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Concept
Cellular Potts model
Summary
In computational biology, a Cellular Potts model (CPM, also known as the Glazier-Graner-Hogeweg model) is a computational model of cells and tissues. 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 formalism can be extended to include cell behaviours such as cell migration, growth and division, and cell signalling. The first CPM was proposed for the simulation of cell sorting by François Graner and James Glazier as a modification of a large-Q Potts model. CPM was then popularized by Paulien Hogeweg for studying morphogenesis.
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. The dynamics of the model are governed by an energy function: the Hamiltonian which describes the energy of a particular configuration of cells in the lattice. In a basic CPM, this energy results from adhesion between cells and resistance of cells to volume changes. The algorithm for updating CPM minimizes this energy.
In order to evolve the model Metropolis-style updates are performed, that is:
choose a random lattice site i
choose a random neighboring lattice site j to copy its ID into i.
calculate the difference in energy () between the original and the proposed new configuration.
accept or reject this copy event based on the change in energy , as follows:
if the new energy is lower, always accept the copy;
if the new energy is higher, accept the copy with probability (the Boltzmann temperature T determines the likelihood of energetically unfavorable fluctuations).
Official source
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