds of acetaldehyde

The 3700 A - 3000 A absorption spectra of CH3CHO and its isotopic compounds such as CH3CDO, CD3CHO and CD3CDO were studied in the gas phase at room temperature and low temperatures. The low resolution spectra of the compounds were recorded by a 1.5 m Baush and Lomb grating spectrograph. The high resolution spectra were recorded by a Ebert spectrograph with the Echelle grating and the holographic grating separately. The multiple reflection cells were used to achieve the long path length. The pressure-path length used for the absorption spectrum of CH 3CHO was up to 100 mm Hg )( 91 . 43mo The emission spectrum and the excitation spectrum of CH3CHO were also recorded in this research. The calculated satellite band patterns \vhich were ob-tailied by the method of Lewis were used to compare with the observed near UV absorption spectrum of acetaldehyde. These calculated satellite band patterns belonged to two cases: namely, the barriers-in-phase case and the barriers- out-of-phase case. Each of the calculated patterns corresponded to a stable conformation of acetaldehyde in the excited state . The comparisons showed that the patterns in the observed absorption spectra corresponded to the H-H eclipsed conformations of acetaldehyde in the excited state . The least squares fitting analysis showed that the barrier heights in the excited state were higher than in the ground state. Finally, the isotopic shifts for the isotopic compounds of acetaldehyde were compared to the compounds with the similar deuterium substitution.

The vibrational spectra and the normal coordinate analysis of thiocarbonye halides /|nby C. R. Subramaniam. -- 260 St. Catharines, Ont. : [s. n.],

The infrared and the Raman spectra of eSelF has been obtained for the first time and has been analysed to give the in-plane normal vibrational frequencies of the molecule, in the ground state. A normal co-ordinate analysis has been carried out for the molecules CSF2, CSClF and eSel 2 using a Urey-Bradley type of potential function and the elements of the [L] matrix elements, the distribution of the potential energy in Urey-Bradley space, and the displacement vector diagrams for the normal modes of vibration for these molecules, have been obtained. The bond for~e constants obtained through the normal co-ordinate analysis, have given some interesting results. The stretching force constant, Kes ' varies markedly with halogen substitution and the force constants KeF and Keel also vary with substitution.

A time-resolved electron paramagnetic resonance spectroscopy study of paramagnetic porphyrins /

There is considerable interest in intramolecular energy transfer, especially in complexes which absorb visible light, because it is crucial to the better understanding of photoharvesting systems in photosynthetic organisms and for utilizing solar energy as well. Porphyrin dimers represent one of the best systems for the exploration of light-induced intramolecular energy transfer. Many kinds of porphyrins and porphyrin dimers have been studied over the past decade, however little attention has been paid to the influence of paramagnetic metals on the behavior of their excited states. In this thesis, Electron Paramagnetic Resonance Spectroscopy (EPR) is used to study such compounds. After light irradiation, porphyrins easily produce a variety of excited states, which are spin polarized and can be detected by the time-resolved (TR) EPR technique. The spin polarized results for vanadyl porphyrins, their electrostatically-coupled dimers, a covalently-linked copper porphyrin-free base porphyrin dimer, and free base porphyrins are presented in this thesis. From these results we can conclude that the spin polarization patterns of vanadyl porphyrins come primarily from the trip-quartet state generated by intersystem crossing (lSC) from the excited sing-doublet state through the trip-doublet state. The spin polarization pattern of electrostatically-coupled vanadyl porphyrin-free base porphyrin dimer is produced by the triplet state of the free base porphyrin half which is coupled to the unpaired electron on the vanadyl ion.

An analysis of the methyl rotation dynamics in the So (x' A) and T (a A) states of thioacetaldehyde from Pyrolysis jet spectra /

