Modeling collective interactions between embedded spheroids and collagen fibers

Tumor-like spheroids are in vitro, three-dimensional cellular collectives consisting of cancerous cells. Embedding these spheroids in an in vitro fibrous environment, such as a collagen network, to mimic the extracellular matrix (ECM) of a tumor provides an essential platform to quantitatively investigate the biophysical mechanisms leading to tumor invasion. To understand the complex interplay between tumor spheroids and ECM, we construct and study a three-dimensional vertex model for tumor spheroids. In such a model, the cells are represented as deformable polyhedrons with cells sharing faces such that there are no gaps between them, otherwise known as confluent. In a bulk model with periodic boundary conditions, we find a rigidity transition as a function of the target cell shape index. For a confluent cellular collective with a finite boundary, and in the presence of lateral extensile and in-plane, radial extensile deformations, we find a significant boundary-bulk effect that is one-cell layer thick. For a cellular collective now embedded in ECM, we explore how the interplay with external ECM fibers affects the morphology and rheology of the cellular collective. We also study the effect of the interplay on the structure of ECM fibers and cell invasion capability. Our study will uncover fundamental, biophysical principles that help drive collective interactions between cells and fibers as well as set the stage for emergent interactions amongst immune cells.