Cellular Potts model

Cellular Potts model

The cellular Potts model 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 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 CPM is evolved by updating the cell lattice one pixel at a time based on a set of probabilistic rules. In this sense, the CPM can be thought of as a generlized cellular automaton ("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.

The primary rule base has three components:
# rules for selecting putative lattice updates
# a "Hamiltonian" or "effective energy" function that is used for calculating the probability of accepting lattice updates.
# 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.

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 original 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:

egin{align}H = & sum_{vec i, vec j ext{neighbors Jleft( au(sigma(vec i)), au(sigma(vec j)) ight) left(1 - delta(sigma(vec i), sigma(vec j)) ight) \+ & sum_{vec i} lambda_ ext{volume} [V(sigma(vec i)) - V_ ext{target}(sigma(vec i))] ^2\+ & sum_{vec i} lambda_ ext{surface} [S(sigma(vec i)) - S_ ext{target}(sigma(vec i))] ^2\end{align}.

Many extensions to the original CPM Hamiltonian control cell behaviors including chemotaxis, elongation and haptotaxis.

References

* [http://biocomplexity.indiana.edu/jglazier/papers.php?action=browse&cat=03a 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

* [http://biocomplexity.indiana.edu/jglazier/ James Glazier] (professional website)
*CompuCell3D, a CPM simulation environment: [http://sourceforge.net/projects/compucell/ Sourceforge]
* [https://simtk.org/home/compucell3d/ SimTK]
* [http://www.nd.edu/~lcls/compucell/linux.htm Notre Dame development site]
* [http://panmental.de/ALifeXIflag Artificial Life model of multicellular morphogenesis with autonomously generated gradients for positional information using the Cellular Potts model]


Wikimedia Foundation. 2010.

Игры ⚽ Поможем сделать НИР

Look at other dictionaries:

  • Potts model — In statistical mechanics, the Potts model, a generalization of the Ising model, is a model of interacting spins on a crystalline lattice. By studying the Potts model, one may gain insight into the behaviour of ferromagnets and certain other… …   Wikipedia

  • List of mathematics articles (C) — NOTOC C C closed subgroup C minimal theory C normal subgroup C number C semiring C space C symmetry C* algebra C0 semigroup CA group Cabal (set theory) Cabibbo Kobayashi Maskawa matrix Cabinet projection Cable knot Cabri Geometry Cabtaxi number… …   Wikipedia

  • Monte Carlo method — Not to be confused with Monte Carlo algorithm. Computational physics …   Wikipedia

  • CompuCell3D — is a three dimensional C++ software Problem Solving Environment for simulations of biocomplexity problems, integrating multiple mathematical [morphogenesis] models. These include the Cellular Potts Model (CPM) which can model cell clustering,… …   Wikipedia

  • CPM — may refer to: Advertising cost per mille, the advert cost per thousand views Cost per impression, the online advert cost per thousand views M=1000 in roman numerals so CPM = C=Cost P=Per M=1,000 as in banner advertising you pay for each 1,000 ad… …   Wikipedia

  • Foam — This article is about the substance formed from trapped gas bubbles. For other uses, see Foam (disambiguation). Soap foam bubbles Contents 1 Definition …   Wikipedia

  • United States — a republic in the N Western Hemisphere comprising 48 conterminous states, the District of Columbia, and Alaska in North America, and Hawaii in the N Pacific. 267,954,767; conterminous United States, 3,022,387 sq. mi. (7,827,982 sq. km); with… …   Universalium

  • performing arts — arts or skills that require public performance, as acting, singing, or dancing. [1945 50] * * * ▪ 2009 Introduction Music Classical.       The last vestiges of the Cold War seemed to thaw for a moment on Feb. 26, 2008, when the unfamiliar strains …   Universalium

  • Ecology — For other uses, see Ecology (disambiguation). Ecology …   Wikipedia

  • Iron Man's armor — refers to the powered metal suit worn by Tony Stark when he assumes his superhero role of Iron Man. The first version of the armor was created by Stark with the help of Ho Yinsen. Unlike most other superheroes, the appearance of Stark s armor has …   Wikipedia

Share the article and excerpts

Direct link
… Do a right-click on the link above
and select “Copy Link”