Visualizing structure and transitions in high-dimensional biological data

Moon, Kevin R.; Dijk, David van; Wang, Zheng; Gigante, Scott; Burkhardt, Daniel; Chen, William S.; Yim, Kristina; Elzen, Antonia van den; Hirn, Matthew; Coifman, Ronald R.; Ivanovа, Natalia; Wolf, Guy; Krishnaswamy, Smita

doi:10.1038/s41587-019-0336-3

Cited by 659 publications

(738 citation statements)

References 73 publications

(99 reference statements)

Supporting

Mentioning

730

Contrasting

Unclassified

Order By: Relevance

“…To visualize the DC tree we adapted M-PHATE and PHATE 30,88 to generate C-PHATE (for Condensation PHATE). At each DC time point, we extracted the intratimepoint kernel K, an n x n matrix that denotes affinities between each of n points.…”

Section: C-phate Visualization Of Electron Micrographs Of the Nerve Rmentioning

confidence: 99%

“…Different from M-PHATE, however, points that are assigned to the same cluster in successive iterations are also connected with a weight in the multi-timepoint kernel. This multitimepoint kernel is plotted via the PHATE algorithm 30 to reveal the hierarchical structure created by DC and to visualize both the dynamics of the condensation process as well as the relationship to one another at all levels of the hierarchy.…”

Section: C-phate Visualization Of Electron Micrographs Of the Nerve Rmentioning

confidence: 99%

See 1 more Smart Citation

Structural and developmental principles of neuropil assembly inC. elegans

Moyle

Barnes

Kuchroo

et al. 2020

Preprint

Self Cite

View full text Add to dashboard Cite

To visualize DC cluster relationships we developed C-PHATE, an extension of PHATE 30 capable of generating a 3D representation of the multigranular structures in the DC hierarchical tree ( Fig. 1a,b; see Methods). Quantitative comparisons of DC/C-PHATE results revealed similar clustering behaviors between the two separately analyzed nervering reconstructions (Adjusted Rand Index (ARI) of 0.7; Extended Data Fig. 1a,b), consistent with the long-accepted qualitative descriptions of the stereotyped structure for the C. elegans nerve ring 3,31 , and recent analyses of neurite adjacencies 22 . Examination of the cluster patterns through the iterations of DC revealed known cell-cell interactions and behavioral circuits ( Fig. 1b,c; Extended Data Fig. 2a,b; [32][33][34][35][36][37][38][39] ), consistent with behavioral and connectomic studies 10,19,20 . The multigranular outputs of the DC/C-PHATE results enabled understanding of the cell-cell interactions within the context of functional circuits, and the functional circuits within the context of the larger bundles of the neuropil.Comparisons of the modularity score, a measure of cluster robustness 40,41 , was highest when the majority of neurites were grouped into four super-clusters ( Fig. 1b; Extended Data Fig. 1a,b; Supplemental Video 1,2; see Methods). Overlaying our analysis of these four super-clusters (see Methods) onto the anatomy of the nerve ring revealed that they correspond to four distinct and tightly grouped bundles within the greater neuropil, circling the pharynx isthmus and stacked along the anterior-posterior axis of the animal. These clusters are herein called S1, S2, S3 and S4 for Stratum 1 etc. (Fig. 1c; Extended Data Fig. 1c-h; Supplemental Video 3 show details of these structures and single-cell identities). The stratified organization of the nerve ring neuropil, resolved here at single neurite level, is reminiscent of laminar organizations in the Drosophila nervous system 42,43 , and in the vertebrate retina and the brain cortex 44,45 .We observed that not all computationally clustered neurites followed simple bundled paths through the neuropil. In Strata 1 (S1), 32 anterior sensory neurons project perpendicular to the nerve ring bundle before making a 180º curl and returning to the anterior limits of the neuropil, where they terminate as synaptic endplates (Fig. 1d; Extended Data Fig. 3a-d; 3,46 ). These uniquely shaped S1 neurons looped at the borders of the S2/S3/S4 bundles. The anterior loops encase ~90% of S2, and the posterior loops encase ~84% of S3 and 100% of S4 ( Fig. 1d-g; Extended Data Fig. 3e-k ; SupplementalVideo 5; Supplemental Table 1). We found that the 32 axons form a six-fold symmetrical honeycomb structure along the neuropil's arc, creating a scaffold that encapsulates the different strata ( Fig. 1g; Extended Data Fig. 3e-h; Supplemental Video 4).The architecture of the neuropil reflects functional segregation of distinct sensory information streams and motor outputs.C. elegans neurons can be divided into three categories ...

