An extension of Modular Response Analysis for global perturbations and robust connectivity inference of gene regulatory networks

Understanding how gene regulatory networks respond to global cell perturbations remains a central challenge in systems biology and network inference. Modular Response Analysis (MRA) provides a mathematical framework to infer gene-to-gene directed connectivity graphs from perturbation experiments; however, classical MRA captures direct gene-to-gene influences, and does not explicitly account for global stimuli that simultaneously change the graph. Here, we introduce MRA ⁺ , an extension of MRA, that incorporates the effect of global perturbations into gene-to-gene graph inference. MRA ⁺ assumes a sequential experimental design in which targeted gene perturbations are followed by the application of a global stimulus, enabling the separation of connectivity changes from direct gene induction. The method estimates network connectivity under induced conditions and quantifies gene-specific induction strengths, which represent contributions to expression changes arising from mechanisms external to the inferred network. In the case of single-cell expression data, we present a bootstrap strategy to assess the robustness of inferred connectivity coefficients and propose a complementary criterion based on sign stability to interpret weak or non-significant estimates. Together, these developments provide a general framework for robust inference of gene connectivity graphs in the presence of global perturbations, applicable to diverse biological and experimental contexts.