Collaborative Research: Inferring Dynamic Topology to Decode and Control Spatiotemporal Structures in Complex Networks

昼夜节律使生物体能够预测和适应可靠的环境事件。视交叉上核（SCN）产生这些精确的每日振荡，但适应环境变化，如季节性日长，这在很大程度上取决于基因和细胞网络结构的重组。本研究的长期目标是：1）创建一个动态的网络映射算法，揭示功能，包括相互作用的功能，2）应用该算法来推断不同条件下的不同系统的功能连接，和3）解决长期存在的问题，最佳的空间层次网络控制。该提案旨在：克服一个重大的数学挑战（创建一个预测性的，数据丰富的网络表示复杂的，非线性动态过程），解决一个重要的生物学问题（解密生物钟的底层交互网络），并将解决方案应用于新的系统控制（通过增强反馈探索网络结构对动物行为的影响）。在目标1中，我们将解决大规模的，复杂网络的拓扑估计问题，利用正交基表示连接函数。在目标2中，我们将网络简化为一个动态等效的小网络。这将被应用到控制夹带的振荡网络使用反向工程相位分配（PA）。在目标3中，我们将应用这些技术来映射拓扑结构，并确定数千个SCN细胞之间的细胞间相位耦合功能。然后，我们将测试网络中的集线器是否代表特定的细胞类型（例如，血管活性肠多肽（vasoactive intestinal polypeptide，VIP），并在同步性的发展和维持中起关键作用。重建网络的预测能力将在时间中断（例如，通过靶向删除细胞，目标3.2）、增强的行为反馈（EBF），目标4）和PA（目标5）。新颖的数学和生物学工具的创新组合（例如，VIP和非VIP细胞中的颜色切换生物发光）将揭示多个SCN耦合途径的作用，并极大地提高我们对SCN中信息处理的时空动力学的理解。 控制论协议EBF和PA将在网络科学中创造一个新的研究范式， 昼夜节律生物学。研究结果将对昼夜节律网络的结构以及重复的日常干扰如何重组这种结构并影响行为提供重要见解。通过从数学的角度来阐述生物学问题，该团队将揭示网络动态与新的计算策略，有助于减轻昼夜节律中断的影响。

Circadian rhythms allow organisms to anticipate and adapt to reliable environmental events. The suprachiasmatic nucleus (SCN) generates these precise daily oscillations and yet adapts to environmental changes like seasonal day length, depending heavily on reorganization of gene and cellular network structures. The long-term goals of this research are to: 1) create a dynamic network-mapping algorithm that reveals features including interaction functions, 2) apply this algorithm to infer functional connectivity of diverse systems under different conditions, and 3) resolve longstanding questions about optimal spatial hierarchies in network control. This proposal aims to: overcome a significant mathematical challenge (to create a predictive, data-rich network representation of complex, nonlinear dynamical processes), solve an important biological problem (to decrypt the underlying interaction network of the circadian clock), and apply the solutions to novel system control (to explore the impact of the network structure on animal behavior through enhanced feedback). In Aim 1, we will solve the large-scale, topology estimation problem of complex networks by the utilization of orthonormal bases for expressing connection functions. In Aim 2, we will reduce the network to a dynamically equivalent small network. This will be applied to control entrainment of oscillatory networks using a reverse engineered phase assignment (PA). In Aim 3, we will apply these techniques to map the topology and identify intercellular phase coupling functions among thousands of SCN cells. We will then test whether hubs within the network represent specific cell types (e.g., vasoactive intestinal polypeptide, VIP) and play key roles in the development and maintenance of synchrony. The predictive power of the reconstructed networks will be tested following chronodisruption (e.g., by targeted deletion of cells, Aim 3.2), enhanced behavioral feedback (EBF), Aim 4) and PA (Aim 5). The innovative combination of novel mathematical and biological tools (e.g., color switching bioluminescence in VIP and non-VIP cells) will reveal the roles of the multiple SCN coupling pathways and greatly improve our understanding of the spatiotemporal dynamics of information processing in the SCN. Control-theoretic protocols, EBF and PA will create a new research paradigm in network science and circadian biology. The research findings will give significant insights into the structure of the circadian network and how repeated daily disruptions can reorganize this structure and impact behavior. By formulating the biological problem from a mathematical viewpoint, the team will reveal network dynamics with novel computational strategies that help mitigate the effects of circadian disruptions.