In this thesis, we have presented our discovery of symmetric presentations of a number of non-abelian simple groups, including the Mathieu group M12. We have given several progenitors, permutation and monomial, including 2*4:(22:3), 2*5:D10, 2*8:((4X2).D4), 3*7:m L2(7), 2*6:(Z3 wr Z2), and 2*24: (2. A5) and their homomorphic images which include 4.(M12:2), the group of automorphisms of M12 and several classical groups. We have given the isomorphism type of each of the group mentioned in the thesis. In each case, a proof of the isomorphism type is provided, either computer-based or by hand. In addition, by hand constructions, using the technique of double coset enumeration, are given for the groups L2(11)X3, L2(11), PGL2(11), S5,(A5XA5):4, A7, and 37:L2(7).

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This thesis contains methods of finding new presentations of finite groups, particularly nonabelian simple groups. We have presented several progenitors such as 2^{*8}:Z_4 wr Z_2, 3^{*3}:_m L(2,7), 2^{*4}:[2:2^2], 2^{*11}:D_{11} and many more on which we've found the mathieu group M12 and 2*[M21:2^2] among their homomorphic images. We give the full monomial automorphism groups of Aut(3^{*2}), Aut(3^{*3}), and Aut(5^{*2}). Included is a proof showing that the full monomial automorphism group of Aut(m^{*n}) is isomorphic to U(m) wr S_n. In addition we have constructed the Cayley Diagrams of PGL(2,7), [3 x A_5]:2, 3:[A_6:2], and 2 x [(3 x L(2,11)):2] using the process of double coset enumeration.

Islet transplantation has proved to be a useful treatment for Type 1 diabetes mellitus, but inadequate supplies of transplantable donor tissue have intensified the need to find a renewable source of β-cells. Human embryonic stem cells (HESC) are pluripotent and may offer a viable alternative to donor islets, but their targeted differentiation to a more specific β-cell phenotype is proving challenging. One strategy to restore β-cell mass is through activation of progenitor cells present in the pancreas. The aim of this study was to isolate and characterise progenitor cells from pancreatic tissue obtained from patients with Congenital Hyperinsulinism of Infancy (CHI). An enzymatic digestion was used to isolate islets from four patients with CHI and CHI-derived cell lines (NES139, NES140, NES140 and NES144) were subsequently derived that had the potential to proliferate in vitro. The previously-described cell line NES2Y was utlised as a control cell line for comparison. Using RT-PCR, exon array, qPCR, immunocytochemistry and Ca2+ microfluorimetry techniques this thesis examines both the molecular and physiological characteristics of these four CHI-derived cell lines to establish their potential as populations of pancreatic progenitor cells. Genotyping revealed that all of the patients carried mutations in the SUR1 gene, ABCC8. Pancreatic endocrine progenitor markers (e.g. PDX1, SOX9 and HLBX9) as well as islet precursor markers (e.g. NKX2.2, NKX6.1, NEUROD1, PAX6 and FOXA2) were identified and their expression was stable over continuous cell culture. However, each of the cell lines failed to express other markers, specifically NGN3, PAX4, and ISLET1. Cell lines developed from each patient then underwent a fibroblast to epithelial-like morphological transition. High-throughput exon array analysis revealed a significant down regulation of ACTA2, VIM and upregulation of CDH1 (q value < 0.05), a gene expression pattern associated with a mesenchymal-to-epithelial transition. Analysis at the mRNA level identified that CHI-derived cell lines expressed those channels and transporters associated with the β-cell function of glucose-stimulated insulin secretion (GSIS). Yet, when expression of all five endocrine hormones was investigated, mRNA expression was undetectable in three CHI-derived cell lines, except for the expression of insulin in NES143. Protein level assessment, however, failed to detect any expression of insulin. Functional studies examining whole cellular calcium dynamics and those underlying GSIS revealed that, whilst ATP (0.1 mM) and histamine (0.1 mM) readily raised intracellular Ca2+, each of the cell lines failed consistently to respond to tolbutamide (0.1 mM), glucose (20 mM), diazoxide (0.1 mM) and KCl (40 mM), except for NES140 which responded to applications of acetylcholine (0.1 mM). Given the display of cellular plasticity, molecular and physiological characteristics, the data show CHI-derived cell lines mimic pancreatic progenitor cell populations. More importantly, they represent islet precursor cells of the secondary transition phase of pancreatic development. Future studies should concentrate on the inductive potential of these cells to produce mature insulin-secreting β-cells.

