This work presents a proof of the dependence of the first eigenvalue for uniformly elliptic partial differential equations on the domain in a less abstract setting than that of Ivo Babushka and Rudolf Vyborny in 1965. The proof contained here, under rather mild conditions on the boundary of the domain, �Ω, demonstrates that the first eigenvalue of elliptic partial differential equation [ �� + �� = 0 �� Ω [ � = 0 �� �Ω depends continuously on the domain in the following sense. If a sequence of domains is such that, then the corresponding first eigenvalues satisfy is the first eigenvalue for [ �� + �� = 0 �� Ω [ � = 0 �� �Ω The work also reviews and utilizes the Sturmian comparison results of John G. Heywood, E. S. Noussair, and Charles A. Swanson. For a continuously parameterized family of domains, say with μ ∈ = [a, b], the continuous dependence of the eigenvalue on the domain combined with the Sturmian comparison results provide a theorem that insures, under certain conditions, that the elliptic partial differential equation [ �� = 0 �� Ω [ � = 0 �� �Ω has a solution which is positive on a nodal domain That is there is a least value of μ [a, b] so that a positive solution u exists for [ �� = 0 �� Ωμ [ � = 0 �� �Ωμ Beyond these results the work contains a theorem that shows for certain types of domains, rectangles in , among them, that there is a critical dimension smaller than which, no solution to the problem [ �� + �� = 0 �� Ω [ � = 0 �� �Ω exists when the eigenvalue is fixed. During the investigations taken up in this work, certain observations were made regarding linear approximations to eigenvalue problems in R2 using a standard numerical approximation scheme. One such observation is that if a linear approximation to an eigenvalue problem contains an incorrect estimate for an eigenvalue, the resulting graphical approximation seems to betray whether or not the estimate was low or high. The observations made do not appear to exist in the literature.

Older adults living with frailty have increased healthcare needs, but require accurate identification for optimal care; nurses’ screening practice is unclear. This cross-sectional survey explored nurses’ frailty screening practices and barriers/facilitators in acute care. Descriptive statistics were generated from 5-point frequency and 101-point scales of frailty screening methods; practice areas were compared using linear regression. Means for barriers and facilitators were generated from a 43-item 6-point Likert-type Theoretical Domains Framework questionnaire. Respondents (n = 228) reported “usually” screening by clinical impression (median = 4, interquartile range = 4-5) and preferring it to formal frailty tools (M = 67.1, SD = 25.7). Practice area influenced general frailty screening (B = 0.81, r = .31, p < .001). The top barrier was belief conducting frailty screening was routine (M = 2.68, SD = 1.42, p > .05). Frailty screening tools supporting clinical judgement and embedded into routine have greater likelihood for uptake.

Protein aggregation is deleterious to human health and detrimental to therapeutic shelf-life. The physical processes that induce aggregation are the same processes that drive productive folding reactions. As such, protein aggregation is a non-productive form of protein folding. To gain insight into the steps that serve as a partition between the folding and aggregation reactions, the folding mechanisms of several β-rich proteins with links to human disease or medicine were examined. In the ALS-linked protein, SOD1, a subpopulation of the unfolded ensemble is found to be a common source of both nonnative structure and frustrated folding. These behaviors are only observed upon the reduction of the intrinsic disulfide bond, indicating that this covalent interaction wards against aggregation. The nonnative structure presents an attractive target for the development of new therapeutic agents. In VH domains from therapeutic mAbs, the intramolecular disulfide bond protects against aggregation. However, it can also introduce complexity to the folding mechanism. This complexity is linked to the formation of a strained orientation of the disulfide bond. This strained orientation of the disulfide in certain VH domains is energetically unfavorable enough to disrupt the formation of the disulfide in the full length mAbs. The novel relationship observed between disulfide orientation, folding complexity, and incomplete oxidation warrants further examination in other Ig domains. Overall, these results demonstrate that mapping the folding free energy landscape for proteins with roles in human disease or therapeutics can provide valuable insights for developing and improving treatment options.

