Multi-cell ECM compaction is predictable via superposition of nonlinear cell dynamics linearized in augmented state space
Name
journal.pcbi.1006798.pdf
Description
Published version
Size
2.87 MB
Format
Adobe PDF
Checksum (MD5)
c8a51877b026c399e81ca13deb05b9a8
Author(s)
Kim, Min-Cheol
Asada, H. Harry
Date Issued
September 20, 2019
Journal
PLoS one
Publisher
Public Library of Science (PLoS)
Citation
Mayalu, Michaëlle N., Min-Cheol Kim and H. Harry Asada. "Multi-cell ECM compaction is predictable via superposition of nonlinear cell dynamics linearized in augmented state space." PLoS one 15 (2019): e1006798 © 2019 The Author(s)
Version
Final published version
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.
Subjects
Ecology
Modelling and Simulation
Computational Theory and Mathematics
Genetics
Ecology, Evolution, Behavior and Systematics
Molecular Biology
Cellular and Molecular Neuroscience
MIT Department
Massachusetts Institute of Technology. Department of Mechanical Engineering
Terms of Use
Creative Commons Attribution 4.0 International license
Persistent DSpace Link
DOI of Published Version
https://doi.org/10.1371/journal.pcbi.1006798
