Phonon spectra and thermodynamic properties of rare gas solids based on empirical and semi-empirical (ab initio) two-body potentials : a comparative study /

We study the phonon dispersion, cohesive and thermal properties of raxe gas solids Ne, Ar, Kr, and Xe, using a variety of potentials obtained from different approaches; such as, fitting to crystal properties, purely ab initio calculations for molecules and dimers or ab initio calculations for solid crystalline phase, a combination of ab initio calculations and fitting to either gas phase data or sohd state properties. We explore whether potentials derived with a certain approaxih have any obvious benefit over the others in reproducing the solid state properties. In particular, we study phonon dispersion, isothermal ajid adiabatic bulk moduli, thermal expansion, and elastic (shear) constants as a function of temperatiue. Anharmonic effects on thermal expansion, specific heat, and bulk moduli have been studied using A^ perturbation theory in the high temperature limit using the neaxest-neighbor central force (nncf) model as developed by Shukla and MacDonald [4]. In our study, we find that potentials based on fitting to the crystal properties have some advantage, particularly for Kr and Xe, in terms of reproducing the thermodynamic properties over an extended range of temperatiures, but agreement with the phonon frequencies with the measured values is not guaranteed. For the lighter element Ne, the LJ potential which is based on fitting to the gas phase data produces best results for the thermodynamic properties; however, the Eggenberger potential for Ne, where the potential is based on combining ab initio quantum chemical calculations and molecular dynamics simulations, produces results that have better agreement with the measured dispersion, and elastic (shear) values. For At, the Morse-type potential, which is based on M0ller-Plesset perturbation theory to fourth order (MP4) ab initio calculations, yields the best results for the thermodynamic properties, elastic (shear) constants, and the phonon dispersion curves.

DNA polymerase activity in trophoblast giant cells in the mouse /

In the developing mouse embryo, the diploid trophectoderm is known to undergo a diploid to giant cell transformation. These cells arise by a process of endoreduplication, characterized by replication of the entire genome without subsequent mitosis or cell division, leading to polyploidy and the formation of giant nuclei. Studies of 13.5 day rat trophoblast derived from the parietal yolk sac have indicated a relatively low rate of DNA polymerase a activity, the noinnal eukaryotic replicase, in comparison to that of DNA polymerase g. These results have suggested that endoreduplication in trophoblast giant cells may not employ the normal replicase enzyme, DNA polymerase a. In order to determine whether a 'switch' from DNA polymerase to DNA polymerase is a necessary concomitant of the diploid to giant cell transformation, two distinct populations of trophoblast giant cells, the primary giant cell derived from the mural trophectoderm and the secondary giant cell derived from the polar trophoectoderm were used. These two populations of trophoblast giant cells can be obtained from the tissue outgrowths of 3.5da blastocysts and the extraembryonic ectoderm (EX) and ectoplacental cone (EPC) of 7.5 day embryos respectively. Tissue outgrowths were treated with aphidicolin, a specific reversible inhibitor of eukaryotic DNA polymerase a, on various days after explantation. The effect of aphidicolin treatment was assessed both qualitatively, using autoradiography and quantitatively by scintillation counting and Feulgen staining. 3 DNA synthesis was measured in control and treated cultures after a Hthymidine pulse. Scintillation counts of the embryo proper revealed that DNA synthesis was consistently inhibited by greater than 907. in the presence of aphidicolin. Inhibition of DNA synthesis in the EX and EPC varied between 81-957. and 82-987. respectively, indicating that most DNA synthesis was mediated by DNA polymerase a, but that a small but significant amount of residual synthesis was indicated. A qualitative approach was then applied to determine whether the apparent residual DNA synthesis was restricted to a subpopulation of giant cells or whether all giant cells displayed a low level of DNA synthesis. Autoradiographs of the ICM of blastocysts and the embryo proper of 7.5da embryos, which acted as diploid control population, was completely inhibited regardless of duration in explant culture. In contrast, primary trophoblast giant cells derived from blastocysts and secondary giant cells derived from the EX and EPC were observed to possess some heavily labelled cells after aphidicolin treatment. These results suggest that although DNA polymerase a is the primary replicating enzyme responsible for endoreduplication in mouse trophoblast giant cells, some nonactivity is also observed. A DNA polymerase assay employing tissue lysates of outgrown 7.5da embryo, EX and EPC tissues was used to attempt to confirm the presence of higher nonactivity in tissues possessing trophoblast giant cells. Employing a series of inhibitors of DNA polymerases, it would appear that DNA polymerase a is the major polymerase active in all tissues of the 7.5da mouse embryo. The nature of the putative residual DNA synthetic activity could not be unequivically determined in this study. Therefore, these results suggest that both primary and secondary trophoblast giant cells possess and use DNA polymerase a in endoreduplicative DNA synthesis. It would appear that the high levels of DNA polymerase g activity reported in trophoblast tissue derived from the 13.5 da rat yolk sac was not a general feature of all endoreduplication.

