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Quantifying Differences in Gene Networks via Graph Curvature
KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Optimization and Systems Theory.
2019 (English)Independent thesis Advanced level (degree of Master (Two Years)), 20 credits / 30 HE creditsStudent thesisAlternative title
Kvantifiering av skillnader i gennätverk genom grafkrökning (Swedish)
Abstract [en]

Fast improvements of technologies for the acquirement of large genomic data through single cell RNA-sequencing have led to a need for new mathematical methods for the analysis of such data. One approach of representing this data that has emerged over the last couple of decades is through graph representations, i.e. as networks that describes how genes interact with each other. There has since then been a development of a multitude of methods based on these so-called co-expression networks for gene analysis. More recently, a notion of curvature has provided a methodology for quantifying differences and similarities in these large graphs, but better understanding of the methods are still needed, especially when the networks considered grows larger and larger.

Pompe disease is a rare genetic disorder caused due to mutations in the GAA gene which codes the enzyme acid alpha glucosidase (GAA). Current treatment involves enzyme replacement therapy and the side effects vary between patients. Here we develop an approach to identify genes and pathways that can reduce the disease pathology by utilizing concominant treatments or reduce the immunogenicity of current treatments.

In this project we use single cell RNA-sequencing of hundreds of cells from real patients to generate networks describing gene interactions. The Ollivier-Ricci curvature is calculated for the large networks using entropy-regulated optimal mass transport.

The top genes we identify by our method have a strong presence in prior literature in association with lysosomal and mitochondrial diseases. This positive verification from scientific literature makes this methodology for narrowing down genes of interest promising.

Abstract [sv]

En snabb utveckling av teknologi kapabel att generera stora genomiska datamängder genom encellig RNA-sekvensering har lett till behovet av nya matematiska metoder för analys av sådan data. Ett sätt att representera denna data som har blivit populärt under de senaste decennierna är genom grafrepresentationer, nätverk som beskriver hur gener interagerar med varandra. Sedan dess har det utvecklats en mängd metoder baserade på dessa nätverk. På senare tid har metoder baserade på grafkrökning skapat ett sätt att differentiera dessa stora grafer, men bättre förståelse av metoderna behövs, särskilt när de nätverken blir större och större.

Pompes sjukdom är en sällsynt genetisk sjukdom orsakad på grund av mutationer i GAA-genen som kodar för enzymet acid alpha glucosidase (GAA). Den nuvarande behandlingen innebär enzymbehandling (ERT) och biverkningarna varierar mellan patienter. Här utvecklar vi ett sätt att identifiera gener som kan förbättra sjukdomen genom att använda sammansatta behandlingar eller minska immunogeniciteten hos nuvarande behandlingar.

I detta projekt använder vi RNA-sekvensering av hundratals celler ifrån patienter för att generera nätverk som beskriver geninteraktioner. Ollivier-Riccikrökningen räknas ut för de stora nätverken genom entropi-regulariserad optimal masstransport.

Generna vi identifierar med vår metod har en stark närvaro i tidigare litteratur i samband med lysosomala och mitokondriska sjukdomar. Denna positiva verifiering från vetenskaplig litteratur gör denna metod för att begränsa gener av intresse lovande.

Place, publisher, year, edition, pages
2019.
Series
TRITA-SCI-GRU ; 2019:223
National Category
Mathematics
Identifiers
URN: urn:nbn:se:kth:diva-253364OAI: oai:DiVA.org:kth-253364DiVA, id: diva2:1326107
External cooperation
Swedish Orphan Biovitrum (SOBI), Stockholm
Subject / course
Optimization and Systems Theory
Educational program
Master of Science - Applied and Computational Mathematics
Supervisors
Examiners
Available from: 2019-06-17 Created: 2019-06-17 Last updated: 2019-06-17Bibliographically approved

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