Thesis: Ph. D., Massachusetts Institute of Technology, Department of Mathematics, 1982 / Bibliography: leaves 78-79. / by John Marshall Lee. / Ph. D. / Ph. D. Massachusetts Institute of Technology, Department of Mathematics

Mémoire numérisé par la Direction des bibliothèques de l'Université de Montréal. / Protein-protein interactions are an integral component of signal transduction pathways. The interactions are mediated by modular domains which are present within the structure of the signalling molecule. These domains include PDZ, SH2, SH3, WW, PTB and LIM domains. hPTP1E is a protein-tyrosine phosphatase which contains within its primary structure a region with homology to Band 4.1 proteins, five PDZ domains and a catalytic domain. While the function of this PTPase remains unknown, the structure of hPTP1E suggest it may recruit several proteins into a multiprotein complex. In order to understand the role of hPTP1E, the protein interactions within its signalling cascade were examined. hPTP1E interacts with ZRP-1 and GEF-5.1 via its second PDZ domain and tuberin via its fourth PDZ domain in the yeast two-hybrid system. In order to characterize these proteins and their interactions, antibodies were generated against ZRP-1 and GEF-5.1. The antibodies which detected the antigen expressed in bacteria were purified by affinity chromatography. The antibodies raised against ZRP-1 and hPTP1E detected proteins of appropriate molecular weights in total cell extracts. HPTP1E is ubiquitously expressed whereas ZRP-1 is restricted to HeLa and MCF-7 cells among the cells tested. Unfortunately, antibodies against GEF-5.1 did not detect a protein of the predicted molecular weight in any of the cell extracts. Immunoprecipitation of hPTP1E fi-om cells overexpressing regions of ZRP-1 and tuberin with a hemaglutinin tag demonstrated the presence of an interaction between the phosphatase and tuberin in vivo. However, ZRP-1 and hPTP1E did not interact under these experimental conditions. Confirmation of the yeast two-hybrid results provides further support for a possible role of hPTP1E in the regulation of endocytosis. Additional molecules involved in the signalling pathways involving hPTP1E were identified by interaction trap. In one study, the proline rich amino terminus of ZRP-1 interacted with several clones encoding a segment of hCDC47 and NtZRP-p33, a clone containing an SH3 domain. The significance of these findings is unknown. HCDC47 is a minichromosome maintenance protein wich regulate DNA replication. Further, a clone called KIAA0769 containing the sequence of NtZRP-p33 depicts the typical structure for a scaffolding protein. Another yeast-two hybrid cDNA library screening using the CDC25 homology domain of GEF-5.1 did not detect an interaction with any GTPase but with 14-3-3E. 14-3-3 proteins are regulatory molecules which interact with various types of proteins by means of a phosphorylated serine residue. Mutational analysis demonstrated that the interaction is dependent on the second serine residue within the consensus sequence RSLSQG found in GEF-5.1. The primary structure of the open reading frame of GEF-5.1 was analyzed using profilescan. The software predicted the presence of several domains including a cNMP binding domain, a LTE domain, a PDZ domain, a rasassociated domain and a CDC25 homology domain. A family of guanidine nucleotide exchange factors may exist as clones KIAA0313 and T14G10 have the same structure. These results indicate a role for GEF-5.1 in Ras signalling pathways. Further, its activity may be regulated by the binding of cNMP molecules and 14-3-3E. The identification of ZRP-1 and GEF-5.1 interacting proteins as well as the analysis of the primary structure of GEF-5.1 have provided additional information about the function of hPTP1E. This cytoplasmic phosphatase may be involved