Cellular Potts model

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|adhesive forces]] to each other and the medium in which they exist. The formalism can be extended to include cell behaviours such as cell migration, cell growth and cell division, and environment sensing. 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 the study of morphogenesis. 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.

Model description

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,

1. choose a lattice site and propose a new cell ID to be assigned to it, and
2. decide if to accept or reject this change based on an energy function called the Hamiltonian.

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:

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

Where i, j are lattice sites, σ_i 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.

The Hamiltonian can be modified to control cell behaviors such as chemotaxis, elongation and haptotaxis by using other sub-lattices containing information such as the concentrations of chemicals.

Extensions

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.

References

• 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 2139985. PMID 18084624.

External links

• James Glazier (professional website)
• CompuCell3D, a CPM simulation environment: Sourceforge
• SimTK
• 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