Hubness reduction improves clustering and trajectory inference in single-cell transcriptomic data.

MOTIVATION: Single-cell RNA-seq (scRNAseq) datasets are characterized by large ambient dimensionality, and their analyses can be affected by various manifestations of the dimensionality curse. One of these manifestations is the hubness phenomenon, i.e. existence of data points with surprisingly large incoming connectivity degree in the datapoint neighbourhood graph. Conventional approach to dampen the unwanted effects of high dimension consists in applying drastic dimensionality reduction. It remains unexplored if this step can be avoided thus retaining more information than contained in the low-dimensional projections, by correcting directly hubness. RESULTS: We investigated hubness in scRNAseq data. We show that hub cells do not represent any visible technical or biological bias. The effect of various hubness reduction methods is investigated with respect to the clustering, trajectory inference and visualization tasks in scRNAseq datasets. We show that hubness reduction generates neighbourhood graphs with properties more suitable for applying machine learning methods; and that it outperforms other state-of-the-art methods for improving neighbourhood graphs. As a consequence, clustering, trajectory inference and visualization perform better, especially for datasets characterized by large intrinsic dimensionality. Hubness is an important phenomenon characterizing data point neighbourhood graphs computed for various types of sequencing datasets. Reducing hubness can be beneficial for the analysis of scRNAseq data with large intrinsic dimensionality in which case it can be an alternative to drastic dimensionality reduction. AVAILABILITY AND IMPLEMENTATION: The code used to analyze the datasets and produce the figures of this article is available from https://github.com/sysbio-curie/schubness. SUPPLEMENTARY INFORMATION: Supplementary data are available at Bioinformatics online.

Modeling Progression of Single Cell Populations Through the Cell Cycle as a Sequence of Switches.

Cell cycle is a biological process underlying the existence and propagation of life in time and space. It has been an object for mathematical modeling for long, with several alternative mechanistic modeling principles suggested, describing in more or less details the known molecular mechanisms. Recently, cell cycle has been investigated at single cell level in snapshots of unsynchronized cell populations, exploiting the new methods for transcriptomic and proteomic molecular profiling. This raises a need for simplified semi-phenomenological cell cycle models, in order to formalize the processes underlying the cell cycle, at a higher abstracted level. Here we suggest a modeling framework, recapitulating the most important properties of the cell cycle as a limit trajectory of a dynamical process characterized by several internal states with switches between them. In the simplest form, this leads to a limit cycle trajectory, composed by linear segments in logarithmic coordinates describing some extensive (depending on system size) cell properties. We prove a theorem connecting the effective embedding dimensionality of the cell cycle trajectory with the number of its linear segments. We also develop a simplified kinetic model with piecewise-constant kinetic rates describing the dynamics of lumps of genes involved in S-phase and G2/M phases. We show how the developed cell cycle models can be applied to analyze the available single cell datasets and simulate certain properties of the observed cell cycle trajectories. Based on our model, we can predict with good accuracy the cell line doubling time from the length of cell cycle trajectory.

Minimum Spanning vs. Principal Trees for Structured Approximations of Multi-Dimensional Datasets.

Construction of graph-based approximations for multi-dimensional data point clouds is widely used in a variety of areas. Notable examples of applications of such approximators are cellular trajectory inference in single-cell data analysis, analysis of clinical trajectories from synchronic datasets, and skeletonization of images. Several methods have been proposed to construct such approximating graphs, with some based on computation of minimum spanning trees and some based on principal graphs generalizing principal curves. In this article we propose a methodology to compare and benchmark these two graph-based data approximation approaches, as well as to define their hyperparameters. The main idea is to avoid comparing graphs directly, but at first to induce clustering of the data point cloud from the graph approximation and, secondly, to use well-established methods to compare and score the data cloud partitioning induced by the graphs. In particular, mutual information-based approaches prove to be useful in this context. The induced clustering is based on decomposing a graph into non-branching segments, and then clustering the data point cloud by the nearest segment. Such a method allows efficient comparison of graph-based data approximations of arbitrary topology and complexity. The method is implemented in Python using the standard scikit-learn library which provides high speed and efficiency. As a demonstration of the methodology we analyse and compare graph-based data approximation methods using synthetic as well as real-life single cell datasets.

Trajectories, bifurcations, and pseudo-time in large clinical datasets: applications to myocardial infarction and diabetes data.

BACKGROUND: Large observational clinical datasets are becoming increasingly available for mining associations between various disease traits and administered therapy. These datasets can be considered as representations of the landscape of all possible disease conditions, in which a concrete disease state develops through stereotypical routes, characterized by "points of no return" and "final states" (such as lethal or recovery states). Extracting this information directly from the data remains challenging, especially in the case of synchronic (with a short-term follow-up) observations. RESULTS: Here we suggest a semi-supervised methodology for the analysis of large clinical datasets, characterized by mixed data types and missing values, through modeling the geometrical data structure as a bouquet of bifurcating clinical trajectories. The methodology is based on application of elastic principal graphs, which can address simultaneously the tasks of dimensionality reduction, data visualization, clustering, feature selection, and quantifying the geodesic distances (pseudo-time) in partially ordered sequences of observations. The methodology allows a patient to be positioned on a particular clinical trajectory (pathological scenario) and the degree of progression along it to be characterized with a qualitative estimate of the uncertainty of the prognosis. We developed a tool ClinTrajan for clinical trajectory analysis implemented in the Python programming language. We test the methodology in 2 large publicly available datasets: myocardial infarction complications and readmission of diabetic patients data. CONCLUSIONS: Our pseudo-time quantification-based approach makes it possible to apply the methods developed for dynamical disease phenotyping and illness trajectory analysis (diachronic data analysis) to synchronic observational data.