Stochastic simulation tools and continuum models for describing two-dimensional collective cell spreading with...

Area of Science:

• Mathematical Biology
• Cell Biology
• Biophysics

Background:

• Two-dimensional collective cell migration assays are crucial for studying cancer and tissue repair.
• These assays involve cell migration and proliferation, both influenced by cell-to-cell crowding.
• Traditional discrete models use nearest-neighbor proliferation with limited crowding effects, leading to logistic growth assumptions that may not always hold true.

Purpose of the Study:

• To develop a generalized proliferation mechanism for discrete models of collective cell migration.
• To address limitations of traditional models regarding crowding effects and logistic growth assumptions.
• To introduce a crowding function that considers density over a wider area.

Main Methods:

• Developed a generalized proliferation mechanism allowing non-nearest neighbor events within a template of concentric rings.
• Introduced a crowding function, f(C), to determine proliferation based on agent density within multiple sites.
• Analyzed the continuum limit of the stochastic model to derive a universal growth function.

Main Results:

• The generalized proliferation mechanism leads to a universal growth function, generalizing the standard logistic growth.
• The continuum model shows good agreement with averaged simulation data for various crowding functions and parameters.
• The match between continuum and discrete models improves with increased interaction range (r) for nonlinear crowding functions.

Conclusions:

• The proposed generalized proliferation mechanism offers a more realistic representation of cell crowding in collective migration.
• The developed continuum model accurately predicts simulation outcomes, particularly for nonlinear crowding effects.
• This work provides a refined mathematical framework for modeling cell proliferation in biological systems like cancer and tissue repair.