|, https://www.frontiersin.org/articles/10.3389/fphy.2018.00061/full#supplementary-material, Creative Commons Attribution License (CC BY). Murray JD. Code includes the extension for cell migration published in. 0597). Contact-inhibited chemotaxis in de novo and sprouting blood-vessel growth. We use essential cookies to perform essential website functions, e.g. Proc Natl Acad Sci USA. (2012) 9:016010. doi: 10.1088/1478-3975/9/1/016010, 56. Annu Rev Conden Matter Phys. In computational biology, a Cellular Potts model is a computational model of cells and tissues. [48]. (1999) 30:183–98. Szabó A, Ünnep R, Méhes E, Twal WO, Argraves WS, Cao Y, et al. Mizutani T, Haga H, Kawabata K. Data set for comparison of cellular dynamics between human AAVS1 locus-modified and wild-type cells. Beatrici CP, Brunnet LG. (2002) 64:327–53. J Exp Med. 7. Collective cell migration: leadership, invasion and segregation. Graner and Glazier have shown that the CPM model with solely differential adhesion, as driving force, is able to generate cell sorting [16]. they're used to log you in. Cates ME, Tailleur J. Motility-induced phase separation. (1992) 38:1092–104. Guidance of collective cell migration by substrate geometry. The cellular Potts model is increasingly being used for the mathematical modeling of a wide range of biological phenomena, including wound healing, tumor growth, and cancer cell migration. (2008) 81:435–60. For ϕ = 0.95 and low density, we observe a double exponential decay with a slower decrease of the autocorrelation function at long time scales independent on the τ value. The differential adhesion hypothesis: a direct evaluation. J Cell Sci. (2015) 114:228102. doi: 10.1103/PhysRevLett.114.228102, 47. J R Soc Interface (2012) 9:3268–78. Learn more. Kabla AJ. These can be converted to PNGs using the provided python script (which assumes a fixed lattice site of 200x200). (2015) 11:e1004280. PLoS ONE (2008) 3:e2093. doi: 10.1016/j.dib.2015.12.053. Both bell- and crater-shape distributions for cell velocity have been predicted by a mathematical model that considers the actin flow [47], connecting persistent motion with crater-shape distribution, in agreement with our findings. (2012) 108:098102. doi: 10.1103/PhysRevLett.108.098102, 12. 36. doi: 10.1529/biophysj.105.061150. Moving forward moving backward: directional sorting of chemotactic cells due to size and adhesion differences. Note that, according to Equation (3) the angle of the driving force ΘM depends on its previous value but does not depend on the direction of the cell movement αM. Bull Math Biol. Phys A (2001) 293:549–58. However, for high density, there is a small deviation and scaled behavior depends on the τ-value, showing the complex behavior generated by the interaction between cells. We would like to thank Luciana Bruno and Fernando Peruani for the fruitful discussions and for their helpful comments on this work. In order to take into account this feedback loop, an alternative way to update the angle ΘM is: where αM(t*)¯ is the mean displacement angle over the last τ MCS, and the other parameters are the same as in Equation (3). We observe that, for any cell density, both the temporal and spatial correlations of the cell velocities are higher when using Equation (5) instead of Equation (3) (see Supplementary Figures 4, 5). Besides, we find that the particular way in which the cell movement direction is updated has important effects on the spatial correlation. Salazar-Ciudad I, Jernvall JM, Newman SA. 53. Phys. Phys Rev E (2011) 84:031927. doi: 10.1103/PhysRevE.84.031927, 13. (2005) 89:912–31. In Figure 6 one can observe that at very short distances (r < 8 pixels) cells are anti-correlated. Work fast with our official CLI. C(t) obtained when considering Equation (5) for ρ = 0.2 is almost independent of the parameter ϕ, whereas for ρ = 0.9 short and long-time behavior of C(t) depends on τ and ϕ in a non trivial manner (see Supplementary Figure 4). doi: 10.1073/pnas.1318967111. J Theor Biol. 8. Since the classical Steinberg experiments, it has been demonstrated that differential adhesion is a key ingredient for cell rearrangement and cell sorting [53, 54]. Cell sorting of two different cell types based on