Improving the realism of the cellular Potts model in simulations of biological cells

Ouchi, Noriyuki; Glazier, James A.; Rieu, Jean-Paul; Upadhyaya, Arpita; Sawada, Yasuji

doi:10.1016/s0378-4371(03)00574-0

Cited by 98 publications

(93 citation statements)

References 16 publications

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“…Adhesion between two cells tends to extend their contact length; it thus contributes negatively to the energy, ϪJ ij P ij , where JϾ0; in agreement with intuition, a higher J describes a stronger adhesion, whereas J ϭ 0 in the absence of adhesion (23,24). This extension is compensated by an elastic cell cortex term, 2 , where P is the perimeter modulus, and P 0i is the target perimeter of cell i.…”

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confidence: 67%

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Cell adhesion and cortex contractility determine cell patterning in the Drosophila retina

Käfer

Hayashi

Marée

et al. 2007

Proc. Natl. Acad. Sci. U.S.A.

185

174

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Because of the resemblance of many epithelial tissues to densely packed soap bubbles, it has been suggested that surface minimization, which drives soap bubble packing, could be governing cell packing as well. We test this by modeling the shape of the cells in a Drosophila retina ommatidium. We use the observed configurations and shapes in wild-type flies, as well as in flies with different numbers of cells per ommatidia, and mutants with cells where Eor N-cadherin is either deleted or misexpressed. We find that surface minimization is insufficient to model the experimentally observed shapes and packing of the cells based on their cadherin expression. We then consider a model in which adhesion leads to a surface increase, balanced by cell cortex contraction. Using the experimentally observed distributions of E-and N-cadherin, we simulate the packing and cell shapes in the wild-type eye. Furthermore, by changing only the corresponding parameters, this model can describe the mutants with different numbers of cells or changes in cadherin expression.cell shape ͉ surface mechanics ͉ Cellular Potts model

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supporting

confidence: 67%

“…In the present example of retina development, we show that interfacial tension should be variable, as described in a second model (23,24). Tension results from an adhesion-driven extension of cell-cell interfaces, balanced by an larger cortical tension (Eq.…”

Section: Constant and Variable Tension Modelsmentioning

confidence: 76%

Cell adhesion and cortex contractility determine cell patterning in the Drosophila retina

Käfer

Hayashi

Marée

et al. 2007

Proc. Natl. Acad. Sci. U.S.A.

185

174

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show abstract

“…S8; note that experimentally applying stretch to the pupal wing is technically very difficult). For numerical simulations, we modified the cell vertex model to control the anisotropic stress environment (supplementary material Appendix S1) (Honda, 1983;Graner and Sawada, 1993;Ouchi et al, 2003;Farhadifar et al, 2007;Käfer et al, 2007;Rauzi et al, 2008). Note that the hexagonal configuration was probably the energy-minimum state in each of the three conditions (Hales, 2001) (Fig.…”

Section: Research Articlementioning

confidence: 99%

The mechanical anisotropy in a tissue promotes ordering in hexagonal cell packing

2013

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SUMMARYMany epithelial tissues pack cells into a honeycomb pattern to support their structural and functional integrity. Developmental changes in cell packing geometry have been shown to be regulated by both mechanical and biochemical interactions between cells; however, it is largely unknown how molecular and cellular dynamics and tissue mechanics are orchestrated to realize the correct and robust development of hexagonal cell packing. Here, by combining mechanical and genetic perturbations along with live imaging and Bayesian force inference, we investigate how mechanical forces regulate cellular dynamics to attain a hexagonal cell configuration in the Drosophila pupal wing. We show that tissue stress is oriented towards the proximal-distal axis by extrinsic forces acting on the wing. Cells respond to tissue stretching and orient cell contact surfaces with the stretching direction of the tissue, thereby stabilizing the balance between the intrinsic cell junction tension and the extrinsic force at the cell-population level. Consequently, under topological constraints of the two-dimensional epithelial sheet, mismatches in the orientation of hexagonal arrays are suppressed, allowing more rapid relaxation to the hexagonal cell pattern. Thus, our results identify the mechanism through which the mechanical anisotropy in a tissue promotes ordering in cell packing geometry.

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“…In particular, the high negative value set for J int N,C prevents cells from fragmenting (we refer to [50,62] for comments). J ext C,C represents instead the adhesive strength between the membranes of two nearby cells, a measure of the quantity of active and exposed cadherins.…”

Section: Extended Cellular Potts Modelmentioning

confidence: 99%

A Hybrid Model Describing Different Morphologies of Tumor Invasion Fronts

Scianna

Preziosi

2012

Math. Model. Nat. Phenom.

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Abstract. The invasive capability is fundamental in determining the malignancy of a solid tumor. Revealing biomedical strategies that are able to partially decrease cancer invasiveness is therefore an important approach in the treatment of the disease and has given rise to multiple in vitro and in silico models. We here develop a hybrid computational framework, whose aim is to characterize the effects of the different cellular and subcellular mechanisms involved in the invasion of a malignant mass. In particular, a discrete Cellular Potts Model is used to represent the population of cancer cells at the mesoscopic scale, while a continuous approach of reaction-diffusion equations is employed to describe the evolution of microscopic variables, as the nutrients and the proteins present in the microenvironment and the matrix degrading enzymes secreted by the tumor. The behavior of each cell is then determined by a balance of forces, such as homotypic (cell-cell) and heterotypic (cell-matrix) adhesions and haptotaxis, and is mediated by the internal state of the individual, i.e. its motility. The resulting composite model quantifies the influence of changes in the mechanisms involved in tumor invasion and, more interestingly, puts in evidence possible therapeutic approaches, that are potentially effective in decreasing the malignancy of the disease, such as the alteration in the adhesive properties of the cells, the inhibition in their ability to remodel and the disruption of the haptotactic movement. We also extend the simulation framework by including cell proliferation which, following experimental evidence, is regulated by the intracellular level of growth factors. Interestingly, in spite of the increment in cellular density, the depth of invasion is not significantly increased, as one could have expected.

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Improving the realism of the cellular Potts model in simulations of biological cells

Cited by 98 publications

References 16 publications

Cell adhesion and cortex contractility determine cell patterning in the Drosophila retina

Cell adhesion and cortex contractility determine cell patterning in the Drosophila retina

The mechanical anisotropy in a tissue promotes ordering in hexagonal cell packing

A Hybrid Model Describing Different Morphologies of Tumor Invasion Fronts

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