This thesis represents a theoretical and numerical investigation of the canonical duality theory, which has been recently proposed as an alternative to the classic and direct methods for non-convex variational problems. These non-convex variational problems arise in a wide range of scientific and engineering applications, such as phase transitions, post-buckling of large deformed beam models, nonlinear field theory, and superconductivity. The numerical discretization of these non-convex variational problems leads to global minimization problems in a finite dimensional space. The primary goal of this thesis is to apply the newly developed canonical duality theory to two non-convex variational problems: a modified version of Ericksen's bar and a problem of Landau-Ginzburg type. The canonical duality theory is investigated numerically and compared with classic methods of numerical nature. Both advantages and shortcomings of the canonical duality theory are discussed. A major component of this critical numerical investigation is a careful sensitivity study of the various approaches with respect to changes in parameters, boundary conditions and initial conditions. / Ph. D.

In recent years, metal-organic frameworks (MOFs) have been identified as promising adsorbents in a number of industrially relevant, yet challenging, separations, including the removal of propane from propane/propylene mixtures and the separation of mixtures of xylene isomers. The highly tuneable nature of MOFs - wherein structures may be constructed from a variety of diverse building blocks – has resulted in the publication of a staggering number of frameworks incorporating a wide range of network topologies, pore shapes and pore diameters. As a result, there are a huge number of candidate adsorbents to consider for a given separation. Molecular simulation techniques allow the identification of those structural features and characteristics of a MOF which exert the greatest influence on the adsorption and separation of the compounds of interest, providing insights which can both guide the selection and accelerate the development of adsorbents for a specific application. The separation of propane/propylene mixtures via adsorption has typically focused on selective adsorption of the olefin, propylene, via specific olefin-adsorbent interactions. These propylene-selective MOFs result in processes which selectively remove the most abundant species in the process stream and are typically characterised by high heats of adsorption, resulting in large adsorption units and adsorbents which are difficult to regenerate. In this work, the capability of MOFs to selectively adsorb propane over propylene is explored, potentially allowing for the design of smaller and more energy-efficient adsorption units. By studying a range of different MOFs as well as carbon-based model pores, it was found that the low-pressure selectivity of the structure is determined by the strength of the electrostatic interaction between propylene and the framework, while the adsorptive preference at industrially-relevant pressures is dominated by the enhanced packing efficiency of propylene over propane. The confinement of C3 molecules, however, may be employed to negate this entropic advantage and guide the development of materials which selectively adsorb propane over propylene. It has recently been reported that the adsorptive preference of a MOF for one xylene isomer over another may be predicted based solely on the pore size distribution of the structure. In this work, the impact of pore size on selectivity was studied systematically in both one-dimensional model pore systems of varying geometries and analogous published MOF structures. The ability of the framework to discriminate between xylene molecules in these systems was found to be determined primarily by the different packing arrangements available to the different isomers – while small pores were found to favour the slimmest of the isomers, larger pores were found to favour the more compact ortho- isomer. Finally, the adsorption and diffusion of xylene isomers in a more complex MOF, UiO-66(Zr), was studied in depth. Simulations were able to correctly predict the previously-reported preference of the MOF for ortho-xylene (oX). The smaller volume of the oX molecule compared to the other isomers was found to be responsible both for an enhanced entropic contribution and higher guest-host interaction energies. The importance of framework flexibility in the diffusion of xylene isomers in UiO-66(Zr) was also explored, with distortion of the structure in response to interaction with adsorbed molecules found to be essential in allowing xylenes to diffuse through the pore space.

