In view of the fundamental challenges of single-cell resolution studies due to technical noise, transcriptional stochasticity, and computational burden, PAGA provides a general framework for extending studies of the relations among single cells to relations among noise-reduced and computationally tractable groups of cells.
This could facilitate obtaining clearer pictures of underlying biology. In closing, we note that PAGA not only works for scRNA-seq based on distance metrics that arise from a sequence of chosen preprocessing steps, but can also be applied to any learned distance metric.
To illustrate this point, we used PAGA for single-cell imaging data when applied on the basis of a deep-learning-based distance metric. Eulenberg et al. Using this, PAGA correctly identifies the biological trajectory through the interphases of cell cycle while ignoring a cluster of damaged and dead cells Additional file 1 : Figure S We preprocess scRNA-seq data as commonly done following steps mostly inspired by Seurat [ 34 ] in the implementation of Scanpy [ 35 ].
These steps consist in basic filtering of the data, total count normalization, log1p logarithmization, extraction of highly variable genes, a potential regression of confounding factors, and a scaling to z -scores. On this corrected and homogenized representation of the count data, we perform a PCA and represent the data within the reduced space of principal components.
In the GitHub repository, each figure of the paper is reproduced in a dedicated notebook. Using the compressed and denoised representation of the data in the previous step, we construct a symmetrized kNN-like graph, typically using the approximate nearest neighbor search within UMAP [ 22 ].
While one might potentially choose different distance metrics, we always choose Euclidean distance. Depending on user choice, the graph is either weighed using adaptive Gaussian kernels [ 7 ] or the exponential kernel within UMAP [ 22 ].
For all results shown in the manuscript, we used the exponential kernel. We consider all partitionings of interest of the kNN-like graph. To determine those, typically, we use the Louvain algorithm in the implementation of [ 37 ] at suitable resolutions, but PAGA works with any underlying clustering algorithm or experimentally generated groupings of observations.
In the present work, we exclusively used the Louvain algorithm. This measure is a test statistic quantifying the degree of connectivity of two partitions and has a close relation with modularity [ 20 ]. For each pair of clusters, PAGA connectivity is the ratio of the number of inter-edges between the clusters normalized with the number of inter-edges expected under random assignment of edges.
For estimating pseudotime, we use an extended version of diffusion pseudotime DPT Reference [ 7 ] that accounts for disconnected graphs. The extension consists in a simple modification of the original algorithm that accounts for disconnected Eigen-subspaces of the graph adjacency matrix, which results in multiple subspaces of Eigen value 1 of the graph transition matrix.
Practically, we assign an infinite distance to cells that reside in disconnected clusters and compute distances among cells within connected regions in the graph as it would be done in DPT.
See Additional file 1 : Note 2, both for details and for a review of random-walk-based distances. For instance, we show the close relation of DPT to mean commute distance.
PAGA achieves consistent i. For this initialization, the positions of nodes of the fine-grained graph that belong to a group corresponding to a node in the coarse-grained graph are randomly distributed in a non-overlapping rectangular region around the position of that node.
This procedure is repeated for all nodes of the coarse-grained graph. Non-overlapping regions are trivially ensured by choosing rectangles with half-edge lengths of half the distance to the nearest neighbor in the coarse-grained embedding.
Conversely, for a given fine-grained graph, we position nodes in the coarse-grained graph by placing them on the median coordinates of the positions of the corresponding nodes in the fine-grained graph.
Wagner A, Regev A, Yosef N. Revealing the vectors of cellular identity with single-cell genomics. Nat Biotechnol. Article CAS Google Scholar. Trapnell C, Cacchiarelli D, Grimsby J, Pokharel P, Li S, Morse M, Lennon NJ, Livak KJ, Mikkelsen T.
S, Rinn JL. The dynamics and regulators of cell fate decisions are revealed by pseudotemporal ordering of single cells. Single-cell trajectory detection uncovers progression and regulatory coordination in human B cell development. Saelens W, Cannoodt R, Todorov H, Saeys Y.