Jet-cooled, laser-induced phosphorescence excitation spectra (LIP) of thioacetaldehyde CH3CHS, CH3CDS, CD3CHS and CD3CDS have been observed over the region 15800 - 17300 cm"^ in a continuous pyrolysis jet. The vibronic band structure of the singlet-triplet n -* n* transition were attributed to the strong coupling of the methyl torsion and aldehydic hydrogen wagging modes . The vibronic peaks have been assigned in terms of two upper electronic state (T^) vibrations; the methyl torsion mode v^g, and the aldehydic hydrogen wagging mode v^^. The electronic origin O^a^ is unequivocally assigned as follows: CH3CHS (16294.9 cm"'' ), CH3CDS (16360.9 cm"'' ), CD3CHS (16299.7 cm"^ ), and CD3CDS (16367.2 cm"'' ). To obtain structural and dynamical information about the two electronic states, potential surfaces V(e,a) for the 6 (methyl torsion) and a (hydrogen wagging) motions were generated by ab initio quantum mechanical calculations with a 6-3 IG* basis in which the structural parameters were fully relaxed. The kinetic energy coefficients BQ(a,e) , B^(a,G) , and the cross coupling term B^(a,e) , were accurately represented as functions of the two active coordinates, a and 9. The calculations reveal that the molecule adopts an eclipsed conformation for the lower Sq electronic state (a=0°,e=0"') with a barrier height to internal rotation of 541.5 cm"^ which is to be compared to 549.8 cm"^ obtained from the microwave experiment. The conformation of the upper T^ electronic state was found to be staggered (a=24 . 68° ,e=-45. 66° ) . The saddle point in the path traced out by the aldehyde wagging motion was calculated to be 175 cm"^ above the equilibrium configuration. The corresponding maxima in the path taken by methyl torsion was found to be 322 cm'\ The small amplitude normal vibrational modes were also calculated to aid in the assignment of the spectra. Torsional-wagging energy manifolds for the two states were derived from the Hamiltonian H(a,e) which was solved variationally using an extended two dimensional Fourier expansion as a basis set. A torsionalinversion band spectrum was derived from the calculated energy levels and Franck-Condon factors, and was compared with the experimental supersonic-jet spectra. Most of the anomalies which were associated with the interpretation of the observed spectrum could be accounted for by the band profiles derived from ab initio SCF calculations. A model describing the jet spectra was derived by scaling the ab initio potential functions. The global least squares fitting generates a triplet state potential which has a minimum at (a=22.38° ,e=-41.08°) . The flatter potential in the scaled model yielded excellent agreement between the observed and calculated frequency intervals.

Orientation of Non-Native 2-Monosubstituted and 2,3-Disubstituted 1,4-Naphthoquinones in the A1 binding site of PSI and the effect on the rate of electron transfer : an electron paramagnetic resonance spectroscopy study

The proce-ss ofoxygenic photosynthesis is vital to life on Earth. the central event in photosynthesis is light induced electron transfer that converts light into energy for growth. Ofparticular significance is the membrane bound multisubunit protein known as Photosystem I (PSI). PSI is a reaction centre that is responsible for the transfer of electrons across the membrane to reduce NADP+ to NADPH. The recent publication ofa high resolution X-ray structure of PSI has shown new information about the structure, in particular the electron transfer cofactors, which allows us to study it in more detail. In PSI, the secondary acceptor is crucial for forward electron transfer. In this thesis, the effect of removing the native acceptor phylloquinone and replacing it with a series of structurally related quinones was investigated via transient electron paramagnetic resonance (EPR) experiments. The orientation of non native quinones in the binding site and their ability to function in the electron transfer process was determined. It was found that PSI will readily accept alkyl naphthoquinones and anthraquinone. Q band EPR experiments revealed that the non-native quinones are incorporated into the binding site with the same orientation of the headgroup as in the native system. X band EPR spectra and deuteration experiments indicate that monosubstituted naphthoquinones are bound to the Al site with their side group in the position occupied by the methyl group in native PSI (meta to the hydrogen bonded carbonyl oxygen). X band EPR experiments show that 2, 3- disubstituted methyl naphthoquinones are also incorporated into the Al site in the same orientation as phylloquinone, even with the presence of a halogen- or sulfur-containing side chain in the position normally occupied by the phytyl tail ofphylloquinone. The exception to this is 2-bromo-3-methyl --.- _. -. - -- - - 4 _._ _ _ - _ _ naphthoquinone which has a poorly resolved spectrum, making determination of the orientation difficuh. All of the non-native quinones studied act as efficient electron acceptors. However, forward electron transfer past the quinone could only be demonstrated for anthraquinone, which has a more negative midpoint potential than phylloquinone. In the case of anthraquinone, an increased rate of forward electron transfer compared to native PSI was found. From these results we can conclude that the rate ofelectron transfer from Al to Fx in native PSI lies in the normal region ofthe Marcus Curve.

Studies in the mass spectra of perfluoroaromatic derivatives of phosphorus and some selected transition metals

The mass spectra and fragmentation of a variety of fluoroaromatic compounds of Group V and some selected transition elements are discussed in some detail, aided by data from metastable defocussed experiments. Results of ,studies on the coupling reaction using unstable organotitanium chloride intermediate species are reported. The preparation of some 5-substituted octafluorodibenzophospho1es is also discussed. Rearrangements under electron bombardment resulting in the loss of heteroatom-fluoride fragments are discussed in the light of presently accepted mechanisms for these processes as are rearrangements observed in compounds involving thionophosphoryl bonds ( p=s ).

