Modeling emergent tissue organization involving high-speed migrating cells in a flow equilibrium

Abstract

There is increasing interest in the analysis of biological tissue, its organization and its dynamics with the help of mathematical models. In the ideal case emergent properties on the tissue scale can be derived from the cellular scale. However, this has been achieved in rare examples only, in particular, when involving high-speed migration of cells. One major difficulty is the lack of a suitable multiscale simulation platform, which embeds reaction-diffusion of soluble substances, fast cell migration and mechanics, and, being of great importance in several tissue types, cell flow homeostasis. In this paper a step into this direction is presented by developing an agent-based mathematical model specifically designed to incorporate these features with special emphasis on high speed cell migration. Cells are represented as elastic spheres migrating on a substrate in lattice-free space. Their movement is regulated and guided by chemoattractants that can be derived from the substrate. The diffusion of chemoattractants is considered to be slower than cell migration and, thus, to be far from equilibrium. Tissue homeostasis is not achieved by the balance of growth and death but by a flow equilibrium of cells migrating in and out of the tissue under consideration. In this sense the number and the distribution of the cells in the tissue is a result of the model and not part of the assumptions. For purpose of demonstration of the model properties and functioning, the model is applied to a prominent example of tissue in a cellular flow equilibrium, the secondary lymphoid tissue. The experimental data on cell speed distributions in these tissues can be reproduced using reasonable mechanical parameters for the simulated cell migration in dense tissue.

The formation of tight tumor clusters affects the efficacy of cell cycle inhibitors: A hybrid model study

“…Among the off-lattice agent-based models of cell colony growth, the cell-centered models are probably the most utilized model frameworks [55,56,57,58,59,60,61,62,63,64], sometimes applied in combination with a continuum description to represent densities or populations of inactive cells, such as nonproliferating, quiescent, or necrotic cell regions [65,66]. More complex models trace cell membrane points or cell–cell boundary interface inputs, as in the vertex-based models [67,68], Voronoi-Delaunay cellular models [69,70], and fluid-based elastic cell models [43,48,71]. The subcellular element models [72,73] explore internal cell complexity by including not only the cell surface but also the intracellular components.…”

Models of Cell Migration

“…This resulted in a model of deformable space-filling polyhedra, where the cells' shapes depended on the cell neighborhood and they exhibited internal viscoelastic dynamics. This approach is most suitable for the modeling of interacting and motile cellular compounds in tissues [155] (see Sect. 7).…”

“…6.2.2). This approach is best applied to fast lymphocytes [120,155] in a chemokine distribution generated by a point source. The high speed of the cells' migration implies that the time scale of chemokine diffusion and cell movement are comparable, and that the chemokine distribution can no longer be modeled by a quasi-steady-state approximation.…”

“…Together with the friction in the tissue, this system is described by coupled Newtonian equations of motion in an overdamped approximation [144,150]. The contact partners of cells are derived from a Delaunay triangulation [150,155] which is locally updated in response to cell movement [170,171]. The mechanical parameters of cell migration are chosen such that the speed distributions of motile lymphocytes in their natural environment [155] are reproduced.…”

A cell based modelling framework for skeletal tissue engineering applications

“…Most cell based models can be characterized as either lattice-based or lattice-free models (reviewed by Alber et al, 2002;Moreira and Deutsch, 2002;Anderson et al, 2007). Cell aggregates of different cellular systems have been studied using lattice free cell based models, such as epidermis (Schaller and Meyer-Hermann, 2007), liver , lymph node (Beyer and Meyer-Hermann, 2007) and tumours (Galle et al, 2006a). Till date, these models have not yet been applied to study specific bone tissue engineering applications (Sengers et al, 2007).…”