in the regulation of processes such as transcription, DNA replication and. Further, an interaction between tuberin and hPTP1E suggests a role for this PTPase in the regulation of endocytosis. / La phosphorylation des protéines est une modification post-traductionelle fréquemment employée pour moduler la transmission des signaux intracellulaires. Il est nécessaire qu'un équilibre du niveau de phosphorylation soit maintenu pour le fonctionnement normal de la cellule sinon des maladies comme le cancer peuvent apparaître. Les enzymes responsables de la phosphorylation des protéines sont les protéines kinases tandis que les protéines phosphatases enlèvent les groupements phosphate. Les résidus phosphorylés dans les protéines sont certains résidus sérines, thréonines et/ou tyrosines. Les différentes enzymes sont classées en deux familles selon leur spécificité. Les protéine-tyrosine phosphatases (PTPase) sont elles-même regroupées dans deux familles selon leur localisation intracellulaire: les PTPases de type récepteur et les phosphatases cytoplasmiques. La structure des phosphatases de type récepteur inclus un domaine extracellulaire, un domaine transmembranaire et un (ou deux) domaine(s) catalytique(s). Les PTPases cytoplasmiques contiennent un domaine catalytique unique et généralement un/ ou des domaine(s) responsable(s) de leur localisation intracellulaire ou impliqué(s) dans des interactions protéine-protéine. Dans notre laboratoire, une phosphatase cytoplasmique dénommée liPTP1E par nous (et PTPL1, PTPBAS, FAP par d'autres) a été isolée. En plus de son domaine catalytique, cette protéine-tyrosine phosphatase contient 1 domaine de type "Band 4.1" qui est impliqué dans la localisation de la protéine à la membrane cellulaire via une interaction avec le cytoskelette, et 5 domaines PDZ. Ces domaines PDZ sont en général impliqués dans les interactions protéineprotéine. Plusieurs études récentes ont tenté de définir la fonction de hPTP1E. Sato et ses collègues ont isolé hPTP1E lors d'un criblage d'une librairie d'ADNc en utilisant le système des deux-hybrides dans la levure avec la partie cytoplasmique du récepteur Fas, comme appât. Ils ont aussi démontré que hPTP1E peut inhiber l'effet apoptotique de Fas. L'apoptose des cellules cibles qui est induit par les lymphocytes T cytotoxiques utiliserait le système Fas. De plus, Fas pourrait être associé à des maladies auto-immunes. En plus, hPTP1E pourrait jouer un rôle dans l'apparition de cellules resistantes aux effets de Fas tel que retrouvées dans les sarcomes de Kaposi chez les sidéens. Malgré des données convaincantes, il reste quand même des doutes quant à l'importance de hPTP1E dans ces maladies. Ainsi une étude publiée n'a pu démontrer une interaction entre les homologues de Fas et hPTP1E chez la souris. Depuis d'autres groupes étudiant les interactions de hPTP1E ont découvert plusieurs protéines qui interagissent avec celle-ci. La première, PARG, est membre de la famille des Rho-GAP, des protéines impliquées dans l'activation des GTPases de type Rho. L'interaction aurait lieu avec le 4ième domaine PDZ de hPTP1E. De plus, le domaine LEVI de RIL interagirait avec hPTP1E via ses 2ième et 4ième domaines PDZ. La fonction biologique de ces interactions n'a toutefois pas été déterminée à ce jour. Pour caractériser la fonction biologique de hPTP1E, nous avons utilisé le système des deux-hybrides de la levure pour identifier des protéines qui interagiraient avec les domaines PDZ de hPTP1E. J'ai ainsi identifié deux protéines nommés ZRP-1 et GEF-5.1, qui se lient à hPTP1E. ZRP-1 possède une structure semblable à celle de zyxin.Ces deux dernières protéines contiennent une région amino-terminale riche en résidus proline et 3 domaines de type LEM à l'extrémité carboxyl terminale. GEF-5.1, d'autre part démontre une homologie marquée aux GEFs de la famille