Bayesian algorithms with applications

Advances in algorithms for approximate sampling from a multivariable target function have led to solutions to challenging statistical inference problems that would otherwise not be considered by the applied scientist. Such sampling algorithms are particularly relevant to Bayesian statistics, since the target function is the posterior distribution of the unobservables given the observables. In this thesis we develop, adapt and apply Bayesian algorithms, whilst addressing substantive applied problems in biology and medicine as well as other applications. For an increasing number of high-impact research problems, the primary models of interest are often sufficiently complex that the likelihood function is computationally intractable. Rather than discard these models in favour of inferior alternatives, a class of Bayesian "likelihoodfree" techniques (often termed approximate Bayesian computation (ABC)) has emerged in the last few years, which avoids direct likelihood computation through repeated sampling of data from the model and comparing observed and simulated summary statistics. In Part I of this thesis we utilise sequential Monte Carlo (SMC) methodology to develop new algorithms for ABC that are more efficient in terms of the number of model simulations required and are almost black-box since very little algorithmic tuning is required. In addition, we address the issue of deriving appropriate summary statistics to use within ABC via a goodness-of-fit statistic and indirect inference. Another important problem in statistics is the design of experiments. That is, how one should select the values of the controllable variables in order to achieve some design goal. The presences of parameter and/or model uncertainty are computational obstacles when designing experiments but can lead to inefficient designs if not accounted for correctly. The Bayesian framework accommodates such uncertainties in a coherent way. If the amount of uncertainty is substantial, it can be of interest to perform adaptive designs in order to accrue information to make better decisions about future design points. This is of particular interest if the data can be collected sequentially. In a sense, the current posterior distribution becomes the new prior distribution for the next design decision. Part II of this thesis creates new algorithms for Bayesian sequential design to accommodate parameter and model uncertainty using SMC. The algorithms are substantially faster than previous approaches allowing the simulation properties of various design utilities to be investigated in a more timely manner. Furthermore the approach offers convenient estimation of Bayesian utilities and other quantities that are particularly relevant in the presence of model uncertainty. Finally, Part III of this thesis tackles a substantive medical problem. A neurological disorder known as motor neuron disease (MND) progressively causes motor neurons to no longer have the ability to innervate the muscle fibres, causing the muscles to eventually waste away. When this occurs the motor unit effectively ‘dies’. There is no cure for MND, and fatality often results from a lack of muscle strength to breathe. The prognosis for many forms of MND (particularly amyotrophic lateral sclerosis (ALS)) is particularly poor, with patients usually only surviving a small number of years after the initial onset of disease. Measuring the progress of diseases of the motor units, such as ALS, is a challenge for clinical neurologists. Motor unit number estimation (MUNE) is an attempt to directly assess underlying motor unit loss rather than indirect techniques such as muscle strength assessment, which generally is unable to detect progressions due to the body’s natural attempts at compensation. Part III of this thesis builds upon a previous Bayesian technique, which develops a sophisticated statistical model that takes into account physiological information about motor unit activation and various sources of uncertainties. More specifically, we develop a more reliable MUNE method by applying marginalisation over latent variables in order to improve the performance of a previously developed reversible jump Markov chain Monte Carlo sampler. We make other subtle changes to the model and algorithm to improve the robustness of the approach.

Analysis of 3 common polymorphisms in the KCNK18 gene in an Australian migraine case-control cohort

Migraine is a common neurological disorder characterised by temporary disabling attacks of severe head pain and associated disturbances. There is significant evidence to suggest a genetic aetiology to the disease however few causal mutations have been conclusively linked to the migraine subtypes Migraine with (MA) or without Aura (MO). The Potassium Channel, Subfamily K, member 18 (KCNK18) gene, coding the potassium channel TRESK, is the first gene in which a rare mutation resulting in a non-functional truncated protein has been identified and causally linked to MA in a multigenerational family. In this study, three common polymorphisms in the KCNK18 gene were analysed for genetic variation in an Australian case-control migraine population consisting of 340 migraine cases and 345 controls. No association was observed for the polymorphisms examined with the migraine phenotype or with any haplotypes across the gene. Therefore even though the KCNK18 gene is the only gene to be causally linked to MA our studies indicate that common genetic variation in the gene is not a contributor to MA.

