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件之间的相互作用，即空间上局部的亚细胞钙升高，称为“钙喷”和“火花”。利用最初在理论物理化学和统计物理中发展起来的技术，推导和分析了与活细胞中大量钙释放部位相关的局部钙浓度的矩。这扩展了由诺贝尔奖获得者霍奇金和赫胥黎提出的用于模拟离子通道打开和关闭的经典“门控变量”方法，以解释细胞内钙离子的短作用范围和细胞内钙离子通道的局部耦合。传统的局部和全局钙反应耦合模型涉及随机模拟方法，这些方法计算量大，往往既无法进行数学分析，也无法进行大规模参数研究。相反，基于矩的细胞内钙反应的全细胞模型是常微分方程组，可以用几何和图形方法来研究。格雷戈里·史密斯(William&Amp；Mary)和学生们开发、验证和基准这个数学建模框架，并随后将其部署在Eric Sobie(西奈山)和Sandor Gyorke(俄亥俄州立大学)的实验室，以解释活细胞钙成像实验，该实验探索心肌细胞中节拍钙循环如何随着药物、突变和疾病的变化而变化。用户友好的软件被生产出来，以帮助其他实验室开发心脏、平滑和横纹肌、神经元和不可兴奋细胞中更现实和更具预测性的钙反应模型。参与该项目的研究生在应用数学和细胞生理学的交界处体验高质量的跨学科科学培训。该项目还扩大和支持了史密斯作为威廉和玛丽生物数学倡议主任的活动，例如，生物建模课程开发，协调跨学科师生期刊俱乐部，指导本科生研究学生，并撰写了一本介绍神经科学专业学生在电生理学背景下的非线性动力学的本科教材(与克里斯托弗·德尔·内格罗共同撰写)。

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).