During mouse embryo gastrulation, the pluripotent epiblast gives rise to the three embryonic germ layers, the ectoderm, mesoderm and endoderm. After somitogenesis begins and pluripotency disappears from the epiblast, bipotent neuromesodermal progenitors (NMPs) drive axis elongation, contributing to the formation of the posterior nervous system, as well as the axial and paraxial mesoderm. Early NMPs arise in the E8.5 mouse embryo, in and near the primitive streak, while late NMPs are found in the tail bud (E9.5 - E13.5). NMP regions are characterized by coexpression of Tbra (Brachyury) and Sox2. Sox1, another neural related transcription factor, has also been detected in NMP regions. Importantly, it has been shown that Sox1 expression increases as NMPs transit from the primitive streak to the tail bud stages. Mouse epiblast derived stem cells (EpiSCs) recapitulate the properties of the post-implantation epiblast and therefore serve as a good in vitro system for the study of early lineage specification events. EpiSCs express pluripotency factors and early differentiation markers, including Sox2, Sox1 and Tbra. Based on studies reporting that EpiSC cultures contain distinct subpopulations that have progressed further into lineage specification, I analyzed the properties of the Tbra expressing EpiSCs and by dissecting their expression profile, I assess whether these cells are pluripotent or they have progressed further into lineage specification, possibly into an NM fate. I show that EpiSC cultures include a large fraction of Tbra/Sox2 double positive cells; however, Nanog expression was detected in the vast majority of Tbra+/Sox2+ EpiSCs suggesting that most of the Tbra+ cells are pluripotent rather than bipotent NMPs. Using a previously published Tbra-GFP reporter cell line, I present that Tbra-GFP+ cells constitute a dynamic fraction of the culture that has not exited pluripotency (as shown by expression of the pluripotency markers), but have adopted an early primitive streak-like character. Similar to the cells of the posterior epiblast, these EpiSCs are in a reversible state and they retain their ability to undergo neural differentiation. In contrast to the overlap of Tbra and Sox2 positivity in self-renewing EpiSCs, it has been shown that Tbra expression is mutually exclusive with expression of Sox1-GFP, that seems to mark a distinct subpopulation with neural-like characteristics. In vitro NMPs can be generated from EpiSCs upon treatment with Fgf2 and the Gsk- 3 antagonist/Wnt agonist CHIRON99021 (FGF/CHI). In these conditions, 80% of the culture becomes Tbra+/Sox2+. Given that Sox1 is present in NMP regions in vivo, I hypothesized that the NMP cultures could contain Tbra+Sox1+ NM bipotent cells. Most importantly, the upregulation of Sox1 at the tail bud stages drove the hypothesis that Sox1 expression could mark the transition from an early- to a late-like NMP state in vitro. In this study, using a Sox1-GFP reporter cell line, I show that Tbra/Sox2/Sox1-GFP triple positive cells emerge in FGF/CHI treated EpiSCs. Importantly, Sox1-GFP+ cells express NMP markers and are enriched in transcripts of Hox genes. The expression profile of Sox1-GFP+ cells resembles the alteration of Hox gene activation that takes place in the caudal progenitor regions during the transition from early NMPs (E8.5) to late NMPs (E9.5-10.5) and hence supports the hypothesis that Sox1-GFP marks NMPs that correspond to the axial progenitors found at tail bud stages. Although the gene activity observed in the Sox1-GFP+ subpopulation correlates with the NM developmental potential, these cells exhibit strong neurogenic capacity, while evidence for their ability to give rise to mesoderm differentiation products is still lacking. Since Tbra and Sox1/Sox2 are not expressed in NMP regions exclusively, but also in mesoderm and neural fated tissues respectively, double rather than single reporter cell lines would be more suitable tools for tracking and isolating bipotent NM progenitors in vivo and in vitro. Here, I present the CRISPR/Cas9-mediated generation of a reliable Tbra-GFP reporter ES cell line that in contrast to the one published before, contains both endogenous Tbra loci intact. By targeting the Sox2 locus in the Tbra-GFP ES cells, I generated a Tbra-GFP/Sox2-tdTomato double reporter ES cell line, that in the future, could help us to dissect the molecular mechanisms underlying the self-renewal and differentiation of NMPs.

