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Pathogenesis of prion diseases in animals is associated with the misfolding of the cellular prion protein PrPC to the infectious form, PrPSc. We hypothesized that an animal’s susceptibility to prions is correlated with the propensity of an animal’s PrPC to adopt a β-sheet, PrPSc-like, conformation. We have developed a method which uses circular dichroism (CD) to directly calculate the relative population of PrP molecules that adopt a β-sheet conformation or the ‘β-state’, as a function of denaturant concentration and pH. We find that the PrP from animals that are more susceptible to prion diseases, like hamsters and mice, adopt the β-state more readily than the PrP from rabbits. The X-ray crystal structure of rabbit PrP reveals a helix-capping motif that may lower the propensity to form the β-state. PrP in the β-state contains both monomeric and octameric β-structured species, and possesses cytotoxic properties.

Pathogenesis of prion diseases in animals is associated with the misfolding of the cellular prion protein PrPC to the infectious form, PrPSc. We hypothesized that an animal’s susceptibility to prions is correlated with the propensity of an animal’s PrPC to adopt a β-sheet, PrPSc-like, conformation. We have developed a method which uses circular dichroism (CD) to directly calculate the relative population of PrP molecules that adopt a β-sheet conformation or the ‘β-state’, as a function of denaturant concentration and pH. We find that the PrP from animals that are more susceptible to prion diseases, like hamsters and mice, adopt the β-state more readily than the PrP from rabbits. The X-ray crystal structure of rabbit PrP reveals a helix-capping motif that may lower the propensity to form the β-state. PrP in the β-state contains both monomeric and octameric β-structured species, and possesses cytotoxic properties.

Single frame ultrasound B-mode image quality is largely governed by the ability to focus the ultrasound beam over a range in depths both in transmission and reception. By developing a comprehensive understanding of acoustic wave propagation two signal processing methods were identified for solving the transmission problem. We made use of both the impulse response using the classical point spread function (PSF) and the spatial sensitivity function (SSF) which describes the spatial distribution at a particular time. Using the angular spectrum method, an accurate analytical model was developed for the field distribution arising from a finite geometry, apodized and focused, plane piston transducer. While there is a thorough understanding of the radiated field arising from uniformly excited plane piston transducers, the focused equivalent (i.e., one that allows a continuous change in phase over the plane piston surface) is incomplete and assumes the Fresnel approximation. Our model addresses the effects of diffraction and evanescent waves without the use of the Fresnel approximation and is applicable at all near- and far-field locations in a lossless medium. The model was analyzed to identify new insights into wave propagation and compared with the Fresnel approximation and the spherically-focused, concave transducer. The piston transducer model was then extended to an attenuating and dispersive medium. After analysing existing models of power-law frequency dependent attenuation, a causal, spherical wave Green’s function was derived from the Navier-Stokes equation for a classical viscous medium. Modifications to the angular spectrum method were presented and used to analyze the radiated field of a focused, planar piston transducer. Finally, after presenting our signal processing strategy for improving imaging spatial resolution through minimization of the SSF, two signal processing methods were derived and analysed in simulation: a deconvolution technique to remove the effects of the ultrasound excitation wave and suppress additive noise from the received ultrasound signal, and a retrospective transmit focusing method that changed the response from a predefined transmit focus to an arbitrary transmit focal depth. Proof-of-concept simulations were presented using a variable number of scatterers and compared with the traditional matched filtering and envelope detection technique.

n個物品之直線排列數與環狀排列數有對應關係，一般而言，具有K-循環節的直線排列之所有情形數若為 ，則 即為所對應的環狀排列數，亦即每K種直線排列對應到同一種環狀排列。本文將直線排列之所有情形依所具有的K-循環節之類別做分割，並導出具有K-循環節之直線排列之所有情形數之計數公式，假設直線排列依 -循環節， -循環節， ， -循環節分類依序有 種不同排列情形，則所有的環狀排列數 。 / There exists a correspondence between ordered arrangements and circular permutations. Generally speaking, suppose the number of ordered arrangements with K-recurring periods is S, then the number of circular permutations is , namely we may assigne each K cases of ordered arrangements with K-recurring periods to a case of circular permutations. This article partitions the total cases of ordered arrangements with indistinguishable objects by means of the different catagories of K-recurring periods and derives a formula to calculate the total number of ordered arrangements with K-recurring periods. Suppose the number of ordered arrangements with -recurring periods、 -recurring periods、 、 -recurring periods is respectively, then the total number of circular permutations is .

