Cellular Potts model

In computational biology, cellular Potts model (CPM) is a computational model of the collective behavior of cellular structures. It allows modelling of many phenomena, such as cell migration, clustering, and growth taking adhesive forces, environment sensing as well as volume and surface-area constraints into account. The first CPM was proposed for the simulation of cell sorting by Graner and Glazier as a modification of a large-Q Potts model. Although the model was developed to model biological cells it can also be used to model individual parts of a biological cell, or even regions of fluid.

The CPM works on a rectangular Euclidean lattice where it represents each cell as a subset of lattice sites sharing the same cell ID (analogical to spin in Potts models in physics). In order to evolve the model Metropolis-style updates are performed, that is,

The Hamiltonian is a central component of every CPM model. It is determined by the configuration of the cell lattice. A basic Hamiltonian proposed by Graner and Glazier included adhesion energies and volume constraints:

${\displaystyle {\begin{aligned}H=\sum _{i,j{\text{ neighbors}}}J\left(\tau (\sigma _{i}),\tau (\sigma _{j})\right)\left(1-\delta (\sigma _{i},\sigma _{j})\right)+\lambda \sum _{i}\left(v(\sigma _{i})-V(\sigma _{i})\right)^{2}.\\\end{aligned}}}$

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