Molecular genetics of migraine

Migraine is a common neurological disorder with a significantly heritable component. It is a complex disease and despite numerous molecular genetic studies, the exact pathogenesis causing the neurological disturbance remains poorly understood. Although several known molecular mechanisms have been associated with an increased risk for developing migraine, there remains significant scope for future studies. The majority of studies have investigated the most plausible candidate genes involved in common migraine pathogenesis utilising criteria that takes into account a combination of physiological functionality in conjunction with regions of genomic association. Thus, far genes involved in neurological, vascular or hormonal pathways have been identified and investigated on this basis. Genome-wide association studies (GWAS) studies have helped to identify novel regions that may be associated with migraine and have aided in providing the basis for further molecular investigations. However, further studies utilising sequencing technologies are required to characterise the genetic basis for migraine.

Studies on the pathophysiology and genetic basis of migraine

Migraine is a neurological disorder that affects the central nervous system causing painful attacks of headache. A genetic vulnerability and exposure to environmental triggers can influence the migraine phenotype. Migraine interferes in many facets of people’s daily life including employment commitments and their ability to look after their families resulting in a reduced quality of life. Identification of the biological processes that underlie this relatively common affliction has been difficult because migraine does not have any clearly identifiable pathology or structural lesion detectable by current medical technology. Theories to explain the symptoms of migraine have focused on the physiological mechanisms involved in the various phases of headache and include the vascular and neurogenic theories. In relation to migraine pathophysiology the trigeminovascular system and cortical spreading depression have also been implicated with supporting evidence from imaging studies and animal models. The objective of current research is to better understand the pathways and mechanisms involved in causing pain and headache to be able to target interventions. The genetic component of migraine has been teased apart using linkage studies and both candidate gene and genome-wide association studies, in family and case-control cohorts. Genomic regions that increase individual risk to migraine have been identified in neurological, vascular and hormonal pathways. This review discusses knowledge of the pathophysiology and genetic basis of migraine with the latest scientific evidence from genetic studies.

A possible role for mitochondrial dysfunction in migraine

Migraine is a common neurological disorder characterised by debilitating head pain and an assortment of additional symptoms which can include nausea, emesis, photophobia, phonophobia and occasionally visual sensory disturbances. Migraine is a complex disease caused by an interplay between predisposing genetic variants and environmental factors. It affects approximately 12 % of studied Caucasian populations with affected individuals being predominantly female. Genes involved in neurological, vascular or hormonal pathways have all been implicated in predisposition towards developing migraine. All of these are nuclear encoded genes, but given the role of mitochondria in a number of neurological disorders and in energy production it is possible that mitochondrial variants may play a role in the pathogenesis of this disease. Mitochondrial DNA has been a useful tool for studying population genetics and human genetic diseases due to the clear inheritance shown through successive generations. Given the clear gender bias found in migraine patients it may be important to investigate X-linked inheritance and mitochondrial-related variants in this disorder. This paper explores the possibility that mitochondrial DNA changes may play a role in migraine. Few variants in the mitochondrial genome have so far been investigated in migraine and new studies should be aimed towards investigating the role of mitochondrial DNA in this common disorder.

