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Duddu AS, Andreas E, Bv H, Grover K, Singh VR, Hari K, Jhunjhunwala S, Cummins B, Gedeon T, Jolly MK. Multistability and predominant hybrid phenotypes in a four node mutually repressive network of Th1/Th2/Th17/Treg differentiation. NPJ Syst Biol Appl 2024; 10:123. [PMID: 39448615 PMCID: PMC11502801 DOI: 10.1038/s41540-024-00433-6] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/15/2024] [Accepted: 09/01/2024] [Indexed: 10/26/2024] Open
Abstract
Elucidating the emergent dynamics of cellular differentiation networks is crucial to understanding cell-fate decisions. Toggle switch - a network of mutually repressive lineage-specific transcription factors A and B - enables two phenotypes from a common progenitor: (high A, low B) and (low A, high B). However, the dynamics of networks enabling differentiation of more than two phenotypes from a progenitor cell has not been well-studied. Here, we investigate the dynamics of a four-node network A, B, C, and D inhibiting each other, forming a toggle tetrahedron. Our simulations show that this network is multistable and predominantly allows for the co-existence of six hybrid phenotypes where two of the nodes are expressed relatively high as compared to the remaining two, for instance (high A, high B, low C, low D). Finally, we apply our results to understand naïve CD4+ T cell differentiation into Th1, Th2, Th17 and Treg subsets, suggesting Th1/Th2/Th17/Treg decision-making to be a two-step process.
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Affiliation(s)
| | - Elizabeth Andreas
- Department of Mathematical Sciences, Montana State University, Bozeman, MT, 59717, USA
| | - Harshavardhan Bv
- Department of Bioengineering, Indian Institute of Science, Bangalore, 560012, India
- IISc Mathematics Initiative, Indian Institute of Science, 560012, Bangalore, India
| | - Kaushal Grover
- School of Computational and Integrative Sciences, Jawaharlal Nehru University, New Delhi, 110067, India
| | - Vivek Raj Singh
- Undergraduate Program, Indian Institute of Science, Bangalore, 560012, India
| | - Kishore Hari
- Department of Bioengineering, Indian Institute of Science, Bangalore, 560012, India
- Department of Physics, Northeastern University, MA, 02115, Boston, USA
- Center for Theoretical Biological Physics, Northeastern University, MA, 02115, Boston, USA
| | | | - Breschine Cummins
- Department of Mathematical Sciences, Montana State University, Bozeman, MT, 59717, USA.
| | - Tomas Gedeon
- Department of Mathematical Sciences, Montana State University, Bozeman, MT, 59717, USA.
| | - Mohit Kumar Jolly
- Department of Bioengineering, Indian Institute of Science, Bangalore, 560012, India.
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Barcenas M, Bocci F, Nie Q. Tipping points in epithelial-mesenchymal lineages from single-cell transcriptomics data. Biophys J 2024; 123:2849-2859. [PMID: 38504523 PMCID: PMC11393678 DOI: 10.1016/j.bpj.2024.03.021] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/11/2023] [Revised: 02/09/2024] [Accepted: 03/15/2024] [Indexed: 03/21/2024] Open
Abstract
Understanding cell fate decision-making during complex biological processes is an open challenge that is now aided by high-resolution single-cell sequencing technologies. Specifically, it remains challenging to identify and characterize transition states corresponding to "tipping points" whereby cells commit to new cell states. Here, we present a computational method that takes advantage of single-cell transcriptomics data to infer the stability and gene regulatory networks (GRNs) along cell lineages. Our method uses the unspliced and spliced counts from single-cell RNA sequencing data and cell ordering along lineage trajectories to train an RNA splicing multivariate model, from which cell-state stability along the lineage is inferred based on spectral analysis of the model's Jacobian matrix. Moreover, the model infers the RNA cross-species interactions resulting in GRNs and their variation along the cell lineage. When applied to epithelial-mesenchymal transition in ovarian and lung cancer-derived cell lines, our model predicts a saddle-node transition between the epithelial and mesenchymal states passing through an unstable, intermediate cell state. Furthermore, we show that the underlying GRN controlling epithelial-mesenchymal transition rearranges during the transition, resulting in denser and less modular networks in the intermediate state. Overall, our method represents a flexible tool to study cell lineages with a combination of theory-driven modeling and single-cell transcriptomics data.
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Affiliation(s)
- Manuel Barcenas
- Department of Mathematics, University of California Irvine, Irvine, California
| | - Federico Bocci
- Department of Mathematics, University of California Irvine, Irvine, California; NSF-Simons Center for Multiscale Cell Fate Research, University of California Irvine, Irvine, California.
| | - Qing Nie
- Department of Mathematics, University of California Irvine, Irvine, California; NSF-Simons Center for Multiscale Cell Fate Research, University of California Irvine, Irvine, California.
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Damaser MS, Valentini FA, Clavica F, Giarenis I. Is the time right for a new initiative in mathematical modeling of the lower urinary tract? ICI-RS 2023. Neurourol Urodyn 2024; 43:1303-1310. [PMID: 38149773 DOI: 10.1002/nau.25362] [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: 11/29/2023] [Accepted: 12/01/2023] [Indexed: 12/28/2023]
Abstract
INTRODUCTION A session at the 2023 International Consultation on Incontinence - Research Society (ICI-RS) held in Bristol, UK, focused on the question: Is the time right for a new initiative in mathematical modeling of the lower urinary tract (LUT)? The LUT is a complex system, comprising various synergetic components (i.e., bladder, urethra, neural control), each with its own dynamic functioning and high interindividual variability. This has led to a variety of different types of models for different purposes, each with advantages and disadvantages. METHODS When addressing the LUT, the modeling approach should be selected and sized according to the specific purpose, the targeted level of detail, and the available computational resources. Four areas were selected as examples to discuss: utility of nomograms in clinical use, value of fluid mechanical modeling, applications of models to simplify urodynamics, and utility of statistical models. RESULTS A brief literature review is provided along with discussion of the merits of different types of models for different applications. Remaining research questions are provided. CONCLUSIONS Inadequacies in current (outdated) models of the LUT as well as recent advances in computing power (e.g., quantum computing) and methods (e.g., artificial intelligence/machine learning), would dictate that the answer is an emphatic "Yes, the time is right for a new initiative in mathematical modeling of the LUT."
