Probabilistic PCA of censored data: accounting for uncertainties in the visualization of high-throughput single-cell qPCR data
Open accessAbstract
Motivation: High-throughput single-cell quantitative real-time polymerase chain reaction (qPCR) is a promising technique allowing for new insights in complex cellular processes. However, the PCR reaction can be detected only up to a certain detection limit, whereas failed reactions could be due to low or absent expression, and the true expression level is unknown. Because this censoring can occur for high proportions of the data, it is one of the main challenges when dealing with single-cell qPCR data. Principal component analysis (PCA) is an important tool for visualizing the structure of high-dimensional data as well as for identifying subpopulations of cells. However, to date it is not clear how to perform a PCA of censored data. We present a probabilistic approach that accounts for the censoring and evaluate it for two typical datasets containing single-cell qPCR data. Results: We use the Gaussian process latent variable model framework to account for censoring by introducing an appropriate noise model and allowing a different kernel for each dimension. We evaluate this new approach for two typical qPCR datasets (of mouse embryonic stem cells and blood stem/progenitor cells, respectively) by performing linear and non-linear probabilistic PCA. Taking the censoring into account results in a 2D representation of the data, which better reflects its known structure: in both datasets, our new approach results in a better separation of known cell types and is able to reveal subpopulations in one dataset that could not be resolved using standard PCA. Availability and implementation: The implementation was based on the existing Gaussian process latent variable model toolbox ( https://github.com/SheffieldML/GPmat ); extensions for noise models and kernels accounting for censoring are available at http://icb.helmholtz-muenchen.de/censgplvm . Contact: fbuettner.phys@gmail.com Supplementary information: Supplementary data are available at Bioinformatics online.
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Some facets of cellular identity are transient in time and space, and temporal processes may progress along trajectories, oscillate, or be influenced by spatial position.
“First, in contexts such as development and physiology, some facets of cellular identity are transient in time and space. Temporal processes may, for example, progress along one or more trajectories (e.g., differentiation); oscillate continuously between cellular states (e.g., the cell cycle98,99 or circadian rhythm100); or be influenced by the physical position and neighborhood of the cell71,93.”
From Revealing the vectors of cellular identity with single-cell genomics (2016) · cites this paper as [93]
The number of required landmarks is related to spatial complexity, introducing the notion of power to detect spatial patterns.
“The number of required landmarks is related to this spatial complexity, introducing the notion of power to detect spatial patterns93.”
From Revealing the vectors of cellular identity with single-cell genomics (2016) · cites this paper as [93]
Canonical structure is likely in most normal tissues (e.g., brain structures) and physiological processes (e.g., embryogenesis).
“While this is a likely situation in most normal tissues (e.g., brain structures71) and physiological processes (e.g., embryogenesis93)”
From Revealing the vectors of cellular identity with single-cell genomics (2016) · cites this paper as [93]
Seurat and a method by Achim et al. combine limited spatial cues for landmark genes with scRNA-seq from dissociated tissue to infer the spatial location of dissociated cells.
“This has inspired the development of two methods, Seurat (A.R. and colleagues)93 and a method by Achim et al.71 that combine limited spatial cues for landmark genes with single-cell RNA-seq of cells from the same type of dissociated tissue to infer the spatial location of the dissociated cells through the patterns reflected by the landmark genes.”
From Revealing the vectors of cellular identity with single-cell genomics (2016) · cites this paper as [93]
Even without new experimental methods, computational techniques can help relate distinct data types across single cells, as was effectively shown for relating spatially resolved in situ hybridization data to scRNA-seq to derive a spatial mapping of cells to positions.
“Even without new experimental methods, computational techniques can help relate distinct data types across single cells, as was effectively shown for relating spatially resolved in situ hybridization data to scRNA-seq to derive a spatial mapping of cells to positions71,93.”
From Revealing the vectors of cellular identity with single-cell genomics (2016) · cites this paper as [93]
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- Authors
- Buettner, F., Moignard, V., Göttgens, B., & Theis, F. J.
- Affiliations
- Wellcome/MRC Cambridge Stem Cell Institute (GB)
- Corresponding author
- Buettner, Florian
- Venue
- Bioinformatics
- Publisher
- Oxford University Press (OUP)
- Published
- 2014-03-10
- Volume
- 30
- Issue
- 13
- Pages
- 1867-1875
- ISSN
- 1367-4803 (ISSN-L)
- 1367-4811
- PMC
- PMC4071202
- OpenAlex
- W2146462627
- Cited by
- 21
- References
- 31
- Citations by year
- 2026: 1 · 2023: 2 · 2020: 5 · 2018: 1 · 2017: 3 · 2016: 4 · 2015: 5
- FWCI
- 1.64
- Type
- journal article
- Language
- en
- Open access
- hybrid
- doi.org
- Locations
- Bioinformatics (publishedVersion, cc-by)
- Europe PMC (PubMed Central) (publishedVersion, cc-by)
- PubMed Central (publishedVersion, cc-by)
- PubMed (publishedVersion)
- Site cant be reached (submittedVersion)
- Funders
- Cancer Research UK (12765)
- Leukaemia and Lymphoma Research
- National Centre for the Replacement, Refinement and Reduction of Animals in Research (G0900729/1)
- Directorate for Biological Sciences
- Medical Research Council (MC_PC_12009)
- Biotechnology and Biological Sciences Research Council (BB/I00050X/1)
- Topics
- Life Sciences › Biochemistry, Genetics and Molecular Biology › Molecular Biology › Single-cell and spatial transcriptomics
- Life Sciences › Biochemistry, Genetics and Molecular Biology › Molecular Biology › Gene expression and cancer classification
- Physical Sciences › Computer Science › Artificial Intelligence › Gaussian Processes and Bayesian Inference
- Keywords
- probabilistic PCA, censored data, single-cell qPCR, Gaussian process latent variable model, detection limit, noise models, kernel selection, high-dimensional data visualization, cell subpopulations, mouse embryonic stem cells
- MeSH terms
- Animals, Probability, Software, Stem Cells, Principal Component Analysis, Mice, Real-Time Polymerase Chain Reaction
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