EPSRC Reference: 
EP/R005125/1 
Title: 
RS Fellow  EPSRC grant (2016): Algebraic and topological approaches for genomic data in molecular biology 
Principal Investigator: 
Harrington, Dr H 
Other Investigators: 

Researcher CoInvestigators: 

Project Partners: 

Department: 
Mathematical Institute 
Organisation: 
University of Oxford 
Scheme: 
EPSRC Fellowship 
Starts: 
02 May 2017 
Ends: 
01 May 2020 
Value (£): 
271,307

EPSRC Research Topic Classifications: 
Algebra & Geometry 
Statistics & Appl. Probability 

EPSRC Industrial Sector Classifications: 
No relevance to Underpinning Sectors 


Related Grants: 

Panel History: 

Summary on Grant Application Form 
Modern science generates data at an unprecedented rate, often including the measurement of genetic sequence information in time. One aim in molecular biology is to understand the processes that generate these data; this can be achieved by exploring different hypotheses that are translated into mathematical equations called models. The main outcome of my research will be a range of new methods to understand models in different scenarios with varying amounts of data. The focus of this proposal is genetic data.
The molecular interactions at the genetic level often involve enzymes and therefore can be described as biochemical reactions (known and hypothesised). In DNA, a family of proteins called recombinases rearrange DNA sequences. The focus here will be on the class of sitespecific recombinases, which only bind to the DNA at certain sites. Biochemically, the DNA is the substrate and the recombinase is the enzyme that catalyses the change.
The mathematical models that study DNA either focus on the changes of the DNA at the nucleotide level or the global structure. Since DNA can be thought of as a string, when a recombinase acts on the DNA, it can also change the knotting of the DNA. The local level analysis mathematically employs algebra, while the global level analysis using topology, a field of mathematics that studies shapes. With recent work by a current PhD student, we have preliminary results that ribbon categories and new theory is required to merge between the local and global view of DNA.
The aim of this project is to develop the mathematical theory and methods further, develop a database of known sitespecific recombinases and resulting DNA knots (which exists for a different class of enzymes called topoisomerases) and then create prediction software. Final extensions are how to take into account uncertainty/noise in either the sequence level data or the global structure experimental image data.
The second part of this project is to consider how a knot's configuration relates to its energy. Understanding the knot energies relates to unknots, which relates to a large unsolved problem in knot theory: Is there a polynomialtime algorithm to detect the unknot.
The methods that I will develop require marrying ideas from pure mathematics (in particular from algebra and topology) with computing, statistics, and techniques from applied mathematics. To combine ideas and techniques from different fields that traditionally do not intersect is an exciting opportunity for interdisciplinary research, and the development of new mathematical ideas. I have experience conducting research projects at this intersection, and employing new methods to gain a new understanding of biological systems.
The advances in mathematical methods and algorithms that result from this project, in combination with datagenerating technologies, will enable to approach and understand realworld biological systems in new ways.

Key Findings 
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Potential use in nonacademic contexts 
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Impacts 
Description 
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Summary 

Date Materialised 


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Project URL: 

Further Information: 

Organisation Website: 
http://www.ox.ac.uk 