Spectral plots and the representation and interpretation of biological data

It is basic question in biology and other fields to identify the char- acteristic properties that on one hand are shared by structures from a particular realm, like gene regulation, protein-protein interaction or neu- ral networks or foodwebs, and that on the other hand distinguish them from other structures. We introduce and apply a general method, based on the spectrum of the normalized graph Laplacian, that yields repre- sentations, the spectral plots, that allow us to find and visualize such properties systematically. We present such visualizations for a wide range of biological networks and compare them with those for networks derived from theoretical schemes. The differences that we find are quite striking and suggest that the search for universal properties of biological networks should be complemented by an understanding of more specific features of biological organization principles at different scales.Comment: 15 pages, 7 figure

An introduction to spectral distances in networks (extended version)

Many functions have been recently defined to assess the similarity among networks as tools for quantitative comparison. They stem from very different frameworks - and they are tuned for dealing with different situations. Here we show an overview of the spectral distances, highlighting their behavior in some basic cases of static and dynamic synthetic and real networks

Guided Graph Spectral Embedding: Application to the C. elegans Connectome

Graph spectral analysis can yield meaningful embeddings of graphs by providing insight into distributed features not directly accessible in nodal domain. Recent efforts in graph signal processing have proposed new decompositions-e.g., based on wavelets and Slepians-that can be applied to filter signals defined on the graph. In this work, we take inspiration from these constructions to define a new guided spectral embedding that combines maximizing energy concentration with minimizing modified embedded distance for a given importance weighting of the nodes. We show these optimization goals are intrinsically opposite, leading to a well-defined and stable spectral decomposition. The importance weighting allows to put the focus on particular nodes and tune the trade-off between global and local effects. Following the derivation of our new optimization criterion and its linear approximation, we exemplify the methodology on the C. elegans structural connectome. The results of our analyses confirm known observations on the nematode's neural network in terms of functionality and importance of cells. Compared to Laplacian embedding, the guided approach, focused on a certain class of cells (sensory, inter- and motoneurons), provides more biological insights, such as the distinction between somatic positions of cells, and their involvement in low or high order processing functions.Comment: 43 pages, 7 figures, submitted to Network Neuroscienc

Streaming visualisation of quantitative mass spectrometry data based on a novel raw signal decomposition method

As data rates rise, there is a danger that informatics for high-throughput LC-MS becomes more opaque and inaccessible to practitioners. It is therefore critical that efficient visualisation tools are available to facilitate quality control, verification, validation, interpretation, and sharing of raw MS data and the results of MS analyses. Currently, MS data is stored as contiguous spectra. Recall of individual spectra is quick but panoramas, zooming and panning across whole datasets necessitates processing/memory overheads impractical for interactive use. Moreover, visualisation is challenging if significant quantification data is missing due to data-dependent acquisition of MS/MS spectra. In order to tackle these issues, we leverage our seaMass technique for novel signal decomposition. LC-MS data is modelled as a 2D surface through selection of a sparse set of weighted B-spline basis functions from an over-complete dictionary. By ordering and spatially partitioning the weights with an R-tree data model, efficient streaming visualisations are achieved. In this paper, we describe the core MS1 visualisation engine and overlay of MS/MS annotations. This enables the mass spectrometrist to quickly inspect whole runs for ionisation/chromatographic issues, MS/MS precursors for coverage problems, or putative biomarkers for interferences, for example. The open-source software is available from http://seamass.net/viz/