A principal component approach to space-based gravitational wave astronomy

The current approach to data analysis for the Laser Interferometry Space Antenna (LISA) depends on the time delay interferometry observables (TDI) which have to be generated before any weak signal detection can be performed. These are linear combinations of the raw data with appropriate time shifts that lead to the cancellation of the laser frequency noises. This is possible because of the multiple occurrences of the same noises in the different raw data. Originally, these observables were manually generated starting with LISA as a simple stationary array and then adjusted to incorporate the antenna's motions. However, none of the observables survived the flexing of the arms in that they did not lead to cancellation with the same structure. The principal component approach is another way of handling these noises that was presented by Romano and Woan which simplified the data analysis by removing the need to create them before the analysis. This method also depends on the multiple occurrences of the same noises but, instead of using them for cancellation, it takes advantage of the correlations that they produce between the different readings. These correlations can be expressed in a noise (data) covariance matrix which occurs in the Bayesian likelihood function when the noises are assumed be Gaussian. Romano and Woan showed that performing an eigendecomposition of this matrix produced two distinct sets of eigenvalues that can be distinguished by the absence of laser frequency noise from one set. The transformation of the raw data using the corresponding eigenvectors also produced data that was free from the laser frequency noises. This result led to the idea that the principal components may actually be time delay interferometry observables since they produced the same outcome, that is, data that are free from laser frequency noise. The aims here were (i) to investigate the connection between the principal components and these observables, (ii) to prove that the data analysis using them is equivalent to that using the traditional observables and (ii) to determine how this method adapts to real LISA especially the flexing of the antenna. For testing the connection between the principal components and the TDI observables a 10x 10 covariance matrix containing integer values was used in order to obtain an algebraic solution for the eigendecomposition. The matrix was generated using fixed unequal arm lengths and stationary noises with equal variances for each noise type. Results confirm that all four Sagnac observables can be generated from the eigenvectors of the principal components. The observables obtained from this method however, are tied to the length of the data and are not general expressions like the traditional observables, for example, the Sagnac observables for two different time stamps were generated from different sets of eigenvectors. It was also possible to generate the frequency domain optimal AET observables from the principal components obtained from the power spectral density matrix. These results indicate that this method is another way of producing the observables therefore analysis using principal components should give the same results as that using the traditional observables. This was proven by fact that the same relative likelihoods (within 0.3%) were obtained from the Bayesian estimates of the signal amplitude of a simple sinusoidal gravitational wave using the principal components and the optimal AET observables. This method fails if the eigenvalues that are free from laser frequency noises are not generated. These are obtained from the covariance matrix and the properties of LISA that are required for its computation are the phase-locking, arm lengths and noise variances. Preliminary results of the effects of these properties on the principal components indicate that only the absence of phase-locking prevented their production. The flexing of the antenna results in time varying arm lengths which will appear in the covariance matrix and, from our toy model investigations, this did not prevent the occurrence of the principal components. The difficulty with flexing, and also non-stationary noises, is that the Toeplitz structure of the matrix will be destroyed which will affect any computation methods that take advantage of this structure. In terms of separating the two sets of data for the analysis, this was not necessary because the laser frequency noises are very large compared to the photodetector noises which resulted in a significant reduction in the data containing them after the matrix inversion. In the frequency domain the power spectral density matrices were block diagonals which simplified the computation of the eigenvalues by allowing them to be done separately for each block. The results in general showed a lack of principal components in the absence of phase-locking except for the zero bin. The major difference with the power spectral density matrix is that the time varying arm lengths and non-stationarity do not show up because of the summation in the Fourier transform.

