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，以确定季节性如何编码在时钟的神经活动中。行为和生理的昼夜节律（约24小时），包括睡眠-觉醒节律，受到太阳每日光照周期的影响，影响身心健康。这些节奏是由大脑的主生物钟驱动的，主生物钟接收来自眼睛的光信息并协调整个身体的生物节律。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。拟议的数学建模和数据分析项目的重点是了解光信号中的信息和不确定性如何被处理和存储在主生物钟中，并通过神经信号向下游传播到睡眠-觉醒网络。 与临床研究人员合作，数学模型将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，以了解暑假引起的睡眠和昼夜节律中断。在一个主要的本科生和西班牙裔服务机构的额外合作者将有助于建模时钟和开发一个数学建模的本科生迷你课程。本科生、研究生和博士后学员将参与研究。该项目由数学科学部数学生物学计划和综合有机系统部神经系统集群共同资助。清醒、睡眠和快速眼动（REM）睡眠的行为状态由脑干和下丘脑神经元群体的网络控制，这些网络的数学建模提供了对它们相互作用的动力学的见解。视交叉上核（SCN）中的主昼夜节律钟控制24小时内的行为定时，并且涉及从细胞内分子“昼夜节律钟”到SCN神经元的电生理反应中的时钟驱动变化、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的生理过程的层次结构。使用数学建模和分析的创新组合，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制的关键方面。返回地图将被用来降低维度，并正式分类昼夜信号和睡眠-觉醒模式的分叉之间的关系。SCN活动的一致性对睡眠-觉醒行为的影响将在理论上建立，这些结果将被应用于了解实验观察到的啮齿动物的背侧和腹侧SCN区域之间的相位关系的变化在季节性光照变化。SCN和睡眠-觉醒网络模型将被结合起来，以调查背腹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;并在小学年龄儿童收集的数据中研究暑假引起的睡眠-觉醒行为变化的机制。项目结果将确定潜在的干预目标，以减轻暑假引起的睡眠和昼夜节律的中断。该奖项反映了NSF的法定使命，并已被认为是值得通过使用基金会的智力价值和更广泛的影响审查标准进行评估的支持。

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.