Section: New Results

Inferring and analysing the networks of molecular elements

Protein structure comparison

We proposed a new distance measure for comparing two protein structures based on their contact map representations [1] . We showed that our novel measure, which we refer to as the maximum contact map overlap (max-CMO) metric, satisfies all properties of a metric on the space of protein representations. Having a metric in that space allows one to avoid pairwise comparisons on the entire database and, thus, to significantly accelerate exploring the protein space compared to no-metric spaces. We showed on a gold standard superfamily classification benchmark set of 6759 proteins that our exact k-nearest neighbour ($k-NN$) scheme classifies up to 224 out of 236 queries correctly and on a larger, extended version of the benchmark with 60; 850 additional structures, up to 1361 out of 1369 queries. Our $k-NN$ classification thus provides a promising approach for the automatic classification of protein structures based on flexible contact map overlap alignments.

Metabolic network analysis

Flux balance analysis (FBA) is one of the most often applied methods on genome-scale metabolic networks. Although FBA uniquely determines the optimal yield, the pathway that achieves this is usually not unique. The analysis of the optimal-yield flux space has been an open challenge. Flux variability analysis is only capturing some properties of the flux space, while elementary mode analysis is intractable due to the enormous number of elementary modes. However, it had been previously found that the space of optimal-yield fluxes decomposes into flux modules. These decompositions allow a much easier but still comprehensive analysis of the optimal-yield flux space. Using the mathematical definition of module introduced by Müller and Bockmayr in 2013, we discovered that flux modularity is rather a local than a global property which opened connections to matroid theory [28] . Specifically, we showed that our modules correspond one-to-one to so-called separators of an appropriate matroid. Employing efficient algorithms developed in matroid theory we are now able to compute the decomposition into modules in a few seconds for genome-scale networks. Using that every module can be represented by one reaction that corresponds to its function, we also presented a method that uses this decomposition to visualise the interplay of modules. We expect the new method to replace flux variability analysis in the pipelines for metabolic networks.

Integrated network analysis

Data on molecular interactions is increasing at a tremendous pace. Since biological functionality primarily operates at the network level, there is a clear need for topology-aware comparison methods. We developed one such method for global network alignment that is fast and robust and can flexibly deal with various scoring schemes taking both node-to-node correspondences as well as network topologies into account [18] . We exploited that network alignment is a special case of the well-studied quadratic assignment problem (QAP). We focused on sparse network alignment, where each node can be mapped only to a typically small subset of nodes in the other network. This corresponds to a QAP instance with a symmetric and sparse weight matrix. We obtained strong upper and lower bounds for the problem by improving a Lagrangian relaxation approach and introduce the open source software tool Natalie 2.0, a publicly available implementation of our method (https://github.com/ls-cwi/natalie ). In an extensive computational study on protein interaction networks for six different species, we found that our new method outperforms alternative established and recent state-of-the-art methods.

Integrative network analysis methods provide robust interpretations of differential high-throughput molecular profile measurements. They are often used in a biomedical context-to generate novel hypotheses about the underlying cellular processes or to derive biomarkers for classification and subtyping. The underlying molecular profiles are frequently measured and validated on animal or cellular models. Therefore the results are not immediately transferable to human. In particular, this is also the case in a study of the recently discovered interleukin-17 producing helper T cells (Th17), which are fundamental for anti-microbial immunity but also known to contribute to autoimmune diseases. We proposed a mathematical model for finding active subnetwork modules that are conserved between two species [19] . These are sets of genes, one for each species, which (1) induce a connected subnetwork in a species-specific interaction network, (2) show overall differential behaviour and (iii) contain a large number of orthologous genes. We proposed a flexible notion of conservation, which turns out to be crucial for the quality of the resulting modules in terms of biological interpretability. We developed an algorithm that finds provably optimal or near-optimal conserved active modules in our model. We applied our algorithm to understand the mechanisms underlying Th17 T cell differentiation in both mouse and human. As a main biological result, we found that the key regulation of Th17 differentiation is conserved between human and mouse.