In this thesis we have presented original homomorphic images of permutations and monomial progenitors. In some cases we have used the double coset enumeration tech- nique to construct the images and for all of the homomorphic images that we have discovered, the isomorphism type of each group is given. The homomorphic images discovered include Linear groups, Alternating groups, and two sporadic simple groups J1 and J2X2 where J1 is the smallest Janko group and J2 is the second Janko sporadic group.

We have investigated several monomial and permutation progenitors, including 2*8 : [8 : 2], 2*18 : [(22 x 3) : (3x2)], 2*16 : [22 : 4], and 2*16 : 24, 5*2 :m [4•22], 5*2 :m [(4x2) :• 2], 103∗2 :m [17 : 2] and 103∗4 :m [17 : 4]. We have discovered original, to the best of our knowledge, symmetric presentations of a number of finite groups, including PSL(2, 7), M12 , A6 : 2, A7 , PSL(2, 25), 25 :• S4, 24 : S3, PSL(2, 271), 12 x PSL(2, 13), and U(3, 7) : 2. We will present our construction of several of these images, including the Mathieu sporadic simple group M12 over the maximal subgroup PSL(2, 11), PSL(2, 17) over D9, PSL(2, 16) : 2 over [24 : 5] and PGL(2, 7) over S3. We will also give our method of finding isomorphism classes of images.

During embryonic development neurons of the cerebral cortex are generated from various progenitor cells that have progressively restricted fate. Understanding the multiple regulatory pathways that regulate the cell cycle kinetics and the identity of neurons is crucial to comprehend the etiology of severe developmental defects such as microcephaly and polymicrogyria and also the evolutionary expansion of the mammalian cerebral cortex. Intermediate progenitors (IPCs) express the transcription factor Tbr2 (a T-box gene) and deletion of this gene causes a decrease in brain size and cortical thickness. However, little is known about the molecular mechanisms regulating behavior of IPCs. In this thesis, I studied the molecular mechanisms regulating cell division and cell fate choices in IPCs using an overexpression system. I show that Tbr2 controls the expression of key genes such as Cdk4, Aspm and Wnt5a by directly binding to upstream regulatory sequences. These downstream targets could explain the role played by Tbr2 in cell cycle, spindle assembly and Wnt signaling in intermediate progenitors. The interaction with Aspm also suggests a possible mechanism of self-renewal of IPCs leading to an expanded generation of cortical neurons and ultimately an increased cortical size. While the role of IPCs in cortical neurogenesis is undisputed, it is widely believed that they contribute only towards supragranular layers. Using a knock-in transgenic mouse line (Tbr2^Cre), I show that IPCs provide glutamatergic neurons (but not GABAergic neurons or GFAP+ astrocytes) towards all cortical layers in a significant proportion (20-40%). I also show that clonally generated neurons disperse within tangential dimension across the cortex significantly closer (142.1 ± 76.8 µm) than unrelated ones (294.9 ± 105.4 µm) though within the confines of a cortical column (300-600 µm). Finally, I describe the similarity in the germinal zones of a large-brained gyrencephalic rodent, agouti and a lissencephalic primate, marmoset. Both these species show similar germinal zone cytoarchitecture and distribution of various progenitors. Further, the number of IPCs is grossly expanded thus demonstrating the conserved role of IPCs in cortical expansion regardless of the folding status of the cortex in these two species.

