Charting cellular differentiation trajectories with Ricci flow.

Complex biological processes, such as cellular differentiation, require intricate rewiring of intra-cellular signalling networks. Previous characterisations revealed a raised network entropy underlies less differentiated and malignant cell states. A connection between entropy and Ricci curvature led to applications of discrete curvatures to biological networks. However, predicting dynamic biological network rewiring remains an open problem. Here we apply Ricci curvature and Ricci flow to biological network rewiring. By investigating the relationship between network entropy and Forman-Ricci curvature, theoretically and empirically on single-cell RNA-sequencing data, we demonstrate that the two measures do not always positively correlate, as previously suggested, and provide complementary rather than interchangeable information. We next employ Ricci flow to derive network rewiring trajectories from stem cells to differentiated cells, accurately predicting true intermediate time points in gene expression time courses. In summary, we present a differential geometry toolkit for understanding dynamic network rewiring during cellular differentiation and cancer.

Random walk with restart on multilayer networks: from node prioritisation to supervised link prediction and beyond.

BACKGROUND: Biological networks have proven invaluable ability for representing biological knowledge. Multilayer networks, which gather different types of nodes and edges in multiplex, heterogeneous and bipartite networks, provide a natural way to integrate diverse and multi-scale data sources into a common framework. Recently, we developed MultiXrank, a Random Walk with Restart algorithm able to explore such multilayer networks. MultiXrank outputs scores reflecting the proximity between an initial set of seed node(s) and all the other nodes in the multilayer network. We illustrate here the versatility of bioinformatics tasks that can be performed using MultiXrank. RESULTS: We first show that MultiXrank can be used to prioritise genes and drugs of interest by exploring multilayer networks containing interactions between genes, drugs, and diseases. In a second study, we illustrate how MultiXrank scores can also be used in a supervised strategy to train a binary classifier to predict gene-disease associations. The classifier performance are validated using outdated and novel gene-disease association for training and evaluation, respectively. Finally, we show that MultiXrank scores can be used to compute diffusion profiles and use them as disease signatures. We computed the diffusion profiles of more than 100 immune diseases using a multilayer network that includes cell-type specific genomic information. The clustering of the immune disease diffusion profiles reveals shared shared phenotypic characteristics. CONCLUSION: Overall, we illustrate here diverse applications of MultiXrank to showcase its versatility. We expect that this can lead to further and broader bioinformatics applications.

Microscopic origin of the scattering pre-peak in aqueous propylamine mixtures: X-ray and neutron experiments versus simulations.

The structure of aqueous propylamine mixtures is investigated through X-ray and neutron scattering experiments, and the scattered intensities compared with computer simulation data. Both sets of data show a prominent scattering pre-peak, which first appears at propylamine mole fraction x ≥ 0.1 around scattering vector k ≈ 0.2 Å-1, and evolves towards k ≈ 0.8 Å-1 for neat propylamine x = 1. The existence of a scattering pre-peak in this mixture is unexpected, specifically in view of its absence in aqueous 1-propanol or aqueous DMSO mixtures. The detailed analysis of the various atom-atom structure factors and snapshots indicates that significant micro-structures exist, which produces correlation pre-peaks in the atom-atom structure factors, positive for like species atom correlations and negative for cross species correlations. The scattering pre-peak depends on how these two contributions cancel out or not. The way the amine group bonds with water produces a pre-peak through an imbalance of the positive and negative scattering contributions, unlike 1-propanol and DMSO, where these 2 contributions compensate exactly. Hence molecular simulations demonstrate how chemical details influence the microscopic segregation in different types of molecular emulsions and can be detected or not by scattering experiments.

Modeling micro-heterogeneity in mixtures: The role of many body correlations.

A two-component interaction model is introduced herein, which allows us to describe macroscopic miscibility with various modes of tunable micro-segregation, ranging from phase separation to micro-segregation, and is in excellent agreement with structural quantities obtained from simulations and the liquid state hypernetted-chain like integral equation theory. The model is based on the conjecture that the many-body correlation bridge function term in the closure relation can be divided into one part representing the segregation effects, which are modeled herein, and the usual part representing random many body fluctuations. Furthermore, the model allows us to fully neglect these second contributions, thus increasing the agreement between the simulations and the theory. The analysis of the retained part of the many body correlations gives important clues about how to model the many body bridge functions for more realistic systems exhibiting micro-segregation, such as aqueous mixtures.