# cellular potts model tutorial

2016; Belmonte et al. Lattice sites that are not occupied by cells are the medium. 662 0 obj <> endobj The direction is stored in a PropertyVector that is used to plot the color and arrows in Gnuplotter. This model specifies CellType which has a VolumeConstraint and a Proliferation plugin. ( Log Out /  CPM describes cells as deformable objects with a certain volume, that can adhere to each other and to the medium in which they live. 1 0000346755 00000 n To model a superdiffusive Levy walk, this waiting time is chosen from an exponential distribution: change_time = time + 20 * rand_gamma(0.5, 5). This model specifies CellType which has a VolumeConstraint and a Proliferation plugin. Furthermore, by incorporating a second role of GDNF as a stimulator of cell proliferation in the ureteric epithelia (Pepicelli et al. Change ), You are commenting using your Facebook account. Because the clusters rotate very slowly, the network is not in equilibrium, but continues to evolve, ever more slowly towards equilibrium, a phenomenon called dynamical arrested. 0000016525 00000 n Change the boundary conditions from circular=constant to x/y=periodic and observe the resulting collective motion. ) 'Q�N�s�˕���9��F��b]jAAL�C�N��PԠ^"o�9���z\�L��~��������@�� p̌*�]U(�e�e�)��{��ȥ�z��+*k���Q����R�s���?Y�84��D��loq؜������ήnkh�=�~U���ǼW��,C���0W�[ ��2�L�� ���pt*63�I)6�ۉ]G��o�޳���v��Ʋ�͞��Q�;���r��� ����c��+. In general, tissue morphogenesis involves multiple feedback regulation loops; the studies review above illustrate that the CPM is a convenient modeling framework to implement such complex events. ) These parameters come from your steppables. 0000005798 00000 n 2012) can, besides vasculogenesis, also explain sprouting from cellular spheroids, an in vitro mechanism thought to be representative for the first steps of angiogenesis (Szabó et al. noted that the diffusion speed for VEGF that was assumed in (Merks et al. 0000004369 00000 n 0000312940 00000 n 0000312613 00000 n The authors proposed that an increased tension at elongated parts of the network could recruit cell–cell adhesion molecules. Other names for the CPM are extended large-q Potts model and Glazier and Graner model. j 0000345765 00000 n 0000008458 00000 n In order to promote or inhibit angiogenesis in these processes, a better understanding of the mechanisms behind blood vessel formation is required. 2019 IEEE/ASME International Conference on Advanced Intelligent Mechatronics (AIM). ( Log Out /  Δ, The cell behavior in the CPM depends on a balance of forces described by a generalized energy, Cyst formation. Formally, a Cellular Potts Model is a time-discrete Markov chain (Markov pro-cess). H One of these (called matrix) is used to represent a matrix with higher adhesivity. In this example, it used to set the stemness (s) of one daughter to 1 and the stemness of the other daughter cell to 0. {\displaystyle \Delta H} “Volume” again). 4C). By incorporating details on the subcellular scale and the microenvironment, more realistic tissue dynamics can be inferred and we can increase our understanding of how mechanisms working on different tissue scales and the intricate interplay among them may promote or inhibit blood vessel formation. 0000007318 00000 n 2008). Hence, it is expected that a large amount of data on multicellular dynamics can be accumulated. ( 2014). However, in early applications of this model, cell movement was taken as a consequence of membrane fluctuations due to cell-cell interactions, or as a response to an external chemotactic gradient. Because the biological structures can be flexibly represented on regular lattices, the CPM can be conveniently interfaced with simulations of a range of physical processes, including reactions within cells, diffusion in extracellular space, and the mechanics of the extracellular matrix (Angermann et al. The CPM simulations are often not yet adequate to assimilate measured data with physical units (Marée et al. This tutorial is aimed at those who wish to understand CompuCell more deeply; to understand how the Potts Model resembles (and differs from) actual cellular phenomenon; and to understand the nuances of the different approaches one must take. 2014; Miyawaki & Niino 2015). 2005). 0000345332 00000 n 0000087767 00000 n 0000344473 00000 n Using an energy function to describe properties of the cells, we found that the interaction between contractile tension along cell–cell junctions and cell–cell adhesion plays an important role not only in determining the dynamics and morphology of cells in the monolayer, but also in influencing whether or not a wound in the monolayer will close. This model show a CPM simulation of a growing cell population in 3D. , trailer 2011), suggesting that including interactions of cells with the ECM is vital for increasing our understanding of the mechanisms of vasculogenesis. School of Mathematics and Physics, The University of Queensland, St. Lucia, Brisbane, Queensland, Australia 4072 The model defines a CPM cell that has two properties: The change in direction is using a VectorRule. Multi-Scale Mathematical Modeling of Prion Aggregate Dynamics and Phenotypes in Yeast Colonies. 0000252791 00000 n This symbol can then be used to distinguish both daughter cells and treat them differently. * 0000346709 00000 n + The authors found that haptokinesis promotes the formation of branches while haptotaxis primarily influenced the degree of sprouting. Corresponding authors, a 0000017949 00000 n μ Observations of tip and stalk cell motility in mouse embryoid bodies and mouse retina assays show that the tip cell position and role is repeatedly taken over by stalk cells further behind on the sprout (Jakobsson et al. Practically, the higher this is set, the more the cell membrane fluctuates and seems raggedy. E-mail: 0000004336 00000 n {\displaystyle \mu } The crypt-like domain is specified by loading an external 8-bit TIFF image file using Lattice/Domain/Image. 2010). z.neufeld@uq.edu.au, b They examined the relationship between doubling time in cell division and relaxation time of the system to its mechanical equilibrium during cystogenesis, and found that the multilumen structures tend to appear when the doubling time is shorter than the relaxation time (Fig. The function and mechanisms of this observed mechanism were not immediately clear and are subject to further studies. 0000006437 00000 n i 0000345116 00000 n 0000071693 00000 n During the process of the mutual induction between these tissues, the UB is formed by budding from the WD and elongates to the MM region, initiating a number of iterative branching events (Michos 2009; Costantini & Kopan 2010). 4B). In vitro studies have revealed that cells involved in cystogenesis acquire apico‐basal polarity during the process, and several cellular activities including proliferation and migration involved in maintaining cell–cell adhesion are coordinated to generate the spherical structure polarized on a tissue scale (Bryant & Mostov 2008; Martin‐Belmonte & Mostov 2008).