Mathematical Institute, Andrew Wiles Building, Woodstock Road, Oxford OX2 6GG
Modelling of complex biological systems
DPhil Project Name and Abstract
Multiscale Modelling of DNA Dynamics supervised by Radek Erban Abstract: Our genetic material is stored in 23 pairs of chromosomes each made up of a single long filament of DNA. The DNA filament is folded into shapes which are in turn folded into progressively larger structures until the entire chromosome is formed. This folding acts to both save space and act as a regulator for the expression levels of genetic information. Over the past 80 years, there have been multiple attempts to model long polymer chains on a variety of scales, varying from macroscopic models of the filament chain, to atomistic models considering forces between individual atoms. These models generally operate on only a single scale, so modellers have to choose between more realistic but computationally expensive models which operate on smaller scales, or faster, less realistic models on larger scales. The research problem which we consider is to investigate whether a multiscale approach could be useful to model dynamics of DNA to allow us to study realistic models on large scales, so that in regions of interest a more detailed, finer model could be used but in regions which are less important a coarser model can be used. This seeks to give the required amount of detail in all regions, while minimizing computational load. One of the big challenges in this DPhil will be ensuring that the multiscale model is consistent and stable between regions whilst being faster and more accurate than existing models. This project falls within the ESPRC 'Biophysics and Soft Matter Physics' research area as the modelling of long biological polymers is an area of biophysics.
DTC Short Projects
As a part of the DTC, at the end of our first year we undertake two short projects, before selecting one of them for our full DPhil. The two projects which I studied were:
Multiscale Modelling of DNA Dynamics supervised by Radek Erban and Yuichi Togashi.
Abstract: Over the past 80 years, there have been multiple attempts to model long polymer chains, which have more recently been used as a model for DNA. Most models consider the filament on only a single scale. In this project we extend one of the first models of polymer dynamics, the Rouse model, to consider a filament with different segments in different resolutions. We also develop a method to increase the resolution in existing segments using the Metropolis-Hastings algorithm. Our multiscale model maintains key statistics of end-to-end distance and diffusion of the filament and makes computational savings when applied to a basic model for the binding of a transcription factor to the DNA filament.
Genotype-Phenotype Maps and L-Systems supervised by Ard Louis.
When studying theoretical evolution, researchers often neglect to look at inherent bias in how likely new phenotypes are to arise through mutations as a property of the genotype-phenotype (GP) map, instead taking a more Darwinian perspective, studying natural selection of phenotypes which are the 'most fit'. In this project we study inherent bias in Lindenmayer systems (L-systems) for theoretical trees, as well as the relationship of this bias with different fitness metrics and complexity. The fitness properties studied have been adapted especially for two-dimensional trees generated by L-systems. In line with results for other model GP maps, we find that L-systems exhibit bias in phenotype selection, and that more complex systems are less likely to be found when sampling from genotypes.
2013-14 Dissertation looking at community detection in the social network of sport coaches with Mason Porter
Summer 2013- 6-week group project at the Oxford Summer School in Computational Biology looking at autocatalytic sets in relation to theories regarding the Origin of Life.
Summer 2012- 10-week short project in networks and theoretical ecology with Mason Porter looking at simulations in MATLAB of extinctions and methods to mitigate further species loss.
2014-current Studying for a DPhil in Systems Biology at Pembroke College, University of Oxford.
2010-2014 Studied for a Masters in Mathematics at St. Anne's College, University of Oxford.