Collective cell migration in 3D extracellular matrix (ECM) is crucial to many physiological and pathological processes. Migrating cells can generate active pulling forces via actin filament contraction, which are transmitted to the ECM fibers and lead to a dynamically evolving force network in the system. Here, we elucidate the role of this force network in regulating collective cell behaviors using a minimal active-particle-on-network (APN) model, in which active particles can pull the fibers and hop between neighboring nodes of the network following local durotaxis. Our model reveals a dynamic transition as the particle number density approaches a critical value, from an “absorbing” state containing isolated stationary small particle clusters, to an “active” state containing a single large cluster undergoing constant dynamic reorganization. This reorganization is dominated by a subset of highly dynamic “radical” particles in the cluster, whose number also exhibits a transition at the same critical density. The transition is underlaid by the percolation of “influence spheres” due to the particle pulling forces. Our results suggest a robust mechanism based on ECM-mediated mechanical coupling for collective cell behaviors in 3D ECM.
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Modeling of Collective Cell Behaviors Interacting With Extracellular Matrix Using Dual Faceted Linearization
Cells interacting over an extracellular matrix (ECM) exhibit
emergent behaviors, which are often observably different from
single-cell dynamics. Fibroblasts embedded in a 3-D ECM, for
example, compact the surrounding gel and generate an
anisotropic strain field, which cannot be observed in single cellinduced
gel compaction. This emergent matrix behavior results
from collective intracellular mechanical interaction and is crucial
to explain the large deformations and mechanical tensions that
occur during embryogenesis, tissue development and wound
healing. Prediction of multi-cellular interactions entails
nonlinear dynamic simulation, which is prohibitively complex to
compute using first principles especially as the number of cells
increase. Here, we introduce a new methodology for predicting
nonlinear behaviors of multiple cells interacting mechanically
through a 3D ECM. In the proposed method, we first apply Dual-
Faceted Linearization to nonlinear dynamic systems describing
cell/matrix behavior. Using this unique linearization method, the
original nonlinear state equations can be expressed with a pair of
linear dynamic equations by augmenting the independent state
variables with auxiliary variables which are nonlinearly
dependent on the original states. Furthermore, we can find a
reduced order latent space representation of the dynamic
equations by orthogonal projection onto the basis of a lower
dimensional linear manifold within the augmented variable
space. Once converted to latent variable equations, we superpose
multiple dynamic systems to predict their collective behaviors.
The method is computationally efficient and accurate as
demonstrated through its application for prediction of emergent
cell induced ECM compaction.
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- Award ID(s):
- 1762961
- NSF-PAR ID:
- 10104619
- Date Published:
- Journal Name:
- 2018 ASME Dynamic Systems and Control Conference
- Volume:
- 1
- Page Range / eLocation ID:
- V001T14A005
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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- Free Publicly Accessible Full Text
-
Accepted Manuscript1.0
- Conference Paper:
- https://doi.org/10.1115/DSCC2018-9164
