Whole-brain functional connectivity (FC) measured with functional MRI (fMRI) evolves over time in meaningful ways at temporal scales going from years (e.g., development) to seconds [e.g., within-scan time-varying FC (tvFC)]. Yet, our ability to explore tvFC is severely constrained by its large dimensionality (several thousands). To overcome this difficulty, researchers often seek to generate low dimensional representations (e.g., 2D and 3D scatter plots) hoping those will retain important aspects of the data (e.g., relationships to behavior and disease progression). Limited prior empirical work suggests that manifold learning techniques (MLTs)—namely those seeking to infer a low dimensional non-linear surface (i.e., the manifold) where most of the data lies—are good candidates for accomplishing this task. Here we explore this possibility in detail. First, we discuss why one should expect tvFC data to lie on a low dimensional manifold. Second, we estimate what is the intrinsic dimension (ID; i.e., minimum number of latent dimensions) of tvFC data manifolds. Third, we describe the inner workings of three state-of-the-art MLTs: Laplacian Eigenmaps (LEs), T-distributed Stochastic Neighbor Embedding (T-SNE), and Uniform Manifold Approximation and Projection (UMAP). For each method, we empirically evaluate its ability to generate neuro-biologically meaningful representations of tvFC data, as well as their robustness against hyper-parameter selection. Our results show that tvFC data has an ID that ranges between 4 and 26, and that ID varies significantly between rest and task states. We also show how all three methods can effectively capture subject identity and task being performed: UMAP and T-SNE can capture these two levels of detail concurrently, but LE could only capture one at a time. We observed substantial variability in embedding quality across MLTs, and within-MLT as a function of hyper-parameter selection. To help alleviate this issue, we provide heuristics that can inform future studies. Finally, we also demonstrate the importance of feature normalization when combining data across subjects and the role that temporal autocorrelation plays in the application of MLTs to tvFC data. Overall, we conclude that while MLTs can be useful to generate summary views of labeled tvFC data, their application to unlabeled data such as resting-state remains challenging.

