Discrete and continuous mathematical models of sharp-fronted collective cell migration and invasion

Area of Science:

• Mathematical Biology
• Computational Biology
• Cellular Dynamics

Background:

• Continuum models using reaction-diffusion equations are standard for cell population spreading.
• Linear diffusion models fail to capture experimentally observed sharp fronts.
• Existing nonlinear models lack clear biological motivation and interpretation.

Purpose of the Study:

• To develop a novel, biologically motivated discrete model for cell population spreading.
• To derive a continuum limit from the discrete model that accurately predicts sharp fronts.
• To provide a framework for modeling cell invasion with well-defined sharp fronts.

Main Methods:

• Developed a stochastic discrete lattice-based model with biologically inspired mechanisms.
• Incorporated agent-based substrate deposition and motility proportional to substrate density.
• Derived a partial differential equation (PDE) model via coarse-graining the discrete model.

Main Results:

• The discrete model successfully mimics experimental observations, including sharp-fronted density profiles.
• Simulations of a circular barrier assay demonstrate model's ability to produce varied front behaviors.
• The derived PDE model accurately approximates averaged data from the discrete simulations.

Conclusions:

• The new discrete model and its PDE approximation offer a biologically motivated approach to cell spreading.
• This framework effectively models populations exhibiting well-defined sharp fronts.
• Open-source code is available for reproducibility and further research.