Epidemiology and genetic architecture of blood pressure: a family based study of Generation Scotland

Hypertension is a major risk factor for cardiovascular disease and mortality, and a growing global public health concern, with up to one-third of the world’s population affected. Despite the vast amount of evidence for the benefits of blood pressure (BP) lowering accumulated to date, elevated BP is still the leading risk factor for disease and disability worldwide. It is well established that hypertension and BP are common complex traits, where multiple genetic and environmental factors contribute to BP variation. Furthermore, family and twin studies confirmed the genetic component of BP, with a heritability estimate in the range of 30-50%. Contemporary genomic tools enabling the genotyping of millions of genetic variants across the human genome in an efficient, reliable, and cost-effective manner, has transformed hypertension genetics research. This is accompanied by the presence of international consortia that have offered unprecedentedly large sample sizes for genome-wide association studies (GWASs). While GWAS for hypertension and BP have identified more than 60 loci, variants in these loci are associated with modest effects on BP and in aggregate can explain less than 3% of the variance in BP. The aims of this thesis are to study the genetic and environmental factors that influence BP and hypertension traits in the Scottish population, by performing several genetic epidemiological analyses. In the first part of this thesis, it aims to study the burden of hypertension in the Scottish population, along with assessing the familial aggregation and heritialbity of BP and hypertension traits. In the second part, it aims to validate the association of common SNPs reported in the large GWAS and to estimate the variance explained by these variants. In this thesis, comprehensive genetic epidemiology analyses were performed on Generation Scotland: Scottish Family Health Study (GS:SFHS), one of the largest population-based family design studies. The availability of clinical, biological samples, self-reported information, and medical records for study participants has allowed several assessments to be performed to evaluate factors that influence BP variation in the Scottish population. Of the 20,753 subjects genotyped in the study, a total of 18,470 individuals (grouped into 7,025 extended families) passed the stringent quality control (QC) criteria and were available for all subsequent analysis. Based on the BP-lowering treatment exposure sources, subjects were further classified into two groups. First, subjects with both a self-reported medications (SRMs) history and electronic-prescription records (EPRs; n =12,347); second, all the subjects with at least one medication history source (n =18,470). In the first group, the analysis showed a good concordance between SRMs and EPRs (kappa =71%), indicating that SRMs can be used as a surrogate to assess the exposure to BP-lowering medication in GS:SFHS participants. Although both sources suffer from some limitations, SRMs can be considered the best available source to estimate the drug exposure history in those without EPRs. The prevalence of hypertension was 40.8% with higher prevalence in men (46.3%) compared to women (35.8%). The prevalence of awareness, treatment and controlled hypertension as defined by the study definition were 25.3%, 31.2%, and 54.3%, respectively. These findings are lower than similar reported studies in other populations, with the exception of controlled hypertension prevalence, which can be considered better than other populations. Odds of hypertension were higher in men, obese or overweight individuals, people with a parental history of hypertension, and those living in the most deprived area of Scotland. On the other hand, deprivation was associated with higher odds of treatment, awareness and controlled hypertension, suggesting that people living in the most deprived area may have been receiving better quality of care, or have higher comorbidity levels requiring greater engagement with doctors. These findings highlight the need for further work to improve hypertension management in Scotland. The family design of GS:SFHS has allowed family-based analysis to be performed to assess the familial aggregation and heritability of BP and hypertension traits. The familial correlation of BP traits ranged from 0.07 to 0.20, and from 0.18 to 0.34 for parent-offspring pairs and sibling pairs, respectively. A higher correlation of BP traits was observed among first-degree relatives than other types of relative pairs. A variance-component model that was adjusted for sex, body mass index (BMI), age, and age-squared was used to estimate heritability