Time-invariant biological networks with feedback loops: structural equation models and structural identifiability.

Area of Science:

• Systems Biology
• Computational Biology
• Network Analysis

Background:

• Biological networks often feature feedback loops, crucial for function but challenging for analysis.
• Existing graphical model methods struggle with feedback loops, leading to unreliable parameter estimates.
• Parameter identifiability is a significant challenge in analyzing biological networks with feedback.

Purpose of the Study:

• To address the structural identifiability problem in time-invariant linear structural equation models (SEMs) with feedback loops.
• To develop a general and efficient solution for parameter identifiability analysis.
• To provide a reliable method for estimating parameters in complex biological networks.

Main Methods:

• Combines Mason's gain with Wright's path coefficient method to generate identifiability equations.
• Derives identifiability matrices to systematically examine the structural identifiability of each unknown parameter.
• Applies the method to a subnetwork of the *C. elegans* neural network for practical illustration.

Main Results:

• A general and efficient solution for structural identifiability analysis of linear SEMs with feedback loops is presented.
• The method avoids complex symbolic or numerical computations, enhancing applicability.
• Demonstrates successful application on a real biological network, validating its practical utility.

Conclusions:

• The proposed method offers a significant breakthrough in analyzing biological networks with feedback loops.
• It provides a reliable framework for parameter estimation, crucial for quantitative biological analyses.
• The generality and efficiency of the method make it broadly applicable to various time-invariant linear SEMs.