the Differential Adhesion Hypothesis (DAH), where the inner (white) cells are more cohesive than the outer (red) cells. Crawling and Gliding: A Computational Model for Shape-Driven Cell Migration Phys Rev Lett. 51. Invasion from a cell aggregate - The roles of active cell motion and mechanical equilibrium. Learn more. Thus, the timing of the cell movement is given by two parameters: the persistence time τ and the autoregressive parameter ϕ, instead of only one as in Beltman et al. Biophys J. The model itself is implemented as node.js modules and can be run within node.js and the web browser. Optimal estimation of cell movement indices from the statistical analysis of cell tracking data. Selmeczi D, Mosler S, Hagedorn P, Larsen N, Flyvbjerg H. Cell motility as persistent random motion: theories from experiments. The MSD obtained for high density is lower than that obtained for low density, as expected. Gonzalez-Rodriguez D, Guevorkian K, Douezan S, Brochard-Wyart F. Soft matter models of developing tissues and tumors. Vertical arrows mark the transition between ballistic and random walk behavior. Marée AFM, Panfilov AV, Hogeweg P. Migration and thermotaxis of Dictyostelium discoideum slugs, a model study. Visualization is not handled by the modules, but example visualizations for 2D (using Canvas) and 3D (using three.js) are included in the "examples" directory. Grima R. Multiscale modeling of biological pattern formation. 27. 5. This complex decay behavior could be the result of the interplay between the parameters τ and ϕ. Keywords: cell motility, cellular Potts model, cell-cell interactions, random walk, cell adhesion, Citation: Guisoni N, Mazzitello KI and Diambra L (2018) Modeling Active Cell Movement With the Potts Model. J Theor Biol. Proc Natl Acad Sci USA. Dunn GA. Characterising a kinesis response: time averaged measures of cell speed and directional persistence. Basel: Birkhäuser (2007). doi: 10.1371/journal.pcbi.1002944, 10. This book shows how the cellular Potts model can be used as a framework for model building and how extended models can achieve even better biological practicality, accuracy, and predictive power. This extension has been used to model the D. discoideum morphogenesis [19–21], to investigate collective cell migration (or motion) in Szabó et al. Scaling MSD with τ2 and the time with τ, we can observe that the scaled behavior is independent of ϕ and τ for ρ = 0.2. 16. Also, for ρ = 0.9, simulations with τ = 10 present a slightly smaller correlation length than simulations with τ = 50 and 100 (9.1, 10.2, and 11.0, respectively). Figure 6 shows C(r) for two different cell densities on the substrate, ρ = 0.2 and 0.9 (solid and dashed lines, respectively), and three different values of τ. 58. Simulation of biological cell sorting using a two-dimensional extended Potts model. Continuous models for cell migration in tissues and applications to cell sorting via differential chemotaxis. doi: 10.1371/journal.pone.0007190, 23. doi: 10.1016/j.cell.2015.01.056, 48. Garcia S, Hannezo E, Elgeti J, Joanny JF, Silberzan P, Gov NS. (2016) 6:793–98. Phys D (2003) 181:157–70. Novel type of phase-transition in a system of self-driven particles. doi: 10.1007/b138451. Data was obtained by averaging between 0 and 4,000 MCS and over 50 and 10 samples, for ρ = 0.2 and 0.9, respectively. Peruani F, Starruß J, Jakovljevic V, Søgaard-Andersen L, Deutsch A, Bär M. Collective motion and nonequilibrium cluster formation in colonies of gliding bacteria. (2013) 9:e1002944. GitHub is home to over 50 million developers working together to host and review code, manage projects, and build software together. The Makefile runs run-2d.js and generates png files and an mp4 movie automatically in the folder output/. This vector can induce a bias on the membrane sites belonging to a cell in the direction given by chemoattractant gradients. NG and KM developed the algorithms and wrote the manuscript. If nothing happens, download GitHub Desktop and try again. These curves display a peak around 14–16 pixels, close to the diameter of a non-interacting cell. Haga H, Irahara C, Kobayashi R, Nakagaki T, Kawabata K. Collective movement of epithelial cells on a collagen gel substrate.