Linking discrete and continuous models of cell birth and migration

Area of Science:

• Mathematical Biology
• Developmental Biology
• Systems Biology

Background:

• Self-organization in biological collectives is crucial but challenging to model.
• Analytical models often lack biological intuition, while discrete models can be computationally intensive.
• Bridging continuous and discrete modeling approaches is essential for understanding collective dynamics.

Purpose of the Study:

• To quantitatively link spatio-temporal dynamics of continuous models with individual-based data.
• To develop a framework for biologically realistic, time-varying cell numbers.
• To improve the translation of continuous model insights into experimentally relevant predictions.

Main Methods:

• Introducing and fitting scaling parameters in continuous models.
• Upscaling rules from a discrete model to a continuous framework.
• Illustrating the approach with zebrafish-skin pattern formation.

Main Results:

• Continuous models with scaling parameters accurately depict agent-based solutions when migration or proliferation act alone.
• Identified discrepancies between discrete and continuous dynamics when both migration and proliferation occur simultaneously.
• Demonstrated that optimal parameters differ when processes act in combination.

Conclusions:

• Scaling parameters can effectively link continuous and discrete models for cell population dynamics.
• The interplay between migration and proliferation presents unique challenges for combined modeling approaches.
• This work enhances the predictive power of mathematical models in developmental biology.