This thesis is focussed on structural and functional studies of a novel glycerophosphodiesterase (GpdQ) from Enterobacter aerogenes. GpdQ is highly promiscuous and is the first known phosphatase which is capable of degrading all three classes of phosphate esters (mono-, di- and triesters). Remarkably, GpdQ is also able to hydrolyse stable aliphatic phosphate esters and has been shown to degrade the hydrolysis product of the nerve agent VX. For these reasons, GpdQ has been realised to have potential as a powerful bioremediator for the removal of organophosphate pesticides and nerve agents. GpdQ is a binuclear metallohydrolase in which one of the metal ions is very weakly bound. Chapter 1 introduces the catalytic mechanisms of binuclear metallohydrolases by examining two related phosphate ester-degrading enzymes. Since one of the main features of catalysis addressed in this thesis are the differential metal binding affinities of GpdQ, Chapter 1 also canvasses a range of other binuclear metallohydrolases with similar behaviour. Chapter 2 examines the structural and evolutionary relationship between GpdQ and a number of other related enzymes. Using genome database searches, the two most closely related enzymes are identified. In performing these searches, a novel, putative binuclear metallohydrolase from Homo sapiens is also discovered. This enzyme, Hsa_aTRACP, is most closely related to PAPs, however construction of a homology model indicates that the active site tyrosine residue of PAP is replaced by histidine. In this respect, it may represent an evolutionary link to Ser/Thr protein phosphatases and GpdQ. The biology and chemistry of this putative enzyme is discussed. PAPs are the only binuclear enzymes with an established heterovalent active site of the type Fe(III)-M(II) (where M=Fe, Zn or Mn) whereas the majority of enzymes in this family have homovalent metal centres, including GpdQ and Ser/Thr protein. This is brought about due to the nature of the coordination sphere imposed by the enzyme. The activity of GpdQ can be reconstituted in the presence of Co(II), Zn(II), Mn(II) and Cd(II). Chapter 3 examines the kinetic properties of a binuclear homovalent system by studying the kinetic properties of Cd(II)-substituted GpdQ and a corresponding model complex. This comparative study leads to the identification of a terminal hydroxide molecule as the likely reaction-initiating nucleophile in Cd(II)-GpdQ with a pKa of 9.4. In Chapter 4, a detailed study of the structural, kinetic and spectroscopic behaviour of Co(II)-substituted GpdQ is presented. This chapter specifically probes the formation of the binuclear active site, the role of the metal ions in catalysis, the identity of the nucleophile and the potential role of any first or second coordination sphere residues in the regulation of enzyme activity, proton donation and metal ion coordination. Based on these findings, a detailed reaction mechanism is proposed in which the substrate itself promotes the formation of the catalytically competent binuclear centre and phosphorolysis occurs following nucleophilic attack by a terminal hydroxide molecule. A potential role of Asn80 (a ligand of one of the metal ions) in regulating both substrate and metal binding, and the role of the bridging hydroxide molecule in the activation of the terminal nucleophile is proposed. Chapter 5 employs a combination of kinetic and spectroscopic techniques to probe the proposed catalytic mechanism of GpdQ in depth. The formation of the catalytically competent binuclear centre is observed in pre-steady state studies, an integral first step in the catalytic mechanism. The dissociation and rate constants associated with formation of the binuclear centre are quantified. The rate of substrate turnover in GpdQ is relatively modest but is enhanced by a structural rearrangement involving the flexible Asn80 ligand. This structural change fine-tunes the reaction mechanism, leading to optimal reactivity. The steady-state kinetic properties of a series of metal ion derivatives (Co(II), Cd(II) and Mn(II)) of GpdQ and their reactivity towards a number of substrates are also compared. These findings lead to the conclusion that the reaction mechanism of GpdQ is modulated by both substrate and metal ion. In this respect, GpdQ is adaptive to the environmental conditions to which it is exposed by employing a flexible mechanistic strategy to achieve catalysis. Chapter 6 correlates the electronic and geometric structure of the binuclear centre in GpdQ as a means to probe specific aspects of the mechanism. This study uses the wild type enzyme and a site-directed mutant (Asn80Asp) to examine the structure of the metal ions at two stages of catalysis. The role of the bridging hydroxide molecule in nucleophilic activation is specifically addressed by monitoring changes in the electronic exchange interaction and other structural parameters as a result of phosphate binding. Also, the coordination environment of the metal ions in both the free enzyme and the phosphate-bound enzyme of wild type and Asn80Asp GpdQ were assessed against the currently proposed structures. The findings in this chapter corroborate the proposed catalytic mechanism of GpdQ. In summary, this project led to a detailed understanding of the mechanism of GpdQ, and provided insight into how both the metal ion composition and the identity of the substrate may modulate this mechanism. The knowledge gained may lead to the design of catalytically more efficient derivatives (mutants) of GpdQ for application in bioremediation.

