Volume and surface constraints in the Cellular Potts Model.pdfVIP

Volume and surface constraints in the Cellular Potts Model 5 0 0 2 c Nikodem J. Poplawski e D Biocomplexity Institute and Department of Physics, Indiana University, 727 East 4 1 Third Street, Swain Hall West 117, Bloomington, IN 47405, USA ] h p - Abstract p m o Glazier and Graner’s Cellular Potts Model is a latticebased stochastic framework c. designed to simulate cell interactions and movement. The dynamics of the cells is s described by the Hamiltonian, which includes the terms representing cell adhesion c i and elasticity. In this paper, we analyze the terms corresponding to the two elastic s y moduli of a deformed isotropic body: the volume constraint which represents cell h compressibility, and the surface area constraint which is related to shear. We propose p [ to replace the surface term by a function of the dimensionless combination of the volume and surface area of a cell. Such a modified Hamiltonian is more consistent 2 v with classical elasticity. 9 2 1 Key words: Cellular Potts Model, differential cell adhesion, cell deformation, 2 elastic energy, elastic moduli 1 5 PACS: 46.05.+b, 46.15.x, 87.18.Bb 0 / s c i s y h 1 Introduction p : v i X Experiment shows that embryonic cell aggregates behave like deformable solids r a at shorttime scales, and like viscous liquids at longtime scales [1,2]. The viscoelastic moduli of the cytoplasm of various cells, as well as solutions of major cytoplasmic biopolymers and various cellular components, have been measured (see Ref. [3] and the references therein). Viscoelastic properties of embryonic tissues can