of BP traits, which ranged from 24% to 32% with pulse pressure (PP) having the lowest estimates. The genetic correlation between BP traits showed a high correlation between systolic (SBP), diastolic (DBP) and mean arterial pressure (MAP) (G: 81% to 94%), but lower correlations with PP (G: 22% to 78%). The sibling recurrence risk ratio (λS) for hypertension and treatment were calculated as 1.60 and 2.04 respectively. These findings confirm the genetic components of BP traits in GS:SFHS, and justify further work to investigate genetic determinants of BP. Genetic variants reported in the recent large GWAS of BP traits were selected for genotyping in GS:SFHS using a custom designed TaqMan® OpenArray®. The genotyping plate included 44 single nucleotide polymorphisms (SNPs) that have been previously reported to be associated with BP or hypertension at genome-wide significance level. A linear mixed model that is adjusted for age, age-squared, sex, and BMI was used to test for the association between the genetic variants and BP traits. Of the 43 variants that passed the QC, 11 variants showed statistically significant association with at least one BP trait. The phenotypic variance explained by these variant for the four BP traits were 1.4%, 1.5%, 1.6%, and 0.8% for SBP, DBP, MAP, and PP, respectively. The association of genetic risk score (GRS) that were constructed from selected variants has showed a positive association with BP level and hypertension prevalence, with an average effect of one mmHg increase with each 0.80 unit increases in the GRS across the different BP traits. The impact of BP-lowering medication on the genetic association study for BP traits has been established, with typical practice of adding a fixed value (i.e. 15/10 mmHg) to the measured BP values to adjust for BP treatment. Using the subset of participants with the two treatment exposure sources (i.e. SRMs and EPRs), the influence of using either source to justify the addition of fixed values in SNP association signal was analysed. BP phenotypes derived from EPRs were considered the true phenotypes, and those derived from SRMs were considered less accurate, with some phenotypic noise. Comparing SNPs association signals between the four BP traits in the two model derived from the different adjustments showed that MAP was the least impacted by the phenotypic noise. This was suggested by identifying the same overlapped significant SNPs for the two models in the case of MAP, while other BP traits had some discrepancy between the two sources

The role of cancer related inflammation, Src family kinases and matrix metalloproteinase 9 in colorectal cancer

Colorectal cancer (CRC) is the third most common cancer in the UK with 41,000 new cases diagnosed in 2011. Despite undergoing potentially curative resection, a significant amount of patients develop recurrence. Biomarkers that aid prognostication or identify patients who are suitable for adjuvant treatments are needed. The TNM staging system does a reasonably good job at offering prognostic information to the treating clinician, but it could be better and identifying methods of improving its accuracy are needed. Tumour progression is based on a complex relationship between tumour behaviour and the hosts’ inflammatory responses. Sustained tumour cell proliferation, evading growth suppressors, resisting apoptosis, replicative immortality, sustained angiogenesis, invasion & metastasis, avoiding immune destruction, deregulated cellular energetics, tumour promoting inflammation and genomic instability & mutation have been identified as hallmarks. These hallmarks are malignant behaviors are what makes the cell cancerous and the more extreme the behaviour the more aggressive the cancer the more likely the risk of a poor outcome. There are two primary genomic instability pathways: Microsatellite Instability (MSI) and Chromosomal Instability (CI) also referred to as Microsatellite Stability (MSS). Tumours arising by these pathways have a predilection for specific anatomical, histological and molecular biological features. It is possible that aberrant molecular expression of genes/proteins that promote malignant behaviors may also act as prognostic and predictive biomarkers, which may offer superior prognostic information to classical prognostic features. Cancer related inflammation has been described as a 7th hallmark of cancer. Despite the systemic inflammatory response (SIR) being associated with more aggressive malignant disease, infiltration by immune cells, particularly CD8+ lymphocytes, at the advancing edge of the tumour have been associated with improved outcome and tumour MSI. It remains unknown if the SIR is associated with tumour MSI and this requires further study. The mechanisms by