This thesis is focussed on structural and functional studies of a novel glycerophosphodiesterase (GpdQ) from Enterobacter aerogenes. GpdQ is highly promiscuous and is the first known phosphatase which is capable of degrading all three classes of phosphate esters (mono-, di- and triesters). Remarkably, GpdQ is also able to hydrolyse stable aliphatic phosphate esters and has been shown to degrade the hydrolysis product of the nerve agent VX. For these reasons, GpdQ has been realised to have potential as a powerful bioremediator for the removal of organophosphate pesticides and nerve agents. GpdQ is a binuclear metallohydrolase in which one of the metal ions is very weakly bound. Chapter 1 introduces the catalytic mechanisms of binuclear metallohydrolases by examining two related phosphate ester-degrading enzymes. Since one of the main features of catalysis addressed in this thesis are the differential metal binding affinities of GpdQ, Chapter 1 also canvasses a range of other binuclear metallohydrolases with similar behaviour. Chapter 2 examines the structural and evolutionary relationship between GpdQ and a number of other related enzymes. Using genome database searches, the two most closely related enzymes are identified. In performing these searches, a novel, putative binuclear metallohydrolase from Homo sapiens is also discovered. This enzyme, Hsa_aTRACP, is most closely related to PAPs, however construction of a homology model indicates that the active site tyrosine residue of PAP is replaced by histidine. In this respect, it may represent an evolutionary link to Ser/Thr protein phosphatases and GpdQ. The biology and chemistry of this putative enzyme is discussed. PAPs are the only binuclear enzymes with an established heterovalent active site of the type Fe(III)-M(II) (where M=Fe, Zn or Mn) whereas the majority of enzymes in this family have homovalent metal centres, including GpdQ and Ser/Thr protein. This is brought about due to the nature of the coordination sphere imposed by the enzyme. The activity of GpdQ can be reconstituted in the presence of Co(II), Zn(II), Mn(II) and Cd(II). Chapter 3 examines the kinetic properties of a binuclear homovalent system by studying the kinetic properties of Cd(II)-substituted GpdQ and a corresponding model complex. This comparative study leads to the identification of a terminal hydroxide molecule as the likely reaction-initiating nucleophile in Cd(II)-GpdQ with a pKa of 9.4. In Chapter 4, a detailed study of the structural, kinetic and spectroscopic behaviour of Co(II)-substituted GpdQ is presented. This chapter specifically probes the formation of the binuclear active site, the role of the metal ions in catalysis, the identity of the nucleophile and the potential role of any first or second coordination sphere residues in the regulation of enzyme activity, proton donation and metal ion coordination. Based on these findings, a detailed reaction mechanism is proposed in which the substrate itself promotes the formation of the catalytically competent binuclear centre and phosphorolysis occurs following nucleophilic attack by a terminal hydroxide molecule. A potential role of Asn80 (a ligand of one of the metal ions) in regulating both substrate and metal binding, and the role of the bridging hydroxide molecule in the activation of the terminal nucleophile is proposed. Chapter 5 employs a combination of kinetic and spectroscopic techniques to probe the proposed catalytic mechanism of GpdQ in depth. The formation of the catalytically competent binuclear centre is observed in pre-steady state studies, an integral first step in the catalytic mechanism. The dissociation and rate constants associated with formation of the binuclear centre are quantified. The rate of substrate turnover in GpdQ is relatively modest but is enhanced by a structural rearrangement involving the flexible Asn80 ligand. This structural change fine-tunes the reaction mechanism, leading to optimal reactivity. The steady-state kinetic properties of a series of metal ion derivatives (Co(II), Cd(II) and Mn(II)) of GpdQ and their reactivity towards a number of substrates are also compared. These findings lead to the conclusion that the reaction mechanism of GpdQ is modulated by both substrate and metal ion. In this respect, GpdQ is adaptive to the environmental conditions to which it is exposed by employing a flexible mechanistic strategy to achieve catalysis. Chapter 6 correlates the electronic and geometric structure of the binuclear centre in GpdQ as a means to probe specific aspects of the mechanism. This study uses the wild type enzyme and a site-directed mutant (Asn80Asp) to examine the structure of the metal ions at two stages of catalysis. The role of the bridging hydroxide molecule in nucleophilic activation is specifically addressed by monitoring changes in the electronic exchange interaction and other structural parameters as a result of phosphate binding. Also, the coordination environment of the metal ions in both the free enzyme and the phosphate-bound enzyme of wild type and Asn80Asp GpdQ were assessed against the currently proposed structures. The findings in this chapter corroborate the proposed catalytic mechanism of GpdQ. In summary, this project led to a detailed understanding of the mechanism of GpdQ, and provided insight into how both the metal ion composition and the identity of the substrate may modulate this mechanism. The knowledge gained may lead to the design of catalytically more efficient derivatives (mutants) of GpdQ for application in bioremediation.

