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

控制理论是工程和数学的交叉学科分支，研究动力系统的行为。它是基于一些非常简单的理念，如反馈循环和稳定性。控制理论关注的是改变系统期望输出的方法，称为参考。当系统的一个或多个输出变量需要随时间跟随某个参考时，控制器操纵系统的输入以获得对系统输出的期望效果。系统可以在几乎任何学科中被有效地定义——它们并不局限于工程或数学。这项提议背后的想法是开发适用于真实生物细胞的新型控制技术。特别地，我们对非线性动力系统在数学上描述的可兴奋细胞的行为感兴趣。细胞和组织的兴奋性是生命的基本功能。它是细胞对刺激作出反应的能力。兴奋性对于神经、肌肉和荷尔蒙等功能的发挥是必要的。细胞兴奋性的基础是它们的离子分布，而离子和分子的分布是由与其质膜结构相关的转运机制决定的。这种结构允许并调节各种形式的离子和分子运输。传统上，实验人员干扰生物系统的能力仅限于严格的预编程协议或更灵活的，但反射受限的，操作员控制的协议。相比之下，实时控制允许研究人员动态探测具有参数扰动的生物系统，这些参数扰动是瞬时系统测量的计算函数，从而提供解决传统方法无法解决的各种未解决问题的能力。一方面有大量的实验数据，另一方面有丰富的可激系统的理论知识。本项目旨在通过探索和设计在真实实验环境中研究和控制可兴奋细胞系统的新技术，弥合理论与实验之间的差距。从长远来看，这种技术将为研究开发与兴奋性细胞功能障碍相关的疾病的有效疗法开辟全新的途径。

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.