The ability to quantify differentiation potential of single cells is a task of critical importance. Here researchers from the University College London demonstrate, using over 7,000 single-cell RNA-Seq profiles, that differentiation potency of a single cell can be approximated by computing the signalling promiscuity, or entropy, of a cell’s transcriptome in the context of an interaction network, without the need for feature selection. They show that signalling entropy provides a more accurate and robust potency estimate than other entropy-based measures, driven in part by a subtle positive correlation between the transcriptome and connectome. Signalling entropy identifies known cell subpopulations of varying potency and drug resistant cancer stem-cell phenotypes, including those derived from circulating tumour cells. It further reveals that expression heterogeneity within single-cell populations is regulated. In summary, signalling entropy allows in silico estimation of the differentiation potency and plasticity of single cells and bulk samples, providing a means to identify normal and cancer stem-cell phenotypes.
The single-cell entropy (SCENT) algorithm
(a) Signalling entropy of single cells as a proxy to their differentiation potential in Waddington’s landscape. Depicted on the left is a population of cells with cells occupying either a pluripotent (magenta), a progenitor (cyan) or a differentiated state (green). The potency state of each cell is determined by a complex function of the transcriptomic profile of the cell. For a given interaction between proteins i and k in the network, signalling in a given cell occurs with a probability pik∼xixk, defining a stochastic matrix P=(pik). In a pluripotent state, there is high demand for phenotypic plasticity, and so promiscuous signalling proteins (that is, those of high connectivity) are highly expressed (red coloured node) with all major differentiation pathways kept at a similar basal activity level (grey edges). The probability of signalling between protein i and k, pik, is therefore 1/ki where ki is the connectivity of protein i in the network. Thus the local signalling entropy around node i is maximal. In a differentiated state, commitment to a specific lineage (activation of a specific signalling pathway shown by red coloured node) means that most pij∼0, except when j=k, so that pik∼1. Thus, local signalling entropy around node i is close to zero. (b) Estimation of signalling entropy. An overall measure of signalling promiscuity of the cell is given mathematically by the signalling entropy rate (SR), which is a weighted average of local signaling entropies Si over all the genes/proteins in the network, with weights specified by π (the steady-state probability satisfying πP=π). It is proposed that SR provides a proxy to the elevation in Waddington’s landscape, quantifying differentiation potential of cells (i.e the number of accessible cell-fates within a given lineage). (c) Quantification of intercellular heterogeneity and reconstruction of lineage trajectories. Estimation of signalling entropy at the single-cell level across a population of cells, allows the distribution of potency states in the population to be determined through Bayes mixture modelling which infers the optimal number of potency states. From this, the heterogeneity of potency states in a cell population is computed using Shannon’s Index. To infer lineage trajectories, SCENT uses a clustering algorithm over dimensionally reduced scRNA-Seq profiles to infer co-expression clusters of cells. Dual assignment of cells to a potency state and co-expression cluster allows the identification of landmarks as bi-clusters in potency-coexpression space. Finally, partial correlations between the expression profiles of the landmarks are used to infer a lineage trajectory network diagram linking cell clusters according to expression similarity, with their height or elevation determined by their potency (signalling entropy).
Availability – Signalling entropy is available as part of the Single Cell Entropy (SCENT) R-package and is freely available from github: https://github.com/aet21/SCENT.