Comparing methods for modelling spreading cell fronts.

Area of Science:

• Mathematical Biology
• Cellular Dynamics
• Statistical Physics

Background:

• Spreading cell fronts are crucial in physiology, often modeled by the Fisher-Kolmogorov equation.
• Continuum models lack individual cell behavior detail and often focus on asymptotic, not transient, dynamics.
• Experimental assays like scratch assays require analysis of transient cell front behavior.

Purpose of the Study:

• To investigate transient and asymptotic behaviors of moving cell fronts.
• To compare discrete models with continuum approximations (mean-field, pair-wise, one-hole).
• To evaluate the performance of different approximations across various parameter spaces.

Main Methods:

• A volume-excluding birth-migration process on a 1D lattice was used for discrete modeling.
• Averaged discrete results were approximated using mean-field, pair-wise, and one-hole methods.
• Performance of approximations was assessed against discrete results for transient and asymptotic behaviors.

Main Results:

• The one-hole approximation accurately predicts asymptotic behavior when cell proliferation outpaces migration.
• Mean-field and pair-wise approximations yield identical asymptotic results, matching discrete models when migration dominates proliferation.
• The pair-wise approximation outperforms mean-field in transient dynamics, despite similar asymptotic predictions.

Conclusions:

• Each approximation is suitable only for specific parameter regimes and behaviors (transient vs. asymptotic).
• Careful selection of approximation methods is essential for accurate predictions in cell front dynamics.
• This work highlights the limitations of continuum models and the importance of discrete approaches for transient phenomena.