Sensitivity analysis on protein-protein interaction networks through deep graph networks

Protein-protein interaction networks (PPINs) provide a comprehensive view of the intricate biochemical processes that take place in living organisms. In recent years, the size and information content of PPINs have grown thanks to techniques that allow for the functional association of proteins. However, PPINs are static objects that cannot fully describe the dynamics of the protein interactions; these dynamics are usually studied from external sources and can only be added to the PPIN as annotations. In contrast, the time-dependent characteristics of cellular processes are described in Biochemical Pathways (BP), which frame complex networks of chemical reactions as dynamical systems. Their analysis with numerical simulations allows for the study of different dynamical properties. Unfortunately, available BPs cover only a small portion of the interactome, and simulations are often hampered by the unavailability of kinetic parameters or by their computational cost. In this study, we explore the possibility of enriching PPINs with dynamical properties computed from BPs. We focus on the global dynamical property of sensitivity, which measures how a change in the concentration of an input molecular species influences the concentration of an output molecular species at the steady state of the dynamical system.

We started with the analysis of BPs via ODE simulations, which enabled us to compute the sensitivity associated with multiple pairs of chemical species. The sensitivity information was then injected into a PPIN, using public ontologies (BioGRID, UniPROT) to map entities at the BP level with nodes at the PPIN level. The resulting annotated PPIN, termed the DyPPIN (Dynamics of PPIN) dataset, was used to train a DGN to predict the sensitivity relationships among PPIN proteins. Our experimental results show that this model can predict these relationships effectively under different use case scenarios. Furthermore, we show that the PPIN structure (i.e., the way the PPIN is "wired") is essential to infer the sensitivity, and that further annotating the PPIN nodes with protein sequence embeddings improves the predictive accuracy.

To the best of our knowledge, the model proposed in this study is the first that allows performing sensitivity analysis directly on PPINs. Our findings suggest that, despite the high level of abstraction, the structure of the PPIN holds enough information to infer dynamic properties without needing an exact model of the underlying processes. In addition, the designed pipeline is flexible and can be easily integrated into drug design, repurposing, and personalized medicine processes.