CDC25 impliquées dans l'activation des GTPases de la famille Ras. Des anticorps ont été générés contre ZRP-1, GEF-5.1 et hPTP1E afin de fournir les outils nécessaires pour mieux caractériser ces différentes protéines. Ainsi, j'ai exprimé et purifié le troisième domaine LIM de ZRP-1 ainsi que le domaine PDZ de GEF-5.1, sous forme de protéines de fusion avec la glutathioneS-transferase (GST). Ces protéines ont servis d'antigène pour générer des anticorps chez le lapin. Des anticorps dirigés contre le deuxième domaine PDZ de hPTP1E étaient déja disponibles dans le laboratoire. Ces anticorps ont été purifiés sur une colonne d'affinité GST. Les anticorps anti-ZRP-1 et anti-hPTP1E détectent tous les deux des protéines du poids moléculaire attendu. HPTP1E est exprimé d'une facon ubiquitaire tandis que l'expression de ZRP-1 est plus restrainte parmi les cellules testées. Toutefois, les immunoglobulines dirigées contre GEF-5.1 ne détectent aucune protéine du poids moléculaire attendu dans un extrait cellulaire brut. Parallèlement, d'autres membres du laboratoire ont démontré une interaction entre la tuberine, le produit du gène TSC2, un oncogène impliqué dans la sclérose tubéreuse, et le quatrième domaine PDZ de hPTP1E. Afin de caractériser ces interactions in vivo, des immunoprécipitations de hPTP1E à partir de cellules dans lesquelles une région de ZRP-1 et/ou de la tuberine étaient surexprimé ont été conduites. Sous les conditions expérimentales utilisées, ZRP-1 n'a pas co-immunoprécipité avec hPTP1E. Cependant une interaction avec la tuberine a été détectée utilisant cette stratégie suggérant que HPTP1E pourrait jouer un rôle dans la modulation de l'endocytose. La structure de ZRP-1 inclus un domaine riche en proline qui n'est pas nécessaire pour son interaction avec hPTP1E mais qui pourrait interagir avec d'autres protéines en particulier avec des protéines contenant un/ ou des domaine(s) SH3. La moitié amino-terminale de ce domaine a été utilisé pour cribler une librairie d'ADNc par le système des deux-hybrides. Un clone appelé NtZRP-p33 contenant un domaine SH3 a été identifié. La conséquence biologique de cette interaction reste toutefois a être déterminée. Cependant, NtZRP-p33 possède une structure suggérant son implication dans la signalisation intracellulaire. Un deuxième criblage de la librairie d'ADNc a été initié pour caractériser les protéines impliquées dans le mécanisme de signalisation de hPTP1E. En utilisant le domaine de GEF-5.1 homologue à CDC25, des clones correspondants à la protéine 14-3-3 ont été isolés. Les protéines 14-3-3 forment une famille de protéines qui régularisent la fonction de plusieurs protéines. Leurs interactions se font via un residu sérine qui est phosphorylé. Des mutations du domaine catalytique ont démontré que l'interaction entre 14-3-3s et GEF-5.1 est dépendante du deuxième sérine de la séquence RSLSQG qui se retrouve immédiatement du coté carboxyl terminale du domaine GEF de la protéine GEF-5.1. Ces résultats suggèrent que l'activité de GEF-5.1 pourrait être modulée par la 14-3-38. En conclusion, les résultats expérimentaux présentés dans ce mémoire indique un rôle potentiel de hPTP1E dans plusieurs fonctions cellulaires. En s'associant à la tuberine, hPTP1E pourrait régulariser l'endocytose. Aussi, cette PTPase pourrait être impliquer dans le cycle cellulaire. Ras étant un activateur de la mitose, HPTP1E pourrait moduler l'activité de Ras par voie de GEF-5.1. Ainsi, hPTP1E pourrait agir comme proto-oncogène ou un gène suppresseur des tumeurs. Zyxin est une protéine qui se retrouve près des sites membranaires en association avec le cytoskelette. Puisque la structure de ZRP-1 et zyxin est semblable, ce dernier sert de modèle pour la fonction de ZRP-1. En collaboration avec hPTP1E, ces deux protéines pourrait régulariser la structure du cytoskelette.