Application of [Lambda] to the fourth perturbation theory in calculating the equation of state of rare gas solids and fcc metals

We have calculated the thermodynamic properties of monatomic fcc crystals from the high temperature limit of the Helmholtz free energy. This equation of state included the static and vibrational energy components. The latter contribution was calculated to order A4 of perturbation theory, for a range of crystal volumes, in which a nearest neighbour central force model was used. We have calculated the lattice constant, the coefficient of volume expansion, the specific heat at constant volume and at constant pressure, the adiabatic and the isothermal bulk modulus, and the Gruneisen parameter, for two of the rare gas solids, Xe and Kr, and for the fcc metals Cu, Ag, Au, Al, and Pb. The LennardJones and the Morse potential were each used to represent the atomic interactions for the rare gas solids, and only the Morse potential was used for the fcc metals. The thermodynamic properties obtained from the A4 equation of state with the Lennard-Jones potential, seem to be in reasonable agreement with experiment for temperatures up to about threequarters of the melting temperature. However, for the higher temperatures, the results are less than satisfactory. For Xe and Kr, the thermodynamic properties calculated from the A2 equation of state with the Morse potential, are qualitatively similar to the A 2 results obtained with the Lennard-Jones potential, however, the properties obtained from the A4 equation of state are in good agreement with experiment, since the contribution from the A4 terms seem to be small. The lattice contribution to the thermal properties of the fcc metals was calculated from the A4 equation of state, and these results produced a slight improvement over the properties calculated from the A2 equation of state. In order to compare the calculated specific heats and bulk moduli results with experiment~ the electronic contribution to thermal properties was taken into account~ by using the free electron model. We found that the results varied significantly with the value chosen for the number of free electrons per atom.

Assessment of chromatin activity in mouse and human tissues

Pancreatic deoxyribonuclease preferentially digests active genes during all phases of the cell cycle including mitosis. Recently, a DNAse I-directed in ~ nick translation technique has been used to demonstrate differences in the DNAse I sensitivity of euchromatic and heterochromatic regions of mitotic chromosomes. This ill ~ technique has been used in this study to ask whether facultative heterochromatin of the inactive X chromosome can be distinguished from the active X chromosome in mouse and human tissues. In addition to this, in ~ nick translation has been used to distinguish constitutive heterochromatin in mouse and human mitotic chromosomes. Based on relative levels of DNAse I sensitivity, the inactive X chromosome could not be distinguished from the active X chromosome in either mouse or human tissues but regions of constitutive heterochromatin could be distinguished by their relative DNAse I insensitivity. The use of !D situ nick translation was also applied to tissue sections of 7.5 day mouse embryos to ask whether differing levels of DNAse I sensitivity could be detected between different tissue types. Differences in DNAse I sensitivities were detected in three tissues examined; embryonic ectoderm, an embryo-derived tissue, and two extraembryonic tissues, extraembryonic ectoderm and ectoplacental cone. Embryonic ectoderm and extraembryonic ectoderm nuclei possessed comparable levels of DNAse I sensitivity while ectoplacental cone was significantly less DNAse I sensitive. This suggests that tissue-specific mechanisms such as chromatin structure may be involved in the regulation of gene activity in certain tissue types. This may also shed some light on possible tissue specific mechanisms regulating X chromosome activity in the developing mouse embryo.