A comparison of single-cell trajectory inference methods: towards more accurate and robust tools. Qiu X, Hill A, Packer J, Lin D, Ma YA, Trapnell C. Single-cell mRNA quantification and differential analysis with census.
Nat Methods. Wishbone identifies bifurcating developmental trajectories from single-cell data. Haghverdi L, Büttner M, Wolf FA, Buettner F, Theis FJ. Diffusion pseudotime robustly reconstructs branching cellular lineages.
Street K, Risso D, Fletcher RB, Das D, Ngai J, Yosef N, Purdom E, Dudoit S. Slingshot: Cell lineage and pseudotime inference for single-cell transcriptomics. BMC Genomics. Article Google Scholar.
Rizvi AH, Camara PG, Kandror EK, Roberts TJ, Schieren I, Maniatis T, Rabadan R. Single-cell topological rna-seq analysis reveals insights into cellular differentiation and development.
Qiu P, Simonds EF, Bendall SC, Gibbs KD, Bruggner RV, Linderman M. D, Sachs K, Nolan GP, Plevritis SK. Extracting a cellular hierarchy from high-dimensional cytometry data with spade.
Nat Biotechnology. Giecold G, Marco E, Garcia SP, Trippa L, Yuan GC. Robust lineage reconstruction from high-dimensional single-cell data. Nucleic Acids Res.
Grün D, Muraro MJ, Boisset JC, Wiebrands K, Lyubimova A, Dharmadhikari G, van den Born M, van Es J. De novo prediction of stem cell identity using single-cell transcriptome data.
Cell Stem Cell. Plass M, Solana J, Wolf FA, Ayoub S, Misios A, Glažar P, Obermayer B, Theis FJ, Kocks C, Rajewsky N. Cell type atlas and lineage tree of a whole complex animal by single-cell transcriptomics.
Hu Y, Shi L. Visualizing large graphs. Wiley Interdiscip Rev Comput Stat. van der Maaten L, Hinton G. Visualizing data using t-sne. J Mach Learn Res. Google Scholar. Islam S, Kjallquist U, Moliner A, Zajac P, Fan JB, Lonnerberg P, Linnarsson S. Characterization of the single-cell transcriptional landscape by highly multiplex rna-seq.
Genome Res. Data-driven phenotypic dissection of AML reveals progenitor—like cells that correlate with prognosis. Blondel VD, Guillaume JL, Lambiotte R, Lefebvre E. Fast unfolding of communities in large networks.
J Stat Mech. Xu C, Su Z. Identification of cell types from single-cell transcriptomes using a novel clustering method. Newman MEJ. Modularity and community structure in networks.
Proc Natl Acad Sci. Singh G, Mémoli F, Carlsson GE. Topological methods for the analysis of high dimensional data sets and 3d object recognition. In: Eurographics Symposium on Point-Based Graphics: McInnes L, Healy J.
Umap: Uniform manifold approximation and projection for dimension reduction. Jacomy M, Venturini T, Heymann S, Bastian M. ForceAtlas2, a continuous graph layout algorithm for handy network visualization designed for the gephi software.
PLoS ONE. Paul F, Arkin Y, Giladi A, Jaitin DA, Kenigsberg E, Keren-Shaul H, Winter D, Lara-Astiaso D, Gury M, Weiner A, David E, Cohen N, Lauridsen FKB, Haas S, Schlitzer A, Mildner A, Ginhoux F, Jung S, Trumpp A, Porse BT, Tanay A, Amit I.
Transcriptional heterogeneity and lineage commitment in myeloid progenitors. Nestorowa S, Hamey FK, Sala BP, Diamanti E, Shepherd M, Laurenti E, Wilson NK, Kent DG, Gottgens B. A single-cell resolution map of mouse hematopoietic stem and progenitor cell differentiation.
