Modelling collective cell motion: are on- and off-lattice models equivalent?

Collective cell motion is central to many biological systems, from tissue morphogenesis to microbial community dynamics. Prior research has shown that eukaryotic cells often exhibit polar alignment of movement, while bacterial systems tend to show apolar alignment. These differences influence how cells organize into functional groups. However, the field lacks a clear framework to distinguish between model-specific behaviors and genuine biological phenomena. This gap motivated the development of various on- and off-lattice computational models to simulate collective motion. Yet, comparing these models remains difficult due to differences in their assumptions and structures. No prior work had resolved how to translate between lattice and non-lattice representations of cell movement. Understanding this distinction is essential for interpreting simulation results accurately. The current paper addresses this challenge by examining how different modeling approaches may produce similar or divergent outcomes.

This study aims to establish criteria for comparing on- and off-lattice models of collective cell motion. The authors seek to determine whether these two modeling approaches can yield equivalent macroscopic behaviors despite their structural differences. They focus on polar and apolar alignment mechanisms, which are key to understanding how cells coordinate movement. By defining prototypical models for each alignment type, the researchers aim to clarify how to translate between lattice and non-lattice frameworks. Their goal is to identify population-level features that remain consistent across different modeling approaches. This work addresses the challenge of distinguishing model-specific effects from general biological patterns. The study also explores how macroscopic descriptions, such as partial differential equations, can help assess model equivalence. Ultimately, the authors hope to provide a framework for interpreting simulation results more reliably.

The researchers defined two types of models: on-lattice and off-lattice, each with polar and apolar alignment rules. They used agent-based modeling to simulate cell interactions and movement. The on-lattice models placed cells on a grid, while off-lattice models allowed free movement in continuous space. They derived macroscopic equations to describe the average behavior of cell populations. By comparing these equations across model types, the authors assessed whether the models produced similar large-scale patterns. They analyzed phase transitions and spatial organization in simulations to identify equivalence criteria. The study also examined how model parameters influenced macroscopic outcomes. This approach allowed the researchers to evaluate whether different modeling frameworks could represent the same biological phenomena.

The study found that on- and off-lattice models can produce similar macroscopic patterns when alignment rules are consistent. Polar alignment models showed ordered movement patterns, while apolar models produced more disordered dynamics. The transition between ordered and disordered states occurred at similar thresholds in both model types. The researchers observed that macroscopic equations derived from the models captured these transitions effectively. The phase behavior of the models was informative for assessing equivalence. The study showed that lattice and non-lattice models could be transformed into one another under certain conditions. The authors demonstrated that the choice of lattice structure did not significantly affect macroscopic outcomes when alignment rules were preserved. These findings suggest that model equivalence can be evaluated through population-level dynamics rather than structural details.

The authors concluded that on- and off-lattice models can be equivalent at the population level when alignment rules are consistent. They proposed that macroscopic patterns and phase transitions serve as useful criteria for comparing different modeling approaches. The study showed that structural differences between models do not necessarily lead to divergent outcomes. The researchers emphasized the importance of focusing on population-level features rather than model-specific details. They suggested that macroscopic equations can help unify different modeling frameworks. The findings indicate that model equivalence depends on the alignment mechanisms rather than the lattice structure. The authors highlighted the need to interpret simulation results in terms of macroscopic behavior. Their work provides a framework for evaluating model equivalence in collective cell motion studies.