Braid groups, mapping class groups, and Torelli groups

This thesis discusses subgroups of mapping class groups of particular surfaces. First, we study the Torelli group, that is, the subgroup of the mapping class group that acts trivially on the first homology. We investigate generators of the Torelli group, and we give an algorithm that factorizes elements of the Torelli group into products of particular generators. Furthermore, we investigate normal closures of powers of standard generators of the mapping class group of a punctured sphere. By using the Jones representation, we prove that in most cases these normal closures have infinite index in the mapping class group. We prove a similar result for the hyperelliptic mapping class group, that is, the group that consists of mapping classes that commute with a fixed hyperelliptic involution. As a corollary, we recover an older theorem of Coxeter (with 2 exceptional cases), which states that the normal closure of the m-th power of standard generators of the braid group has infinite index in the braid group. Finally, we study finite index subgroups of braid groups, namely, congruence subgroups of braid groups. We discuss presentations of these groups and we provide a topological interpretation of their generating sets.

The role of inflammation in vascular function and pregnancy outcome in the pregnant stroke prone spontaneously hypertensive rat

During pregnancy, the maternal cardiovascular system undergoes major adaptation. One of these changes is a 40-50 % increase in circulating blood volume which requires a systemic remodelling of the vasculature in order to regulate maternal blood pressure and maximise blood supply to the developing placenta and fetus. These changes are broadly conserved between humans and rats making them an appropriate pre-clinical model in which to study the underlying mechanisms of pregnancy-dependent cardiovascular remodelling. Whilst women are normally protected against cardiovascular disease; pregnancy marks a period of time where women are susceptible to cardiovascular complications. Cardiovascular disease is the leading cause of maternal mortality in the United Kingdom; in particular hypertensive conditions are among the most common complications of pregnancy. One of the main underlying pathologies of these pregnancy complications is thought to be a failure of the maternal cardiovascular system to adapt. The remodelling of the uterine arteries, which directly supply the maternal-fetal interface, is paramount to a healthy pregnancy. Failure of the uterine arteries to remodel sufficiently can result in a number of obstetric complications such as preeclampsia, fetal growth restriction and spontaneous pregnancy loss. At present, it is poorly understood whether this deficient vascular response is due to a predisposition from existing maternal cardiovascular risk factors, the physiological changes that occur during pregnancy or a combination of both. Previous work in our group employed the stroke prone spontaneously hypertensive rat (SHRSP) as a model to investigate pregnancy-dependent remodelling of the uterine arteries. The SHRSP develops hypertension from 6 weeks of age and can be contrasted with the control strain, the Wistar Kyoto (WKY) rat. The phenotype of the SHRSP is therefore reflective of the clinical situation of maternal chronic hypertension during pregnancy. We showed that the SHRSP exhibited a deficient uterine artery remodelling response with respect to both structure and function accompanied by a reduction in litter size relative to the WKY at gestational day (GD) 18. A previous intervention study using nifedipine in the SHRSP achieved successful blood pressure reduction from 6 weeks of age and throughout pregnancy; however uterine artery remodelling and litter size at GD18 was not improved. We concluded that the abnormal uterine artery remodelling present in the SHRSP was independent of chronic hypertension. From these findings, we hypothesised that the SHRSP could be a novel model of spontaneously deficient uterine artery remodelling in response to pregnancy which was underpinned by other as yet unidentified cardiovascular risk factors. In Chapter 1 of this thesis, I have characterised the maternal, placental and fetal phenotype in pregnant (GD18) SHRSP and WKY. The pregnant SHRSP exhibit features of left ventricular hypertrophy in response to pregnancy and altered expression of maternal plasma biomarkers which have been previously associated with hypertension in human pregnancy. I developed a protocol for accurate dissection of the rat uteroplacental unit using qPCR