On the equation of state and atomic mean square displacement of crystals

We have presented a Green's function method for the calculation of the atomic mean square displacement (MSD) for an anharmonic Hamil toni an . This method effectively sums a whole class of anharmonic contributions to MSD in the perturbation expansion in the high temperature limit. Using this formalism we have calculated the MSD for a nearest neighbour fcc Lennard Jones solid. The results show an improvement over the lowest order perturbation theory results, the difference with Monte Carlo calculations at temperatures close to melting is reduced from 11% to 3%. We also calculated the MSD for the Alkali metals Nat K/ Cs where a sixth neighbour interaction potential derived from the pseudopotential theory was employed in the calculations. The MSD by this method increases by 2.5% to 3.5% over the respective perturbation theory results. The MSD was calculated for Aluminum where different pseudopotential functions and a phenomenological Morse potential were used. The results show that the pseudopotentials provide better agreement with experimental data than the Morse potential. An excellent agreement with experiment over the whole temperature range is achieved with the Harrison modified point-ion pseudopotential with Hubbard-Sham screening function. We have calculated the thermodynamic properties of solid Kr by minimizing the total energy consisting of static and vibrational components, employing different schemes: The quasiharmonic theory (QH), ).2 and).4 perturbation theory, all terms up to 0 ().4) of the improved self consistent phonon theory (ISC), the ring diagrams up to o ().4) (RING), the iteration scheme (ITER) derived from the Greens's function method and a scheme consisting of ITER plus the remaining contributions of 0 ().4) which are not included in ITER which we call E(FULL). We have calculated the lattice constant, the volume expansion, the isothermal and adiabatic bulk modulus, the specific heat at constant volume and at constant pressure, and the Gruneisen parameter from two different potential functions: Lennard-Jones and Aziz. The Aziz potential gives generally a better agreement with experimental data than the LJ potential for the QH, ).2, ).4 and E(FULL) schemes. When only a partial sum of the).4 diagrams is used in the calculations (e.g. RING and ISC) the LJ results are in better agreement with experiment. The iteration scheme brings a definitive improvement over the).2 PT for both potentials.

Phonon dispersion curves and atomic mean square displacement for several fcc and bcc materials

The atomic mean square displacement (MSD) and the phonon dispersion curves (PDC's) of a number of face-centred cubic (fcc) and body-centred cubic (bcc) materials have been calclllated from the quasiharmonic (QH) theory, the lowest order (A2 ) perturbation theory (PT) and a recently proposed Green's function (GF) method by Shukla and Hiibschle. The latter method includes certain anharmonic effects to all orders of anharmonicity. In order to determine the effect of the range of the interatomic interaction upon the anharmonic contributions to the MSD we have carried out our calculations for a Lennard-Jones (L-J) solid in the nearest-neighbour (NN) and next-nearest neighbour (NNN) approximations. These results can be presented in dimensionless units but if the NN and NNN results are to be compared with each other they must be converted to that of a real solid. When this is done for Xe, the QH MSD for the NN and NNN approximations are found to differ from each other by about 2%. For the A2 and GF results this difference amounts to 8% and 7% respectively. For the NN case we have also compared our PT results, which have been calculated exactly, with PT results calculated using a frequency-shift approximation. We conclude that this frequency-shift approximation is a poor approximation. We have calculated the MSD of five alkali metals, five bcc transition metals and seven fcc transition metals. The model potentials we have used include the Morse, modified Morse, and Rydberg potentials. In general the results obtained from the Green's function method are in the best agreement with experiment. However, this improvement is mostly qualitative and the values of MSD calculated from the Green's function method are not in much better agreement with the experimental data than those calculated from the QH theory. We have calculated the phonon dispersion curves (PDC's) of Na and Cu, using the 4 parameter modified Morse potential. In the case of Na, our results for the PDC's are in poor agreement with experiment. In the case of eu, the agreement between the tlleory and experiment is much better and in addition the results for the PDC's calclliated from the GF method are in better agreement with experiment that those obtained from the QH theory.

