Stochastic modeling and identification of emergent behaviors of an Endothelial Cell population in angiogenic pattern formation

Abstract

Despite a high level of stochasticity and heterogeneity, a population of biological cells can collectively construct a complex structure that emerges from individual cell behaviors. Endothelial Cells (ECs), for example, create a vascular network with a tubular structure through interactions with the surrounding scaffold and other cells. Individual cells make a series of discrete decisions whether to migrate, proliferate, or die, leading to network pattern formation. This paper presents a methodology for deriving agent behavior models from EC time lapse data in an in vitro micro-fluidic environment. Individual cells are modeled as stochastic agents that detect growth factors (chemical molecules) and the scaffold conditions, and that make stochastic phenotype state transitions. Based on observed behaviors, a model is obtained for predicting the behavior of a population of interacting cells, which will sprout out, form a tubular structure, and create a branch to generate a vascular network − the process referred to as angiogenesis. A Maximum Likelihood method for estimating model parameters from angiogenesis process time lapse data is then presented. The identified mechanism of emergent pattern formation, although investigated in the context of angiogenesis, provides useful insights for swarm and modular robotics.