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Multi-Cell ECM compaction is predictable via superposition of nonlinear cell dynamics linearized in augmented state space

Mayalu, Michaëlle N. and Kim, Min-Cheol and Asada, Harry (2019) Multi-Cell ECM compaction is predictable via superposition of nonlinear cell dynamics linearized in augmented state space. PLoS Computational Biology, 15 (9). Art. No. e1006798. ISSN 1553-734X. PMCID PMC6774565. https://resolver.caltech.edu/CaltechAUTHORS:20190123-125910370

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[img] PDF (S1 Fig. Focal adhesion dynamics on an elastic substrate) - Supplemental Material
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[img] PDF (S2 Fig. Composition of ECM fiber network model) - Supplemental Material
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[img] Video (MPEG) (S1 Video. Comparison between original nonlinear simulation and latent variable superposition simulation of two-cell interaction embedded within cylindrical ECM) - Supplemental Material
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[img] Video (MPEG) (S2 Video. Comparison between two-cell latent variable superposition simulation and single cell latent variable simulation) - Supplemental Material
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[img] Video (MPEG) (S3 Video. Two-cell latent variable superposition simulation at varied spacing between 2 cells embedded within cylindrical ECM) - Supplemental Material
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[img] Video (MPEG) (S4 Video. Multi-cell latent variable superposition simulation depicting comparison of ECM compaction between heterogeneous distributions of cells) - Supplemental Material
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[img] PDF (S1 Text. Contains Appendix A: Nonlinear dynamics of cell-ECM interaction for computational model, Appendix B: Least squares estimation for identification of the parameter matrices A, B, C, G involved in the latent space state equations, Appendix C...) - Supplemental Material
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[img] PDF (S1 Table. List of simulation parameters) - Supplemental Material
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Abstract

Cells interacting through an extracellular matrix (ECM) exhibit emergent behaviors resulting from collective intercellular interaction. In wound healing and tissue development, characteristic compaction of ECM gel is induced by multiple cells that generate tensions in the ECM fibers and coordinate their actions with other cells. Computational prediction of collective cell-ECM interaction based on first principles is highly complex especially as the number of cells increase. Here, we introduce a computationally-efficient method for predicting nonlinear behaviors of multiple cells interacting mechanically through a 3-D ECM fiber network. The key enabling technique is superposition of single cell computational models to predict multicellular behaviors. While cell-ECM interactions are highly nonlinear, they can be linearized accurately with a unique method, termed Dual-Faceted Linearization. This method recasts the original nonlinear dynamics in an augmented space where the system behaves more linearly. The independent state variables are augmented by combining auxiliary variables that inform nonlinear elements involved in the system. This computational method involves a) expressing the original nonlinear state equations with two sets of linear dynamic equations b) reducing the order of the augmented linear system via principal component analysis and c) superposing individual single cell-ECM dynamics to predict collective behaviors of multiple cells. The method is computationally efficient compared to original nonlinear dynamic simulation and accurate compared to traditional Taylor expansion linearization. Furthermore, we reproduce reported experimental results of multi-cell induced ECM compaction.


Item Type:Article
Related URLs:
URLURL TypeDescription
https://doi.org/10.1371/journal.pcbi.1006798DOIArticle
https://doi.org/10.1101/526426DOIDiscussion Paper
https://doi.org/10.1371/journal.pcbi.1006798.s001DOIS1 Fig.
https://doi.org/10.1371/journal.pcbi.1006798.s002DOIS2 Fig.
https://doi.org/10.1371/journal.pcbi.1006798.s003DOIS1 Video
https://doi.org/10.1371/journal.pcbi.1006798.s004DOIS2 Video
https://doi.org/10.1371/journal.pcbi.1006798.s005DOIS3 Video
https://doi.org/10.1371/journal.pcbi.1006798.s006DOIS4 Video
https://doi.org/10.1371/journal.pcbi.1006798.s007DOIS1 Text
https://doi.org/10.1371/journal.pcbi.1006798.s008DOIS1 Table
https://www.ncbi.nlm.nih.gov/pmc/articles/PMC6774565/PubMed CentralArticle
ORCID:
AuthorORCID
Mayalu, Michaëlle N.0000-0002-9678-0157
Kim, Min-Cheol0000-0001-6649-9463
Additional Information:© 2019 Mayalu et al. This is an open access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited. Received: January 17, 2019; Accepted: June 12, 2019; Published: September 20, 2019. Data Availability: All relevant data are within the manuscript and its Supporting Information files. This material is based on work supported by the National Science Foundation (NSF) under grant number CMMI-1762961, Singapore-MIT Alliance of Research and Technology (SMART), and NSF Science and Technology Center (STC) on Emergent Behaviors in Integrated Cellular Systems (EBICS) under Grant CBET-0939511. The funders had no role in study design, data collection and analysis, decision to publish, or preparation of the manuscript. The authors have declared that no competing interests exist. The authors would like to thank Prof. Roger D. Kamm (MIT) and Taher Saif (UIUC) for their biological insights and advice of the studied system. Author Contributions: Conceptualization: Michaëlle N. Mayalu, H. Harry Asada. Data curation: Michaëlle N. Mayalu. Formal analysis: Michaëlle N. Mayalu, H. Harry Asada. Funding acquisition: H. Harry Asada. Investigation: Michaëlle N. Mayalu, H. Harry Asada. Methodology: Michaëlle N. Mayalu, H. Harry Asada. Project administration: H. Harry Asada. Resources: Min-Cheol Kim. Software: Min-Cheol Kim. Supervision: Min-Cheol Kim, H. Harry Asada. Validation: Michaëlle N. Mayalu, Min-Cheol Kim. Visualization: Michaëlle N. Mayalu, Min-Cheol Kim. Writing – original draft: Michaëlle N. Mayalu, Min-Cheol Kim, H. Harry Asada. Writing – review & editing: Michaëlle N. Mayalu, Min-Cheol Kim, H. Harry Asada.
Funders:
Funding AgencyGrant Number
NSFCMMI-1762961
Singapore-MIT Alliance of Research and TechnologyUNSPECIFIED
NSFCBET-0939511
Issue or Number:9
PubMed Central ID:PMC6774565
Record Number:CaltechAUTHORS:20190123-125910370
Persistent URL:https://resolver.caltech.edu/CaltechAUTHORS:20190123-125910370
Official Citation:Mayalu MN, Kim M-C, Asada HH (2019) Multi-cell ECM compaction is predictable via superposition of nonlinear cell dynamics linearized in augmented state space. PLoS Comput Biol 15(9): e1006798. https://doi.org/10.1371/journal. pcbi.1006798
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:92432
Collection:CaltechAUTHORS
Deposited By: Tony Diaz
Deposited On:23 Jan 2019 22:19
Last Modified:31 Oct 2019 18:02

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