Prime Rational Functions and Integral Polynomials

Let f(x) be a complex rational function. In this work, we study conditions under which f(x) cannot be written as the composition of two rational functions which are not units under the operation of function composition. In this case, we say that f(x) is prime. We give sufficient conditions for complex rational functions to be prime in terms of their degrees and their critical values, and we derive some conditions for the case of complex polynomials. We consider also the divisibility of integral polynomials, and we present a generalization of a theorem of Nieto. We show that if f(x) and g(x) are integral polynomials such that the content of g divides the content of f and g(n) divides f(n) for an integer n whose absolute value is larger than a certain bound, then g(x) divides f(x) in Z[x]. In addition, given an integral polynomial f(x), we provide a method to determine if f is irreducible over Z, and if not, find one of its divisors in Z[x].

X-ray diffraction of a gram-negative bacterial membrane mimetic

This thesis applies x-ray diffraction to measure he membrane structure of lipopolysaccharides and to develop a better model of a LPS bacterial melilbrane that can be used for biophysical research on antibiotics that attack cell membranes. \iVe ha'e Inodified the Physics department x-ray machine for use 3.'3 a thin film diffractometer, and have lesigned a new temperature and relative humidity controlled sample cell.\Ve tested the sample eel: by measuring the one-dimensional electron density profiles of bilayers of pope with 0%, 1%, 1G :VcJ, and 100% by weight lipo-polysaccharide from Pse'udo'lTwna aeTuginosa. Background VVe now know that traditional p,ntibiotics ,I,re losing their effectiveness against ever-evolving bacteria. This is because traditional antibiotic: work against specific targets within the bacterial cell, and with genetic mutations over time, themtibiotic no longer works. One possible solution are antimicrobial peptides. These are short proteins that are part of the immune systems of many animals, and some of them attack bacteria directly at the membrane of the cell, causing the bacterium to rupture and die. Since the membranes of most bacteria share common structural features, and these featuret, are unlikely to evolve very much, these peptides should effectively kill many types of bacteria wi Lhout much evolved resistance. But why do these peptides kill bacterial cel: '3 , but not the cells of the host animal? For gramnegative bacteria, the most likely reason is that t Ileir outer membrane is made of lipopolysaccharides (LPS), which is very different from an animal :;ell membrane. Up to now, what we knovv about how these peptides work was likely done with r !10spholipid models of animal cell membranes, and not with the more complex lipopolysa,echaricies, If we want to make better pepticies, ones that we can use to fight all types of infection, we need a more accurate molecular picture of how they \vork. This will hopefully be one step forward to the ( esign of better treatments for bacterial infections.

Alicaligenes faecalis : identification and study of its antagonistic properties against Botrytis cinerea

A Gram negative aerobic flagellated bacterium with fungal growth inhibitory properties was isolated from a culture of Trichoderma harzianum. According to its cultural characteristics and biochemical properties it was identified as a strain of Alcaligenes (aeca/is Castellani and Chalmers. Antisera prepared in Balbc mice injected with live and heat-killed bacterial cells gave strong reactions with the homologous immunogen and with ATCC 15554, the type strain of A. taeca/is, but not with Escherichia coli or Enterobacter aerogens in immunoprecipitation and dot immunobinding assays. Growth of Botrytis cinerea Pers. and several other fungi was significantly affected when co-cultured with A. taeca/is on solid media. Its detrimental effect on germination and growth of B. cinerea has been found to be associated with antifungal substances produced by the bacterium and released into the growth medium. A biotest for the antibiotic substances, based on their inhibitory effect on germination of B. cinerea conidia, was developed. This biotest was used to study the properties of these substances, the conditions in which they are produced, and to monitor the steps of their separation during extraction procedures. It has been found that at least two substances could be involved in the antagonistic interaction. One of these is a basic volatile substance and has been identified as ammonia. The other substance is a nonvolatile, dialysable, heat stable, polar compound released into the growth medium. After separation of growth medium samples by Sephadex G-10 column chromatography a single peak with a molecular weight below 700 Daltons exhibited inhibitory activity. From its behaviour in electrophoretic separation in agarose gels it seems that this is a neutral or slightly positively charged.

Rapid [Gamma]-amino acid synthesis and the inhibition of the growth and development of oblique banded leaf-roller larvae

The hypothesis that rapid y-aminobutyric acid (GABA) accumulation is a plant defense against phytophagous insects was investigated. Simulation of mechanical damage resulting from phytophagous insect activity increased soybean (Glycine max L.) leaf GABA 10- to 25-fold within 1 to 4 min. Pulverizing leaf tissue resulted in a value of 2. 15 (±O. 11 SE) ~mol GABA per gram fresh weight. Increasing the GABA levels in a synthetic diet from 1.6 to 2.6 Jlffiol GABA per gram fresh weight reduced the growth rates, developmental rates, total biomass (50% reduction), and survival rates (30% reduction) of cultured Oblique banded leaf-roller (OBLR) (Choristonellra rosacealla Harris) larvae. In field experiments OBLR larvae were found predominantly on young terminal leaves which have a reduced capacity to produce GABA in response to mechanical damage. Glutamate decarboxylase (GAD) is a cytosolic enzyme which catalyses the decarboxylation of L-Glu to GABA. GAD is a calmodulin binding enzyme whose activity is stimulated dramatically by increased cytosolic H+ or Ca2 + ion concentrations. Phytophagous insect activity will disrupt the cellular compartmentation of H+ and Ca2 +, activate GAD and subsequent GABA accumulation. In animals GABA is a major inhibitory neurotransmitter. The possible mechanisms resulting in GABA inhibited growth and development of insects are discussed.

