Disease progression in biosystems is not always a steady process but is occasionally abrupt. It is important but challenging to signal critical transitions in complex biosystems. In this study, based on the theoretical framework of dynamic network biomarkers (DNBs), we propose a model-free method, edge-based relative entropy (ERE), to identify temporal key biomolecular associations/networks that may serve as DNBs and detect early-warning signals of the drastic state transition during disease progression in complex biological systems. Specifically, by combining gene‒gene interaction (edge) information with the relative entropy, the ERE method converts gene expression values into network entropy values, quantifying the dynamic change in a biomolecular network and indicating the qualitative shift in the system state. The proposed method was validated using simulated data and real biological datasets of complex diseases. The applications show that for certain diseases, the ERE method helps to reveal so-called “dark genes” that are non-differentially expressed but with high ERE values and of essential importance in both gene regulation and prognosis. The proposed method effectively identified the critical transition states of complex diseases at the network level. Our study not only identified the critical transition states of various cancers but also provided two types of new prognostic biomarkers, positive and negative edge biomarkers, for further practical application. The method in this study therefore has great potential in personalized disease diagnosis.

中文翻译：

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基于边缘的相对熵作为生物系统关键转变的敏感指标

生物系统中的疾病进展并不总是一个稳定的过程，有时是突然的。在复杂的生物系统中发出关键转变信号很重要，但也具有挑战性。在本研究中，基于动态网络生物标志物（DNB）的理论框架，我们提出了一种无模型方法，基于边缘的相对熵（ERE），来识别可作为DNB并早期检测的时间关键生物分子关联/网络。 -复杂生物系统疾病进展期间剧烈状态转变的警告信号。具体来说，ERE方法通过将基因-基因相互作用（边缘）信息与相对熵相结合，将基因表达值转换为网络熵值，量化生物分子网络的动态变化并指示系统状态的质变。使用复杂疾病的模拟数据和真实生物数据集验证了所提出的方法。应用表明，对于某些疾病，ERE方法有助于揭示所谓的“暗基因”，这些基因非差异表达但具有高ERE值，对基因调控和预后都至关重要。该方法有效地识别了网络层面复杂疾病的关键过渡状态。我们的研究不仅确定了各种癌症的关键过渡状态，还提供了两种新的预后生物标志物，即阳性边缘生物标志物和阴性边缘生物标志物，以供进一步的实际应用。因此，本研究的方法在个性化疾病诊断方面具有巨大的潜力。