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.

A hybrid modeling framework integrating a highly specific mechanistic model with highly abstract empirical model is presented. With the growing interest in the scientific and medical community for identification of therapeutic targets in treatment of disease, it is necessary to develop predictive models that can describe cellular behavior in response to environmental cues. Intracellular signaling pathways form complex networks that regulate cellular response in both health and disease. Mechanistic (or white-box) models of biochemical networks are often unable to explain comprehensive cellular response due to lack of knowledge and/or intractable complexity (especially in events distal from the cell membrane). Empirical (or black-box) models may provide a less than accurate representation of cellular response due to data deficiency and/or loss of mechanistic detail. In the proposed framework, we use a mechanistic model to capture early signaling events and apply the resulting generated internal signals (along with external inputs) to a downstream empirical sub-model. The key construct in the approach is the treatment of a cell’s biochemical network as an encoder that creates a functional internal representation of external environmental cues. The signals derived from this representation are then used to inform downstream behaviors. Using this idea, we are able to create a comprehensive framework that describes important mechanisms with sufficient detail, while representing complex or unknown mechanisms in a more abstract form. The model is verified using published biological data describing T-Cells in immune response.

This paper presents a modeling framework for an intracellular signaling network based on formalisms derived from the fundamental concepts in probability theory. Cellular behavior is mediated by a network of intracellular protein activations that originate at the membrane in response to stimulation of cell surface receptors. Multiple protein signal transductions occur concurrently through diverse pathways triggered by different extracellular cues. Through crosstalk, these pathways intersect at various node proteins. The state of a particular node protein is dependent on the binding order of molecules from various pathways. The probability of a particular binding order is evaluated using state dependent transduction time probabilities associated with each pathway. In this way, the probability of the cell to be in a given internal state is tracked and used to gain insight into the cell’s phenotypic behavior. A simulation example illustrates the approach. Future work will incorporate the proposed method into the development of a feedback control strategy for the development of an in silico control design of endothelial cell migration during angiogenesis.