Modular response analysis reformulated as a multilinear regression problem

Motivation: Modular response analysis (MRA) is a well-established method to infer biological networks from perturbation data. Classically, MRA requires the solution of a linear system, and results are sensitive to noise in the data and perturbation intensities. Due to noise propagation, applications to networks of 10 nodes or more are difficult.Results: We propose a new formulation of MRA as a multilinear regression problem. This enables to integrate all the replicates and potential additional perturbations in a larger, over-determined, and more stable system of equations. More relevant confidence intervals on network parameters can be obtained, and we show competitive performance for networks of size up to 1000. Prior knowledge integration in the form of known null edges further improves these results.

Automated summary

The traditional method of modular response analysis (MRA) is difficult to apply to networks with 10 or more nodes due to sensitivity to noise in the data and perturbation intensities. We propose a new formulation of MRA as a multilinear regression problem, which allows for integration of all replicates and potential additional perturbations in a larger and more stable system of equations. This approach provides more relevant confidence intervals for network parameters and shows competitive performance for networks up to size 1000. Integration of known null edges further improves the results.