Cellular Potts model
This article may be confusing or unclear to readers. In particular, the article does not clearly define the object it is about.. (March 2016) (Learn how and when to remove this template message)
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,
- choose a lattice site and propose a new cell ID to be assigned to it, and
- decide if to accept or reject this change based on an energy function called the Hamiltonian.
The Hamiltonian is a central component of every CPM. It is determined by the configuration of the cell lattice. A basic Hamiltonian proposed by Graner and Glazier included adhesion energies and volume constraints:
Where i, j are lattice sites, σi is the cell at site i, τ(σ) is the cell type of cell σ, J is the boundary coefficient determining the adhesion between two cells of types τ(σ),τ(σ'), δ is the Kronecker delta, v(σ) is the volume of cell σ, V(σ) is the target volume, λ is a Lagrange multiplier determining the strength of the volume constraint.
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.
Multiscale and hybrid modeling using CPM
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. Open source software Bionetsolver can be used to integrate intracellular dynamics with CPM algorithm.
- Graner, Fraçois; Glazier, James (1992). "Simulation of biological cell sorting using a two-dimensional extended Potts model" (PDF). Phys. Rev. Lett. 69 (13): 2013–7. Bibcode:1992PhRvL..69.2013G. doi:10.1103/PhysRevLett.69.2013.
- Szabó, A; Merks, RM (2013). "Cellular potts modeling of tumor growth, tumor invasion, and tumor evolution". Frontiers in Oncology. 3. doi:10.3389/fonc.2013.00087.
- Andasari, Vivi; Roper, Ryan T; Swat, Maciej H; Chaplain, MA (2012). "Integrating intracellular dynamics using CompuCell3D and Bionetsolver: applications to multiscale modelling of cancer cell growth and invasion". PLOS ONE. 7: e33726. Bibcode:2012PLoSO...733726A. doi:10.1371/journal.pone.0033726. PMC . PMID 22461894.
- Chen, Nan; Glazier, James A.; Izaguirre, Jesus A.; Alber, Mark S. (2007). "A parallel implementation of the Cellular Potts Model for simulation of cell-based morphogenesis". Computer Physics Communications. 176 (11–12): 670–681. Bibcode:2007CoPhC.176..670C. doi:10.1016/j.cpc.2007.03.007. PMC .
- James Glazier (professional website)
- CompuCell3D, a CPM simulation environment: Sourceforge
- Notre Dame development site
- Artificial Life model of multicellular morphogenesis with autonomously generated gradients for positional information using the Cellular Potts model
- Stochastic cellular automata