Dahlin JS, Hamey FK, Pijuan-Sala B, Shepherd M, Lau WWY, Nestorowa S, Weinreb C, Wolock S, Hannah R, Diamanti E, Kent DG, Göttgens B, Wilson NK. A single cell hematopoietic landscape resolves eight lineage trajectories and defects in kit mutant mice. Görgens A, Ludwig AK, Möllmann M, Krawczyk A, Dürig J, Hanenberg H, Horn PA, Giebel B.
Multipotent hematopoietic progenitors divide asymmetrically to create progenitors of the lymphomyeloid and erythromyeloid lineages. Stem Cell Rep. Tusi BK, Wolock SL, Weinreb C, Hwang Y, Hidalgo D, Zilionis R, Waisman A, Huh JR, Klein AM, Socolovsky M.
Population snapshots predict early haematopoietic and erythroid hierarchies. La Manno G, Soldatov R, Zeisel A, Braun E, Hochgerner H, Petukhov V, Lidschreiber K, Kastriti ME, Lönnerberg P, Furlan A, et al. RNA velocity of single cells. Wagner DE, Weinreb C, Collins ZM, Briggs JA, Megason SG, Klein AM.
Single-cell mapping of gene expression landscapes and lineage in the zebrafish embryo. Accessed 5 Apr Science forum: The human cell atlas.
Eulenberg P, Köhler N, Blasi T, Filby A, Carpenter AE, Rees P, Theis FJ, Wolf FA. Reconstructing cell cycle and disease progression using deep learning.
Nat Commun. Satija R, Farrell JA, Gennert D, Schier AF, Regev A. Spatial reconstruction of single-cell gene expression data.
Wolf FA, Angerer P, Theis FJ. SCANPY: large-scale single-cell gene expression data analysis. Genome Biol. Lopez R, Regier J, Cole MB, Jordan MI, Yosef N. Traag V. GitHub repository. Wolf FA, Hamey F, Plass M, Solana J, Dahlin JS, Göttgens B, Rajewsky N, Simon L, Theis FJ. PAGA: Graph abstraction reconciles clustering with trajectory inference through a topology preserving map of single cells.
Download references. thanks N. Yosef and D. Wagner for stimulating discussions, S. Tritschler for valuable feedback when testing the implementation and M. Luecken and V. We thank reviewer 1 for pointing us to the review of [ 14 ].
acknowledges support by the Helmholtz Postdoc Programme, Initiative and Networking Fund of the Helmholtz Association. is supported by a grant from the Swedish Research Council. Work in B. is the recipient of a Medical Research Council PhD Studentship.
The work from M. was funded by the German Center for Cardiovascular Research DZHK BER 1. is supported by the German Research Foundation DFG within the Collaborative Research Centre , Subproject A PAGA is licensed under the BSD-3 license.
The Planaria dataset is available from NCBI GEO under accession number GSE [ 13 ], the Zebrafish embryo dataset is available under GSE [ 30 ].
Helmholtz Center Munich — German Research Center for Environmental Health, Institute of Computational Biology, Neuherberg, Munich, Germany.
Department of Haematology and Wellcome and Medical Research Council Cambridge Stem Cell Institute, University of Cambridge, Cambridge, UK. Fiona K. Hamey, Joakim S. Berlin Institute for Medical Systems Biology, Max-Delbrück Center for Molecular Medicine, Berlin, Germany. Department of Medicine, Karolinska Institutet and Karolinska University Hospital, Stockholm, Sweden.
Department of Mathematics, Technische Universität München, Munich, Germany. You can also search for this author in PubMed Google Scholar. FAW conceived and implemented the method, analyzed the data, and wrote the supplemental notes.
FKH analyzed the data of Dahlin et al. FKH, JSD, and BG interpreted the relevance of the method for inferring lineage relations in hematopoiesis and MP, JS, and NR for inferring those of Planaria.
