The study of how cells interact to produce tissue development, homeostasis, or diseases was, until recently, almost purely experimental. Now, multi-cell computer simulation methods, ranging from relatively simple cellular automata to complex immersed-boundary and finite-element mechanistic models, allow in silico study of multi-cell phenomena at the tissue scale based on biologically observed cell behaviors and interactions such as movement, adhesion, growth, death, mitosis, secretion of chemicals, chemotaxis, etc. This tutorial introduces the lattice-based Glazier–Graner–Hogeweg (GGH) Monte Carlo multi-cell modeling and the open-source GGH-based CompuCell3D simulation environment that allows rapid and intuitive modeling and simulation of cellular and multi-cellular behaviors in the context of tissue formation and subsequent dynamics. We also present a walkthrough of four biological models and their associated simulations that demonstrate the capabilities of the GGH and CompuCell3D.

A self-propelled particle model is introduced to study cell sorting occurring in some living organisms. This allows us to evaluate the influence of intrinsic cell motility separately from differential adhesion with fluctuations, a mechanism previously shown to be sufficient to explain a variety of cell rearrangement processes. We find that the tendency of cells to actively follow their neighbors greatly reduces segregation time scales. A finite-size analysis of the sorting process reveals clear algebraic growth laws as in physical phase-ordering processes, albeit with unusual scaling exponents. DOI: 10.1103/PhysRevLett.100.248702 PACS numbers: 87.17.ÿd, 05.65.+b, 64.75.ÿg Regeneration after tissue dissociation and reaggregation of some species of sponges, sea urchins, and hydras has been investigated in a series of experiments [1]. These phenomena involve cell sorting: Initially mixed cells form clusters, similarly to domain growth processes in physics. To explain cell sorting, Steinberg [2] proposed the differential adhesion hypothesis (DAH), which postulates that local rearrangements depend on the adhesion and motility properties of the different types of cells involved.Experiments have verified some of the DAH postulates. Surface tension measurements in chicken embryonic tissues [3] and determination of adhesive forces between pairs of Hydra cells [4] confirmed the relative magnitudes necessary to favor tissue envelopment: Ectodermic cells are less cohesive than endodermic cells. It was also shown that random membrane ruffling induces effective cell motion [5]. However, the coherent component of cellular flow must also be considered, as in viscoelastic fluids [6]. Remarkable experiments on Hydra performed in two spatial dimensions by Rieu et al. [7,8] discriminate between random and coherent motion contributions to cell segregation, showing that, during aggregate rounding or sorting, endodermic cell dynamics is dominated by the coherent behavior of ectodermic cells. Also, short-range spatial correlations corresponding to parallel displacement of adjacent cells were observed. The diffusive properties of cells were also measured. In all cases, diffusion was found to be normal only beyond a trapping time during which cells keep the same neighbors. This time is smaller for endodermic cells immersed in the ectoderm.Cell-sorting phenomena, such as Hydra regeneration from random cellular aggregates, have been simulated in the seminal work by Graner and Glazier in 1992 [9], later extended by Hogeweg and co-workers [10] (hereafter the GGH model). In the GGH model, cells are represented on a site-labeled lattice. A connected group of sites with the same label stands for a cell, and an energy function accounts for surface tension between adjacent cells while keeping the cell sizes fluctuating around specified targets.Monte Carlo simulations showed that sorting may occur, with less adhesive cells engulfing the more adhesive ones. However, this type of approach cannot easily account for locally coherent active cell mo...

Somitogenesis, the formation of the body's primary segmental structure common to all vertebrate development, requires coordination between biological mechanisms at several scales. Explaining how these mechanisms interact across scales and how events are coordinated in space and time is necessary for a complete understanding of somitogenesis and its evolutionary flexibility. So far, mechanisms of somitogenesis have been studied independently. To test the consistency, integrability and combined explanatory power of current prevailing hypotheses, we built an integrated clock-and-wavefront model including submodels of the intracellular segmentation clock, intercellular segmentation-clock coupling via Delta/Notch signaling, an FGF8 determination front, delayed differentiation, clock-wavefront readout, and differential-cell-cell-adhesion-driven cell sorting. We identify inconsistencies between existing submodels and gaps in the current understanding of somitogenesis mechanisms, and propose novel submodels and extensions of existing submodels where necessary. For reasonable initial conditions, 2D simulations of our model robustly generate spatially and temporally regular somites, realistic dynamic morphologies and spontaneous emergence of anterior-traveling stripes of Lfng. We show that these traveling stripes are pseudo-waves rather than true propagating waves. Our model is flexible enough to generate interspecies-like variation in somite size in response to changes in the PSM growth rate and segmentation-clock period, and in the number and width of Lfng stripes in response to changes in the PSM growth rate, segmentation-clock period and PSM length.

The formation of body segments (somites) in vertebrate embryos is accompanied by molecular oscillations (segmentation clock). Interaction of this oscillator with a wave traveling along the body axis (the clock-and-wavefront model) is generally believed to control somite number, size, and axial identity. Here we show that a clock-and-wavefront mechanism is unnecessary for somite formation. Non-somite mesoderm treated with Noggin generates many somites that form simultaneously, without cyclic expression of Notch-pathway genes, yet have normal size, shape, and fate. These somites have axial identity: The Hox code is fixed independently of somite fate. However, these somites are not subdivided into rostral and caudal halves, which is necessary for neural segmentation. We propose that somites are self-organizing structures whose size and shape is controlled by local cell-cell interactions.