Alternating regimes of motion in a model with cell-cell interactions.

Cellular movement is a complex dynamic process, resulting from the interaction of multiple elements at the intra- and extracellular levels. This epiphenomenon presents a variety of behaviors, which can include normal and anomalous diffusion or collective migration. In some cases, cells can get neighborhood information through chemical or mechanical cues. A unified understanding about how such information can influence the dynamics of cell movement is still lacking. In order to improve our comprehension of cell migration we have considered a cellular Potts model where cells move actively in the direction of a driving field. The intensity of this driving field is constant, while its orientation can evolve according to two alternative dynamics based on the Ornstein-Uhlenbeck process. In one case, the next orientation of the driving field depends on the previous direction of the field. In the other case, the direction update considers the mean orientation performed by the cell in previous steps. Thus, the latter update rule mimics the ability of cells to perceive the environment, avoiding obstacles and thus increasing the cellular displacement. Different cell densities are considered to reveal the effect of cell-cell interactions. Our results indicate that both dynamics introduce temporal and spatial correlations in cell velocity in a friction-coefficient and cell-density-dependent manner. Furthermore, we observe alternating regimes in the mean-square displacement, with normal and anomalous diffusion. The crossovers between diffusive and directed motion regimes are strongly affected by both the driving field dynamics and cell-cell interactions. In this sense, when cell polarization update grants information about the previous cellular displacement, the duration of the diffusive regime decreases, particularly in high-density cultures.

RPE Cell and Sheet Properties in Normal and Diseased Eyes.

Previous studies of human retinal pigment epithelium (RPE) morphology found spatial differences in density: a high density of cells in the macula, decreasing peripherally. Because the RPE sheet is not perfectly regular, we anticipate that there will be differences between conditions and when and where damage is most likely to begin. The purpose of this study is to establish relationships among RPE morphometrics in age, cell location, and disease of normal human and AMD eyes that highlight irregularities reflecting damage. Cadaveric eyes from 11 normal and 3 age-related macular degeneration (AMD) human donors ranging from 29 to 82 years of age were used. Borders of RPE cells were identified with phalloidin. RPE segmentation and analysis were conducted with CellProfiler. Exploration of spatial point patterns was conducted using the "spatstat" package of R. In the normal human eye, with increasing age, cell size increased, and cells lost their regular hexagonal shape. Cell density was higher in the macula versus periphery. AMD resulted in greater variability in size and shape of the RPE cell. Spatial point analysis revealed an ordered distribution of cells in normal and high spatial disorder in AMD eyes. Morphometrics of the RPE cell readily discriminate among young vs. old and normal vs. diseased in the human eye. The normal RPE sheet is organized in a regular array of cells, but AMD exhibited strong spatial irregularity. These findings reflect on the robust recovery of the RPE sheet after wounding and the circumstances under which it cannot recover.

Far-from-equilibrium growth of magnetic thin films with Blume-Capel impurities.

We investigate the irreversible growth of (2+1)-dimensional magnetic thin films. The spin variable can adopt three states (s(I)=±1,0), and the system is in contact with a thermal bath of temperature T. The deposition process depends on the change of the configuration energy, which, by analogy to the Blume-Capel Hamiltonian in equilibrium systems, depends on Ising-like couplings between neighboring spins (J) and has a crystal field (D) term that controls the density of nonmagnetic impurities (s(I)=0). Once deposited, particles are not allowed to flip, diffuse, or detach. By means of extensive Monte Carlo simulations, we obtain the phase diagram in the crystal field vs temperature parameter space. We show clear evidence of the existence of a tricritical point located at D(t)/J=1.145(10) and k(B)T(t)/J=0.425(10), which separates a first-order transition curve at lower temperatures from a critical second-order transition curve at higher temperatures, in analogy with the previously studied equilibrium Blume-Capel model. Furthermore, we show that, along the second-order transition curve, the critical behavior of the irreversible growth model can be described by means of the critical exponents of the two-dimensional Ising model under equilibrium conditions. Therefore, our findings provide a link between well-known theoretical equilibrium models and nonequilibrium growth processes that are of great interest for many experimental applications, as well as a paradigmatic topic of study in current statistical physics.