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Tan ZC, Meyer AS. The structure is the message: Preserving experimental context through tensor decomposition. Cell Syst 2024; 15:679-693. [PMID: 39173584 PMCID: PMC11366223 DOI: 10.1016/j.cels.2024.07.004] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/03/2024] [Revised: 06/25/2024] [Accepted: 07/22/2024] [Indexed: 08/24/2024]
Abstract
Recent biological studies have been revolutionized in scale and granularity by multiplex and high-throughput assays. Profiling cell responses across several experimental parameters, such as perturbations, time, and genetic contexts, leads to richer and more generalizable findings. However, these multidimensional datasets necessitate a reevaluation of the conventional methods for their representation and analysis. Traditionally, experimental parameters are merged to flatten the data into a two-dimensional matrix, sacrificing crucial experiment context reflected by the structure. As Marshall McLuhan famously stated, "the medium is the message." In this work, we propose that the experiment structure is the medium in which subsequent analysis is performed, and the optimal choice of data representation must reflect the experiment structure. We review how tensor-structured analyses and decompositions can preserve this information. We contend that tensor methods are poised to become integral to the biomedical data sciences toolkit.
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Affiliation(s)
- Zhixin Cyrillus Tan
- Bioinformatics Interdepartmental Program, University of California, Los Angeles (UCLA), Los Angeles, CA, USA.
| | - Aaron S Meyer
- Bioinformatics Interdepartmental Program, University of California, Los Angeles (UCLA), Los Angeles, CA, USA; Department of Bioengineering, UCLA, Los Angeles, CA, USA; Jonsson Comprehensive Cancer Center, UCLA, Los Angeles, CA, USA; Eli and Edythe Broad Center of Regenerative Medicine and Stem Cell Research, UCLA, Los Angeles, CA, USA.
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2
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Ramirez A, Orcutt-Jahns BT, Pascoe S, Abraham A, Remigio B, Thomas N, Meyer AS. Integrative, high-resolution analysis of single cells across experimental conditions with PARAFAC2. BIORXIV : THE PREPRINT SERVER FOR BIOLOGY 2024:2024.07.29.605698. [PMID: 39131377 PMCID: PMC11312543 DOI: 10.1101/2024.07.29.605698] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 08/13/2024]
Abstract
Effective tools for exploration and analysis are needed to extract insights from large-scale single-cell measurement data. However, current techniques for handling single-cell studies performed across experimental conditions (e.g., samples, perturbations, or patients) require restrictive assumptions, lack flexibility, or do not adequately deconvolute condition-to-condition variation from cell-to-cell variation. Here, we report that the tensor decomposition method PARAFAC2 (Pf2) enables the dimensionality reduction of single-cell data across conditions. We demonstrate these benefits across two distinct contexts of single-cell RNA-sequencing (scRNA-seq) experiments of peripheral immune cells: pharmacologic drug perturbations and systemic lupus erythematosus (SLE) patient samples. By isolating relevant gene modules across cells and conditions, Pf2 enables straightforward associations of gene variation patterns across specific patients or perturbations while connecting each coordinated change to certain cells without pre-defining cell types. The theoretical grounding of Pf2 suggests a unified framework for many modeling tasks associated with single-cell data. Thus, Pf2 provides an intuitive universal dimensionality reduction approach for multi-sample single-cell studies across diverse biological contexts.
