Structural Identifiability of Cyclic Graphical Models of Biological Networks with Latent Variables

TL;DR

This paper introduces an efficient algorithm for analyzing the structural identifiability of cyclic biological network models with latent variables, avoiding symbolic computation and providing high-resolution parameter identifiability.

Contribution

It presents a novel method using symbolic polynomial equations and matrix operations to determine parameter identifiability in complex cyclic networks with latent variables.

Findings

Validated on benchmark models

Successfully applied to influenza A virus network

Avoids symbolic computation for efficiency

Abstract

An efficient structural identifiability analysis algorithm is developed in this study for a broad range of network structures. The proposed method adopts the Wright's path coefficient method to generate identifiability equations in forms of symbolic polynomials, and then converts these symbolic equations to binary matrices (called identifiability matrix). Several matrix operations are introduced for identifiability matrix reduction with system equivalency maintained. Based on the reduced identifiability matrices, the structural identifiability of each parameter is determined. A number of benchmark models are used to verify the validity of the proposed approach. Finally, the network module for influenza A virus replication is employed as a real example to illustrate the application of the proposed approach in practice. The proposed approach can deal with cyclic networks with latent variables. The key advantage is that it intentionally avoids symbolic computation and is thus highly efficient. Also, this method is capable of determining the identifiability of each single parameter and is thus of higher resolution in comparison with many existing approaches. Overall, this study provides a basis for systematic examination and refinement of graphical models of biological networks from the identifiability point of view, and it has a significant potential to be extended to more complex network structures or high-dimensional systems.