Biological tissues can fluidize by tuning their internal degrees of freedom

Simple vertex models have effectively captured various mechanical characteristics of biological tissues, including rigidity transitions. These cell-based models contain parameters like preferred cell perimeters, which govern the system's mechanics and dynamics. Tissues are often modeled as having a specific, fixed distribution of such cell-scale parameters, characterized by an average value and a width. Inspired by the success of physical learning rules in resistor and spring networks to design materials that can learn tasks, we wonder whether biological tissues could be tuning these internal degrees of freedom to achieve design goals. As a first test of this idea, we allow cell-scale parameters in vertex models to vary as new learning degrees of freedom. We keep the overall distributions of these parameters fixed, but allow them to swap spatial locations, and minimize a simple cost function which is the total mechanical energy. Incorporating these transient degrees of freedom, in addition to the physical degrees of freedom represented by the vertex positions, alters the high dimensional energy landscape. We find that as we introduce the preferred cell perimeters as transient degrees of freedom, the system can find a lower energy state, so that the rigidity transition occurs at a lower average value of the perimeter. In other words, with the mechanical energy as the cost function, the system tunes itself to fluidize more easily. Moreover, there is an optimal width of the initial cell perimeter distribution to facilitate learning. Adding perimeter or area stiffnesses or preferred cell areas as new degrees of freedom, on the other hand, does not change the rigidity transition of tissues. Through analysis of tissue structural features in presence of learning degrees of freedom, we propose certain predictive metrics to ascertain whether real epithelial tissues leverage these extra degrees of freedom when performing specific functions.