Fig 1.
Overview of the tree dimension test for trajectory presence.
The input is multivariate data. A Euclidean minimum spanning tree (EMST) is computed on the data points. Trajectory inferential test statistic S is computed from tree dimension measure Td of the EMST. A log-normal null distribution of S is derived from the null population following a spherical multivariate normal distribution with no trajectory patterns. A p-value of the observed statistic S is computed to quantify statistical significance for the presence of a trajectory pattern.
Fig 2.
Trees, dimensions, and dimension measures.
Each tree dimension is highlighted by a different color. (A) A one-dimensional tree, or a path graph, with tree dimension measure Td = 1. (B) A two-dimensional tree with Td = 1.5. (C) A two-dimensional tree with Td = 2. (D) A three-dimensional tree with Td = 3.
Fig 3.
Two trees of the same number of vertices and their tree dimension measure Td, diameter Dm and number of leaves L.
The color of a vertex indicates a unique tree dimension. (A) The tree is two dimensional with Td=2, Dm=6 and L=4. (B) The tree is four dimensional with Td=2.28, Dm=6 and L=8.
Fig 4.
Approximating the empirical null distribution of trajectory test statistic S.
BIC, AIC, and KS test p-values of (A) log-normal (lnorm), (B) gamma, and (C) normal (norm) distributions after they (red curves) were fit to simulated null test statistic S values (histograms).
Fig 5.
Two pathways of contrasting tissue specificity during the development of seven mouse tissues.
EMSTs linking tissue samples are derived from expression levels of genes on each pathway. Vertices are samples colored by tissue type. (A) The Wnt signaling pathway is of high tissue specificity in gene expression dynamics, with developing samples of the same tissue type forming unique trajectory segments. (B) The mismatch repair pathway, of low tissue specificity in gene expression dynamics, shows mingled samples of different tissue types.
Fig 6.
Trajectory presence testing on 229 simulated single-cell datasets.
(A) ROC curves and AUROC scores for TDT effect size S/N, number of leaves L and tree diameter Dm. (B) PR curves and AUPR scores for the three methods. (C) The PCA plot of a multifurcating trajectory patterns, points represent cell and the axes gene expression, and the EMST representation of trajectory pattern, with each point representing a cell. Text shows p-values of each method when applied on the dataset. (D) PCA and EMST plots of a looping trajectory pattern. (E) PCA and EMST plots of a multifurcating trajectory. (F)–(H) PCA and EMST plots of datasets with no significant trajectory patterns.
Fig 7.
Trajectory presence testing on 110 real single-cell datasets.
(A) ROC curves and AUC scores for TDT effect size S/N, number of leaves L and tree diameter Dm. (B) PR curves and AUC scores for the three methods. (C) The PCA plot and EMST representation of trajectory patterns in single-cell human lung adenocarcinoma cancer cell lines data. Points represent cells. Text shows p-values of each method when applied on the dataset. (D) PCA and EMST plots of a trajectory pattern in human female germline single-cell data (E) PCA and EMST plots of a trajectory pattern in planaria single-cell data. (F)–(H) PCA and EMST plots of datasets with no significant trajectory patterns.
Fig 8.
Empirical runtime of TDT on simulated single-cell data with varying number of cells.
The runtime includes 100 simulations to estimate parameters for the null distribution. The horizontal axis represents the number of cells. The vertical axis is the runtime in minutes. Time was recorded on a 2015 Apple Macbook Pro laptop computer with 2.2 GHz Quad-Core Intel Core i7 processor using a single thread.
Fig 9.
Distinct cellular and pathway trajectories in single-cell data of embryonic stem cells.
Cells are clustered into five groups indicated by the colors. (A) Observed gene expression data of embryonic stem cells in the first three principal components. (B) The EMST of the entire transcriptome suggests a strong trajectory pattern at the cellular level. (C)-(F) EMST representations of trajectory patterns in embryonic stem cells using gene expression on the pathways of (C) renin, (D) proteasome, (E) mismatch repair, and (F) hedgehog.
Fig 10.
Tissue specificity of gene expression dynamics of 40 biological pathways during human and mouse development.
(A) Pathways are ranked by average tissue specificity during mammalian development computed from transcriptome data in seven tissue types in human and mouse. (B) Pathway tissue specificity is conserved between developing mouse and human. Each point is a pathway and the axes represent its tissue specificity scores for mouse and human, respectively.
Fig 11.
Gene expression dynamics of most and least tissue-specific pathways during mammalian development.
Seven tissue types are coded by colors. PCA and EMSTs of expression of genes on (A) calcium signaling, (B) Wnt signaling, (C) mismatch repair, and (D) ribosome pathways during human development. (E)–(H) PCA and EMSTs of gene expression dynamics of the same four pathways during mouse development.