Functional analysis of missense variants in the TRESK (KCNK18) K+ channel

A loss of function mutation in the TRESK K2P potassium channel (KCNK18), has recently been linked with typical familial migraine with aura. We now report the functional characterisation of additional TRESK channel missense variants identified in unrelated patients. Several variants either had no apparent functional effect, or they caused a reduction in channel activity. However, the C110R variant was found to cause a complete loss of TRESK function, yet is present in both sporadic migraine and control cohorts, and no variation in KCNK18 copy number was found. Thus despite the previously identified association between loss of TRESK channel activity and migraine in a large multigenerational pedigree, this finding indicates that a single non-functional TRESK variant is not alone sufficient to cause typical migraine and highlights the genetic complexity of this disorder. Migraine is a common, disabling neurological disorder with a genetic, environmental and in some cases hormonal component. It is characterized by attacks of severe, usually unilateral and throbbing headache, can be accompanied by nausea, vomiting and photophobia and is clinically divided into two main subtypes, migraine with aura (MA) when a migraine is accompanied by transient and reversible focal neurological symptoms and migraine without aura (MO)1. The multifactorial and clinical heterogeneity of the disorder have considerably hindered the identification of common migraine susceptibility genes and most of our current understanding comes from the studies of familial hemiplegic migraine (FHM), a rare monogenic autosomal dominant form of MA2. So far, the three susceptibility genes that have been convincingly identified in FHM families all encode ion channels or transporters: CACNA1A encoding the α1 subunit of the Cav2.1 calcium channel3, SCN1A encoding the Nav1.1 sodium channel4 and ATP1A2 encoding the α2 subunit of the Na+/K+ pump5. It is believed that mutations in these genes may lead to increased efflux of glutamate and potassium in the synapse and thereby cause migraine by rendering the brain more susceptible to cortical spreading depression (CSD)6 which is thought to play a role in initiating a migraine attack7,8. However, these genes have not to date been implicated in common forms of migraine9. Nevertheless, current opinion suggests that typical migraine, like FHM, is also disorder of neuronal excitability, ion homeostasis and neurotransmitter release10,11,12. Mutations in the SLC4A4 gene encoding the sodium-bicarbonate cotransporter NBCe1, have recently been implicated in several different forms of migraine13, and a variety of genes involved in glutamate homeostasis (PGCP, MTDH14 and LRP115) and a cation channel (TRPM8)15 have also recently been implicated in migraine via genome-wide association studies. Ion channels are therefore highly likely to play an important role in the pathogenesis of typical migraine. TRESK (KCNK18), is a member of the two-pore domain (K2P) family of potassium channels involved in the control of cellular electrical excitability16. Regulation of TRESK activity by the calcium-dependent phosphatase calcineurin17, as well as its expression in dorsal root ganglia (DRG)18 and trigeminal ganglia (TG)19,20 has led to a proposed role for this channel in a variety of pain pathways. In a recent study, a frameshift mutation (F139Wfsx24) in TRESK was identified in a large multigenerational pedigree where it co-segregated perfectly with typical MA and a significant genome-wide linkage LOD score of 3.0. Furthermore, functional analysis revealed that this mutation caused a complete loss of TRESK function and that the truncated subunit was also capable of down regulating wild-type channel function. This therefore highlighted KCNK18 as potentially important candidate gene and suggested that TRESK dysfunction might play a possible role in the pathogenesis of familial migraine with visual aura20. Additional screening for KCNK18 mutations in unrelated sporadic migraine and control cohorts also identified a number of other missense variants; R10G, A34V, C110R, S231P and A233V20. The A233V variant was found only in the control cohort, whilst A34V was identified in a single Australian migraine proband for which family samples were not available, but it was not detected in controls. By contrast, the R10G, C110R, and S231P variants were found in both migraineurs and controls in both cohorts. In this study, we have investigated the functional effect of these variants to further probe the potential association of TRESK dysfunction with typical migraine.

Investigation of the role of the GABRG2 gene variant in migraine

Migraine is the most common neurological disorder worldwide affecting about 12% of the worldwide population. This disorder has been classed into two main types of migraine—with and without aura. While a number of factors can influence the onset of migraine, a major factor is that of genetics. The GABAA gene encodes for the GABAA receptor. Along with other receptors, the GABAA receptor is involved in the mediation of neuronal activities. In this study, a GABRG2 gene (GABAA receptor gamma-2-subunit) SNP (rs211037) was genotyped on a migraine case–control population of 546 (273 affected and an equal number of healthy) individuals. Using specifically designed primers, a high resolution melt (HRM) assay was carried out in the genotyping process. After genotyping, results were compared in the case and control populations. Analysis of results showed no significant differences in the allele frequencies between case and control populations. Similarly no differences were detected for subtypes or for a specific gender of migraine (p > 0.05). Although this gene has been previously found to be involved in febrile seizures and there is some co-morbidity between epilepsy and migraine, we decided to investigate this marker for involvement in migraine. The results did not support a role for the tested GABRG2 variant in migraine.

The role of the MTHFR gene in migraine

Migraine is a common neurological disorder and is characterized by debilitating head pain and an assortment of additional symptoms which can include nausea, emesis, photophobia, phonophobia, and occasionally, visual sensory disturbances. A number of genes have been implicated in the pathogenesis of this disease, including genes involved in regulating the vascular system. Of particular importance are the methylenetetrahydrofolate reductase (MTHFR) gene and the role it plays in migraine with aura. Migraine with aura has previously been shown to have a significant comorbidity with stroke, making the vascular class of genes a priority for migraine studies. In this report, we outline the importance of the MTHFR gene in migraine and also discuss the use of a genetic isolate to investigate MTHFR genetic variants. From this study, 3 MTHFR single nucleotide polymorphisms showing association with migraine in the Norfolk Island population have been identified, thus reinforcing the potential role of MTHFR in migraine susceptibility. Further studies will continue to build a gene profile of variants involved in the complex disease migraine and improve understanding of the underlying genetic causes of this disorder.

