Multi-scale modeling in morphogenesis: a critical analysis of the cellular Potts model

Area of Science:

• Theoretical biology
• Mathematical modeling
• Computational biology

Background:

• Cellular Potts models (CPMs) are increasingly used in theoretical biology to simulate biological development.
• CPMs offer sub-cellular spatial resolution, suitable for problems involving multiple spatial and temporal scales.
• Despite their application, CPMs have received limited attention from mathematical theory.

Purpose of the Study:

• To theoretically analyze Cellular Potts models (CPMs).
• To investigate the dynamical properties of CPM updating rules for intercellular interactions.
• To understand CPM behavior across different temporal scales and potential extensions to unbounded systems.

Main Methods:

• Theoretical analysis of CPM updating rules.
• Investigation of CPM behavior on finite and unbounded lattices.
• Integration of CPMs into a general multiscale modeling framework.

Main Results:

• CPMs demonstrate degenerate long-time behavior, characterized by cell extinction irrespective of interaction structures.
• Analysis of spatio-temporal limits for CPMs on unbounded systems was explored.
• Surface fluctuations in CPMs impose significant limitations on their mechanistic and phenomenological applications.

Conclusions:

• The inherent cell-death dynamic in CPMs limits their utility for long-term biological simulations.
• CPM limitations highlight the need for refined modeling approaches for tissue-scale emergent behavior.
• Further theoretical development is required to fully exploit CPMs in mechanistic and phenomenological biological modeling.