Collaborative Research: Nonsmooth Maps, Coupled Oscillators and Seasonal Variation of Sleep and Circadian Rhythms

该项目将开发和分析生物钟信号及其对睡眠-觉醒调节的控制的数学模型，以确定生物钟的神经活动如何编码季节性。行为和生理上的昼夜节律（~24小时），包括睡眠-觉醒节律，受太阳每日光照周期的影响，影响身心健康。这些节律是由大脑的主生物钟驱动的，它接收来自眼睛的光信息，并协调全身的生物节律。在现代生活中，暴露在人造光下会破坏内部生理节律和环境光定时之间的关键联系。提出的数学建模和数据分析项目侧重于理解光信号中的信息和不确定性如何在主生物钟中被处理和存储，并通过神经信号向下游传播到睡眠-觉醒网络。在与一名临床研究人员的合作中，数学模型将被应用于描述小学学龄儿童在学年和夏季的光照和睡眠的数据，以了解暑假对睡眠和昼夜节律的干扰。另一名主要为本科生和西班牙裔服务的机构的合作者将为时钟建模并为本科生开发一门数学建模迷你课程。本科生、研究生和博士后将参与研究。该项目由数学科学部数学生物学项目和综合有机体系统神经系统集群部门联合资助。清醒、睡眠和快速眼动（REM）睡眠的行为状态是由脑干和下丘脑神经元群网络控制的，这些网络的数学模型提供了对它们相互作用动态的见解。视交叉上核（SCN）中的主昼夜节律钟控制着24小时内的行为时间，涉及一系列生理过程，从细胞内分子“昼夜节律钟”到SCN神经元电生理反应的时钟驱动变化，再到SCN神经网络的集体信号传导及其调节睡眠-觉醒行为的动态作用。利用数学建模和分析的创新结合，将在多个空间和时间尺度上探索睡眠-觉醒行为的光依赖性昼夜节律调节的关键方面。返回图将用于降低维数，并正式分类昼夜节律信号和睡眠-觉醒模式分支之间的关系。SCN活动的一致性对睡眠-觉醒行为的影响将从理论上建立，这些结果将用于理解实验观察到的季节性光照变化下啮齿动物SCN背侧和腹侧区域相位关系的变化。SCN和睡眠-觉醒网络模型将结合起来研究背-腹侧相互作用在门控光对SCN活动的影响中的作用；量化人类生物钟对不稳定的光照时间表的敏感性；并通过收集的小学学龄儿童的数据来研究暑假引起的睡眠-觉醒行为变化的潜在机制。项目结果将确定干预措施的潜在目标，以减轻暑假引起的睡眠和昼夜节律中断。该奖项反映了美国国家科学基金会的法定使命，并通过使用基金会的知识价值和更广泛的影响审查标准进行评估，被认为值得支持。

This project will develop and analyze mathematical models for circadian clock signaling and its control of sleep-wake regulation to determine how seasonality is encoded in the neural activity of the clock. Circadian (~24 hour) rhythms in behavior and physiology, including sleep-wake rhythms, are entrained by the sun's daily light cycle and affect physical and mental health. These rhythms are driven by the brain's master circadian clock, which receives light information from the eyes and coordinates biological rhythms throughout the body. In modern life, exposure to artificial light can erode the crucial tie between internal physiological rhythms and environmental light timing. The proposed mathematical modeling and data analysis projects focus on understanding how information and uncertainty in light signals are processed and stored in the master circadian clock and propagated downstream to sleep-wake networks through neural signaling. In collaboration with a clinical researcher, the mathematical models will be applied to data describing light exposure and sleep in elementary school-aged children during the school year and summer to understand summer vacation-induced disruptions to sleep and circadian rhythms. An additional collaborator at a primarily undergraduate and Hispanic-serving institution will contribute to modeling the clock and developing a mathematical modeling mini-course for undergraduate students. Undergraduate, graduate and postdoctoral trainees will be involved in the research. This project is funded jointly by the Division of Mathematical Sciences Mathematical Biology Program and the Division of Integrative Organismal Systems Neural Systems Cluster.Behavioral states of waking, sleep, and rapid eye movement (REM) sleep are governed by networks of brainstem and hypothalamic neuronal populations, and mathematical modeling of these networks provides insights into the dynamics of their interactions. The master circadian clock in the suprachiasmatic nucleus (SCN) controls the timing of behavior across the 24 hour day and involves a hierarchy of physiological processes from the intracellular molecular "circadian clock," to clock-driven variations in the electrophysiological responses of SCN neurons, to the collective signaling of the SCN neural network and its dynamic role modulating sleep-wake behavior. Using an innovative combination of mathematical modeling and analysis, key aspects of light-dependent circadian modulation of sleep-wake behavior will be explored at multiple spatial and temporal scales. Return maps will be used to reduce dimensionality and formally classify the relationship between circadian signaling and bifurcations in sleep-wake patterning. Effects of coherence of SCN activity on sleep-wake behavior will be established theoretically, and these results will be applied to understand experimentally observed changes in phase relationships between dorsal and ventral SCN regions in rodents under seasonal light variation. SCN and sleep-wake network models will be combined to investigate the role of dorsal-ventral interactions in gating light effects on SCN activity; to quantify sensitivity of the human clock to erratic light schedules; and to examine mechanisms underlying summer vacation-induced changes in sleep-wake behavior in data collected in elementary school-aged children. Project results will identify potential targets for interventions to alleviate summer vacation-induced disruptions to sleep and circadian rhythms.This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.