A reduced order systems approach to prediction of emergent behaviors of cellular systems

Populations of cells interacting within an extracellular matrix (ECM) exhibit spatiotemporal behaviors that are usually described through complex and extensive mechanisms. However, mechanistic computational models become intractable as the cell population increases. Here, we develop a reduced order agent-based framework derived from the empirical treatment of simulation data obtained from detailed single-cell mechanistic computational models. The key construct within this approach is the linearization and subsequent superposition of single-cell agent models to explain the emergent behavior among multiple cells. First, simulation data is obtained from a detailed single-cell mechanistic computational model. In order to increase linear variation, nonlinear force terms are considered within the data. Then, the technique of Partial Least Squares Regression (PLSR) is used to linearly approximate the simulation data. A linear state transition equation representing a single-cell agent is formulated in latent variable space using the results from the PLSR approximation. Finally, an algorithm is developed were linearized agents are superposed to predict multi-cellular interactions. Using this method, computational expense and time are decreased significantly and sufficient mechanistic detail is retained in the simulation. The method is applied to cell-ECM interactions, and ECM remodeling during cell migration.