NGCM-0060: Reduction of high-dimensional stochastic simulations of biochemical network models

Biological models of systems, such as in the study of fundamental biology of stem cells, or the initiation and
evolution of cancer, involve large number of variables undergoing reactions at multiple time-scales, and need
to capture variability at single cell level. In order to account for this stochasticity, continuous time Markov
(CTM) processes are used to describe (and simulate) the system. Even for very simple systems that may be
computationally tractable, in order to gain insight into how systemic properties might depend on the many
variables, or the many parameters characterising component reactions, it is customary to reduce them to
simpler models, such as those involving stochastic differential equations (SDE), which can then be held
answerable to empirical or theoretical queries. It is a challenging task to find suitable tractable descriptions
that remain faithful to the complexity of behaviour of large simulation models. This project will build upon
formalisms that focus on slow-scale trajectories between fixed points of deterministic systems and
reinterprets them in the language of correspondence between optics and mechanics, where shortest path
constraints determines the trajectories of particles in mechanics or light rays. This correspondence will
provide criteria of acceptance of model reduction outcomes that are amenable to such a shortest path
description. By providing a simulation based test-bed for these ideas, the project will explore the
applicability of qualitative descriptions of high-dimensional data that is commonplace in the fields of singlecell
genomic descriptions of the differentiation pathways of stem cells and development of cancer cells.

This project is run through participation in the EPSRC Centre for Doctoral Training in Next Generation Computational Modelling (http://ngcm.soton.ac.uk). For details of our 4 Year PhD programme, please see http://www.findaphd.com/search/PhDDetails.aspx?CAID=331&LID=2652

For a details of available projects click here http://www.ngcm.soton.ac.uk/projects/index.html