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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. 

Filopodia have a key role in sensing both chemical and mechanical cues in surrounding extracellular matrix (ECM). However, quantitative understanding is still missing in the filopodial mechanosensing of local ECM stiffness, resulting from dynamic interactions between filopodia and the surrounding 3D ECM fibers. Here we present a method for characterizing the stiffness of ECM that is sensed by filopodia based on the theory of elasticity and discrete ECM fiber. We have applied this method to a filopodial mechanosensing model for predicting directed cell migration toward stiffer ECM. This model provides us with a distribution of force and displacement as well as their time rate of changes near the tip of a filopodium when it is bound to the surrounding ECM fibers. Aggregating these effects in each local region of 3D ECM, we express the local ECM stiffness sensed by the cell and explain polarity in the cellular durotaxis mechanism.