Multi-Cell ECM compaction is predictable via superposition of nonlinear cell dynamics linearized in augmented state space
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.
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.Attached Files
Published - journal.pcbi.1006798.pdf
Submitted - 526426.full.pdf
Supplemental Material - journal.pcbi.1006798.s001.pdf
Supplemental Material - journal.pcbi.1006798.s002.pdf
Supplemental Material - journal.pcbi.1006798.s003.mp4
Supplemental Material - journal.pcbi.1006798.s004.mp4
Supplemental Material - journal.pcbi.1006798.s005.mp4
Supplemental Material - journal.pcbi.1006798.s006.mp4
Supplemental Material - journal.pcbi.1006798.s007.pdf
Supplemental Material - journal.pcbi.1006798.s008.pdf
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Additional details
- PMCID
- PMC6774565
- Eprint ID
- 92432
- Resolver ID
- CaltechAUTHORS:20190123-125910370
- CMMI-1762961
- NSF
- Singapore-MIT Alliance of Research and Technology
- CBET-0939511
- NSF
- Created
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2019-01-23Created from EPrint's datestamp field
- Updated
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2023-06-01Created from EPrint's last_modified field