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

• Published in: PLoS computational biology Vol. 15; no. 9; p. e1006798
• Main Authors: Mayalu, Michaëlle N, Kim, Min-Cheol, Asada, H Harry
• Format: Journal Article
• Language: English
• Published: United States Public Library of Science 01.09.2019; Public Library of Science (PLoS)
• Subjects: Biology; Biology and Life Sciences; Biomechanical Phenomena - physiology; Biomechanics; Cell adhesion & migration; Cell culture; Cell interactions; Cell Physiological Phenomena - physiology; Collagen; Compaction; Computational efficiency; Computer and Information Sciences; Computer applications; Computer simulation; Decomposition; Dynamical systems; Elastic Modulus - physiology; Equations of state; Extracellular matrix; Extracellular Matrix - physiology; Fiber optic networks; Fibers; Fibroblasts; First principles; Forecasts and trends; Gene expression; Independent variables; Linearization; Mathematical models; Mechanical engineering; Methods; Models, Biological; Nonlinear Dynamics; Nonlinear equations; Nonlinear systems; Physical Sciences; Physiological aspects; Physiology; Predictions; Principal components analysis; Pseudopodia - physiology; Research and Analysis Methods; State variable; Taylor series; Viscoelasticity; Wound care; Wound healing; Wounds; United States; United States > US; Massachusetts; California
• ISSN: 1553-7358; 1553-734X; 1553-7358
• DOI: 10.1371/journal.pcbi.1006798

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.