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Affiliation(s)
- Margot S Damaser
- Department of Biomedical Engineering, Lerner Research Institute, Cleveland Clinic, Cleveland, Ohio, USA
- Advanced Platform Technology Center, Louis Stokes Cleveland Department of Veterans Affairs Medical Center, Cleveland, Ohio, USA
| | - Françoise A Valentini
- Physical Medicine and Rehabilitation Department, Rothschild Hospital, Sorbonne Université, Paris, France
| | - Francesco Clavica
- ARTORG Center for Biomedical Engineering Research, University of Bern, Bern, Switzerland
- Department of Urology, Inselspital, Bern University Hospital, University of Bern, Bern, Switzerland
| | - Ilias Giarenis
- Department of UroGynaecology, Norfolk and Norwich University Hospital, Norwich, UK
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Zhou P, Bocci F, Li T, Nie Q. Spatial transition tensor of single cells. Nat Methods 2024; 21:1053-1062. [PMID: 38755322 PMCID: PMC11166574 DOI: 10.1038/s41592-024-02266-x] [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: 07/03/2023] [Accepted: 04/02/2024] [Indexed: 05/18/2024]
Abstract
Spatial transcriptomics and messenger RNA splicing encode extensive spatiotemporal information for cell states and transitions. The current lineage-inference methods either lack spatial dynamics for state transition or cannot capture different dynamics associated with multiple cell states and transition paths. Here we present spatial transition tensor (STT), a method that uses messenger RNA splicing and spatial transcriptomes through a multiscale dynamical model to characterize multistability in space. By learning a four-dimensional transition tensor and spatial-constrained random walk, STT reconstructs cell-state-specific dynamics and spatial state transitions via both short-time local tensor streamlines between cells and long-time transition paths among attractors. Benchmarking and applications of STT on several transcriptome datasets via multiple technologies on epithelial-mesenchymal transitions, blood development, spatially resolved mouse brain and chicken heart development, indicate STT's capability in recovering cell-state-specific dynamics and their associated genes not seen using existing methods. Overall, STT provides a consistent multiscale description of single-cell transcriptome data across multiple spatiotemporal scales.
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Affiliation(s)
- Peijie Zhou
- Department of Mathematics, University of California, Irvine, Irvine, CA, USA
- Center for Machine Learning Research, Peking University, Beijing, China
- AI for Science Institute, Beijing, China
- National Engineering Laboratory for Big Data Analysis and Applications, Beijing, China
| | - Federico Bocci
- Department of Mathematics, University of California, Irvine, Irvine, CA, USA
| | - Tiejun Li
- LMAM and School of Mathematical Sciences, Peking University, Beijing, China
| | - Qing Nie
- Department of Mathematics, University of California, Irvine, Irvine, CA, USA.
- Department of Cell and Developmental Biology, University of California, Irvine, Irvine, CA, USA.
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Krause AL, Gaffney EA, Jewell TJ, Klika V, Walker BJ. Turing Instabilities are Not Enough to Ensure Pattern Formation. Bull Math Biol 2024; 86:21. [PMID: 38253936 PMCID: PMC10803432 DOI: 10.1007/s11538-023-01250-4] [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: 11/10/2023] [Accepted: 12/22/2023] [Indexed: 01/24/2024]
Abstract
Symmetry-breaking instabilities play an important role in understanding the mechanisms underlying the diversity of patterns observed in nature, such as in Turing's reaction-diffusion theory, which connects cellular signalling and transport with the development of growth and form. Extensive literature focuses on the linear stability analysis of homogeneous equilibria in these systems, culminating in a set of conditions for transport-driven instabilities that are commonly presumed to initiate self-organisation. We demonstrate that a selection of simple, canonical transport models with only mild multistable non-linearities can satisfy the Turing instability conditions while also robustly exhibiting only transient patterns. Hence, a Turing-like instability is insufficient for the existence of a patterned state. While it is known that linear theory can fail to predict the formation of patterns, we demonstrate that such failures can appear robustly in systems with multiple stable homogeneous equilibria. Given that biological systems such as gene regulatory networks and spatially distributed ecosystems often exhibit a high degree of multistability and nonlinearity, this raises important questions of how to analyse prospective mechanisms for self-organisation.
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Affiliation(s)
- Andrew L Krause
- Department of Mathematical Sciences, Durham University, Upper Mountjoy Campus, Stockton Road, Durham, DH1 3LE, UK.
| | - Eamonn A Gaffney
- Wolfson Centre for Mathematical Biology, Mathematical Institute, University of Oxford, Oxford, OX2 6GG, UK
| | - Thomas Jun Jewell
- Wolfson Centre for Mathematical Biology, Mathematical Institute, University of Oxford, Oxford, OX2 6GG, UK
| | - Václav Klika
- Department of Mathematics, FNSPE, Czech Technical University in Prague, Trojanova 13, 120 00, Prague, Czech Republic
| | - Benjamin J Walker
- Department of Mathematical Sciences, University of Bath, Bath, BA2 7AY, UK
- Department of Mathematics, University College London, London, WC1E 6BT, UK
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