Effects of large anphiphilic ligands upon the spectra and kinetics of cytochrome C oxidase

Cytoch ro me c oxidase (ferrocytochrome c : 02 oxidoreductase ; EC 1.9. 3.1) is the terminal enzyme in the mitochondrial electron transport chain, catalyzing the transfer of electrons from ferrocytochrome c to molecular oxygen. The effects of two large amphiphilic molecules - valinomycin and dibucaine upon the spectra of the isolated enzyme and upon the activity of both isolated enzyme and enzyme in membrane systems are investigated by using spectrophotometric and oxygen electrode techniques. The results show that both valinomycin and dibucaine change the Soret region of the speetrum and cause a partial inhibition in a concentration range higher than that in which they act as ionophores. It is concluded that both valinomycin and dibucaine binding induce a conformational change of the protein structure which modifies the spectrum of the a3 CUB centre and diminishes the rate of electron transfer between cytochrome a and the binuclear centre.

Developing a numerical inverse-theory-based extraction of orientation-dependent relaxation rates from partially- relaxed spectra

Second-rank tensor interactions, such as quadrupolar interactions between the spin- 1 deuterium nuclei and the electric field gradients created by chemical bonds, are affected by rapid random molecular motions that modulate the orientation of the molecule with respect to the external magnetic field. In biological and model membrane systems, where a distribution of dynamically averaged anisotropies (quadrupolar splittings, chemical shift anisotropies, etc.) is present and where, in addition, various parts of the sample may undergo a partial magnetic alignment, the numerical analysis of the resulting Nuclear Magnetic Resonance (NMR) spectra is a mathematically ill-posed problem. However, numerical methods (de-Pakeing, Tikhonov regularization) exist that allow for a simultaneous determination of both the anisotropy and orientational distributions. An additional complication arises when relaxation is taken into account. This work presents a method of obtaining the orientation dependence of the relaxation rates that can be used for the analysis of the molecular motions on a broad range of time scales. An arbitrary set of exponential decay rates is described by a three-term truncated Legendre polynomial expansion in the orientation dependence, as appropriate for a second-rank tensor interaction, and a linear approximation to the individual decay rates is made. Thus a severe numerical instability caused by the presence of noise in the experimental data is avoided. At the same time, enough flexibility in the inversion algorithm is retained to achieve a meaningful mapping from raw experimental data to a set of intermediate, model-free

Phonon spectra and temperature variation of thermodynamic properties of fcc metals via Finnis-Sinclair type many body potentials: Sutton-Chen and improved Sutton-Chen models

Volume(density)-independent pair-potentials cannot describe metallic cohesion adequately as the presence of the free electron gas renders the total energy strongly dependent on the electron density. The embedded atom method (EAM) addresses this issue by replacing part of the total energy with an explicitly density-dependent term called the embedding function. Finnis and Sinclair proposed a model where the embedding function is taken to be proportional to the square root of the electron density. Models of this type are known as Finnis-Sinclair many body potentials. In this work we study a particular parametrization of the Finnis-Sinclair type potential, called the "Sutton-Chen" model, and a later version, called the "Quantum Sutton-Chen" model, to study the phonon spectra and the temperature variation thermodynamic properties of fcc metals. Both models give poor results for thermal expansion, which can be traced to rapid softening of transverse phonon frequencies with increasing lattice parameter. We identify the power law decay of the electron density with distance assumed by the model as the main cause of this behaviour and show that an exponentially decaying form of charge density improves the results significantly. Results for Sutton-Chen and our improved version of Sutton-Chen models are compared for four fcc metals: Cu, Ag, Au and Pt. The calculated properties are the phonon spectra, thermal expansion coefficient, isobaric heat capacity, adiabatic and isothermal bulk moduli, atomic root-mean-square displacement and Gr\"{u}neisen parameter. For the sake of comparison we have also considered two other models where the distance-dependence of the charge density is an exponential multiplied by polynomials. None of these models exhibits the instability against thermal expansion (premature melting) as shown by the Sutton-Chen model. We also present results obtained via pure pair potential models, in order to identify advantages and disadvantages of methods used to obtain the parameters of these potentials.

