Modeling multi-cellular systems using sub-cellular elements

TL;DR

This paper presents a flexible, grid-free model for simulating large multi-cellular systems using sub-cellular elements, capturing cell shape dynamics and biological complexity, with applications in tumor growth and embryogenesis.

Contribution

The paper introduces a novel sub-cellular element model that enables adaptive cell shapes and integrates intra-cellular biology, bridging detailed and coarse-grained multi-cellular modeling approaches.

Findings

Model effectively simulates epithelial sheet dynamics.

Connects detailed sub-cellular models to PDE-based approaches.

Proposes efficient algorithms for large-scale simulations.

Abstract

We introduce a model for describing the dynamics of large numbers of interacting cells. The fundamental dynamical variables in the model are sub-cellular elements, which interact with each other through phenomenological intra- and inter-cellular potentials. Advantages of the model include i) adaptive cell-shape dynamics, ii) flexible accommodation of additional intra-cellular biology, and iii) the absence of an underlying grid. We present here a detailed description of the model, and use successive mean-field approximations to connect it to more coarse-grained approaches, such as discrete cell-based algorithms and coupled partial differential equations. We also discuss efficient algorithms for encoding the model, and give an example of a simulation of an epithelial sheet. Given the biological flexibility of the model, we propose that it can be used effectively for modeling a range of multi-cellular processes, such as tumor dynamics and embryogenesis.