Cells interacting over an extracellular matrix (ECM) exhibit
emergent behaviors, which are often observably different from
singlecell dynamics. Fibroblasts embedded in a 3D 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 multicellular 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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Unsupervised manifold learning of collective behavior
Collective behavior is an emergent property of numerous complex systems, from financial markets to cancer cells to predatorprey ecological systems. Characterizing modes of collective behavior is often done through human observation, training generative models, or other supervised learning techniques. Each of these cases requires knowledge of and a method for characterizing the macrostate(s) of the system. This presents a challenge for studying novel systems where there may be little prior knowledge. Here, we present a new unsupervised method of detecting emergent behavior in complex systems, and discerning between distinct collective behaviors. We require only metrics, d (1) , d (2) , defined on the set of agents, X , which measure agents’ nearness in variables of interest. We apply the method of diffusion maps to the systems ( X , d ( i ) ) to recover efficient embeddings of their interaction networks. Comparing these geometries, we formulate a measure of similarity between two networks, called the map alignment statistic (MAS). A large MAS is evidence that the two networks are codetermined in some fashion, indicating an emergent relationship between the metrics d (1) and d (2) . Additionally, the form of the macroscale organization is encoded in the covariances among the two sets of diffusion map components. Using these covariances we discern between different modes of collective behavior in a datadriven, unsupervised manner. This method is demonstrated on a synthetic flocking model as well as empirical fish schooling data. We show that our state classification subdivides the known behaviors of the school in a meaningful manner, leading to a finer description of the system’s behavior.
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 Award ID(s):
 1848576
 NSFPAR ID:
 10290194
 Editor(s):
 Grilli, Jacopo
 Date Published:
 Journal Name:
 PLOS Computational Biology
 Volume:
 17
 Issue:
 2
 ISSN:
 15537358
 Page Range / eLocation ID:
 e1007811
 Format(s):
 Medium: X
 Sponsoring Org:
 National Science Foundation
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