Mathematical tools for analysis of genome function, linkage disequilibrium structure and disease gene prediction

Abstract

Next-generation sequencing (NGS) help to identify disease-causing genes underlying any given monogenic or complex disease. Concurrently, mathematical tools and statistical methods, includ- ing machine learning algorithms, are rapidly evolving and together, these technologies represent the new frontier of research and clinical management on a path leading toward personalised medicine.

This thesis has been divided into three main sections. Firstly, the Linkage disequilibrium (LD) patterns were observed to understand the combined impact of recombination, natural selection, genetic drift and mutation. LD is the non-random association of alleles at different loci in a given population. To this end, LD patterns were constructed using 454 whole-genome sequences (WGS) from the Wellderly study based on the Malécot Morton model (exponential distributions with restricted parameters). Therefore, the extent of the LD was computed for genic, intergenic, exon and intron regions. The main result demonstrated that significant differences between exonic, intronic and intergenic components demonstrate that fine-scale LD structure provides important insights into genome function, which cannot be revealed by LD analysis of much lower resolution array-based genotyping and conventional linkage maps.

Secondly, machine learning methodologies were applied to classify genes into four groups: essential genes, Mendelian genes, genes associated with complex disorders, and non-essential–non-disease genes. To this end, the dataset was extracted from published studies of biological and functional properties of the genes. Hence, different supervised machine learning (ML) models were studied to select the most important features relevant for classifying genes. Simultaneously, Bayesian inference in a Gaussian graphical model (BGGM) was carried out to investigate recognising the significant features to enclose genes. Once the relevant features had been selected, a proposed unsupervised ML approach was developed to cluster genes into those four groups. The combined analysis of genomic data for gradient boosting and random forest models showed that more than 50% of the variance was explained and the results from BGMM showed that the connectivity between these gene metrics was 40%. The proposed unsupervised model showed an improvement for classifying genes into Mendelian group. However, results suggested that some genes involved in developing Mendelian disorders overlap with complex disorders.


Thirdly, a polygenic risk score (PRS) was developed to quantify the cumulative effect of low- penetrance genetic variants on breast cancer (BC), following the hypothesis that the polygenic component has an important impact on BC patients, as do BRCAs variants. Genome data from POSH and WTCCC were used to generate the PRS. This score was computed based on the surprisal theory. As a result, relative genome information per individual (RGI) was estimated to understand how unusual a genome is related to the reference genome. Thus, a person with a higher RGI has a more unusual genome. Likewise, a lower RGI corresponds to having more common alleles, and therefore a less surprising genome. The PRS for women who carry BRCA1/2 mutations or intermediate-risk/common variants demonstrated the hypothesis that the BC cases contain a strong inherited polygenic component. Furthermore, the polygenic component carriers tend to have more significant changes in allele frequencies compared to BRCA1 and BRCA2 variants.

This thesis presents methodological contributions to predictive models based on machine learning techniques and mathematical programming, together with relevant insights into disease mechanisms and potential treatment options.

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Identifiers

ORCID for Andrew Collins: orcid.org/0000-0001-7108-0771

ORCID for Reuben Pengelly: orcid.org/0000-0001-7022-645X

ORCID for William Tapper: orcid.org/0000-0002-5896-1889

ORCID for Mahesan Niranjan: orcid.org/0000-0001-7021-140X

ORCID for Benjamin Macarthur: orcid.org/0000-0002-5396-9750

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