Cellular Potts model
It is used to simulate individual and collective cell behavior, tissue morphogenesis and cancer development.
CPM describes cells as deformable objects with a certain volume, that can adhere to each other and to the medium in which they live.
The first CPM was proposed for the simulation of cell sorting by François Graner and James A. Glazier as a modification of a large-Q Potts model.
[1] CPM was then popularized by Paulien Hogeweg for studying morphogenesis.
[2] Although the model was developed to describe biological cells, it can also be used to model individual parts of a biological cell, or even regions of fluid.
The CPM consists of a rectangular Euclidean lattice, where each cell is a subset of lattice sites sharing the same cell ID (analogous to spin in Potts models in physics).
Lattice sites that are not occupied by cells are the medium.
In order to evolve the model Metropolis-style updates are performed, that is: The original model proposed by Graner and Glazier contains cells of two types, with different adhesion energies for cells of the same type and cells of a different type.
Each cell type also has a different contact energy with the medium, and the cell volume is assumed to remain close to a target value.
Cells with a lower J value for their membrane contact will stick together more strongly.
Therefore, different patterns of cell sorting can be simulated by varying the J values.
Over time, the CPM has evolved from a specific model of cell sorting to a general framework with many extensions, some of which are partially or entirely off-lattice.
[3] Various cell behaviours, such as chemotaxis, elongation and haptotaxis can be incorporated by extending either the Hamiltonian, H, or the change in energy
Auxiliary sub-lattices may be used to include additional spatial information, such as the concentrations of chemicals.
In CPM, cells can be made to move in the direction of higher chemokine concentration, by increasing the probability of copying the ID of site j into site i when the chemokine concentration is higher at j.
Core GGH (or CPM) algorithm which defines the evolution of the cellular level structures can easily be integrated with intracellular signaling dynamics, reaction diffusion dynamics and rule based model to account for the processes which happen at lower (or higher) time scale.
[4] Open source software Bionetsolver can be used to integrate intracellular dynamics with CPM algorithm.