In modern educational technology we have the ability to capture click-stream interaction data from a student as they work on educational problems within an online environment. This provides us with an opportunity to identify student behaviours within the data (captured by the online environment) that are predictive of student success or failure. The constraints that exist within an educational setting provide the ability to associate these student behaviours to specific educational outcomes. This information could be then used to inform environments that support student learning while improving a student’s metacognitive skills. In this dissertation, we describe how reading behaviour clusters were extracted in an experiment in which students were embedded in a learning environment where they read documents and answered questions. We tracked their keystroke level behaviour and then applied clustering techniques to find pedagogically meaningful clusters. The key to finding these clusters were categorizing the questions as to their level in Bloom’s educational taxonomy: different behaviour patterns predicted success and failure in answering questions at various levels of Bloom. The clusters found in the first experiment were confirmed through two further experiments that explored variations in the number, type, and length of documents and the kinds of questions asked. In the final experiment, we also went beyond the actual keystrokes and explored how the pauses between keystrokes as a student answers a question can be utilized in the process of determining student success. This research suggests that it should be possible to diagnose learner behaviour even in “ill-defined” domains like reading. It also suggests that Bloom’s taxonomy can be an important (even necessary) input to such diagnosis.

The MDM2 and MDM4 oncoproteins are both involved in regulating the tumour suppressor, p53. While the MDM2–p53 interface is structurally and biophysically well characterised, the MDM4-p53 interaction has only recently attracted researchers’ attentions. The goal of this project was to establish structural and chemical ground rules for the disruption of the interactions between the N-terminal domains of MDM2/4 and p53, which is an attractive anticancer strategy. In the current work, successful recombinant production and purification protocols for both the N-terminal domains of MDM2 (i.e. MDM2-N, residues 11-118) and MDM4 (MDM4-N, residues 14-111) have been established, yielding protein in sufficient quantity and quality for analysis using nuclear magnetic resonance spectroscopy (NMR). Two screening strategies were employed to identify small-molecule antagonists of the MDM2-N:p53 interaction. First, a virtual screening exercise identified several compounds that were shown (by NMR) to bind to MDM2-N with μM KDs. Docking studies supported by NMR chemical shift perturbation analysis suggested proposals for binding modes. The results are discussed in relation to the previously reported binding to MDM2-N of well-characterised inhibitors of the MDM2:p53 interaction such as Nutlin-3. Second, a fragment-based library was screened against MDM2-N using TROSY-type NMR spectra to monitor binding. Several hits were identified and the results are discussed with regard to the “druggability” of the MDM2-N p53 interaction. To better understand the p53-binding groove of MDM4-N, multidimensional NMR was used to investigate the structure and backbone dynamics of double-isotopically labelled samples of MDM4-N, both free (i.e. apo-MDM4-N) and in complexes with a p53-derived peptide or Nutlin-3. The apo-MDM4-N is more conformationally dynamic than MDM2, since it contains unstructured regions. These regions appear to become structured upon binding of a ligand. MDM4 appears to bind its ligand through conformational selection and/or an induced fit mechanism involving reorganization of key sub-sites within the binding groove. This study highlighted Abstract differences between Nutlin-3 and peptide binding that suggest the rational design of specific inhibitors of the MDM4:p53 interaction.

Peptide recognition domains (PRD) bind to short linear motifs on their biological partners and are found in several cellular pathways including those found to be critical in tumorigenesis. In this study, I aimed to generate peptide probes against PRDs present on proteins involved in ovarian cancer. Using bioinformatics, I identified 66 potential PRDs present on these proteins. I then used peptide phage display to successfully generate peptides against 27 of the 66 domains. To validate my results, I performed an extensive literature review and structural analysis. For several cases, the phage-display derived binding preferences are similar to previously reported studies. However, for a subset of domains, I identified non-canonical binding preferences that have not been reported previously in literature. The binding preferences obtained in this study can be used to design intracellular probes for studying the role of these PRDs in biological pathways important in ovarian cancer.

Peptide recognition domains (PRD) bind to short linear motifs on their biological partners and are found in several cellular pathways including those found to be critical in tumorigenesis. In this study, I aimed to generate peptide probes against PRDs present on proteins involved in ovarian cancer. Using bioinformatics, I identified 66 potential PRDs present on these proteins. I then used peptide phage display to successfully generate peptides against 27 of the 66 domains. To validate my results, I performed an extensive literature review and structural analysis. For several cases, the phage-display derived binding preferences are similar to previously reported studies. However, for a subset of domains, I identified non-canonical binding preferences that have not been reported previously in literature. The binding preferences obtained in this study can be used to design intracellular probes for studying the role of these PRDs in biological pathways important in ovarian cancer.

Traditional (or commercial) CRM is a well-defined domain but there is currently no generally accepted definition of what constitutes CRM in the not for profit (NfP) sector. Not for profit organisations are organisations which exist for a social purpose, are independent of the State, and which re-invest all of their financial surpluses in the services they offer or in the organisation itself. This research aims to answer the question "What exactly is CRM as applied to the NfP sector, what are its boundaries and what functions should an NfP CRM information system perform?" Grounded Theory Method (GTM) within a Design Science framework was used to collect, analyse, categorise, generalise and structure data from a number of NfP organisations and NfP information systems suppliers. An NfP CRM model was constructed from this data in the form of three multi-level taxonomies. The main taxonomy relates to generic and reusable information system requirements both functional and non-functional. Within this taxonomy the high-level categorisations of commercial CRM, namely "Marketing, "Sales" and "Service", are greatly extended to reflect the special needs of the NfP sector and in particular a much broader definition of "customer". The two minor taxonomies relate to issues of CRM strategy and CRM systems architecture which need to be considered alongside the system requirements. In addition to and resulting from the taxonomies, an over-arching definition of NfP CRM was developed. NfP organisations now have a framework that will enable them to know what to expect of CRM systems and from which they can select requirements to build their own specification of information system needs. Using the requirements taxonomy for this task will make the process of requirements analysis and specification easier, quicker, cheaper and more complete than using traditional methods. The framework will also allow NfP system suppliers to know what NfP organisations expect of their systems and will assist them with the specification of new system features. The minor taxonomies will provide NfP organisations with a series of strategic issues and systems architecture options that should be considered when implementing a CRM system. This research also demonstrates how GTM can be utilised: as the development phase of Design Research, as a general method of domain analysis, and as a tool to develop a taxonomy of reusable information system requirements.