which colorectal cancer cells locally invade through the bowel remain uncertain, but connective tissue degradation by matrix metalloproteinases (MMPs) such as MMP-9 have been implicated. MMP-9 has been found in the cancer cells, stromal cells and patient circulation. Although tumoural MMP-9 has been associated with poor survival, reports are conflicting and contain relatively small sample sizes. Furthermore, the influence of high serum MMP-9 on survival remains unknown. Src family kinases (SFKs) have been implicated in many adverse cancer cell behaviors. SFKs comprise 9 family members BLK, C-SRC, FGR, FYN, HCK, LCK, LYN, YES, YRK. C-SRC has been the most investigated of all SFKs, but the role of other SFKs in cellular behaviors and their prognostic value remains largely unknown. The development of Src inhibitors, such as Dasatinib, has identified SFKs as a potential therapeutic target for patients at higher risk of poor survival. Unfortunately, clinical trials so far have not been promising but this may reflect inadequate patient selection and SFKs may act as useful prognostic and predictive biomarkers. In chapter 3, the association between cancer related inflammation, tumour MSI, clinicopathological factors and survival was tested in two independent cohorts. A training cohort consisting of n=182 patients and a validation cohort of n=677 patients. MSI tumours were associated with a raised CRP (p=0.003). Hypoalbuminaemia was independently associated with poor overall survival in TNM stage II cancer (HR 3.04 (95% CI 1.44 – 6.43);p=0.004), poor recurrence free survival in TNM stage III cancer (HR 1.86 (95% 1.03 – 3.36);p=0.040) and poor overall survival in CI colorectal cancer (HR 1.49 (95% CI 1.06 – 2.10);p=0.022). Interestingly, MSI tumours were associated with poor overall survival in TNM stage III cancer (HR 2.20 (95% CI 1.10 – 4.37);p=0.025). In chapter 4, the role of MMP-9 in colorectal cancer progression and survival was examined. MMP-9 in the tissue was assessed using IHC and serum expression quantified using ELISA. Serum MMP-9 was associated with cancer cell expression (Spearman’s Correlation Coefficient (SCC) 0.393, p<0.001)) and stromal expression (SCC 0.319, p=0.002). Serum MMP-9 was associated with poor recurrence-free (HR 3.37 (95% CI 1.20 – 9.48);p=0.021) and overall survival (HR 3.16 (95% CI 1.22 – 8.15);p=0.018), but tumour MMP-9 was not survival or MSI status. In chapter 5, the role of SFK expression and activation in colorectal cancer progression and survival was studied. On PCR analysis, although LYN, C-SRC and YES were the most highly expressed, FGR and HCK had higher expression profiles as tumours progressed. Using IHC, raised cytoplasmic FAK (tyr 861) was independently associated with poor recurrence free survival in all cancers (HR 1.48 (95% CI 1.02 – 2.16);p=0.040) and CI cancers (HR 1.50 (95% CI 1.02 – 2.21);p=0.040). However, raised cytoplasmic HCK (HR 2.04 (95% CI 1.11 – 3.76);p=0.022) was independently associated with poor recurrence-free survival in TNM stage II cancers. T84 and HT29 cell lines were used to examine the cellular effects of Dasatinib. Cell viability was assessed using WST-1 assay and apoptosis assessed using an ELISA cell death detection assay. Dasatinib increased T84 tumour cell apoptosis in a dose dependent manner and resulted in reduced expression of nuclear (p=0.008) and cytoplasmic (p=0.016) FAK (tyr 861) expression and increased nuclear FGR expression (p=0.004). The results of this thesis confirm that colorectal cancer is a complex disease that represents several subtypes of cancer based on molecular biological behaviors. This thesis concentrated on features of the disease related to inflammation in terms of genetic and molecular characterisation. MSI cancers are closely associated with systemic inflammation but despite this observation, they retain their relatively improved survival. MMP-9 is a feature of tissue remodeling during inflammation and is also associated with degradation of connective tissue, advanced T-stage and poor outcome when measured in the serum. The lack of stromal quantification due to TMA use rather than full sections makes the value of tumoural MMP-9 immunoreactivity in the prognostication and its association with MSI unknown and requires further study. Finally, SFK activation was also associated with SIR, however, only cytoplasmic HCK was independently associated with poor survival in patients with TNM stage II disease, the group of patients where identifying a novel biomarker is most needed. There is still some way to go before these biomarkers are translated into clinical practice and future work needs to focus on obtaining a reliable and robust scientific technique with validation in an adequately powered independent cohort.