Isolation and analysis of a corprinus cinereus DNA fragment showing homology to a fimbrial cDNA from ustilago violacea

Surface proteinaceous fibrils, termed fimbriae, were first identified on gram negative bacteria in the 1940s. Fungal fimbriae, discovered some 25 years later, are found on members of all fungal classes. In the present study, polyclonal antiserum raised against the fimbrial proteins of U. vio/acea were used in order to identify antigenically related proteins from Coprinus cinereus and Schizophy//um commune. Two polypeptides with molecular masses of 37 and 39 kDa from C. cinereus were observed and confirm earlier results. A single previously unidentified 50 kDa polypeptide in S. commune crossreacted with the antiserum. The 50 kDa protein was found to consist of 3 isoforms with isoelectric points ranging from 5.6 to 5.8. A fimbrial cDNA derived from U. vio/acea was used to identify DNA restriction fragments from C. cinereus and S. commune showing homology to the fimbrial transcript of U. vio/acea. Heterologous hybridization with this cDNA was used in order to screen a C. cinereus genomic DNA library. A single clone, A2-3A, with a 14 kbp insert showed strong homology to the pfim3-1 cDNA. The region of homology, a 700 bp Xba I fragment, was subcloned into pUG19. This plasmid was refered to as pXX8. DNA sequence determinations of pXX8 and adjacent fragments from A2-3A suggested that the cloned DNA was a portion of the rONA repeat encoding the small subunit rRNA. DNA sequence analysis of pfim3-1 yielded an incomplete open reading frame. The predicted amino acid sequence codes for a 206 amino acid, 22 kDa polypeptide which contains a domain similar to a transmembrane domain from rat leukocyte antigen, GDS3. As well, an untranslated 576 nucleotide domain showed 81 % homology to pXX8 and 830/0 homology to the 188 rRNA sequence of Ustilago maydis. This sequence was found adjacent to a region of adenine-thymine base pairs presumed to represent the polyadenylation sequence of the fimbrial transcript. The size and extent of homology is sufficient to account for the hybridization of pfim3-1 to rDNA. It is suggested that this domain represents a completely novel regulatory domain within eukaryotes that may enable the observed rapid regeneration of fimbriae in U. violacea.

Study of new yeast strains as novel starter cultures for Riesling icewine production

Icewine is a sweet dessert wine fermented from the juice of grapes naturally frozen on the vine. The production of Icewine faces many challenges such as sluggish fermentation, which often yields wines with low ethanol, and an accumulation of high concentration of volatile acidity, mainly in the form of acetic acid. This project investigated three new yeast strains as novel starter cultures for Icewine fermentation with particular emphasis on reducing acetic acid production: a naturally occurring strain of S. bayanus/S. pastorianus isolated from Icewine grapes, and two hybrids between S. cerevisiae and S. bayanus, AWRI 1571 and AWRI 1572. These strains were evaluated for sugar consumption patterns and metabolic production of ethanol, glycerol and acetic acid, and were compared to the performance of a standard commercial wine yeast KI-VI116. The ITS rONA region of the two A WRI crosses was also analyzed during fermentations to assess their genomic stability. Icewine fermentations were performed in sterile filtered juice, in the absence of indigenous microflora, and also in unfiltered juice in order to mirror commercial wine making practices. The hybrid A WRI 1572 was found to be a promising candidate as a novel starter culture for Icewine production. I t produced 10.3 % v/v of ethanol in sterile Riesling Icewine fermentations and 11.2 % v/v in the unfiltered ones within a reasonable fermentation time (39 days). Its acetic acid production per gram sugar consumed was approximately 30% lower in comparison with commercial wine yeast K I -V 1116 under both sterile filtered and unfiltered fermentations. The natural isolate S. bayanus/S. pastorianus and AWRI 1571 did not appear to be suitable for commercial Icewine production. They reached the target ethanol concentration of approximately 10 % v/v in 39 day fermentations and also produced less acetic acid as a function of both time and sugar consumed in sterile fermentations compared to KI-V1116. However, in unfiltered fermentations, both of them failed to produce the target concentration of ethanol and accumulated high concentration of acetic acid. Both A WRI crosses displayed higher loss of or reduced copies in ITS rDNA region from the S. bayanus parent compared to the S. cerevisiae parent; however, these genomic losses could not be related to the metabolic profile.

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.