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Affiliation(s)
- Andrew Ramirez
- Department of Bioengineering, University of California, Los Angeles (UCLA), CA, USA
| | | | - Sean Pascoe
- Department of Bioengineering, University of California, Los Angeles (UCLA), CA, USA
- Department of Molecular Biosciences, Northwestern University, Evanston, IL, USA
| | - Armaan Abraham
- Department of Bioengineering, University of California, Los Angeles (UCLA), CA, USA
| | | | | | - Aaron S. Meyer
- Department of Bioengineering, University of California, Los Angeles (UCLA), CA, USA
- Jonsson Comprehensive Cancer Center, UCLA, CA, USA
- Eli and Edythe Broad Center of Regenerative Medicine and Stem Cell Research, UCLA, CA, USA
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Hung EC, Hodzic E, Tan ZC, Meyer AS. Censored Least Squares for Imputing Missing Values in PARAFAC Tensor Factorization. BIORXIV : THE PREPRINT SERVER FOR BIOLOGY 2024:2024.07.05.602272. [PMID: 39026852 PMCID: PMC11257416 DOI: 10.1101/2024.07.05.602272] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 07/20/2024]
Abstract
Tensor factorization is a dimensionality reduction method applied to multidimensional arrays. These methods are useful for identifying patterns within a variety of biomedical datasets due to their ability to preserve the organizational structure of experiments and therefore aid in generating meaningful insights. However, missing data in the datasets being analyzed can impose challenges. Tensor factorization can be performed with some level of missing data and reconstruct a complete tensor. However, while tensor methods may impute these missing values, the choice of fitting algorithm may influence the fidelity of these imputations. Previous approaches, based on alternating least squares with prefilled values or direct optimization, suffer from introduced bias or slow computational performance. In this study, we propose that censored least squares can better handle missing values with data structured in tensor form. We ran censored least squares on four different biological datasets and compared its performance against alternating least squares with prefilled values and direct optimization. We used the error of imputation and the ability to infer masked values to benchmark their missing data performance. Censored least squares appeared best suited for the analysis of high-dimensional biological data by accuracy and convergence metrics across several studies.
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Affiliation(s)
- Ethan C Hung
- Computational and Systems Biology, University of California, Los Angeles (UCLA), USA
| | | | | | - Aaron S Meyer
- Department of Bioengineering, UCLA, USA
- Jonsson Comprehensive Cancer Center, UCLA, USA
- Eli and Edythe Broad Center of Regenerative Medicine and Stem Cell Research, UCLA, USA
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Muñoz-Lasso DC, Mollá B, Sáenz-Gamboa JJ, Insuasty E, de la Iglesia-Vaya M, Pook MA, Pallardó FV, Palau F, Gonzalez-Cabo P. Frataxin Deficit Leads to Reduced Dynamics of Growth Cones in Dorsal Root Ganglia Neurons of Friedreich’s Ataxia YG8sR Model: A Multilinear Algebra Approach. Front Mol Neurosci 2022; 15:912780. [PMID: 35769335 PMCID: PMC9236133 DOI: 10.3389/fnmol.2022.912780] [Citation(s) in RCA: 2] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/04/2022] [Accepted: 05/17/2022] [Indexed: 11/14/2022] Open
Abstract
Computational techniques for analyzing biological images offer a great potential to enhance our knowledge of the biological processes underlying disorders of the nervous system. Friedreich’s Ataxia (FRDA) is a rare progressive neurodegenerative inherited disorder caused by the low expression of frataxin, which is a small mitochondrial protein. In FRDA cells, the lack of frataxin promotes primarily mitochondrial dysfunction, an alteration of calcium (Ca2+) homeostasis and the destabilization of the actin cytoskeleton in the neurites and growth cones of sensory neurons. In this paper, a computational multilinear algebra approach was used to analyze the dynamics of the growth cone and its function in control and FRDA neurons. Computational approach, which includes principal component analysis and a multilinear algebra method, is used to quantify the dynamics of the growth cone (GC) morphology of sensory neurons from the dorsal root ganglia (DRG) of the YG8sR humanized murine model for FRDA. It was confirmed that the dynamics and patterns of turning were aberrant in the FRDA growth cones. In addition, our data suggest that other cellular processes dependent on functional GCs such as axonal regeneration might also be affected. Semiautomated computational approaches are presented to quantify differences in GC behaviors in neurodegenerative disease. In summary, the deficiency of frataxin has an adverse effect on the formation and, most importantly, the growth cones’ function in adult DRG neurons. As a result, frataxin deficient DRG neurons might lose the intrinsic capability to grow and regenerate axons properly due to the dysfunctional GCs they build.
