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，如季节性的白天长度，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)建立一种揭示交互功能等特征的动态网络映射算法；2)应用该算法推断不同系统在不同条件下的功能连通性；3)解决长期存在的网络控制中最优空间层次的问题。该提案旨在：克服一个重大的数学挑战（创建一个复杂、非线性动态过程的预测、数据丰富的网络表示），解决一个重要的生物学问题（解密生物钟的潜在相互作用网络），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Aim 1中，我们将通过使用正交基来表示连接函数来解决复杂网络的大规模拓扑估计问题。在目标2中，我们将把网络简化为一个动态等效的小网络。这将应用于使用反向工程相位分配（PA）控制振荡网络的夹带。在Aim 3中，我们将应用这些技术来绘制拓扑并识别数千个SCN细胞之间的细胞间期耦合功能。然后，我们将测试网络中的枢纽是否代表特定的细胞类型（例如，血管活性肠多肽，VIP），并在同步的发展和维持中发挥关键作用。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，Aim 3.2），增强行为反馈（EBF）， Aim 4)和PA （Aim 5）之后进行测试。新颖的数学和生物学工具（如VIP细胞和非VIP细胞的颜色切换生物发光）的创新结合将揭示多种SCN耦合途径的作用，并大大提高我们对SCN中信息处理的时空动态的理解。

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.