Modeling of Collective Cell Behaviors Interacting With Extracellular Matrix Using Dual Faceted Linearization

Abstract

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 cell-induced 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.