BACKGROUND: 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. RESULTS: 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. CONCLUSION: 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.

Understanding the inductive bias of Deep Graph Networks (DGNs) is crucial because it reveals how these models generalize from training data to unseen data. Discovering these learning assumptions, and their alignment to the task’s characteristics, allows informed architectural design choices and facilitates interpretation. With this goal, we analyze the different inductive biases of DGNs by relating the node-level explanations produced by explainable AI (XAI) methods to known network science measures of lower-order (local) and higher-order (increasingly global) connectivity. We then apply graph signal processing to refine this analysis at the granularity of the graph frequency spectrum spanned by the explanation signals. Our main finding is that different DGNs focus on different regions of the graph frequency spectrum, and in particular, high-frequency DGNs generalize by focusing on lower-order graph connectivity, while low-frequency DGNs generalize by recognizing higher-order graph structures. This characterization is first derived on synthetic benchmarks by showing that explanations align with network science measures sitting at the two extremes of the spectrum (Katz centrality in the high frequencies, and Fiedler eigenvector scores in the low frequencies). Moving to real-world chemical benchmarks, this result is generalized by showing that inductive biases do indeed lie on a continuum that corresponds to sub-regions of the frequency spectrum.

Generalization in machine learning involves introducing inductive biases that restrict the solution space of the learning problem, allowing for the inductive leap.In this paper, we show the existence of different inductive biases between convolutional and recursive Deep Graph Networks (DGN) by applying Explainable AI (XAI) methods as model inspection techniques.We show that different architectures can perfectly solve the given tasks by learning different labelling policies.Our results promote the usage of different architectures to address a task and raise warnings on the assessment of XAI techniques as their benchmarks may contain more ground truths than those provided.* Research partly funded by PNRR -M4C2 -Investimento 1.3, Partenariato Esteso PE00000013 -"FAIR -Future Artificial Intelligence Research" -Spoke 1 "Human-centered AI", funded by the European Commission under the NextGeneration EU programme.

MOTIVATION: Dynamical properties of biochemical pathways (BPs) help in understanding the functioning of living cells. Their in silico assessment requires simulating a dynamical system with a large number of parameters such as kinetic constants and species concentrations. Such simulations are based on numerical methods that can be time-expensive for large BPs. Moreover, parameters are often unknown and need to be estimated. RESULTS: We developed a framework for the prediction of dynamical properties of BPs directly from the structure of their graph representation. We represent BPs as Petri nets, which can be automatically generated, for instance, from standard SBML representations. The core of the framework is a neural network for graphs that extracts relevant information directly from the Petri net structure and exploits them to learn the association with the desired dynamical property. We show experimentally that the proposed approach reliably predicts a range of diverse dynamical properties (robustness, monotonicity, and sensitivity) while being faster than numerical methods at prediction time. In synergy with the neural network models, we propose a methodology based on Petri nets arc knock-out that allows the role of each molecule in the occurrence of a certain dynamical property to be better elucidated. The methodology also provides insights useful for interpreting the predictions made by the model. The results support the conjecture often considered in the context of systems biology that the BP structure plays a primary role in the assessment of its dynamical properties. AVAILABILITY AND IMPLEMENTATION: https://github.com/marcopodda/petri-bio (code), https://zenodo.org/record/7610382 (data).