Segregation-pattern reorientation of a granular mixture on a horizontally oscillating tray

Molecular dynamics simulations of a multicellular model with cell-cell interactions and Hippo signaling pathway

The transcriptional coactivator Yes-associated protein (YAP)/transcriptional co-activator with PDZ binding motif (TAZ) induces cell proliferation through nuclear localization at low cell density. Conversely, at extremely high cell density, the Hippo pathway, which regulates YAP/TAZ, is activated. This activation leads to the translocation of YAP/TAZ into the cytoplasm, resulting in cell cycle arrest. Various cancer cells have several times more YAP/TAZ than normal cells. However, it is not entirely clear whether this several-fold increase in YAP/TAZ alone is sufficient to overcome proliferation inhibition (contact inhibition) under high-density conditions, thereby allowing continuous proliferation. In this study, we construct a three-dimensional (3D) mathematical model of cell proliferation incorporating the Hippo-YAP/TAZ pathway. Herein, a significant innovation in our approach is the introduction of a novel modeling component that inputs cell density, which reflects cell dynamics, into the Hippo pathway and enables the simulation of cell proliferation as the output response. We assume such 3D model with cell-cell interactions by solving reaction and molecular dynamics (MD) equations by applying adhesion and repulsive forces that act between cells and frictional forces acting on each cell. We assume Lennard-Jones (12-6) potential with a softcore character so that each cell secures its exclusive domain. We set cell cycles composed of mitotic and cell growth phases in which cells divide and grow under the influence of cell kinetics. We perform mathematical simulations at various YAP/TAZ levels to investigate the extent of YAP/TAZ increase required for sustained proliferation at high density. The results show that a twofold increase in YAP/TAZ levels of cancer cells was sufficient to evade cell cycle arrest compared to normal cells, enabling cells to continue proliferating even under high-density conditions. Finally, this mathematical model, which incorporates cell-cell interactions and the Hippo-YAP/TAZ pathway, may be applicable for evaluating cancer malignancy based on YAP/TAZ levels, developing drugs to suppress the abnormal proliferation of cancer cells, and determining appropriate drug dosages. The source codes are freely available.

Self-replicating segregation patterns in horizontally vibrated binary mixture of granules

Fluidized granular mixtures of various particle sizes exhibit intriguing patterns as different species segregate and condense. However, understanding the segregation dynamics is hindered by the inability to directly observe the time evolution of the internal structure. We discover self-replicating bands within a quasi-2D container subjected to horizontal agitation, resulting in steady surface waves. Through direct observation of surface flow and evolving internal structures, we reveal the crucial role of coupling among segregation, surface flow, and hysteresis in granular fluidity. We develop Bonhoeffer-van der Pol type equations grounded in experimental observations, reproducing complex band dynamics, such as replication, oscillation, and breathing. It suggests the similarity between pattern formation in granular segregation and that in reaction-diffusion systems.

Self-organization of agitated microspheres on various substrates

The vibration dynamics of relatively large granular grains is extensively treated in the literature, but comparable studies on the self-assembly of smaller agitated beads are lacking. In this work, we investigate how the particle properties and the properties of the underlying substrate surface affect the dynamics and self-organization of horizontally agitated monodisperse microspheres with diameters between 3 and 10 μm. Upon agitation, the agglomerated hydrophilic silica particles locally leave traces of particle monolayers as they move across the flat uncoated and fluorocarbon-coated silicon substrates. However, on the micromachined silicon tray with relatively large surface roughness, the agitated silica agglomerates form segregated bands reminiscent of earlier studies on granular suspensions or Faraday heaps. On the other hand, the less agglomerated hydrophobic polystyrene particles form densely occupied monolayer arrangements regardless of the underlying substrate. We explain the observations by considering the relevant adhesion and friction forces between particles and underlying substrates as well as those among the particles themselves. Interestingly, for both types of microspheres, large areas of the fluorocarbon-coated substrates are covered with densely occupied particle monolayers. By qualitatively examining the morphology of the self-organized particle monolayers using the Voronoi approach, it is understood that these monolayers are highly disordered, i.e., multiple symmetries coexist in the self-organized monolayers. However, more structured symmetries are identified in the monolayers of the agitated polystyrene microspheres on all the substrates, albeit not all precisely positioned on a hexagonal lattice. On the other hand, both the silica and polystyrene monolayers on the bare silicon substrates transition into less disordered structures as time progresses. Using Kelvin probe force microscopy measurements, we show that due to the tribocharging phenomenon, the formation of particle monolayers is promoted on the fluorocarbon surface, i.e., a local electrostatic attraction exists between the particle and the substrate.

Segregation and phase inversion of strongly and weakly fluctuating Brownian particle mixtures and a chain of such particle mixtures in spherical containers

We investigate the segregation pattern formation of strongly and weakly fluctuating Brownian particle mixtures confined in a three-dimensional spherical container. We consider systems where the particle motion is restricted by the harmonic external trapping potential and the container edge wall. In such systems, two segregation patterns are observed. When the container radius is sufficiently large, more weakly fluctuating particles accumulate near the center of the container than strongly fluctuating particles. On the other hand, the distributions of the strongly and weakly fluctuating particles are inverted when the container radius is small. With no external trapping potentials, we find similar segregation and phase inversion if the particles construct a chain (heterofluctuating polymer) and are confined in a three-dimensional spherical container. We could apply these phenomena in the study of biopolymer behavior, such as chromosomes in the cell nucleus.

The timescales of granular segregation in horizontally shaken monolayers

The results of an experimental investigation of segregation phenomenon in thin layers of a binary multi-particle system on a horizontal vibrating tray are discussed. Complex structures are observed to emerge from initially mixed states and result from interaction of individual particles. Qualitatively different segregation states are found which have disparate timescales and these are shown to have a systematic dependence on the control parameters.