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...

The authors study the arrangement of cells in undifferentiated vegetable tissues of five different species. The distribution of the number of sides, the average area (an), perimeter (pn) and side length (ln) of n-sided cells are determined as well as the correlation between the number of sides of a cell and of its neighbours. The results show that vegetable cellular nets obey Aboav-Weaire's law. They also discuss Lewis' law and a possible relation between (pn) and n. The analysis of these structures provides a different example of random cellular structures and helps to show general aspects of the ideal one.

Thermal growth of silicon oxide films on Si in dry O 2 is modeled as a dynamical system, assuming that it is basically a reaction-diffusion phenomenon. Relevant findings of the last decade are incorporated, as structure and composition of the oxide/Si interface and O 2 transport and reaction at initial stages of growth. The present model departs from the well-established Deal and Grove framework ͓B. E. Deal and A. S. Grove, J. Appl. Phys. 36, 3770 ͑1965͔͒ indicating that its basic assumptions, steady-state regime, and reaction between O 2 and Si at a sharp oxide/Si interface are only attained asymptotically. Scaling properties of these model equations are explored, and experimental growth kinetics, obtained for a wide range of growth parameters including the small thickness range, are shown to be well described by the model.

We perform extensive Potts model simulations of three-dimensional dry foam coarsening. Starting with 2.25 million bubbles, we have enough statistics to fulfill the three constraints required for the study of statistical scale invariance: first, enough time for the transient to end and reach the scaling state; then, enough time in the scaling state itself to characterize its properties; and finally, enough bubbles at the end to avoid spurious finite size effects. In the scaling state, we find that the average surface area of the bubbles increases linearly with time. The geometry ͑bubble shape and size͒ and topology ͑number of faces and edges͒, as well as their correlations, become constant in time. Their distributions agree with the data of the literature. We present an analytical model ͑universal, up to parameters extracted from the simulations͒ for a disordered foam minimizing its free energy, which agrees with the simulations. We discuss the limitations of the simulations and of the model.

Mesenchymal cell crawling is a critical process in normal development, in tissue function, and in many diseases. Quantitatively predictive numerical simulations of cell crawling thus have multiple scientific, medical, and technological applications. However, we still lack a low-computational-cost approach to simulate mesenchymal three-dimensional (3D) cell crawling. Here, we develop a computationally tractable 3D model (implemented as a simulation in the CompuCell3D simulation environment) of mesenchymal cells crawling on a two-dimensional substrate. The F€ urth equation, the usual characterization of meansquared displacement (MSD) curves for migrating cells, describes a motion in which, for increasing time intervals, cell movement transitions from a ballistic to a diffusive regime. Recent experiments have shown that for very short time intervals, cells exhibit an additional fast diffusive regime. Our simulations' MSD curves reproduce the three experimentally observed temporal regimes, with fast diffusion for short time intervals, slow diffusion for long time intervals, and intermediate time -interval-ballistic motion. The resulting parameterization of the trajectories for both experiments and simulations allows the definition of time-and length scales that translate between computational and laboratory units. Rescaling by these scales allows direct quantitative comparisons among MSD curves and between velocity autocorrelation functions from experiments and simulations. Although our simulations replicate experimentally observed spontaneous symmetry breaking, short-timescale diffusive motion, and spontaneous cell-motion reorientation, their computational cost is low, allowing their use in multiscale virtual-tissue simulations. Comparisons between experimental and simulated cell motion support the hypothesis that short-time actomyosin dynamics affects longertime cell motility. The success of the base cell-migration simulation model suggests its future application in more complex situations, including chemotaxis, migration through complex 3D matrices, and collective cell motion.