Figure 1.
Cell-surface interaction in the cellular Potts model is regulated by the surface energy coefficients.
Three cells with cell indices 1, 2 and 3, respectively, each one covering several lattice sites, interact with each other at the cell surfaces. The cells 1 and 3 are of type A, depicted in dark grey, the cell 3 is of type B, depicted in light grey. The strength of the interaction depends on the cell types. There are also interactions between the cells and the medium (white, cell index 0). Possible boundary interactions are not shown.
Figure 2.
A mechanistic multiscale framework is characterized by the coupling of multiple spatial and temporal scales on the basis of abstracted rules.
The assumed intercellular interaction may depend on an interplay with cellular characteristics and intercellular details. By determining the distinctive characteristics at the tissue level and their comparison with experimental observation, it can be tested wether a specific mechanism explains the behavior of an experimentally studied cell system.
Figure 3.
Cell surface fluctuations are the central device in the realization of the multiscale concept in CPMs.
Both the rules of intercellular interaction and the considered cellular characteristics are eventually coded, via the Hamiltonian or directly for extended models, into an expression that regulates the intensity of CPM-cells' surface fluctuations. Additional technical parameters are integrated into the Hamiltonian to be able to suppress phenomenologically unrealistic behavior. The actual impact of the Hamiltonian on the intensity of CPM cells' surface fluctuations is attenuated by a voter-like portion in the transition rates. The surface fluctuations drive simultaneously the actual behavior of a CPM at the cellular scale, the specifics of intercellular interaction and the emerging behavior at the tissue scale. Single aspects of the cellular properties in the model, for instance the cell shape flexibility, the magnitude of random cell displacements or the cells' surface roughness, and of the intercellular interaction, like the strength of intercellular adhesion, cannot be controlled individually but are interlinked with each other. Likewise, purely model-technical control parameters such as the cellular integrity, that is the property of CPM cells to span over connected, essentially convex lattice domains, are coupled indirectly with biologically interpretable cellular and intercellular properties. The emerging tissue scale behavior is solely rooted in the specified characteristics of the CPM cells' surface fluctuations and not linked directly to cellular and intracellular specifics.