All biological processes are fundamentally inter-molecular interactions. In order to understand, and hence control, biomolecular structure and function, methods are required that probe biological systems at the molecular level, ideally with those molecules being in their native environment. The research summarized herein has at its core the development and application of ultra violet (UV)-visible spectrophotometric techniquies for this prupose, in particular circular dichrosim (CD) and linear dichrosim (LD) but also absorbance, fluorescence and resonance light scattering. The spectroscopy is complemented by fundamental theoretical work on molecular structure and reactivity that forms the basis for designing molecules to bind to biomolecules for a particular structural or functional effect. A brief summary of the contributions of the listed publications to our understanding of 'Molecular aspects of biololecule structure and function' is given below under five headings: Circular dichroism theory Molecular geometry and reactivity Small molecule-macromolecule interactions: spectroscopic probes of inter-molecular geometries Molecular design for nucleic acid structure and control Spectroscopic probes of biomolecule structure: instrumentation and application In general terms these correspond to successive phases of the research programme, however, all areas have been present since the first publications in 1983 and can be traced weaving through all subsequent activity.

Thesis (M.A.)--Virginia Polytechnic Institute and State University, 1990. / Abstract. Also available via the Internet.

Thesis (Ph.D. in Molecular Biology) -- University of Colorado Denver, 2008. / Typescript. Includes bibliographical references (leaves 155-167). Free to UCD affiliates. Online version available via ProQuest Digital Dissertations;