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

一个复杂的模拟方法被开发来研究全细胞内钙动力学和钙处理的构件之间的相互作用，空间局部化的亚细胞钙升高被称为“钙泡”和“火花”。" 使用最初在理论物理化学和统计物理学中开发的技术，方程推导和分析与活细胞中大量钙释放位点相关的局部钙浓度的时刻。 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范围作用和细胞内钙通道的局部耦合。 耦合的局部和全局钙响应的传统模型涉及随机模拟方法，其计算密集型并且通常禁止数学分析和大规模参数研究。 相反，细胞内钙响应的基于矩的全细胞模型是可以使用几何和图形方法研究的常微分方程系统。 格雷戈里·史密斯（威廉&玛丽）和学生开发，验证和基准测试这个数学建模框架，随后，部署在实验室的埃里克索比（西奈山）和Sandor Gyorke（俄亥俄州）解释活细胞钙成像实验，该实验探测心肌细胞中的心跳间钙循环如何响应药物、突变、用户友好的软件，以协助其他实验室在他们的发展更现实和预测模型的钙反应在心脏，平滑肌，横纹肌，神经元和非兴奋细胞。 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培训。该项目还扩大和支持史密斯的活动，作为威廉玛丽生物数学倡议主任，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介绍神经科学专业非线性动力学的本科文本的作者（与克里斯托弗·德尔内格罗）。

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).