Comparing a discrete and continuum model of the intestinal crypt

Area of Science:

• Computational biology
• Mathematical modeling
• Cell dynamics

Background:

• Discrete cell-level models are increasingly used for population dynamics, incorporating factors like cell heterogeneity.
• Analyzing large parameter spaces in discrete models requires extensive simulations, hindering generalization.
• Coarse-graining discrete models into continuum models offers a path to analytical insights.

Purpose of the Study:

• To apply coarse-graining techniques to a discrete cell dynamics model of the intestinal crypt.
• To analyze the resulting continuum model for insights into cell population stability.
• To validate continuum model predictions against discrete simulations and experimental data.

Main Methods:

• Developed a discrete cell-level model for intestinal crypt dynamics.
• Coarse-grained the discrete model to derive a continuum model.
• Analyzed the continuum model to identify regions of steady-state solutions.
• Compared continuum model predictions with discrete simulations and murine intestinal crypt data.

Main Results:

• The analysis of the continuum model identified a limited parameter space for biologically realistic, steady-state solutions.
• Continuum model predictions demonstrated good agreement with underlying discrete simulations.
• Model predictions also showed good agreement with experimental data from murine intestinal crypts.

Conclusions:

• Coarse-graining discrete cell models to continuum models is a viable approach for gaining analytical insights.
• The study highlights specific parameter constraints for stable cell population dynamics in the intestinal crypt.
• The developed continuum model serves as a validated tool for understanding intestinal crypt cell dynamics.