Association study of calcitonin gene-related polypeptide-alpha (CALCA) gene polymorphism with migraine

Migraine is a neurological disorder that is associated with increased levels of calcitonin gene-related peptide (CGRP) in plasma. CGRP, being one of the mediators of neurogenic inflammation and a phenomenon implicated in the pathogenesis of migraine headache, is thus suggested to have an important role in migraine pathophysiology. Polymorphisms of the CALCA gene have been linked to Parkinson's disease, ovarian cancer and essential hypertension, suggesting a functional role for these polymorphisms. Given the strong evidence linking CGRP and migraine, it is hypothesised that polymorphisms in the CALCA gene may play a role in migraine pathogenesis. Seemingly non functional intronic polymorphisms are capable of disrupting normal RNA processing or introducing a splice site in the transcript. A 16 bp deletion in the first intron of the CALCA gene has been reported to be a good match for the binding site for a transcription factor expressed strongly in neural crest derived cells, AP-2. This deletion also eliminates an intron splicing enhancer (ISE) that may potentially cause exon skipping. This study investigated the role of the 16 bp intronic deletion in the CALCA gene in migraineurs and matched control individuals. Six hundred individuals were genotyped for the deletion by polymerase chain reaction followed by fragment analysis on the 3130 Genetic Analyser. The results of this study showed no significant association between the intronic 16 bp deletion in the CALCA gene and migraine in the tested Australian Caucasian population. However, given the evidence linking CGRP and migraine, further investigation of variants with this gene may be warranted.

Genome-wide association study reveals three susceptibility loci for common migraine in the general population

Migraine is a common, heterogeneous and heritable neurological disorder. Its pathophysiology is incompletely understood, and its genetic influences at the population level are unknown. In a population-based genome-wide analysis including 5,122 migraineurs and 18,108 non-migraineurs, rs2651899 (1p36.32, PRDM16), rs10166942 (2q37.1, TRPM8) and rs11172113 (12q13.3, LRP1) were among the top seven associations (P < 5 × 10(-6)) with migraine. These SNPs were significant in a meta-analysis among three replication cohorts and met genome-wide significance in a meta-analysis combining the discovery and replication cohorts (rs2651899, odds ratio (OR) = 1.11, P = 3.8 × 10(-9); rs10166942, OR = 0.85, P = 5.5 × 10(-12); and rs11172113, OR = 0.90, P = 4.3 × 10(-9)). The associations at rs2651899 and rs10166942 were specific for migraine compared with non-migraine headache. None of the three SNP associations was preferential for migraine with aura or without aura, nor were any associations specific for migraine features. TRPM8 has been the focus of neuropathic pain models, whereas LRP1 modulates neuronal glutamate signaling, plausibly linking both genes to migraine pathophysiology.

Identification of molecular genetic factors that influence migraine

Migraine is a common neurological disorder with a strong genetic basis. However, the complex nature of the disorder has meant that few genes or susceptibility loci have been identified and replicated consistently to confirm their involvement in migraine. Approaches to genetic studies of the disorder have included analysis of the rare migraine subtype, familial hemiplegic migraine with several causal genes identified for this severe subtype. However, the exact genetic contributors to the more common migraine subtypes are still to be deciphered. Genome-wide studies such as genome-wide association studies and linkage analysis as well as candidate genes studies have been employed to investigate genes involved in common migraine. Neurological, hormonal and vascular genes are all considered key factors in the pathophysiology of migraine and are a focus of many of these studies. It is clear that the influence of individual genes on the expression of this disorder will vary. Furthermore, the disorder may be dependent on gene–gene and gene–environment interactions that have not yet been considered. In addition, identifying susceptibility genes may require phenotyping methods outside of the International Classification of Headache Disorders II criteria, such as trait component analysis and latent class analysis to better define the ambit of migraine expression.

Association between migraine and a functional polymorphism at the dopamine β-hydroxylase locus