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Affiliation(s)
- Diana C. Muñoz-Lasso
- Chemical Biology Group, Department of Biomedical Engineering, Eindhoven University of Technology (TU/e), Eindhoven, Netherlands
| | - Belén Mollá
- Department of Genetics, Faculty of Biological Sciences, University of Valencia, Valencia, Spain
- CIBER de Enfermedades Raras (CIBERER), Valencia, Spain
| | - Jhon J. Sáenz-Gamboa
- Brain Connectivity Laboratory, Joint Unit FISABIO & Prince Felipe Research Centre (CIPF), Valencia, Spain
- Regional Ministry of Health in Valencia, Hospital Sagunto (CEIB-CSUSP), Valencia, Spain
- CIBER de Salud Mental (CIBERSAM), Valencia, Spain
| | | | - Maria de la Iglesia-Vaya
- Brain Connectivity Laboratory, Joint Unit FISABIO & Prince Felipe Research Centre (CIPF), Valencia, Spain
- Regional Ministry of Health in Valencia, Hospital Sagunto (CEIB-CSUSP), Valencia, Spain
- CIBER de Salud Mental (CIBERSAM), Valencia, Spain
| | - Mark A. Pook
- Biosciences, Brunel University London, Uxbridge, United Kingdom
| | - Federico V. Pallardó
- CIBER de Enfermedades Raras (CIBERER), Valencia, Spain
- Department of Physiology, Faculty of Medicine and Dentistry, University of Valencia, Valencia, Spain
- Biomedical Research Institute INCLIVA, Valencia, Spain
| | - Francesc Palau
- CIBER de Enfermedades Raras (CIBERER), Valencia, Spain
- Department of Genetic and Molecular Medicine IPER, Institut de Recerca Sant Joan de Déu, Hospital Sant Joan de Déu, Barcelona, Spain
- Division of Pediatrics, University of Barcelona School of Medicine and Health Sciences, Barcelona, Spain
| | - Pilar Gonzalez-Cabo
- CIBER de Enfermedades Raras (CIBERER), Valencia, Spain
- Department of Physiology, Faculty of Medicine and Dentistry, University of Valencia, Valencia, Spain
- Biomedical Research Institute INCLIVA, Valencia, Spain
- *Correspondence: Pilar Gonzalez-Cabo,
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Roy SS, Taguchi YH. Identification of genes associated with altered gene expression and m6A profiles during hypoxia using tensor decomposition based unsupervised feature extraction. Sci Rep 2021; 11:8909. [PMID: 33903618 PMCID: PMC8076323 DOI: 10.1038/s41598-021-87779-7] [Citation(s) in RCA: 5] [Impact Index Per Article: 1.7] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/09/2021] [Accepted: 04/05/2021] [Indexed: 11/09/2022] Open
Abstract
Although hypoxia is a critical factor that can drive the progression of various diseases, the mechanism underlying hypoxia itself remains unclear. Recently, m6A has been proposed as an important factor driving hypoxia. Despite successful analyses, potential genes were not selected with statistical significance but were selected based solely on fold changes. Because the number of genes is large while the number of samples is small, it was impossible to select genes using conventional feature selection methods with statistical significance. In this study, we applied the recently proposed principal component analysis (PCA), tensor decomposition (TD), and kernel tensor decomposition (KTD)-based unsupervised feature extraction (FE) to a hypoxia data set. We found that PCA, TD, and KTD-based unsupervised FE could successfully identify a limited number of genes associated with altered gene expression and m6A profiles, as well as the enrichment of hypoxia-related biological terms, with improved statistical significance.
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Affiliation(s)
- Sanjiban Sekhar Roy
- School of Computer Science and Engineering, Vellore Institute of Technology, Vellore, India
| | - Y-H Taguchi
- Department of Physics, Chuo University, Tokyo, 112-8551, Japan.
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