Sub-modular resolution analysis by network mixture models

Inferring the structure of networks usually involves the attempt of retrieving their modular organization and knowing its possible interpretation, while quantifying the involved computational complexity through the methods and algorithms to be used. In protein interactomics, it is assumed that even the most recently created interactomes are known only up to a certain degree of coverage and accuracy, due to both experimental and computational limitations. Therefore, we need to infer from the measured interactomes about real interactomes as much as we infer from samples relative to a reference population. In order to exploit additional information sources, it is common to integrate multiple omic data and pursue method fusion. Particularly after the advent of high-throughput technologies, the increased complexity of data-intensive applications has determined an important role for network inference. Consequently, advances in spectral clustering, community detection algorithms and modularity optimization methods have been proposed, according to both deterministic and probabilistic solutions. We have considered the two kinds of approaches, and applied some of the available methods to two human interactomes obtained from high-throughput small-scale experiments and mass spectrometry measurements. The main motivation of this study is refining the resolution spectrum at which protein modularity maps can be studied. First, we started by a coarse-grained interactome decomposition through core and community structures, and by applying sub-sampling to the interactome adjacency matrix. Then, we switched to stochastic methods to uncover fine-grained interactome components, and applied both variational and mixture statistical models. Lastly, we integrated our analysis with the biological validation of the retrieved modules. Overall, the proposed approach shows potential for calibrating modularity detection in protein interactomes at different resolutions.