Since their discovery in 1953, adenoviruses have significantly contributed to the understanding of virus-host cell interactions, including mechanistic details of cellular processes such as cell cycle control and alternative RNA splicing. Among the first characterized adenoviral genes were the virus-associated RNAs (VA RNAI/II), which are produced in massive amount during a lytic infection. The VA RNAs perform multiple functions and are required for a successful adenovirus life cycle. More recently, it was shown that the VA RNAs are processed into small viral miRNAs, so-called mivaRNAs, which interfere with the function of the cellular RNAi/miRNA machinery. In papers I and II, we focused on a structural and functional characterization of the mivaRNAs using two approaches. Firstly, we created a model system where the predicted miRNA-like function of mivaRNAI could be investigated, without interfering with other VA RNA functions. This was accomplished by construction of recombinant adenoviruses, in which the seed sequence of mivaRNAI was altered. The results showed that in cell culture experiments the mivaRNAI seed sequence mutants grew as the wild type virus, suggesting that the mivaRNAs are not required during the lytic phase of an adenovirus infection. Secondly, we showed that the VA RNAs from different human adenoviruses (Ad4, Ad5, Ad11 and Ad37) undergo the same type of Dicer-dependent processing into mivaRNAs, which subsequently are loaded onto the RNA induced silencing complex (RISC), albeit with different efficiencies. In paper III, we demonstrated that the promoter proximal region of the adenovirus major late promoter (MLP) produces a novel non-canonical class of small RNAs, which we termed the MLP-TSS-sRNAs. Surprisingly the MLP-TSS-sRNA maintains the m7G-cap structure while bound to Ago2 containing RISC. These complexes are functional suppressing expression of target mRNAs with complementary binding site. Most importantly, the MLP-TSS-sRNA limits the efficiency of viral DNA replication probably through a targeting of the E2B mRNAs, which are transcribed in the antisense orientation. In conclusion, the MLP-TSS-sRNA represents the first viral small RNA, which has been shown to have a function as a regulator of an adenovirus infection.

QCD at non-zero baryon density is expected to have a critical point where the finite temperature crossover at zero density turns into a first order phase transition. To identify this point, we use the canonical ensemble approach to scan the temperaturedensity plane through lattice QCD simulations with Wilson-type fermions. In order to scan a wide range of the phase diagram, we develop an algorithm, the ”winding number expansion method” (WNEM) to fix the numerical instability problem due to the discrete Fourier transform for calculating the projected determinant. For a given temperature, we measure the chemical potential as a function of the baryon number and look for the signal of a first order phase transition. We carry out simulations using clover fermions with mπ ≈ 800MeV on 63 × 4 lattices. As a benchmark, we run simulations for the four degenerate flavor case where we observe a clear signal of the first order phase transition. In the two flavor case we do not see any signal for temperatures as low as 0.83 Tc. To gauge the discretization errors, we also run a set of simulations using Wilson fermions and compare the results to those from the clover fermion. The three flavor case is close to realistic QCD with two light u and d quarks and one heavier s quark. Any hint of the existence of the first order phase transition and, particularly, its critical end point will be valuable for the planned relativistic heavy-ion experiments to search for such a point. In the three flavor case we found a clear signal for the first order phase transition, the critical point is located at a temperature of 0.93(2) Tc and a baryon chemical potential of 3.25(7) Tc. Since the quark mass in our present simulation is relatively heavy, we would like to repeat it with lighter quark masses and larger volumes.

This thesis presents a development of classical canonical formalism and the usual transition schema to quantum dynamics. The question of transition from relativistic mechanics to relativistic quantum dynamics is answered by developing a homogeneous formalism which is relativistically invariant. Using this formalism the Klein-Gordon equation is derived as the relativistic analog of the Schroedinger equation. Using this formalism further, a method of generating other relativistic equations (with spin) is presented.