Transient and Pulsed Electron Paramagnetic Resonance Spectroscopy on Type I Photosynthetic Reaction Centers

Two time-resolved EPR techniques, have been used to study the light induced electron transfer(ET) in Type I photosynthetic reaction centers(RCs). First, pulsed EPR was used to compare PsaA-M688H and PsaB-M668H mutants of Chlamydomonas reinhardtii and Synechosystis sp. PCC 6803.The out-of-phase echo modulation curves combined with other EPR and optical data show that the effect of the mutations is species dependent. Second, transient and pulsed EPR data are presented which show that PsaA-A660N and PsaB-A640N mutations in C. reinhardtii alter the relative quantum yield of ET in the A- and B-branches of PS I. Third, transient EPR studies on RCs from Heliobacillus mobilis that have been exposed to oxygen show partial inhibition of ET. In the RCs in which ET still occurs, the ET kinetics and EPR spectra show evidence of oxidation of some but not all of the, BChl g and BChl g' to Chl a.

The Fast Regulation of Photosynthesis in Diatoms: an inquiry into the physiological and physical origins of non-photochemical chlorophyll fluorescence quenching.

Diatoms are renowned for their robust ability to perform NPQ (Non-Photochemical Quenching of chlorophyll fluorescence) as a dissipative response to heightened light stress on photosystem II, plausibly explaining their dominance over other algal groups in turbulent light environs. Their NPQ mechanism has been principally attributed to a xanthophyll cycle involving the lumenal pH regulated reversible de-epoxidation of diadinoxanthin. The principal goal of this dissertation is to reveal the physiological and physical origins and consequences of the NPQ response in diatoms during short-term transitions to excessive irradiation. The investigation involves diatom species from different originating light environs to highlight the diversity of diatom NPQ and to facilitate the detection of core mechanisms common among the diatoms as a group. A chiefly spectroscopic approach was used to investigate NPQ in diatom cells. Prime methodologies include: the real time monitoring of PSII excitation and de-excitation pathways via PAM fluorometry and pigment interconversion via transient absorbance measurements, the collection of cryogenic absorbance spectra to measure pigment energy levels, and the collection of cryogenic fluorescence spectra and room temperature picosecond time resolved fluorescence decay spectra to study excitation energy transfer and dissipation. Chemical inhibitors that target the trans-thylakoid pH gradient, the enzyme responsible for diadinoxanthin de-epoxidation, and photosynthetic electron flow were additionally used to experimentally manipulate the NPQ response. Multifaceted analyses of the NPQ responses from two previously un-photosynthetically characterised species, Nitzschia curvilineata and Navicula sp., were used to identify an excitation pressure relief ‘strategy’ for each species. Three key areas of NPQ were examined: (i) the NPQ activation/deactivation processes, (ii) how NPQ affects the collection, dissipation, and usage of absorbed light energy, and (iii) the interdependence of NPQ and photosynthetic electron flow. It was found that Nitzschia cells regulate excitation pressure via performing a high amplitude, reversible antenna based quenching which is dependent on the de-epoxidation of diadinoxanthin. In Navicula cells excitation pressure could be effectively regulated solely within the PSII reaction centre, whilst antenna based, diadinoxanthin de-epoxidation dependent quenching was implicated to be used as a supplemental, long-lasting source of excitation energy dissipation. These strategies for excitation balance were discussed in the context of resource partitioning under these species’ originating light climates. A more detailed investigation of the NPQ response in Nitzschia was used to develop a comprehensive model describing the mechanism for antenna centred non-photochemical quenching in this species. The experimental evidence was strongly supportive of a mechanism whereby: an acidic lumen triggers the diadinoxanthin de-epoxidation and protonation mediated aggregation of light harvesting complexes leading to the formation of quencher chlorophyll a-chlorophyll a dimers with short-lived excited states; quenching relaxes when a rise in lumen pH triggers the dispersal of light harvesting complex aggregates via deprotonation events and the input of diadinoxanthin. This model may also be applicable for describing antenna based NPQ in other diatom species.

Electron Transfer Involving the Phylloquinone (A1) Cofactor of Photosystem I Examined with Time Resolved Absorbance and Electron Paramagnetic Resonance Spectroscopy

