Control-based Continuation of Solutions and Bifurcations in Dynamic-Clamp-Constructed Hybrid Bursting Systems

Control theory is an interdisciplinary branch of engineering and mathematics that deals with the behaviour of dynamical systems. It is built up around a few very simple ideas, such as feedback loop and stability. Control theory concerns itself with means by which to alter the desired output of a system, called the reference. When one or more output variables of a system need to follow a certain reference over time, a controller manipulates the inputs to a system to obtain the desired effect on the output of the system. Systems can usefully be defined in almost any discipline - they are not confined to engineering or mathematics. The idea behind this proposal is to develop novel control techniques applicable to real biological cells. In particular, we are interested in the behaviour of excitable cells, described mathematically by nonlinear dynamical systems.Excitability of cells and tissues is a basic function of life. It is the ability of cells to respond to stimuli. Excitability is necessary for the functioning of nerves, muscles, and hormones, among other things. The basis for the excitability of cells is their ion distribution, and the distribution of ions and molecules is determined by transport mechanisms associated with their plasma membrane structure. This structure permits and regulates various forms of ionic and molecular transport. The ability of experimentalists to perturb biological systems has traditionally been limited to rigid pre-programmed protocols or more flexible, but reflex constrained, operator-controlled protocols. In contrast, real-time control allows the researcher to dynamically probe a biological system with parameter perturbations that are calculated functions of instantaneous system measurements, thereby providing the ability to address diverse unanswered questions that are not amenable to traditional approaches.There is a great deal of experimental data on one hand and a wealth of theoretical knowledge about excitable systems on the other. This project aims to bridge the gap between theory and experiments by exploring and designing novel techniques for investigation and control of excitable cell systems in real experimental settings. In a long term, such a technology will open completely new avenues for research in development of effective therapies for diseases associated with excitable cell dysfunction.

As well as the specific academic beneficiaries listed in the Academic Beneficiaries section, the public and a wider academic community will benefit from the increase in knowledge about basic excitable cell physiology and thus brain, heart and muscles function as well as regulation of hormonal secretion. This project also has a great scope towards the medical community, clinical neuroscience and public health. Sectors of the pharmaceutical industry working to develop effective drug therapies for diseases based on excitable cell disorders will also benefit from the proposed work. Indirectly, and in the long term, people suffering from such diseases may also benefit. Therefore, there is the potential for beneficial impact on both the health and wealth of the UK. The ability of an excitable cell to generate a response (in the form of action potential spike or burst) is an important guide to its health. Research into numerous diseases such as neurological disorders, high blood pressure, angina, abnormal heart rhythms, diabetes, etc. has found deficits in ion channels function and specifically the ability to correctly respond to stimuli. This has led to the current idea that these diseases may be classed as channelopathies . Therefore, the mechanisms that we will study in our research will be incorporated into the body of knowledge about these debilitating diseases, for example, informing the development of animal models of disease, which amongst other things, pharmaceutical companies extensively utilise as part of the drug development process. The social impact and economic costs of the diseases mentioned above are enormous. Therefore our work will benefit society from the advances we make in investigating mechanisms that may underlie such diseases, and will benefit the economy both in terms of costs saved in care for patients suffering from these conditions, and also in profits from pharmaceuticals developed and sold by UK-based companies. We acknowledge that these indirect benefits may take several years before they are realised. Following my recent appointment at the University of Bristol as a Lecturer in Engineering Mathematics, the impact of this award on my prospects, as an independent researcher, will be large as it will allow me to start up my intended research programme. The proposed study is highly ambitious, and will draw on the experience of leading researchers at the University of Bristol. It will use interdisciplinary approaches, such as mathematical modelling, computer programming and iterative cycles with wet-lab experiments to validate the models and test model predictions. I have personally developed and analysed the models to be used in this study, and this project will allow me to gain further knowledge and develop a number of new skills. Due to its unprecedented character this project will most likely lead to a number of high impact publications to be generated in the course of the work.