A cell-centered, agent-based framework that enables flexible environment granularities

Derivation of continuum models from discrete models of mechanical forces in cell populations

In certain discrete models of populations of biological cells, the mechanical forces between the cells are center based or vertex based on the microscopic level where each cell is individually represented. The cells are circular or spherical in a center based model and polygonal or polyhedral in a vertex based model. On a higher, macroscopic level, the time evolution of the density of the cells is described by partial differential equations (PDEs). We derive relations between the modelling on the micro and macro levels in one, two, and three dimensions by regarding the micro model as a discretization of a PDE for conservation of mass on the macro level. The forces in the micro model correspond on the macro level to a gradient of the pressure scaled by quantities depending on the cell geometry. The two levels of modelling are compared in numerical experiments in one and two dimensions.

Impact of Force Function Formulations on the Numerical Simulation of Centre-Based Models

Centre-based or cell-centre models are a framework for the computational study of multicellular systems with widespread use in cancer modelling and computational developmental biology. At the core of these models are the numerical method used to update cell positions and the force functions that encode the pairwise mechanical interactions of cells. For the latter, there are multiple choices that could potentially affect both the biological behaviour captured, and the robustness and efficiency of simulation. For example, available open-source software implementations of centre-based models rely on different force functions for their default behaviour and it is not straightforward for a modeller to know if these are interchangeable. Our study addresses this problem and contributes to the understanding of the potential and limitations of three popular force functions from a numerical perspective. We show empirically that choosing the force parameters such that the relaxation time for two cells after cell division is consistent between different force functions results in good agreement of the population radius of a two-dimensional monolayer relaxing mechanically after intense cell proliferation. Furthermore, we report that numerical stability is not sufficient to prevent unphysical cell trajectories following cell division, and consequently, that too large time steps can cause geometrical differences at the population level.

Epithelial Migration and Non-adhesive Periderm Are Required for Digit Separation during Mammalian Development

The fusion of digits or toes, syndactyly, can be part of complex syndromes, including van der Woude syndrome. A subset of van der Woude cases is caused by dominant-negative mutations in the epithelial transcription factor Grainyhead like-3 (GRHL3), and Grhl3^-/-mice have soft-tissue syndactyly. Although impaired interdigital cell death of mesenchymal cells causes syndactyly in multiple genetic mutants, Grhl3^-/- embryos had normal interdigital cell death, suggesting alternative mechanisms for syndactyly. We found that in digit separation, the overlying epidermis forms a migrating interdigital epithelial tongue (IET) when the epithelium invaginates to separate the digits. Normally, the non-adhesive surface periderm allows the IET to bifurcate as the digits separate. In contrast, in Grhl3^-/- embryos, the IET moves normally between the digits but fails to bifurcate because of abnormal adhesion of the periderm. Our study identifies epidermal developmental processes required for digit separation.