Thermodynamic properties and Debye-Waller factor of fee materials

We have calculated the equation of state and the various thermodynamic properties of monatomic fcc crystals by minimizing the Helmholtz free energy derived in the high temperature limit for the quasiharmonic theory, QH, and the lowest-order (cubic and quartic), 'A2, anharmonic terms of the perturbation theory, PT. The total energy in each case is obtained by adding the static energy. The calculation of the thermal properties was carried out for a nearest-neighbour central-force model of the fcc lattice by means of the appropriate thermodynamic relations. We have calculated the lattice constant, the thermal expansion, the coefficient of volume expansion, the specific heat at constant volume and at constant pressure, the isothermal and adiabatic bulk moduli, and the Griineisen parameter, for the rare-gas solids Kr and Xe, and gold. Morse potential and modified Morse potential were each used to represent the atomic interaction for the three fcc materials. For most of the calculated thermodynamic properties from the QH theory, the results for Kr and Xe with the modified Morse potential show an improvement over the results for the Morse potential when compared with the experimental data. However, the results of the 'A 2 equation of state with the modified Morse potential are in good agreement with experiment only in the case of the specific heat at constant volume and at constant pressure. For Au we have calculated the lattice contribution from the QH and 'A 2 PT and the electronic contribution to the thermal properties. The electronic contribution was taken into account by using the free electron model. The results of the thermodynamic properties calculated with the modified Morse potential were similar to those obtained with the Morse potential. U sing the minimized equation of state we also calculated the Mossbauer recoilless fraction for Kr and Xe and the Debye-Waller factor (DWF) for Pb, AI, eu, Ag, and Au. The Mossbauer recoilless fraction was obtained for the above two potentials and Lennard-Jones potential. The L-J potential gives the best agreement with experiment for Kr. No experimental data exists for Xe. At low temperature the calculated DWF results for Pb, AI, and eu show a good agreement with experimental values, but at high temperature the experimental DWF results increase very rapidly. For Ag the computed values were below the expected results at all temperatures. The DWF results of the modified Morse potential for Pb, AI, eu and Ag were slightly better than those of the Morse potential. In the case of Au the calculated values were in poor agreement with experimental results. We have calculated the quasiharmonic phonon dispersion curves for Kr, Xe, eu, Ag, and Au. The calculated and experimental results of the frequencies agree quite well for all the materials except for Au where the longitudinal modes show serious discrepancies with the experimental results. In addition, the two lowest-order anharmonic contributions to the phonon frequency were derived using the Green's function method. The A 2 phonon dispersion curves have been calculated only for eu, and the results were similar to those of the QH dispersion curves. Finally, an expression for the Griineisen parameter "( has been derived from the anharmonic frequencies, and calculated for these materials. The "( results are comparable with those obtained from the thermodynamic definition.

An anharmonic contribution to the Helmholtz free energy O(lambda 6)

The anharmonic contributions of order A6 to the Helmholtz free energy for a crystal in which every atom is on a site of inversion symmetry, have been evaluated The cor~esponding diagrams in the various orders of the perturbation theory have been presented The validity of the expressions given is for high temperatures. Numerical calculations for the diagrams which contribute to the free energy have been worked out for a nearest-n~ighbour central-force model of a facecentered cubic lattice in the high-temperature limit and in the leading term and the Ludwig approximations. The accuracy of the Ludwig approximation in evaluating the Brillouin-zone sums has been investigated. Expansion for all diagrams in the high-temperature limit has been carried out The contribution to the specific heat involves a linear as well as cubic term~ We have applied Lennard-Jones, Morse and Exponential 6 types of potentials. A comparison between the contribution to the free energy of order A6 to that of order A4 has been made.

