U.S.-Mexico Collaborative Research: Bursting Electrical Activity of Excitable Cells; Mathematical Models Based on Averaged Slow Dynamics

美国-墨西哥合作研究：可兴奋细胞的电活动爆发；

• 批准号: 8803573
• 负责人: John Rinzel
• 金额: $ 0.47万
• 依托单位: National Institutes of Health
• 依托单位国家: 美国
• 项目类别: Interagency Agreement
• 财政年份: 1988
• 资助国家: 美国
• 起止时间: 1988-08-01 至 1991-01-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=8803573&HistoricalAwards=false
• 关键词: U.S.; Mexico; Collaborative; Research; Bursting

This award will support collaborative research visits between researchers at the U.S. National Institutes of Health under the direction of Dr. John Rinzel and researchers at the Universidad Nacional Autonoma de Mexico (UNAM) under the leadership of Dr. Humberto Carrillo. For over 30 years, mathematical models have been formulated and used to describe and interpret the electrical activity (action potentials) of various nerve, muscle, and secretory cells. However, long-time behavior often involves dynamics on two different time scales, e.g., action potentials (time scale of msec) and variation of second messengers such as intracellular calcium (tens of seconds). The researchers intend to study such behavior using models that include the short-time averaged influence of action potentials but not the detailed time courses of individual events. As a model problem, they will consider the phenomenon of bursting electrical oscillations. The approach will involve both numerical and analytical methods and, in particular, the mathematical technique of averaging. They will derive and analyze biophysically detailed, "averaged" differential equations for the slow dynamics of bursting. The formulation and study of an idealized, analytically tractable model with important generic properties will be useful in elucidating the qualitative character of all such models. The work will proceed simultaneously at both institutions with extensive computations done in Bethesda and rigorous justification of averaging in Mexico City. The approach will allow a biophysical description and interpretation. Furthermore, it will provide insight into the important role played by slow variables as well as into new and interesting mathematical questions related to the method of averaging.

该奖项将支持 John Rinzel 博士领导下的美国国立卫生研究院研究人员与 Humberto Carrillo 博士领导下的墨西哥国立自治大学 (UNAM) 研究人员之间的合作研究访问。 30 多年来，数学模型已被制定并用于描述和解释各种神经、肌肉和分泌细胞的电活动（动作电位）。 然而，长时间行为通常涉及两个不同时间尺度上的动态，例如动作电位（毫秒的时间尺度）和第二信使（例如细胞内钙）的变化（数十秒）。 研究人员打算使用包含动作电位的短时平均影响但不包含单个事件的详细时间过程的模型来研究此类行为。 作为一个模型问题，他们将考虑突发电振荡现象。 该方法将涉及数值方法和分析方法，特别是平均数学技术。 他们将推导出并分析生物物理上详细的“平均”微分方程，以了解爆发的缓慢动态。 具有重要通用属性的理想化、分析上易于处理的模型的制定和研究将有助于阐明所有此类模型的定性特征。 这项工作将在两个机构同时进行，在贝塞斯达进行大量计算，并在墨西哥城进行严格的平均计算。 该方法将允许生物物理学描述和解释。 此外，它将深入了解慢变量所发挥的重要作用，以及与平均方法相关的新的有趣的数学问题。