Subcellular Genetic Populations

Abstract

Absolute quantification of mtDNA is an important task in the study of health conditions related to mtDNA heteroplasmy. This absolute quantification can be carried out through applying Bayesian inference methods to qPCR fluorescence data. There is also scope for absolute quantification through analysis of scRNAseq data. The qPCR process is described by a binomial branching process that gives rise to a Hidden Markov Model. The Metropolis Hastings (MH) algorithm (a Markov Chain Monte Carlo method) is implemented on qPCR single cell experimental data in order to infer parameters given by the model. Additionally, we investigate the use of a variation of MH, the Adaptive Metropolis algorithm. Inference results are compared between these two algorithms, combined with comparisons of various execution times. Our discussion analyses the Markov chains, and suggests further avenues for exploration, including the application of these methods to other forms of data e.g. data from ddPCR.

Lay Summary

Mitochondrial DNA (mtDNA) makes up only a small portion of the total DNA in a eukaryotic cell. However, due to its relatively high mutation rate, it has significant implications for ageing and health issues. Many medical conditions are associated with changes in the structure of mtDNA, including cancers and Parkinson’s disease. Analysing the quantity of mutant mtDNA present in single cells (termed heteroplasmy) is a key step in tackling these health issues. Reliable measurements need to be taken in order to understand how heteroplasmy changes with time. A challenge arises from the fact that measurement processes are intrinsically noisy – a variety of different heteroplasmic states could give rise to identical measurements and data. We can attempt to infer the absolute quantity of mutant mtDNA by building a mathematical model of the measurement process itself. We can determine this quantity by applying algorithms which perturb randomly around an initial guess, accepting those which are ‘likely’ given an appropriate dataset. The accepted guesses yield a probability distribution (the posterior) for the quantities we wish to infer.

Background

Model

Inference

Results

Discussion

Summary

Full Results Figures

References & Glossary

Acknowledgements

This project was conducted under the supervision of Dr Nick Jones within the Systems and Signals Group at Imperial College London. Thanks to Nick for his supervision and support, as well as Juvid Aryaman for providing expertise and guidance throughout. Thanks also to Prof Michael Sternberg, Prof Michael PH Stumpf, and others involved in conducting and overseeing the MSc in Bioinformatics and Theoretical Systems Biology, in particular Dr Suhail A Isalam for his technical support. Finally, thanks to the Wellcome Trust for their support.

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