A new class of whole cell models with bidirectional coupling of local (subcellular) and global (cellular) calcium responses

开发了一种复杂的模拟方法来研究整个细胞内钙动力学与钙处理的构建块之间的相互作用，空间定位的亚细胞钙升高被称为“钙泡”和“火花”。利用最初在理论物理化学和统计物理中开发的技术，推导并分析了与活细胞中大量钙释放位点相关的局部钙浓度矩的方程。这扩展了经典的“门控变量”方法来模拟离子通道的打开和关闭——由诺贝尔奖获得者霍奇金和赫胥黎引入——以解释细胞内钙的短距离作用和细胞内钙通道的局部耦合。传统的局部和全局耦合钙响应模型涉及随机模拟方法，计算量大，通常禁止数学分析和大规模参数研究。相反，基于时刻的细胞内钙反应的全细胞模型是常微分方程系统，可以使用几何和图形方法进行研究。Gregory Smith （William & Mary）和学生们开发、验证和测试了这个数学模型框架，并随后将其部署到Eric Sobie （Mount Sinai）和Sandor Gyorke （Ohio State）的实验室中，以解释活细胞钙成像实验，探索心肌细胞中钙循环如何在药物、突变和疾病的影响下发生变化。用户友好软件的生产，以协助其他实验室在他们的心脏，平滑肌，横纹肌，神经元和不可兴奋细胞的钙反应更现实和预测模型的发展。参与该项目的研究生在应用数学和细胞生理学的界面上体验高质量的跨学科科学训练。该项目还扩展并支持Smith作为William & Mary生物数学倡议主任的活动，例如，生物建模的课程开发，跨学科师生期刊俱乐部的协调，本科研究生的指导，以及在电生理学背景下向神经科学专业学生介绍非线性动力学的本科文本的作者（与Christopher Del Negro）。

A sophisticated simulation method is developed to investigate the interactions between whole cell intracellular calcium dynamics and the building blocks of calcium handling, spatially localized subcellular calcium elevations known as "calcium puffs" and "sparks." Using techniques originally developed in theoretical physical chemistry and statistical physics, equations are derived and analyzed for the moments of the local calcium concentration associated with the large number of calcium release sites in living cells. This extends the classical "gating variable" approach to modeling the opening and closing of ion channels - introduced by Nobel prize winners Hodgkin and Huxley - to account for the short range of action of intracellular calcium and local coupling of intracellular calcium channels. Traditional models of coupled local and global calcium responses involve stochastic simulation methods that are computationally intensive and often prohibit both mathematical analysis and large-scale parameters studies. Conversely, moment-based whole cell models of intracellular calcium responses are systems of ordinary differential equations that can be studied using geometric and graphical approaches. Gregory Smith (William & Mary) and students develop, validate, and benchmark this mathematical modeling framework and, subsequently, deploy it in the laboratories of Eric Sobie (Mount Sinai) and Sandor Gyorke (Ohio State) to interpret live cell calcium imaging experiments that probe how beat-to-beat calcium cycling in heart muscle cells changes in response to drugs, mutations, and disease.User-friendly software is produced to assist other laboratories in their development of more realistic and predictive models of calcium responses in cardiac, smooth, and striated muscle, neurons, and non-excitable cells. Graduate students involved in this project experience high-quality interdisciplinary scientific training at the interface of applied mathematics and cell physiology. The project also expands and supports Smith's activities as Director of the William & Mary Biomathematics Initiative, e.g., curriculum development in biological modeling, coordination of an interdisciplinary faculty-student journal club, mentoring of undergraduate research students, and authorship of an undergraduate text introducing neuroscience majors to nonlinear dynamics in the context of electrophysiology (with Christopher Del Negro).