The dependence of the electron transfer (ET) rate on the Photosystem I (PSI) cofactor phylloquinone (A1) is studied by time-resolved absorbance and electron paramagnetic resonance (EPR) spectroscopy. Two active branches (A and B) of electron transfer converge to the FX cofactor from the A1A and A1B quinone. The work described in Chapter 5 investigates the single hydrogen bond from the amino acid residue PsaA-L722 backbone nitrogen to A1A for its effect on the electron transfer rate to FX. Room temperature transient EPR measurements show an increase in the rate for the A1A- to FX for the PsaA-L722T mutant and an increased hyperfine coupling to the 2-methyl group of A1A when compared to wild type. The Arrhenius plot of the A1A- to FX ET in the PsaA-L722T mutant suggests that the increased rate is probably the result of a slight change in the electronic coupling between A1A- and FX. The reasons for the non-Arrhenius behavior are discussed. The work discussed in Chapter 6 investigates the directionality of ET at low temperature by blocking ET to the iron-sulfur clusters FX, FA and FB in the menB deletion mutant strain of Synechocyctis sp. PCC 6803, which is unable to synthesize phylloquinone, by incorporating the high midpoint potential (49 mV vs SHE) 2,3-dichloro-1,4-naphthoquinone (Cl2NQ) into the A1A and A1B binding sites. Various EPR spectroscopic techniques were implemented to differentiate between the spectral features created from A and B- branch electron transfer. The implications of this result for the directionality of electron transfer in PS I are discussed. The work discussed in Chapter 7 was done to study the dependence of the heterogeneous ET at low temperature on A1 midpoint potential. The menB PSI mutant contains plastiquinone-9 in the A1 binding site. The solution midpoint potential of the quinone measures 100 mV more positive then wild-type phylloquinone. The irreversible ET to the terminal acceptors FA and FB at low temperature is not controlled by the forward step from A1 to FX as expected due to the thermodynamic differences of the A1 cofactor in the two active branches A and B. Alternatives for the ET heterogeneity are discussed.

Montage et caractérisation d’un système de spectroscopie Raman accordable en longueur d’onde utilisant des réseaux de Bragg comme filtre : application aux nanotubes de carbone

La spectroscopie Raman est un outil non destructif fort utile lors de la caractérisation de matériau. Cette technique consiste essentiellement à faire l’analyse de la diffusion inélastique de lumière par un matériau. Les performances d’un système de spectroscopie Raman proviennent en majeure partie de deux filtres ; l’un pour purifier la raie incidente (habituellement un laser) et l’autre pour atténuer la raie élastique du faisceau de signal. En spectroscopie Raman résonante (SRR), l’énergie (la longueur d’onde) d’excitation est accordée de façon à être voisine d’une transition électronique permise dans le matériau à l’étude. La section efficace d’un processus Raman peut alors être augmentée d’un facteur allant jusqu’à 106. La technologie actuelle est limitée au niveau des filtres accordables en longueur d’onde. La SRR est donc une technique complexe et pour l’instant fastidieuse à mettre en œuvre. Ce mémoire présente la conception et la construction d’un système de spectroscopie Raman accordable en longueur d’onde basé sur des filtres à réseaux de Bragg en volume. Ce système vise une utilisation dans le proche infrarouge afin d’étudier les résonances de nanotubes de carbone. Les étapes menant à la mise en fonction du système sont décrites. Elles couvrent les aspects de conceptualisation, de fabrication, de caractérisation ainsi que de l’optimisation du système. Ce projet fut réalisé en étroite collaboration avec une petite entreprise d’ici, Photon etc. De cette coopération sont nés les filtres accordables permettant avec facilité de changer la longueur d’onde d’excitation. Ces filtres ont été combinés à un laser titane : saphir accordable de 700 à 1100 nm, à un microscope «maison» ainsi qu’à un système de détection utilisant une caméra CCD et un spectromètre à réseau. Sont d’abord présentés les aspects théoriques entourant la SRR. Par la suite, les nanotubes de carbone (NTC) sont décrits et utilisés pour montrer la pertinence d’une telle technique. Ensuite, le principe de fonctionnement des filtres est décrit pour être suivi de l’article où sont parus les principaux résultats de ce travail. On y trouvera entre autres la caractérisation optique des filtres. Les limites de basses fréquences du système sont démontrées en effectuant des mesures sur un échantillon de soufre dont la raie à 27 cm-1 est clairement résolue. La simplicité d’accordabilité est quant à elle démontrée par l’utilisation d’un échantillon de NTC en poudre. En variant la longueur d’onde (l’énergie d’excitation), différentes chiralités sont observées et par le fait même, différentes raies sont présentes dans les spectres. Finalement, des précisions sur l’alignement, l’optimisation et l’opération du système sont décrites. La faible acceptance angulaire est l’inconvénient majeur de l’utilisation de ce type de filtre. Elle se répercute en problème d’atténuation ce qui est critique plus particulièrement pour le filtre coupe-bande. Des améliorations possibles face à cette limitation sont étudiées.