Additional file 1: Figure S1. Quality control and batch effect correction in scRNA-Seq, related to Figure 1 A. Violin plots showing the number of expressed genes, the number of reads uniquely mapped against the reference genome, and the fraction of mitochondrial genes compared to all genes per cell in scRNA-Seq data. B. Box plot showing the number of genes (left) and the number of uniquely mapped reads (right) per cell in each identified cell type in scRNA-Seq data. C. tSNE plot visualization of the sample source for all 70,201 cells. Each dot is a cell. Different colors represent different samples. D. tSNE plot visualization of unsupervised clustering analysis for all 70,201 cells based on scRNA-Seq data after quality control, which gave rise to 31 distinct clusters. Figure S2. Gene Ontology (GO) analysis of the DEGs for each cell type was performed and the representative enriched GO terms are presented, related to Figure 1. Figure S3. Expression of selected marker genes along the differentiation trajectory, related to Figure 2 A. tSNE plot demonstrating cell cycle regression (left). Visualization of myogenic differentiation trajectory by cell cycle phases (G1, S, and G2/M) (right). B. Donut plots showing the percentages of cells in G1, S, and G2M phase at different cell states. C. Expression levels of cell cycle-related genes in the myogenic cells organized into the Monocle trajectory. D. Expression levels of muscle related genes in the myogenic cells organized into the Monocle trajectory. Figure S4. Unsupervised clustering analysis for all cells in scATAC-Seq data and myogenic-specific scATAC-seq peaks, related to Figure 4 A-C. tSNE plot visualization of the sample source for all 48514 cells in scATAC-Seq. Each dot is a cell. Different colors represent different pigs (A), different embryonic stages (B), or different samples (C). D. tSNE plot visualization of unsupervised clustering analysis for all 48514 cells after quality control in scATAC-Seq data, which gave rise to 15 distinct clusters. E. tSNE plot visualization of myogenic cells and other cells. Clusters 4 and 8 in Figure S4D were annotated as myogenic cells due to their high levels of accessibility of marker genes associated with myogenic lineage. F. Genome browser view of myogenic-specific peaks at the TSS of MyoG and Myf5 for myogenic cells and other cells in the scATAC-seq dataset. Figure S5. Percentage distribution of open chromatin elements in scATAC-Seq data, related to Figure 4 A. Distribution of open chromatin elements in each snATAC-seq sample. B. Distribution of open chromatin elements in snATAC-seq of myogenic cell types. C. Percentage distribution of open chromatin elements among DAPs in myogenic cell types. Figure S6. Integrative analysis of transcription factors and target genes, related to Figure 5 A. tSNE depiction of regulon activity (“on-blue”, “off-gray”), TF gene expression (red scale), and expression of predicted target genes (purple scale) of MyoG, FOSB, and TCF12. B. Corresponding chromatin accessibility in scATAC data for TFs and predicted target genes are depicted. Figure S7. Pseudotime-dependent chromatin accessibility and gene expression changes, related to Figure 7. The first column shows the dynamics of the 10× Genomics TF enrichment score. The second column shows the dynamics of TF gene expression values, and the third and fourth columns represent the dynamics of the SCENIC-reported target gene expression values of corresponding TFs, respectively. Figure S8. Myogenesis related gene expression in DMD (Duchenne muscular dystrophy) mice. Comparison of RNA-seq data of flexor digitorum short (FDB), extensor digitorum long (EDL), and soleus (SOL) in DMD and wild-type mice including 2- month and 5-month age. A. The expression levels of myogenesis related genes (Myod1, Myog, Myf5, Pax7). B. The expression levels of related genes that were upregulated during porcine embryonic myogenesis (EGR1, RHOB, KLF4, SOX8, NGFR, MAX, RBFOX2, ANXA6, HES6, RASSF4, PLS3, SPG21). C. The expression levels of related genes that were downregulated during porcine embryonic myogenesis COX5A, HOMER2, BNIP3, CNCS). Data were obtained from the GEO database (GSE162455; WT, n = 4; DMD, n = 7). Figure S9. Genome browser view of differentially accessible peaks at the TSS of EGR1 and RHOB between myogenic cells in the scATAC-seq dataset, related to Figure 8. Figure S10. Functional analysis of EGR1 in myogenesis, related to Figure 8 A-B. EdU assays for the proliferation of pig primary myogenic cells (A) and C2C12 myoblasts following EGR1 overexpression. C. qPCR analysis of the mRNA levels of cell cycle regulators in C2C12 cells following EGR1 overexpression. D. Immunofluorescence staining for MyHC in C2C12 cells following EGR1 overexpression and differentiation for 3 d. Then, the fusion index was calculated. Figure S11. Functional analysis of RHOB in myogenesis, related to Figure 8 A-B. EdU assays for proliferation of pig primary myogenic cells (A) and C2C12 myoblasts following RHOB overexpression. C. qPCR analysis of the mRNA levels of cell-cycle regulators in C2C12 cells following RHOB overexpression. D. Immunofluorescence staining for MyHC in C2C12 cells following RHOB overexpression and differentiation for 3 d. Then, the fusion index was calculated.

Data submittedInput data for tsne and violin plots

Molecular simulation trajectories represent high-dimensional data. Such data can be visualized by methods of dimensionality reduction. Non-linear dimensionality reduction methods are likely to be more efficient than linear ones due to the fact that motions of atoms are non-linear. Here we test a popular non-linear t-distributed Stochastic Neighbor Embedding (t-SNE) method on analysis of trajectories of 200 ns alanine dipeptide dynamics and 208 μs Trp-cage folding and unfolding. Furthermore, we introduce a time-lagged variant of t-SNE in order to focus on rarely occurring transitions in the molecular system. This time-lagged t-SNE efficiently separates states according to distance in time. Using this method it is possible to visualize key states of studied systems (e.g., unfolded and folded protein) as well as possible kinetic traps using a two-dimensional plot. Time-lagged t-SNE is a visualization method and other applications, such as clustering and free energy modeling, must be done with caution.

