Department of Mathematics
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Ph.D. Physics, Arizona State University, 2008
Post-doctoral Research Associate, University of York, 2008-2013
Leverhulme Trust Early Career Fellow, 2014-2016
My research is mostly focused on mathematical and biophysical models of viral assembly, evolution and their life cycle in a cell. Additionally I have also been interested in the development of computational tools for predicting RNA folding and kinetics, as RNA dynamics is often involved in the regulation of gene expression in ssRNA viruses. My work involves a variety of mathematics, physics and computational science such as stochastic simulation techniques, molecular dynamics, and normal mode analysis and aims to provide a systems approach to understanding viral infections.
RNA structure prediction
Given an RNA sequence of N letters (A,U,G,C) which have specific pairing rules (A-U, G-C, G-U), the goal of RNA structure prediction is to identify the nucleotides of the sequence which are base-paired and those that are single stranded, i.e. an RNA fold. The challenging aspect of RNA structure prediction is the extremely high number of RNA folds that are possible for a sequence of N letters. Each RNA fold will have a probability of occurrence and often it is the most probable states which are of interest. Using computational algorithms, one can explore the combinatorics of the space of RNA folds and make predictions on which folds are more likely and develop kinetic models which study how a given RNA sequence can transition between different folds, an important aspect of gene regulation in ssRNA viruses.
Viruses are usually built from many identical copies of a single protein which self-assemble into a protective spherical shell, or capsid, which houses the virus's genome. Viral capsids typically have icosahedral symmetry and are built from a combination of pentamers and hexamers. Mathematical models can be used to study the assembly process (i.e. how the individual proteins that make up the shell come together into larger structures) as well as probe questions around how the viral genome can be packaged into the protective shell simultaneously with capsid assembly.
Viral life cycles
During a viral infection, the cellular machinery is hijacked by the virus and forced to produce viral proteins and eventually new viral particles which go on to infect other cells. The various processes that need to be completed by the virus, such as the production of viral proteins and assembly of new virus, needs to be properly coordinated so that viral proteins are produced in abundance before assembly begins. Exploring the temporal coordination of virus assembly and eventual exit from the cell requires a systems approach, i.e. an approach in which various viral and host proteins along with the viral genome work together via various feedback mechanisms to regulate the timing of assembly and viral protein production.
Viral Evolution and Quasi-species Theory
Virus undergo rapid mutation and adaptation in response to various environmental pressures. The most common evolutionary pressure on a virus is from the attack of the host immune response. Mathematical disruptions of viral evolution have been around, the most famous being the Eigen model, which use a generic mathematical function to describe viral fitness. Using the insights from virus assembly and viral life cycles my collaborators and I hope to develop more realistic fitness functions to study viral evolution and viral Quasi-species which are rooted in virus biology.
Mathematical Biology and Chemistry Research Group
I have Ph.D. projects available in numerical and physical models of viral systems as well as on the study of the combinatorics, determination, and kinetic modelling of RNA secondary structure. All of my projects are heavily computational based and prospective students should be comfortable with computer coding and numerical simulations.