Collaborative research: Multiscale modeling of the physiological interactions between sleep and circadian systems

了解睡眠/觉醒行为与昼夜（~24小时）节律之间的相互作用，通过视交叉上核（SCN）在大脑中进行协调，对于应对与轮班工作，时差以及更普遍的24小时社会生活相关的挑战至关重要。 当这些系统没有得到最佳调整时，就会对身心健康、工作表现和驾驶等关键任务产生负面影响。调查这些相互作用是困难的，因为它们发生在一系列的空间和时间尺度上，不容易与目前的实验技术同时解决。 时间尺度从神经元放电的毫秒计时到昼夜节律的24小时周期，再到睡眠和昼夜节律发生失调的天数和周数。 空间尺度的范围从胞内蛋白质转录和翻译动力学（其在SCN神经活动中产生24小时节律性）到参与睡眠状态调节的神经群体之间的突触相互作用，再到动物的最终可观察到的睡眠/觉醒行为。 最近的进展，在确定昼夜节律和睡眠/觉醒调节系统的解剖学和生理学提供了必要的细节，为构建这些系统的基于生理学的数学模型。该项目的三个目标是开发、分析和整合数学模型，以弥合问题的不同时间和空间尺度。该项目将解决以下关键问题：（1）不同睡眠状态，特别是快速眼动睡眠，在睡眠行为与昼夜节律同步中的作用;（2）SCN电生理学如何将神经元信号转化为分子信号，从而改变昼夜节律;和（3）SCN和调节睡眠和觉醒状态的神经群之间的间接突触投射的性质，所述睡眠和觉醒状态在实验记录的大鼠睡眠/觉醒模式中支配24小时节律。不同的睡眠状态对睡眠和昼夜节律同步的作用将通过采用耦合到SCN的睡眠/觉醒调节网络的神经元群体模型来研究。 为了量化同步的数学基础和促进去极化的快速眼动睡眠循环的特征，将耦合振荡器理论中开发的基于相位图的分析技术应用于模型。 为了了解神经元和分子信号如何整合在SCN神经元中，将视交叉上核神经元的Hodgkin-Huxley型模型与细胞内分子钟的基于Goodwin振荡器的模型联系起来。 模型分析将确定神经元突触投射在毫秒时间尺度上的作用的机制，通过电生理学和由此产生的细胞内钙动力学介导，干扰钙依赖的24小时振荡的分子钟。 SCN和睡眠/觉醒调节网络之间的前馈和反馈突触投射将通过将来自睡眠/觉醒和昼夜节律网络的神经元群体模型的模拟睡眠/觉醒模式拟合到24小时实验大鼠睡眠记录来研究。 结果将提供网络结构和耦合机制的约束和预测。 在数学上，这些项目将推进多尺度建模技术，深入了解涉及极限环和磁滞环振荡器的耦合振荡器系统，研究对模型动态的确定性和随机性贡献，并展示使用实验数据约束网络模型的新方法。 两名研究生和至少四名本科生将通过参与项目进行数学神经科学和动力系统的跨学科研究培训。 对于教育推广，将为高中代数课程开发睡眠/清醒建模教学模块，以使学生在个人高度相关的背景下进行建模，这些背景与轮班工作，时差和青少年睡眠阶段延迟等问题有关。

Understanding the interactions between sleep/wake behavior and the circadian (~24 hour) rhythm, coordinated in the brain by the suprachiasmatic nucleus (SCN), is fundamentally important for coping with challenges associated with shift work, jet lag, and, more generally, life in our 24-hour society. When these systems are not optimally aligned, there are negative implications for physical and mental health, job performance, and key tasks such as driving. Investigating these interactions is difficult since they take place on a range of spatial and temporal scales that are not easily addressed simultaneously with current experimental techniques. Temporal scales vary from the millisecond timing of neuron firing to the 24 hour period of the circadian rhythm to the days and weeks over which misalignment of sleep and circadian rhythms occurs. Spatial scales range from the intracellular protein transcription and translation dynamics that generate 24 hour rhythmicity in SCN neural activity to synaptic interactions between neural populations involved in the regulation of sleep states to the ultimately observable sleep/wake behavior of the animal. Recent advances in identifying the anatomy and physiology of circadian and sleep/wake regulatory systems provide the necessary details for constructing physiologically-based mathematical models of these systems. The three aims of this project undertake the development, analysis, and integration of mathematical models to bridge the disparate temporal and spatial scales of the problem. The project will address the following key questions: (1) the role of different sleep states, particularly rapid eye movement sleep, in the synchronization of sleep behavior with the circadian rhythm; (2) how SCN electrophysiology translates neuronal signals into molecular signals that act to shift the circadian clock; and (3) the nature of the indirect synaptic projections between the SCN and neural populations regulating sleep and wake states that govern the 24 hour rhythm in experimentally recorded rat sleep/wake patterning. The role of different sleep states on synchronization of sleep and circadian rhythms will be investigated by employing a neuronal population model of the sleep/wake regulatory network coupled to the SCN. To quantify the mathematical basis for synchronization and the characteristics of rapid eye movement sleep cycling that promote desynchronization, phase map based analytical techniques developed in coupled oscillator theory will be applied to the model. To understand how neuronal and molecular signals are integrated in SCN neurons, a Hodgkin-Huxley-type model for neurons in the suprachiasmatic nucleus will be linked to a Goodwin-oscillator-based model for the intracellular molecular clock. Model analysis will identify the mechanisms by which the actions of neuronal synaptic projections on a millisecond time scale, mediated through electrophysiology and resultant intracellular calcium dynamics, perturb the calcium-dependent 24 hour oscillations of the molecular clock. The feedforward and feedback synaptic projections between the SCN and the sleep/wake regulatory network will be investigated by fitting simulated sleep/wake patterning from neuronal population models of sleep/wake and circadian networks to 24 hour experimental rat sleep recordings. Results will provide constraints on and predictions for network structure and coupling mechanisms. Mathematically, the projects will advance techniques for multiscale modeling, provide insights into coupled oscillator systems involving both limit cycle and hysteresis loop oscillators, investigate deterministic and stochastic contributions to model dynamics, and demonstrate novel methodologies for using experimental data to constrain network models. Two graduate students and at least four undergraduate students will be trained in interdisciplinary research in mathematical neuroscience and dynamical systems through their participation in the projects. For educational outreach, a sleep/wake modeling teaching module will be developed for high school algebra classes to expose students to modeling in a personal, highly relevant context that relates to issues such as shift work, jet lag, and the well-documented sleep phase delay in teenagers.