Mechanisms underlying Retinoic acid-induced chemoattraction in molluscan neurons

Retinoic acid, a derivative of vitamin A, is known to play diverse roles in development and regeneration. Previous research in the mollusc Lymnaea stagnalis has shown that a gradient of all-trans retinoic acid attracts the growth cones of cultured neurons. The present study investigates the sub-cellular mechanisms within the growth cones of Lymnaea pedal A neurons which mediate the attractive response to a gradient of alltrans retinoic acid. In this study, the mechanism of growth cone turning is shown to be local, as neurites mechanically isolated from their cell body retain the capacity to turn towards an exogenous gradient of all-trans retinoic acid. The turning response is dependent on the initiation of protein synthesis and calcium influx, but does not appear to involve signaling through protein kinase C (PKC). The retinoid X receptor (RXR), which classically functions as a transcription factor, was also shown to be involved in the turning response, functioning locally through a non-genomic pathway. These data show, for the first time in any species, that all-trans retinoic acid's chemotropic action involves a local mechanism involving non-genomic signaling through the RXR. As retinoic acid is known to playa role in regeneration, understanding the mechanisms underlying retinoic acid signaling may lead to further advances in regenerative neuroscience.

Identification of novel retinoid receptors and their roles in vertebrate and invertebrate nervous systems

In vertebrates, signaling by retinoic acid (RA) is known to play an important role in embryonic development, as well as organ homeostasis in the adult. In organisms such as adult axolotls and newts, RA is also important for regeneration of the CNS, limb, tail, and many other organ systems. RA mediates many of its effects in development and regeneration through nuclear receptors, known as retinoic acid receptors (RARs) and retinoid X receptors (RXRs). This study provides evidence for an important role of the RA receptor, RAR~2, in ,( '. regeneration ofthe spinal cord and tail of the adult newt. It has previously been proposed that the ability of the nervous system to regenerate might depend on the presence or absence of this RAR~2 isoform. Here, I show for the very first time, that the regenerating spinal cord of the adult newt expresses this ~2 receptor isoform, and inhibition of retinoid signaling through this specific receptor with a selective antagonist inhibits tail and spinal cord regeneration. This provides the first evidence for a role of this receptor in this process. Another species capable of CNS ~~generation in the adult is the invertebrate, " Lymnaea stagnalis. Although RA has been detected in a small number of invertebrates (including Lymnaea), the existence and functional roles of the retinoid receptors in most invertebrate non-chordates, have not been previously studied. It has been widely believed, however, that invertebrate non-chordates only possess the RXR class of retinoid receptors, but not the RARs. In this study, a full-length RXR cDNA has been cloned, which was the first retinoid receptor to be discovered in Lymnaea. I then went on to clone the very first full-length RAR eDNA from any non-chordate, invertebrate species. The functional role of these receptors was examined, and it was shown that normal molluscan development was altered, to varying degrees, by the presence of various RXR and RAR agonists or antagonists. The resulting disruptions in embryogenesis ranged from eye and shell defects, to complete lysis of the early embryo. These studies strongly suggest an important role for both the RXR and RAR in non-chordate development. The molluscan RXR and RAR were also shown to be expressed in the adult, nonregenerating eNS, as well as in individual motor neurons regenerating in culture. More specifically, their expression displayed a non-nuclear distfibution, suggesting a possible non-genomic role for these 'nuclear' receptors. It was shown that immunoreactivity for the RXR was present in almost all regenerating growth cones, and (together with N. Farrar) it was shown that this RXR played a novel, non-genomic role in mediating growth cone turning toward retinoic acid. Immunoreactivity for the novel invertebrate RAR was also found in the regenerating growth cones, but future work will be required to determine its functional role in nerve cell regeneration. Taken together, these data provide evidence for the importance of these novel '. retinoid receptors in development and regeneration, particularly in the adult nervous system, and the conservation of their effects in mediating RA signaling from invertebrates to vertebrates.

Identification and characterization of retinoic acid-induced morphological and electrophysiological changes in an invertebrate nervous system

