Quantitative analyses of biological networks such as key biological parameter estimation necessarily call for the use of graphical models. While biological networks with feedback loops are common in reality, the development of graphical model methods and tools that are capable of dealing with feedback loops is still in its infancy. Particularly, inadequate attention has been paid to the parameter identifiability problem for biological networks with feedback loops such that unreliable or even misleading parameter estimates may be obtained. In this study, the structural identifiability analysis problem of time-invariant linear structural equation models (SEMs) with feedback loops is addressed, resulting in a general and efficient solution. The key idea is to combine Mason's gain with Wright's path coefficient method to generate identifiability equations, from which identifiability matrices are then derived to examine the structural identifiability of every single unknown parameter. The proposed method does not involve symbolic or expensive numerical computations, and is applicable to a broad range of time-invariant linear SEMs with or without explicit latent variables, presenting a remarkable breakthrough in terms of generality. Finally, a subnetwork structure of the C. elegans neural network is used to illustrate the application of the authors' method in practice.

中文翻译：

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具有反馈回路的时不变生物网络：结构方程模型和结构可识别性。

生物网络的定量分析，如关键生物参数估计，必然需要使用图形模型。虽然具有反馈回路的生物网络在现实中很常见，但能够处理反馈回路的图形模型方法和工具的开发仍处于起步阶段。特别是，对于具有反馈回路的生物网络的参数可识别性问题没有给予足够的重视，因此可能会获得不可靠甚至误导性的参数估计。在这项研究中，解决了具有反馈回路的时不变线性结构方程模型 (SEM) 的结构可识别性分析问题，从而得到了一个通用且有效的解决方案。关键思想是将梅森的收益与赖特结合起来 s 路径系数方法生成可识别性方程，然后从中导出可识别性矩阵以检查每个单个未知参数的结构可识别性。所提出的方法不涉及符号或昂贵的数值计算，适用于范围广泛的具有或不具有显式潜变量的时不变线性扫描电镜，在通用性方面取得了显着突破。最后，利用秀丽隐杆线虫神经网络的子网结构来说明作者方法在实践中的应用。并且适用于范围广泛的具有或不具有显式潜变量的时不变线性SEM，在一般性方面取得了显着突破。最后，利用秀丽隐杆线虫神经网络的子网结构来说明作者方法在实践中的应用。并且适用于范围广泛的具有或不具有显式潜变量的时不变线性SEM，在一般性方面取得了显着突破。最后，利用秀丽隐杆线虫神经网络的子网结构来说明作者方法在实践中的应用。