Suppression of anomalous dynamics by random pinning in three-dimensional confluent tissues

We numerically investigate the supercooled glassy dynamics of a three-dimensional Voronoi model for confluent cellular tissues, focusing on the effect of randomly pinning a fraction of cells. The dynamics are analyzed in both rigid and floppy regimes, tuned by the shape index. Unpinned floppy systems exhibit anomalous sub-Arrhenius temperature dependence of the structural relaxation time, a sub-diffusive mean-squared-displacement regime, and the preservation of the Stokes-Einstein (SE) relation across all temperatures-signatures of mean-field-like dynamics. In contrast, rigid systems show conventional super-Arrhenius behavior and a breakdown of the SE relation at low temperatures. Introducing random pinning systematically alters these behaviors: it suppresses the anomalous sub-diffusive regime in floppy systems, shifts their relaxation from sub-Arrhenius toward nearly Arrhenius behavior, and induces a breakdown of the SE relation in the supercooled regime. In rigid systems, pinning enhances dynamic heterogeneity, making the relaxation more super-Arrhenius and reducing the SE breakdown exponent. Pinning also increases the mean string length of cooperative string-like motion, raises the T1-transition rate in floppy systems, and strengthens the exponential correlation between this rate and the population of very small cell-cell interfaces, bringing these measures close to the values seen in rigid systems. These results demonstrate that geometrical constraint imposed by random pinning suppresses the unique anomalous glassy dynamics of under-constrained floppy confluent tissues, restoring conventional glass-forming behavior by enhancing geometric constraints and modifying the underlying energy landscape.