The vitamin A metabolite, retinoic acid (RA) is known to play an important role in the development, patterning and regeneration of nervous tissue, both in the embryo and in the adult. Classically, RA is known to mediate the transcription of target genes through the binding and activation ofits nuclear receptors: the retinoic acid receptors (RARs) and retinoid X receptors (RXRs). Recently, mounting evidence from many animal models has implicated a number of RA-mediated effects operating independently of gene transcription, and thus highlights nove~ nongenornic actions of RA. For example, recent work utilizing cultured neurons from the pond snaa Lymnaea stagnalis, has shown that RA can elicit a regenerative response, growth cone turning, independently of "classical" transcriptional activation While this work illustrates a novel regeneration-inducing effect in culture, it is currently -unknown whether RA also induces regeneration in situ. This study has sought to determine RA's regenerative effucts at the morphological and molecular levels by utilizing an in situ approach focusing on a single identified dopaminergic neuron which possesses a known "mapped" morphology within the CNS. These studies show, for the first time in an invertebrate, that RA can increase neurite outgrowth of dopaminergic cells that have undergone a nerve-crush injury. Utilizing Western blot analysis, it was shown that this effect appears to be independent of any changes in whole CNS expression levels of either the RAR or RXR. Additionally, utilizing immunohistochemistry, to examine protein localization, there does not appear to be any obvious changes in the RXR expression level at the crush site. Changes in cell morphology such as neurity extension are known to be modulated by changes in neuronal firing activity. It has been previously shown that exposure to RA over many days can lead to changes in the electrophysiological properties of cultured Lymnaea neurons; however, no studies have investigated whether short-term exposure to RA can elicit electrophysiological changes and/or changes in firing pattern of neurons in Lymnaea or any other species. The studies performed here show, for the first time in any species, that short-tenn treatment with RA can elicit significant changes in the firing properties of both identified dopaminergic neurons and peptidergic neurons. This effect appears to be independent of protein synthesis, activation of protein kinase A or phospholipase C, and calcium influx but is both dose-dependent and isomer-dependent. These studies provide evidence that the RXR, but not RAR, may be involved, and that intracellular calcium concentrations decrease upon RAexposure with a time course, dose-dependency and isomer-dependency that coincide with the RA-induced electrophysiological changes. Taken together, these studies provide important evidence highlighting RA as a multifunctional molecule, inducing morphological, molecular and electrophysiological changes within the CNS, and highlight the many pathways through which RA may operate to elicit its effects.

Elucidation of the Retinoid Signalling Pathway Involved in Axon Guidance in Lymnaea stagnalis and Xenopus laevis

The vitamin A metabolite, retinoic acid (RA), is known to play a crucial role in several developmental processes including axial patterning and differentiation. More recently, RA has been implicated in the regenerative process acting through its classical signaling pathway, the nuclear receptors, retinoic acid receptor (RAR) and retinoid X receptor (RXR), to mediate gene transcription. Moreover, RA has been shown to act as a guidance molecule for growth cones of regenerating motorneurons of the pond snail, Lymnaea stagnalis. Our lab has recently shown that RA can induce this morphological response independent of nuclear transcription, however, the role of the retinoid receptors in RA-induced chemoattraction is still unknown. Here, I show that the retinoid receptors, RXR and RAR, may mediate the growth cones response to the metabolically active retinoic acid isomers, all-trans and 9-cis RA, in Lymnaea stagnalis. Data presented here show that both an RXR and RAR antagonist can block growth cone turning in response to application of both isomers. Because no prior investigations have shown growth cone turning of individual vertebrate neurons, I aimed to show that both retinoic acid isomers were capable of inducing growth cone turning of embryonic spinal cord neurons in the frog, Xenopus laevis. For the first time in Xenopus, I showed that both all-trans and 9-cis RA were able to induce significantly more neurite outgrowth from cultured embryonic spinal cord neurons and induce positive growth cone turning of individual growth cones. In addition, I showed that the presence of the RXR antagonist, HX531, blocked 9-cis RA-induced growth cone turning and the RARβ antagonist, LE135, blocked all-trans RA-induced growth cone turning in this species. Evidence provided here shows for the first time, conservation of retinoic acid-induced growth cone turning in a vertebrate model system. In addition, these data show that the receptors involved in this morphological response may be the same in vertebrates and invertebrates.

Investigating the role of retinoic acid in the vertebrate and invertebrate nervous system

Please consult the paper edition of this thesis to read. It is available on the 5th Floor of the Library at Call Number: Z 9999.5 B56 D64 2007

Niagara's Parks (1897)

Issued jointly by: Commissioners for the Queen Victoria Niagara Falls Park, and Commissioners of the State Reservation at Niagara.