show abstract

Section: C-phate Visualization Of Electron Micrographs Of the Nerve Rmentioning

confidence: 99%

Section: C-phate Visualization Of Electron Micrographs Of the Nerve Rmentioning

confidence: 99%

Structural and developmental principles of neuropil assembly inC. elegans

Moyle

Barnes

Kuchroo

et al. 2020

Preprint

Self Cite

View full text Add to dashboard Cite

show abstract

“…To test if the total MLI trajectory can be resolved by other trajectory inference algorithms, we applied a parallel approach using PHATE. PHATE was developed for visualization of branching data structures, with preservation of both local and global similarities (Moon et al 2019). The PHATE-generated trajectory ordered the MLI reconstructions along a linear arrangement that reflected a pseudo-temporal gradient ( Figure 7D), and was confirmed by our expertdirected staging metric ( Figure 7E).…”

Section: Trajectory Inference By Phate Reveals the Early Emergence Ofmentioning

confidence: 99%

Morphological pseudotime ordering and fate mapping reveals diversification of cerebellar inhibitory interneurons

Wang

Lefebvre

2020

Preprint

View full text Add to dashboard Cite

Understanding how diverse neurons are assembled into circuits requires a framework for describing cell types and their developmental trajectories. Here, we combined genetic fate mapping and pseudo-temporal profiling to resolve the diversification of cerebellar inhibitory interneurons based on morphology. The molecular layer interneurons (MLIs) derive from a common progenitor but comprise a diverse population of dendritic-, somatic-, and axon initial segment-targeting interneurons. MLIs are classically divided into two types. However, their morphological heterogeneity suggests an alternate model of one continuously varying population. Through clustering and trajectory inference of 811 MLI reconstructions at maturity and during development, we show that MLIs divide into two discrete classes but also present significant within-class heterogeneity. Pseudotime trajectory mapping uncovered the emergence of distinct phenotypes during migration and axonogenesis, well before neurons reach their final positions. Our study illustrates the utility of quantitative single-cell methods to morphology for defining the diversification of neuronal subtypes. Figure 2. Morphological heterogeneity among MLIs. (A) Left: Immunostaining of MLIs (Parvalbumin, cyan) and PCs (co-labeled by Parvalbumin and Calbindin, cyan and red, respectively) show the ML space in which MLIs reside. PC somata are enveloped by BC axons (white arrowhead). Right: Inverted image of four fluorescently-labelled MLIs. The lower MLI (pink arrowhead) has canonical BC morphologies, including axonal basket terminals around the PC somata (asterisks). The two upper MLIs (teal arrowhead) have canonical SC morphologies and reside within the upper ML. The faintly labelled MLI (blue arrowhead) has SC morphologies but reside within the lower ML. (B) Reconstruction of canonical BC from panel A, with complete dendritic arbor traced in orange, and complete axonal arbor traced in blue. (C) Reconstruction of canonical SC from panel A (cell on far right). (D-F) Representative images of MLIs with mixtures of BC and SC characteristics. Top: inverted fluorescence image; Bottom: reconstruction with dendritic (orange) and axonal (blue) traces. (D) MLI located in the middle ML with SC dendritic features, and a long horizontal axon (arrow) with descending basket collaterals (asterisks). (E) MLI located in the lower ML with SC-like dendritic and axonal arbors. (F) MLI located in the upper ML with a long horizontal axon (arrow) and two descending axon collaterals with basket formations around PC somas (asterisks). All scale bars are 50 μm.

show abstract

“…For example, scRNA-seq profiling of the adult mouse nervous system uncovers new cell classes and types across regions, providing a clearer picture of cell diversity by region and a reference atlas for studying the mammalian nervous system [3]. There are several machine learning algorithms developed to analyze the single-cell gene expression matrix [4], including visualization [5], imputation [6], data integration [7] and prediction of perturbation responses [8].…”

Section: Introductionmentioning

confidence: 99%

“…We present a novel perspective to integrate scRNA-seq expression data. 4. We demonstrate that Transformers [20] can be used for general sparse and high-dimensionality data by visualizing the embedding results.…”

mentioning

confidence: 99%

Multitask learning for Transformers with application to large-scale single-cell transcriptomes

Pang

Tegnér

2020

Preprint

View full text Add to dashboard Cite

Recent progress in machine learning provides competitive methods for bioinformatics in many traditional topics, such as transcriptomes sequence and single-cell analysis. However, discovering biomedical correlation of cells that are present across large-scale data sets remains challenging. Our attention-based neural network module with 300 million parameters is able to capture biological knowledge in a data-driven way. The module contains high-quality embedding, taxonomy analysis and similarity measurement. We tested the model on Mouse Brain Atlas, which consists of 160,000 cells and 25,000 genes. Our module obtained some interesting findings that have been verified by biologists and got better performance when benchmarked against autoencoder and principal components analysis.

show abstract

Visualizing structure and transitions in high-dimensional biological data

Cited by 659 publications

References 73 publications

Structural and developmental principles of neuropil assembly inC. elegans

Structural and developmental principles of neuropil assembly inC. elegans

Morphological pseudotime ordering and fate mapping reveals diversification of cerebellar inhibitory interneurons

Multitask learning for Transformers with application to large-scale single-cell transcriptomes

Contact Info

Product

Resources

About