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

点击翻译按钮获取中文摘要

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.