Migraine is a common neurological disorder with a significant genetic component. Although a number of linkage and association studies have been undertaken, the number and identity of all migraine susceptibility genes has yet to be defined. The existence of dopaminergic hypersensitivity in migraine has been recognised on a pharmacological basis and some studies have reported genetic association between migraine and dopamine-related gene variants. Our laboratory has previously reported association of migraine with a promoter STR marker in the dopamine beta hydroxylase (DBH) gene. In the present study, we analysed two additional DBH markers in two independent migraine case–control cohorts. These two markers are putative functional SNPs, one within the promoter (−1021C→T) and another SNP (+1603C→T) in exon 11 of the DBH gene. The results showed a significant association for allelic and genotypic frequency distribution between the DBH marker in the promoter and migraine in the first (P = 0.004 and P = 0.012, respectively) and the second (P = 0.013 and P = 0.031, respectively) tested cohorts. There was no association observed between either genotype and/or allelic frequencies for the DBH marker located in exon 11 and migraine (P ≥ 0.05). The promoter DBH marker, reported associated with migraine in this study, has been shown to affect up to 52% of plasma DBH activity. Varying DBH activity levels have been postulated to be involved in migraine process with an increase of dopamine, resulting from a lower DBH activity shown positively correlated with migraine severity. It is plausible that the functional promoter variant of DBH may play a role in the migraine disorder.

Investigation between the S377G3 GATA-4 polymorphism and migraine

Migraine is a common and painful neurological disorder, with genetic and environmental components. Several conditions have been shown to be comorbid with migraine, notably a cardiac malformation affecting the interatrial septum and leading to patent foramen ovale (PFO). Mutations in the development regulatory gene GATA-4, located on human chromosome 8p23.1-p22, have been found to be responsible for some cases of congenital heart defects including PFO. To determine whether the GATA-4 gene is involved in migraine, the present study performed an association analysis of a common GATA-4 variant that results in a change of amino acid (S377G), in a large case/control population (275 unrelated Caucasian migraineurs versus 275 control individuals). The results showed that there was no significant association for this polymorphism between migraine and controls (χ² = 0.84, P = 0.66). Thus it appears that the GATA-4 (S377G) mutation does not play a significant role in common migraine susceptibility.

Investigation of Gamma-aminobutyric acid (GABA) A receptors genes and migraine susceptibility

Background Migraine is a neurological disorder characterized by recurrent attacks of severe headache, affecting around 12% of Caucasian populations. It is well known that migraine has a strong genetic component, although the number and type of genes involved is still unclear. Prior linkage studies have reported mapping of a migraine gene to chromosome Xq 24–28, a region containing a cluster of genes for GABA A receptors (GABRE, GABRA3, GABRQ), which are potential candidate genes for migraine. The GABA neurotransmitter has been implicated in migraine pathophysiology previously; however its exact role has not yet been established, although GABA receptors agonists have been the target of therapeutic developments. The aim of the present research is to investigate the role of the potential candidate genes reported on chromosome Xq 24–28 region in migraine susceptibility. In this study, we have focused on the subunit GABA A receptors type ε (GABRE) and type θ (GABRQ) genes and their involvement in migraine. Methods We have performed an association analysis in a large population of case-controls (275 unrelated Caucasian migraineurs versus 275 controls) examining a set of 3 single nucleotide polymorphisms (SNPs) in the coding region (exons 3, 5 and 9) of the GABRE gene and also the I478F coding variant of the GABRQ gene. Results Our study did not show any association between the examined SNPs in our test population (P > 0.05). Conclusion Although these particular GABA receptor genes did not show positive association, further studies are necessary to consider the role of other GABA receptor genes in migraine susceptibility.

Gene expression studies in multiple sclerosis

Multiple sclerosis (MS) is a serious neurological disorder affecting young Caucasian individuals, usually with an age of onset at 18 to 40 years old. Females account for approximately 60x of MS cases and the manifestation and course of the disease is highly variable from patient to patient. The disorder is characterised by the development of plaques within the central nervous system (CNS). Many gene expression studies have been undertaken to look at the specific patterns of gene transcript levels in MS. Human tissues and experimental mice were used in these gene-profiling studies and a very valuable and interesting set of data has resulted from these various expression studies. In general, genes showing variable expression include mainly immunological and inflammatory genes, stress and antioxidant genes, as well as metabolic and central nervous system markers. Of particular interest are a number of genes localised to susceptible loci previously shown to be in linkage with MS. However due to the clinical complexity of the disease, the heterogeneity of the tissues used in expression studies, as well as the variable DNA chips/membranes used for the gene profiling, it is difficult to interpret the available information. Although this information is essential for the understanding of the pathogenesis of MS, it is difficult to decipher and define the gene pathways involved in the disorder. Experiments in gene expression profiling in MS have been numerous and lists of candidates are now available for analysis. Researchers have investigated gene expression in peripheral mononuclear white blood cells (PBMCs), in MS animal models Experimental Allergic Encephalomyelitis (EAE) and post mortem MS brain tissues. This review will focus on the results of these studies.