**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 *p*_{ik}∼*x*_{i}*x*_{k}, defining a stochastic matrix *P=(p*_{ik}). 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, p*_{ik}, is therefore 1/*k*_{i} where *k*_{i} 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 *p*_{ij}*∼0*, except when *j=k,* so that *p*_{ik}*∼*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 *S*_{i} 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.

Teschendorff AE, Enver T. (2017) **Single-cell entropy for accurate estimation of differentiation potency from a cell’s transcriptome.** *Nat Commun* 8:15599. [abstract]