Calcific aortic valve disease (CAVD) is associated with increased presence of myofibroblasts, osteoblastic cells and, occasionally, adipocytes and chondrocytes in lesions. The ectopic cell types in diseased valves may be elaborated by an unidentified multipotent progenitor subpopulation within the valve interstitial cells (VICs) that populate the valve interstitium. Notably, lesions form preferentially in the fibrosa layer, the stiffer layer of the valve leaflet. It has been shown that differentiation of VICs to myofibroblasts and osteoblasts is modulated by matrix stiffness. However, the molecular mechanisms involved in mediating stiffness-dependent mechanotransduction remain obscure. The objectives of this thesis were: (1) to determine whether VICs contain a subpopulation of multipotent mesenchymal progenitor cells and to measure the frequencies of the mesenchymal progenitors and osteoprogenitors; (2) to determine the role of β-catenin and matrix stiffness in transforming growth factor-β1 (TGF-β1)-induced myofibroblast differentiation of VICs; and (3) to preliminarily investigate the involvement of four and a half LIM domains protein 2 (FHL2) in CAVD and stiffness-dependent mechanotransduction downstream of RhoA in VICs. Firstly, VICs were found to contain a subpopulation of mesenchymal progenitors that are inducible to osteogenic, myofibroblastic, adipogenic, and chondrogenic lineages. The frequencies of mesenchymal progenitors and osteoprogenitors were significantly higher than other reported sources. Secondly, it was demonstrated that β-catenin is required in TGF-β1-induced, matrix stiffness-regulated myofibroblast differentiation. Notably, TGF-β1 was only able to induce β-catenin nuclear translocation and myofibroblast differentiation on matrices with fibrosa-like stiffness, but not on matrices with ventricularis-like stiffness. Thirdly, FHL2 was found to be upregulated and colocalized with runt-related transcriptional factor 2 (Runx2) in lesions in the fibrosa layer of diseased valves, suggesting its role in osteogenic processes in CAVD. Notably, increasing matrix stiffness increased FHL2 nuclear translocation and RhoA activity in VICs. Preliminary data showed that matrix stiffness regulates FHL2 nuclear translocation via RhoA activity. These results suggest that differentiation of the rich valve progenitor subpopulation, regulated by both mechanical and biochemical cues, may contribute to the preferential occurrence of ectopic cell types in the fibrosa in CAVD. More broadly, these results highlight the critical role of mechanical environment in modulating cellular biochemical signaling.

The neocortex is the most recently evolved part of the mammalian brain which is involved in a repertoire of higher order brain functions, including those that separate humans from other animals. Humans have evolved an expanded neocortex over the course of evolution through a massive increase in neuron number (compared to our close relatives-­‐‑ the chimpanzees) in spite of sharing similar gestation time frames. So what do humans do differently compared to chimpanzees within the same time frame during their development? This dissertation addresses this question by comparing the developmental progression of neurogenesis between humans and chimpanzees using cerebral organoids as the model system. The usage of cerebral organoids, has enabled us to compare the development of both the human neocortex, and the chimpanzee neocortex from the very initiation of the neural phase of embryogenesis until very long periods of time. The results obtained so far suggest that the genetic programs underlying the development of the chimpanzee neocortex and the human neocortex are not very different, but rather the difference lies in the timing of the developmental progression. These results show that the chimpanzee neocortex spends lesser time in its proliferation phase, and allots lesser time to the generation of its neurons than the human neocortex. In more scientific terms, the neurogenic phase of the neocortex is shorter in chimpanzees than it is in humans. This conclusion is supported by (1) an earlier onset of gliogenesis in chimpanzees compared to humans which is indicative of a declining neurogenic phase, (2) an earlier increase in the chimpanzee neurogenic progenitors during development, compared to humans, (3) a higher number of stem cell– like progenitors in human cortices compared to chimpanzees, (4) a decline in neurogenic areas within the chimpanzee cerebral organoids over time compared to human cerebral organoids.