A node-based version of the cellular Potts model

Abstract

The cellular Potts model (CPM) is a lattice-based Monte Carlo method that uses an energetic formalism to describe the phenomenological mechanisms underlying the biophysical problem of interest. We here propose a CPM-derived framework that relies on a node-based representation of cell-scale elements. This feature has relevant consequences on the overall simulation environment. First, our model can be implemented on any given domain, provided a proper discretization (which can be regular or irregular, fixed or time evolving). Then, it allowed an explicit representation of cell membranes, whose displacements realistically result in cell movement. Finally, our node-based approach can be easily interfaced with continuous mechanics or fluid dynamics models. The proposed computational environment is here applied to some simple biological phenomena, such as cell sorting and chemotactic migration, also in order to achieve an analysis of the performance of the underlying algorithm. This work is finally equipped with a critical comparison between the advantages and disadvantages of our model with respect to the traditional CPM and to some similar vertex-based approaches.

Simulating Heterogeneous Tumor Cell Populations

“…Despite the longterm degenerate behavior of the cellular Potts model and the modeling limitations imposed by the central role of surface fluctuations [47], efforts to map the parameters of the model formalism to physical and biological properties of cells suggest it to be a powerful tool for investigating a large range of biological questions [46]. In addition, the cellular Potts model has been extended and enhanced in useful ways, for example: a parallel processing implementation that can efficiently simulate a population of 10 7 or more cells [48]; and a node-based version that can be implemented on any given domain, so long as it is a proper discretization (regular or irregular, fixed or time-evolving), and can easily interface with continuous mechanics or fluid dynamics models [49]. Beginning with Sulsky and Childress [59], cell-centered Voronoi models of cell sorting have been used to study cell tissue dynamics [60] and estimate the strength of cell-cell interactions under the differential adhesion hypothesis [61].…”

“…The off-lattice hybrid discrete-continuum model [40] is an example of cells-as-points off-lattice. The cellular Potts model [41–49] is an example of cells composed of sub-elements on a lattice. The sub-cellular viscoelastic model [50] is an example of cells composed as sub-elements off-lattice.…”

Adapting a Plant Tissue Model to Animal Development: Introducing Cell Sliding into VirtualLeaf

“…The new sliding operator strengthens the similarity of the VirtualLeaf and the CPM, to the extent that our updated VirtualLeaf model can be seen as an ‘off-lattice’ version of the CPM. A related generalization of the CPM was introduced by Scianna and Preziosi (2016), who have introduced a node-based version of the CPMs. In this generalization, the cells can be represented on any tessellation, which has the advantage that the method can be interfaced with a wider range of methods for continuum mechanics where using arbitrary meshes is useful, e.g., for the finite-element method.…”

“…The CPM (Graner and Glazier 1992; Glazier and Graner 1993) is run on a regular lattice. The node-based CPM (Scianna and Preziosi 2016) can be run on irregular lattices. VirtualLeaf takes the CPM ‘off the lattice,’ with the current restriction that tissues must be confluent.…”

Seven Challenges in the Multiscale Modelling of Multicellular Tissues

“…A variety of multiscale modelling approaches have been developed for multicellular tissues (Fletcher et al, 2017). These approaches generally either discretise space into a regular (Lehotzky & Zupanc, 2019) or irregular (Scianna & Preziosi, 2016) lattice, or allow cells to move continuously in space (Drasdo & Höhme, 2005). Such approaches also vary in their geometric description: cells may be treated as point-like particles or prescribed shapes such as ellipsoids (Xu et al, 2008); or cell shape may be more complex and dynamic, evolving according to a balance of forces (Farhadifar et al, 2007) or stochastic fluctuations (Graner & Glazier, 1992).…”