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From the spectral plot of the (normalized) graph Laplacian, the essential qualitative properties of a network can be simultaneously deduced. Given a class of empirical networks, reconstruction schemes for elucidating the evolutionary dynamics leading to those particular data can then be developed. This method is exemplified for protein-protein interaction networks. Traces of their evolutionary history of duplication and divergence processes are identified. In particular, we can identify typical specific features that robustly distinguish protein-protein interaction networks from other classes of networks, in spite of possible statistical fluctuations of the underlying data.
The determination of protein functions is one of the most challenging problems of the post-genomic era. The sequencing of entire genomes and the possibility to access genes co-expression patterns has moved the attention from the study of single prote
Aligning protein-protein interaction (PPI) networks of different species has drawn a considerable interest recently. This problem is important to investigate evolutionary conserved pathways or protein complexes across species, and to help in the iden
Machine-learning models that learn from data to predict how protein sequence encodes function are emerging as a useful protein engineering tool. However, when using these models to suggest new protein designs, one must deal with the vast combinatoria
Potts models and variational autoencoders (VAEs) have recently gained popularity as generative protein sequence models (GPSMs) to explore fitness landscapes and predict the effect of mutations. Despite encouraging results, quantitative characterizati
We develop a theoretical approach to the protein folding problem based on out-of-equilibrium stochastic dynamics. Within this framework, the computational difficulties related to the existence of large time scale gaps in the protein folding problem a