probes specific for each layer. This allowed me to make an accurate and specific statement about gene expression in the SHRSP GD18 placenta; where oxidative stress related gene markers were increased in the vascular compartments. The majority of SHRSP placenta presented at GD18 with a blackened ring which encircled the tissue. Further investigation of the placenta using western blot for caspase 3 cleavage determined that this was likely due to increased cell death in the SHRSP placenta. The SHRSP also presented with a loss of one particular placental cell type at GD18: the glycogen cells. These cells could have been the target of cell death in the SHRSP placenta or were utilised early in pregnancy as a source of energy due to the deficient uterine artery blood supply. Blastocyst implantation was not altered but resorption rate was increased between SHRSP and WKY; indicating that the reduction in litter size in the SHRSP was primarily due to late (>GD14) pregnancy loss. Fetal growth was not restricted in SHRSP which led to the conclusion that SHRSP sacrifice part of their litter to deliver a smaller number of healthier pups. Activation of the immune system is a common pathway that has been implicated in the development of both hypertension and adverse pregnancy outcome. In Chapter 2, I proposed that this may be a mechanism of interest in SHRSP pregnancy and measured the pro-inflammatory cytokine, TNFα, as a marker of inflammation in pregnant SHRSP and WKY and in the placentas from these animals. TNFα was up-regulated in maternal plasma and urine from the GD18 SHRSP. In addition, TNFα release was increased from the GD18 SHRSP placenta as was the expression of the pro-inflammatory TNFα receptor 1 (Tnfr1). In order to investigate whether this excess TNFα was detrimental to SHRSP pregnancy, a vehicle-controlled intervention study using etanercept (a monoclonal antibody which works as a TNFα antagonist) was carried out. Etanercept treatment at GD0, 6, 12 and 18 resulted in an improvement in pregnancy outcome in the SHRSP with an increased litter size and reduced resorption rate. Furthermore, there was an improved uterine artery function in GD18 SHRSP treated with etanercept which was associated with an improved uterine artery blood flow over the course of gestation. In Chapter 3, I sought to identify the source of this detrimental excess of TNFα by designing a panel for maternal leukocytes in the blood and placenta at GD18. A population of CD3- CD161+ cells, which are defined as rat natural killer (NK) cells, were increased in number in the SHRSP. Intracellular flow cytometry also identified this cell type as a source of excess TNFα in blood and placenta from pregnant SHRSP. I then went on to evaluate the effects of etanercept treatment on these CD3- CD161+ cells and showed that etanercept reduced the expression of CD161 and the cytotoxic molecule, granzyme B, in the NK cells. Thus, etanercept limits the cytotoxicity and potential damaging effect of these NK cells in the SHRSP placenta. Analysing the urinary peptidome has clinical potential to identify novel pathways involved with disease and/or to develop biomarker panels to aid and stratify diagnosis. In Chapter 4, I utilised the SHRSP as a pre-clinical model to identify novel urinary peptides associated with hypertensive pregnancy. Firstly, a characterisation study was carried out in the kidney of the WKY and SHRSP. Urine samples from WKY and SHRSP taken at pre-pregnancy, mid-pregnancy (GD12) and late pregnancy (GD18) were used in the peptidomic screen. In order to capture peptides which were markers of hypertensive pregnancy from the urinary peptidomic data, I focussed on those that were only changed in a strain dependent manner at GD12 and 18 and not pre-pregnancy. Peptide fragments from the uromodulin protein were identified from this analysis to be increased in pregnant SHRSP relative to pregnant WKY. This increase in uromodulin was validated at the SHRSP kidney level using qPCR. Uromodulin has previously been identified to be a candidate molecule involved in systemic arterial hypertension but not in hypertensive pregnancy thus is a promising target for further study. In summary, we have characterised the SHRSP as the first model of maternal chronic hypertension during pregnancy and identified that inflammation mediated by TNFα and NK cells plays a key role in the pathology. The evidence presented in this thesis establishes the SHRSP as a pre-clinical model for pregnancy research and can be continued into clinical studies in pregnant women with chronic hypertension which remains an area of unmet research need.