The advance in single-cell profiling technologies and the development in computational algorithms provide the opportunity to reconstruct pseudo temporal trajectory with branch point of cellular development. On the other hand, theories such as dynamical network biomarkers (DNB) theory have been recently proposed to characterize the pre-transition state in biological systems. Few studies have validated whether the branch point identified in pseudo time is the critical point in dynamical system. In this study, the dynamical behavior of the branch point on the pseudo trajectory has been investigated. We study the pseudo temporal trajectories reconstructed by Wishbone and diffusion pseudotime analysis (DPT) algorithms, as well as the simulated trajectory. DNB theory is applied to justify the bifurcating event on the pseudo trajectories. Our results demonstrate that the branch point recovered by Wishbone and DPT algorithms is confirmed as a transition state in cell differentiation process by DNB theory. Furthermore, we show that an appropriate DNB group will amplify the comprehensive index of critical event as defined in DNB theory. Our study provides biological insights on pseudo trajectory with branch point in a dynamical view and also indicates that DNB theory may serve as a benchmark to check the validity of branch point.

中文翻译：

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分化轨迹的一个分支点是通过单细胞数据的动态网络生物标记分析揭示的分叉事件。

单细胞分析技术的进步和计算算法的发展提供了利用细胞发展的分支点重建伪时间轨迹的机会。另一方面，近来提出了诸如动态网络生物标记（DNB）理论之类的理论来表征生物系统中的过渡前状态。很少有研究证实伪时间中确定的分支点是否是动力学系统的关键点。在这项研究中，研究了伪轨迹上分支点的动力学行为。我们研究了由Wishbone和扩散伪时间分析（DPT）算法重建的伪时间轨迹，以及模拟的轨迹。DNB理论被应用来证明伪轨迹上的分叉事件是合理的。我们的结果表明，通过DNB理论将Wishbone和DPT算法回收的分支点确定为细胞分化过程中的过渡状态。此外，我们表明，适当的DNB组将放大DNB理论中定义的关键事件的综合指数。我们的研究从动力学角度提供了具有分支点的伪轨迹的生物学见解，并指出DNB理论可以作为检验分支点有效性的基准。