**Supervisors**: Ramon Grima, Guido Sanguinetti

**Project description**:

A particularly important quantity of interest in computational biology is the first-passage time (FPT), that is, the time it takes a particular biological process to cross a certain threshold. For example, the time it takes cells to respond to external signals by expressing certain genes and the extinction time of epidemic diseases. One could use this approach to also provide guarantees for synthetic biology systems e.g. that the systems will not reach a state which is dangerous in a finite time. However FPT problems are notoriously difficult to solve mathematically. Recently the Grima and Sanguinetti groups showed that the FPT problem can be formulated exactly as a Bayesian inference problem. This novel formulation allows us to the derivation of an efficient approximation scheme that relies on the solution of a small set of ordinary differential equations. In this project the successful student will take forward the new approach by applying it to several problems of interest in molecular, ecological, population and synthetic biology. The student will also systematically explore the accuracy of the new approach, uncover the limits of its applicability and extend it using methods from machine learning and statistical physics. The successful applicant will have a Bachelors degree in Physics, Applied Mathematics or a similar qualification. Previous experience in machine learning, Bayesian computation or statistical physics is not necessary as all training will be provided. An interest in learning the biology background to the problems of interest is a must. The successful candidate will join the group of Dr. Ramon Grima in the Centre for Synthetic and Systems Biology at the University of Edinburgh and interact on a weekly basis with the Sanguinetti group in the School of Informatics. |