In addition to its canonical role in aminoacylation, threonyl-tRNA synthetase (TARS) possesses pro-angiogenic activity that is susceptible to the TARS-specific antibiotic borrelidin. However, the therapeutic benefit of borrelidin is offset by its strong toxicity to living cells. The removal of a single methylene group from the parent borrelidin generates BC194, a modified compound with significantly reduced toxicity but comparable anti-angiogenic potential. Biochemical analyses revealed that the difference in toxicities was due to borrelidin's stimulation of amino acid starvation at ten-fold lower concentrations than BC194. However, both compounds were found to inhibit in vitro and in vivo models of angiogenesis at sub-toxic concentrations, suggesting a similar mechanism that is distinct from the toxic responses. Crystal structures of TARS in complex with each compound indicated that the decreased contacts in the BC194 structure may render it more susceptible to competition with the canonical substrates and permit sufficient aminoacylation activity over a wider concentration of inhibitor. Conversely, both borrelidin and BC194 induce identical conformational changes in TARS, providing a rationale for their comparable effects on angiogenesis. The mechanisms of TARS and borrelidin-based compounds on angiogenesis were subsequently tested using zebrafish and cell-based models. These data revealed ectopic branching, non-functional vessels, and increased cell-cell contracts following BC194-treatment or knockdown of TARS expression, suggesting a role for the enzyme in the maturation and guidance of nascent vasculature. Using various TARS constructs this function was found to be dependent on two interactions or activities associated with the TARS enzyme that are distinct from its canonical aminoacylation activity. Furthermore, observations that TARS may influence VEGF expression and purinergic signaling suggest the possibility for a receptor-mediated response. Taken together, the results presented here demonstrate a clear role for TARS in angiogenesis, independent of its primary function in translation. Although the exact molecular mechanisms through which TARS and borrelidin regulate this activity remain to be determined, these data provide a foundation for future investigations of TARS's function in vascular biology and its use as a target for angiogenesis-based therapy.

Tidal freshwater forest restoration after dam removal has been unexplored to date. This study elucidated pre-dam forest composition, as well as post-dam edaphic and microtopographical attributes and woody species recruiting along a narrow ecotone of a 29.3-ha tidal freshwater wetland. The ≈65-year-old historical forest (15 species, 200 stems ha-1) and ≈7-year-old contemporary forest (40 species and 11,009 stems ha-) community dominants were dissimilar (Fraxinus spp. vs. Liquidambar styraciflua, respectively). Pre-dam environmental conditions were unknown. Post-dam edaphic water content, organic matter, redox potential and microtopography differed significantly across tidal sites but were less variable in non-tidal sites. Shifts in the contemporary woody community composition and the concomitant increase in stem density and seedling:sapling ratios with elevation likely owed to significant changes in microtopography and edaphic attributes. Developing ecotones that contain variable microtopography may be extremely important for successful natural woody recruitment after dam removal from a tidal freshwater system.

Coordinated inductive and morphogenetic processes of gastrulation establish the zebrafish body plan. Gastrulation includes massive cell rearrangements to generate the three germ layers and shape the embryonic body. Three modes of cell migration must occur during vertebrate gastrulation and include: epiboly, internalization of the presumptive mesendoderm and convergent extension (C&E). C&E movements narrow the germ layers mediolaterally (convergence) and elongate them anteroposteriorly (extension) to define the embryonic axis. The molecular mechanisms regulating coordinated cell migrations remain poorly understand and studying these has become of great interest to researchers. Understanding cell migration during development is highly relevant to a number of human physiological processes. Abnormal cell migration during early development can lead to congenital defects, with improper cell migration during adult life potentially leading to the invasion and metastasis of cancer. By studying cell migration events, in vivo, new insights are to be found to both the function and malfunction of key embryonic and postembryonic migratory events. The non-canonical Wnt pathway has been identified as an evolutionarily conserved signaling pathway, regulating C&E cell movements during vertebrate gastrulation. With the absence of the non-canonical Wnts (ncWnts), Wnt5 and Wnt11, during zebrafish development leading to a shorter and broader body axis with defects in elongation during segmentation resulting in undulation of the notochord. While it is clear ncWnts are necessary for C&E, many of the downstream effectors regulating these cell movements have not been defined. Previous research has shown that activation of ncWnt signaling through Wnt5 or Wnt11 results in an increase in intracellular Ca2+ during zebrafish gastrulation. To determine if the Ca2+/Calmodulin-dependent protein kinase, CaMK-II, is a potential downstream target of the Ca2+ increases during ncWnt activation, CaMK-II’s role in C&E was assessed. This study identifies camk2b1 and camk2g1 as being necessary for C&E movements, and outlines the phenotype of the overall embryo as well as individual cells of camk2b1 and camk2g1 morphants. The defects of CaMK-II morphants are specifically linked to alterations in C&E cell movements, while cell fate and proliferation are unaffected. An increase in CaMK-II activation during gastrulation produces similar C&E defects, demonstrating the specificity of CaMK-II’s activation in facilitating these highly coordinated cellular movements. We show that CaMK-II is working downstream Wnt 11 and in parallel to JNK signaling during gastrulation C&E. Overall, these data identify CaMK-II as a required component of C&E movements during zebrafish development, downstream ncWnt signaling, and altering cell migration through changes in cell shape