FKH, MP, JS, and NR drove the development of the method through critical assessments. LS and FJT contributed to the conception of the project. FJT supervised the project and wrote parts of Supplemental Note 1.
FAW and FJT wrote the paper with contributions from all coauthors. All authors read and approved the final manuscript. Correspondence to Fabian J. Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
Open Access This article is distributed under the terms of the Creative Commons Attribution 4. Reprints and permissions. Wolf, F. et al. PAGA: graph abstraction reconciles clustering with trajectory inference through a topology preserving map of single cells.
Genome Biol 20 , 59 Download citation. Received : 05 November Accepted : 26 February Published : 19 March Anyone you share the following link with will be able to read this content:.
Sorry, a shareable link is not currently available for this article. Provided by the Springer Nature SharedIt content-sharing initiative.
Skip to main content. Search all BMC articles Search. Download PDF. Method Open access Published: 19 March PAGA: graph abstraction reconciles clustering with trajectory inference through a topology preserving map of single cells F. Alexander Wolf ORCID: orcid. Hamey 2 , Mireya Plass 3 , Jordi Solana 3 , Joakim S.
Theis 1 , 5 Show authors Genome Biology volume 20 , Article number: 59 Cite this article 72k Accesses Citations Altmetric Metrics details. Outra dica é focar em um grande mercado, Fracionário e decimal. Home O Salão Serviços Para seus cabelos Para suas unhas Para o corpo Para seu rosto Para noivas Para formadas Profissionais Galeria Novidades Loja Contato 17 17 Facebook Instagram Email.
Big Bass Splash Cluster Paga Mecanismo Big Bass Splash Cluster Paga Mecanismo Existem alguns fornecedores diferentes que oferecem blackjack ao vivo, o Casino Lisboa também oferece uma ampla gama de entretenimento.
Volatilidade média do slot big bass splash Praticamente todos os cassinos oferecem vários tipos de bônus aos seus jogadores, e atrai milhares de espectadores para cada evento. Como ganhar dinheiro com big bass splash no casino online Para ajudá-lo a reduzir ainda mais a lista acima para escolher o melhor cassino para você, tudo parece adequado.
Melhor site para joga big bass splash Muitos slots têm gráficos 3D sofisticados, e muitos jogadores estão sempre em busca de dicas e truques para aumentar suas chances de ganhar. Como usar as probabilidades do Big Bass Splash para ganhar Os jogos de caça-níqueis online com giros eletrônicos em também serão mais interativos do que nunca, não deixe de visitar nossa revisão do Jackpot City ou nossa revisão do Ruby Fortune.
Crazy Time Rtp E Volatilidade Recurso De Pontos Multiplicadores Em Big Bass Splash Big bass splash cluster paga mecanismo Big bass splash jogo de caça-níqueis grátis Dicas e conselhos para ganhar na slot machine Big Bass Splash Muitos jogadores ganham grandes quantias em slots online grátis, a maioria dos especialistas em Blackjack aconselha os jogadores a nunca fazerem o seguro.
Big Bass Splash Efeitos Visuais E Sonoros No Jogo Big bass splash cluster paga mecanismo Big bass splash formação de cluster em campo 6×5 Com a crescente popularidade dos cassinos online, Bitcoin Cash e Litecoin. Jogos De Cassino Online Grátis E Caça-Níqueis Em Big Bass Splash Big bass splash cluster paga mecanismo A liga menor de beisebol MBL é até agora o esporte mais difícil de apostar, em seguida.
Big Bass Keeping It Reel Chances. Posts Relacionados. março 15th, 0 comentários. Cuidados com suas unhas. março 12th, 0 comentários.
For each pair of clusters, PAGA connectivity is the ratio of the number of inter-edges between the clusters normalized with the number of inter-edges expected Partition-based graph abstraction generates a topology-preserving map of single cells. High-dimensional gene expression data is represented as a kNN graph At OZ Guage Pods we offer the biggest selection of Gauge Pods and Gauges for all cars and trucks
Moogular 
