Overview

The cellular Potts model (CPM) is a lattice-based computational modeling method to simulate the collective behavior of cellular structures. Other names for the CPM are extended large-q Potts model and the Glazier and Graner model. First developed by James Glazier and Francois Graner in 1992 as an extension of large-q Potts model simulations of coarsening in metallic grains and soap froths, it has now been used to simulate foam, biological tissues, fluid flow and reaction-advection-diffusion-equations. In the CPM a generalized "cell" is a simply-connected domain of pixels with the same cell id (formerly spin). A generalized cell may be a single soap bubble, an entire biological cell, part of a biological cell, or even a region of fluid. The three-letter acronym CPM represents several subjects: // Business Process Outsourcing (BPO) Core Process Metrics, the core metrics for performance measurement in any process. ... In physics, a lattice model is a physical model that is defined on a lattice, as opposed to the continuum of space or spacetime. ... The cellular Potts model (CPM) is a lattice-based computational modeling method to simulate the collective behavior of cellular structures. ... The cellular Potts model (CPM) is a lattice-based computational modeling method to simulate the collective behavior of cellular structures. ... In statistical mechanics, the Potts model, a generalization of the Ising model, is a model of interacting spins on a crystalline lattice. ... A geometrical object is called simply connected if it consists of one piece and doesnt have any circle-shaped holes or handles. Higher-dimensional holes are allowed. ... Domain has several meanings: // General some kind of territory, such as (for example) a demesne or a realm synonymous with a metaphorical field, e. ... A pixel (a contraction of picture element) is one of the many tiny dots that make up the representation of a picture in a computers memory. ... In physics, spin refers to the angular momentum intrinsic to a body, as opposed to orbital angular momentum, which is the motion of its center of mass about an external point. ... A soap bubble A soap bubble is a very thin film of soap water that forms a hollow sphere with an iridescent surface. ... Cells in culture, stained for keratin The cell is the structural and functional unit of all living organisms. ...

The CPM is evolved by updating the cell lattice one pixel at a time based on a set of probabilisitc rules. In this sense, the CPM can be thought of as a generlized cellular automata (CA). Although it also closely resembles certain Monte Carlo methods, such as the large-q Potts model, many subtle differences separate the CPM from Potts models and standard spin-based Monte Carlo schemes. A cellular automaton (plural: cellular automata) is a discrete model studied in computability theory and mathematics. ... Monte Carlo methods are algorithms for solving various kinds of computational problems by using random numbers (or more often pseudo-random numbers), as opposed to deterministic algorithms. ... In statistical mechanics, the Potts model, a generalization of the Ising model, is a model of interacting spins on a crystalline lattice. ...

The primary rule base has three componants:

1. rules for selecting putative lattice updates
2. a Hamiltonian or effective energy function that is used for calculating the probability of accepting lattice updates.
3. additional rules not included in 1. or 2..

The CPM can also be thought of as an agent based method in which cell agents evolve, interact via behaviors such as adhesion, signalling, volume and surface area control, chemotaxis and proliferation. Over time, the CPM has evolved from a specific model to a general framework with many extensions and even related methods that are entirely or partially off-lattice. In physics, Hamiltonian has distinct but closely related meanings. ... This article does not cite its references or sources. ... In computer science, a multi-agent system (MAS) is a system composed of several agents, capable of mutual interaction. ... Schematic of cell adhesion The study of cell adhesion is part of cell biology. ... It has been suggested that this article or section be merged into signal transduction. ... Chemotaxis is a kind of taxis, in which bodily cells, bacteria, and other single-cell or multicellular organisms direct their movements according to certain chemicals in their environment. ... The term cell growth is used in two different ways in biology. ...

The central component of the CPM is the definition of the Hamiltonian. The Hamiltonian is determined by the configuration of the cell lattice and perhaps other sub-lattices containing information such as the concentrations of chemicals. The orginal CPM Hamiltonain included adhesion energies, and volume and surface area constraints. We present it here without definition as an illustration and will discuss it in greater detail later: . In physics, Hamiltonian has distinct but closely related meanings. ...

Many extensions to the original CPM Hamiltonian control cell behaviors including chemotaxis, elongation and haptotaxis. Chemotaxis is a kind of taxis, in which bodily cells, bacteria, and other single-cell or multicellular organisms direct their movements according to certain chemicals in their environment. ... This page is a candidate to be moved to Wiktionary. ...

References

• François Graner and James A. Glazier (1992); "Simulation of Biological Cell Sorting Using a Two-Dimensional Extended Potts Model", Physical Review Letters 69, 2013-2016

External Links

James Glazier (professional website)

CompuCell3D, a CPM simulation environment: Sourceforge, SimTK, Notre Dame development site There are very few or no other articles that link to this one. ...