Background: in biological systems ion channel proteins sit in cell membranes and selectively allow the passage of particular types of ions, creating currents. Ion currents are important for many biological processes, for instance: regulating ionic concentrations within cells; passing signals (such as nerve impulses); or co-ordinating contraction of muscle (skeletal muscle and also the heart, diaphragm, gut, uterus etc.). Mathematical ion channel electrophysiology models have been used for thousands of studies since their development by Hodgkin & Huxley in 1952 , and are the basis for whole research fields, such as cardiac modelling and brain modelling . It has been suggested that there are problems in identifying which set of equations is most appropriate as an ion channel model. Often it appears different structures and/or parameter values could fit the training data equally well, but may make different predictions in new situations .
Aim: we have been developing novel experimental designs to provide more information about ion channel behaviour from shorter experiments. We would like to improve our techniques - to describe the ion current and also to characterise drug binding to ion channels (which can physically block them and reduce the current that flows to zero, sometimes leading to fatal heart rhythm changes). It is difficult to measure the rate at which drug/ion channel binding occurs and whether it occurs when the channels are open, closed, or both. These factors may be crucial in determining whether novel pharmaceutical compounds are likely to have side effects or not, and there is a need to develop efficient ways to measure them.
Approach: this project will involve computational biophysical modelling (efficient numerical solution of nonlinear ODE systems); the application of statistical techniques to quantify our uncertainty in model parameters and model equations/structure; and some wet-lab laboratory electrophysiology experiments. We will design more information-rich experiments to reduce our uncertainty in the models we develop  and work closely with labs to test out experiments we design and improve them.
A. L. Hodgkin and A. F. Huxley, "A quantitative description of membrane current and its application to conduction and excitation in nerve," J. Physiol., vol. 117, pp. 500-544, 1952.
D. Noble, A. Garny, and P. J. Noble, "How the Hodgkin - Huxley equations inspired the Cardiac Physiome Project," vol. 11, pp. 2613-2628, 2012.
M. Fink and D. Noble, "Markov models for ion channels : versatility versus identifiability and speed," Philos. Trans. A. Math. Phys. Eng. Sci., vol. 367, no. 1896, pp. 2161-79, Jun. 2009.
G. R. Mirams, P. Pathmanathan, R. A. Gray, P. Challenor, and R. H. Clayton, "White paper: Uncertainty and variability in computational and mathematical models of cardiac physiology.," J. Physiol., Mar. 2016.
The MAML programme: The MAML doctoral training programme focuses on innovative modelling, simulation and data analysis to study real-world problems in medicine and biology. Maintaining a healthy society creates major challenges in areas including ageing, cancer, drug resistance, chronic disease and mental health. Addressing such challenges necessitates continuing development and implementation of a raft of new mathematical approaches and their integration with experimental and clinical science. Students will apply mathematical approaches (from areas such as dynamic modelling, informatics, network theory, scientific computation and uncertainty quantification) to research projects at the forefront of biomedical and life sciences identified through well-established collaborations with both academic and industrial partners.
MAML students will be provided with an excellent training environment within the Centre for Mathematical Medicine and Biology and collaborating departments. Students will undertake tailored training, complemented by broadening, soft-skills, wet-lab (where appropriate) and student-led activities. There will also be opportunities for training and exchanges with world-leading partners.
Applications: Please follow the instructions at the MAML website: http://www.nottingham.ac.uk/mathematics/maml
Applicants for the MAML programme should have at least a 2:1 degree in mathematics, statistics or a similarly quantitative discipline (such as physics, engineering, or computer science).
Completed applications and references should be submitted by Wednesday 28 February 2018.
For any enquiries please email: [email protected]