Peptides are a promising class of therapeutic candidates due to their high specificity and affinity for cellular protein targets. However, peptides are susceptible to protease degradation and are typically not cell-permeable. In efforts to design more effective peptide drug discovery systems, investigators have discovered that incorporation of non-canonical amino acids (ncAAs) and macrocyclization overcome these limitations, making peptides more drug-like. In this work, we exploit the promiscuity of wild-type aminoacyl-tRNA synthetases (aaRSs) to ‘mischarge’ ncAAs onto tRNA and ribosomally incorporate them into peptides using a cell-free translation system. We have demonstrated the ability to incorporate five ncAAs into a single peptide with near-wild type yield and fidelity. We also demonstrated the in situ incorporation of ncAAs containing azide and alkyne functionalities, enabling the use of CuAAC (click chemistry) to generate triazole-bridged cyclic peptides. When combined with bisalkylation of peptides containing two cysteines via an α,α’-dibromo-m-xylene linker, we created bicyclic peptides which are structurally similar to the highly bioactive knotted peptide natural products. Biological display methods, such as mRNA display, are powerful peptide discovery tools based on their ability to generate libraries of >1014 unique peptides. We combined our ability to incorporate ncAAs with our bicyclization technique adapted for use with mRNA display to create knotted peptide library scaffolds. We performed side-by-side monocyclic and bicyclic in vitro selections against a model protein (streptavidin). Both selections resulted in peptides with mid-nM affinity, and the bicyclic selection yielded a peptide with remarkable protease resistance. We used a new library that enables the generation of a diverse collection of linear, monocyclic and bicyclic scaffolds in one pot, increasing the likelihood of target-ligand conformational alignment. We performed a second selection against streptavidin and revealed a nearly unanimous preference for linear peptides containing an HPQ motif, a known streptavidin-binding sequence. However, when we used these libraries for in vitro selection against a biological target, DNA repair protein XRCC4, we did not observe convergence. In summary, we have developed a novel technique for production of bicyclic peptide libraries. These highly-constrained protease-stable scaffolds can be used as platforms to identify high affinity, drug-like ligands using mRNA display.

It is increasingly being realised that localised deviations from the average structure can play an important role in a material's properties, and hence an understanding of these deviations is essential when constructing a coherent picture of a system. In this thesis, both neutron and X-ray total scattering data have been collected and used to reveal information on three canonical systems: the high-temperature superconductor YBa₂Cu₃O_7-x; the parent compound of the colossal magnetoresistive manganites, LaMnO₃; and the oldest known magnetic material, Fe₃O₄. Reverse Monte Carlo refinements-using the RMCProfile implementation of the algorithm-have been used as the principal analysis technique, and the functionality of the RMCProfile program has been extended to allow the refinement of magnetic systems involving substitutional disorder. For YBa₂Cu₃O_7-x, the focus of this thesis is on the apical Cu{O bond length. This is shown to have a bimodal distribution, but correlations in the displacements of both atoms disguise this fact in the average structure, thus resolving the apparent controversy that had existed between local- and average-structure probes. LaMnO₃ displays (what was thought to be) a simple order{disorder transition that results in the Jahn-Teller distortion becoming invisible in the average structure above ~ 750 K. Here it is shown that in fact the transition is more complicated, and involves a change in the symmetry of the Jahn-Teller distortion, whereby the long Mn-O bonds move from being opposite one another in the octahedra to being adjacent to one another. This new distortion still breaks the degeneracy of the system, and is consistent with a wide range of existing observations. Finally the low temperature structure of Fe₃O₄ is examined using the updated RMCProfile code. The refinements show sensitivity to local structure variations, producing a bimodal Fe atom bond valence distribution. In addition, the refined magnetic spin configuration is presented, providing the first detailed description of the low-temperature magnetic structure. It is found to be a canted ferrimagnet, and appears to be consistent with Cc symmetry.