一种用于探索生物钟网络同步的Kuramoto相位模型
A Kuramoto phase model to explore the synchronisation of a network of circadian clocks
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中文总结 AI 辅助
该研究基于Kuramoto模型提出细胞群体生物钟模型，引入相位依赖耦合机制，分析其渐近相位同步条件。通过小波分解提取振荡特征，用准蒙特卡罗滤波算法校准模型，比较野生型和Cry2基因敲除情况，揭示了表型差异及相关机制。
中文摘要 AI 辅助
我们基于从Kuramoto模型导出的振荡器网络，提出了一种细胞群体中生物钟的模型。振荡器之间的耦合由全局相互作用项描述，但我们引入了一种依赖相位的耦合机制，使得振荡器仅在对应于昼夜节律周期特定阶段的周期特定间隔内相互作用。我们分析证明，只要满足初始相位分布和耦合窗口长度的特定条件，这个修改后的系统就能实现完全渐近相位同步。为了将这个理论框架与实验观察联系起来，我们引入了一种基于小波分解的信号处理程序，从Per2::荧光素酶报告基因轨迹中提取定量振荡特征。然后，我们使用两步准蒙特卡罗滤波算法，根据野生型和Cry2基因敲除肝细胞球体的数据集对模型进行校准。比较分析揭示了显著的表型差异，表明Cry2基因敲除条件改变了模型参数的可识别性格局，并引入了新的补偿机制，这些机制将初始群体异质性与长期宏观信号衰减混淆在一起。
英文摘要
We propose a model of the circadian clock in a population of cells based on a network of oscillators, derived from the Kuramoto model. The coupling between oscillators is described by a global interaction term but we introduce a phase-dependent coupling mechanism, such that oscillators interact only within a specific interval of the cycle corresponding to a specific stage of the circadian cycle. We analytically demonstrate that this modified system achieves complete asymptotic phase synchronisation, provided specific conditions on the initial phase distribution and the coupling window length are met. To bridge this theoretical framework with experimental observations, we introduce a signal processing procedure based on wavelet decomposition to extract quantitative oscillatory features from Per2::luciferase reporter traces. We then calibrate the model against datasets from both wild type and Cry2 knockout hepatocyte spheroids using a two-step quasi-Monte Carlo filtering algorithm. The comparative analysis reveals significant phenotypic divergence, showing that the Cry2KO condition alters the identifiability landscape of the model's parameters and introduces new compensatory mechanisms that confound the initial population heterogeneity with long-term macroscopic signal decay.