Scripts used for analysis of V1 and V2 Datasets.seurat_v1.R - initialize seurat object from 10X Genomics cellranger outputs. Includes filtering, normalization, regression, variable gene identification, PCA analysis, clustering, tSNE visualization. Used for v1 datasets. merge_seurat.R - merge two or more seurat objects into one seurat object. Perform linear regression to remove batch effects from separate objects. Used for v1 datasets. subcluster_seurat_v1.R - subcluster clusters of interest from Seurat object. Determine variable genes, perform regression and PCA. Used for v1 datasets.seurat_v2.R - initialize seurat object from 10X Genomics cellranger outputs. Includes filtering, normalization, regression, variable gene identification, and PCA analysis. Used for v2 datasets. clustering_markers_v2.R - clustering and tSNE visualization for v2 datasets. subcluster_seurat_v2.R - subcluster clusters of interest from Seurat object. Determine variable genes, perform regression and PCA analysis. Used for v2 datasets.seurat_object_analysis_v1_and_v2.R - downstream analysis and plotting functions for seurat object created by seurat_v1.R or seurat_v2.R. merge_clusters.R - merge clusters that do not meet gene threshold. Used for both v1 and v2 datasets. prepare_for_monocle_v1.R - subcluster cells of interest and perform linear regression, but not scaling in order to input normalized, regressed values into monocle with monocle_seurat_input_v1.R monocle_seurat_input_v1.R - monocle script using seurat batch corrected values as input for v1 merged timecourse datasets. monocle_lineage_trace.R - monocle script using nUMI as input for v2 lineage traced dataset. monocle_object_analysis.R - downstream analysis for monocle object - BEAM and plotting. CCA_merging_v2.R - script for merging v2 endocrine datasets with canonical correlation analysis and determining the number of CCs to include in downstream analysis. CCA_alignment_v2.R - script for downstream alignment, clustering, tSNE visualization, and differential gene expression analysis.

Additional file 4: S2 Table. Number of SNPs, genomic location and coordinates for each gene in the t-SNE plot.

BackgroundBy employing a high-dimensionality approach, this study aims to identify mechanistically relevant cellular immune signatures that predict poor outcomes.MethodsThis prospective study recruited 39 children with sepsis admitted to the intensive care unit and 19 healthy age-matched children. Peripheral blood mononuclear cells were studied with mass cytometry. Unique cell subsets were identified in the paediatric sepsis immunome and depicted with t-distributed stochastic neighbour embedding (tSNE) plots. Network analysis was performed to quantify interactions between immune subsets. Enriched immune subsets were included in a model for distinguishing sepsis and validated by flow cytometry in an independent cohort.ResultsThe median (interquartile range) age and paediatric sequential organ failure assessment (pSOFA) score in this cohort was 5.6(2.0, 11.3) years and 6.6 (IQR: 2.5, 10.1), respectively. High-dimensionality analyses of the immunome in sepsis revealed a loss of coordinated communication between immune subsets, particularly a loss of regulatory/inhibitory interaction between cell types, fewer interactions between cell subsets, and fewer negatively correlated edges than controls. Four independent immune subsets (CD45RA−CX3CR1+CTLA4+CD4+ T cells, CD45RA−17A+CD4+ T cells CD15+CD14+ monocytes, and Ki67+ B cells) were increased in sepsis and provide a predictive model for diagnosis with area under the receiver operating characteristic curve, AUC 0.90 (95% confidence interval, CI 0.82–0.98) in the discovery cohort and AUC 0.94 (95% CI 0.83–1.00) in the validation cohort.ConclusionThe sepsis immunome is deranged with loss of regulatory/inhibitory interactions. Four immune subsets increased in sepsis could be used in a model for diagnosis and prediction of poor outcomes.

Figure S6. Unidimensional bar graphs of medication class prescribing frequency by region. Bar graphs of each of the top 10 medication classes prescribed (by percentage of individual prescriber prescriptions) for each of 24 medical specialty groupings, plotted for each of 10 Federal Regions. Note that drug class prescribing percentages are mean levels, and truncated at 21% to make the visualizations informative. (ZIP 5280 kb)

Data submittedInput data for tsne and violin plots

This datatable contains all excitatory cells (slc17a7+) across anterior, intermediate, and posterior sections of the basolateral amygdala. Metadata includes:- gene: denotes gene expressed within given cell- quant: quantified expression of a given gene, normalized so that quantification of each gene adds to 1 for a given cell- X & Y: cell position in space- position: denotes which section the cells came from (anterior intermediate, or posterior)- tsne1 & tsne2: plot these to get tsne visualization (perplexity = 35, max iteration = 6350)- cluster: cells labelled cluster 1-6 - according to hierarchical clustering (distance = Euclidean, method = Ward D2)