Testing and overcoming the limitations of modular response analysis

Modular response analysis (MRA) is an effective method to infer biological networks from perturbation data. However, it has several limitations such as strong sensitivity to noise, need of performing independent perturbations that hit a single node at a time, and linear approximation of dependencies within the network. Previously, we addressed the sensitivity of MRA to noise by reinterpreting MRA as a multilinear regression problem. We demonstrated the advantages of this approach over the conventional MRA and other known inference methods, particularly in handling noise measurements and nonlinear networks. Here, we provide new contributions to complement this theory. First, we overcome the need of perturbations to be independent, thereby augmenting MRA applicability. Second, using analysis of variance and lack-of-fit tests, we can now assess MRA compatibility with the data and identify the primary source of errors. In cases where nonlinearity prevails, we propose extending the model to a second-order polynomial. Third, we demonstrate how to effectively use prior knowledge about a network. We validated these results using 4 networks with known dynamics (3, 4, and 6 nodes) and 40 simulated networks, ranging from 10 to 200 nodes. Finally, we incorporated these innovations into our R software package MRARegress to offer a comprehensive, extended theory for MRA and to facilitate its use by the community. Mathematical aspects, tests details, and scripts are provided as Supplementary Information (see 'Data Availability Statement').