From coffee beans flowing in a chute to cells remodelling in a living tissue, a wide variety of close-packed collective systems— both inert and living—have the potential to jam. The collective can sometimes flow like a fluid or jam and rigidify like a solid. The unjammed-to-jammed transition remains poorly understood, however, and structural properties characterizing these phases remain unknown. Using primary human bronchial epithelial cells, we show that the jamming transition in asthma is linked to cell shape, thus establishing in that system a structural criterion for cell jamming. Surprisingly, the collapse of critical scaling predicts a counter-intuitive relationship between jamming, cell shape and cell–cell adhesive stresses that is borne out by direct experimental observations. Cell shape thus provides a rigorous structural signature for classification and investigation of bronchial epithelial layer jamming in asthma, and potentially in any process in disease or development in which epithelial dynamics play a prominent role.

As an injury heals, an embryo develops, or a carcinoma spreads, epithelial cells systematically change their shape. In each of these processes cell shape is studied extensively whereas variability of shape from cell-to-cell is regarded most often as biological noise. But where do cell shape and its variability come from? Here we report that cell shape and shape variability are mutually constrained through a relationship that is purely geometrical. That relationship is shown to govern processes as diverse as maturation of the pseudostratified bronchial epithelial layer cultured from non-asthmatic or asthmatic donors, and formation of the ventral furrow in the Drosophila embryo. Across these and other epithelial systems, shape variability collapses to a family of distributions that is common to all. That distribution, in turn, is accounted for by a mechanistic theory of cell-cell interaction showing that cell shape becomes progressively less elongated and less variable as the layer becomes progressively more jammed. These findings suggest a connection between jamming and geometry that spans living organisms and inert jammed systems, and thus transcends system details. Although molecular events are needed for any complete theory of cell shape and cell packing, observations point to the hypothesis that jamming behavior at larger scales of organization sets overriding geometrical constraints.

Coordinated motions of close-packed multicellular systems typically generate cooperative packs, swirls, and clusters. These cooperative motions are driven by active cellular forces, but the physical nature of these forces and how they generate collective cellular motion remain poorly understood. Here, we study forces and motions in a confined epithelial monolayer and make two experimental observations: 1) the direction of local cellular motion deviates systematically from the direction of the local traction exerted by each cell upon its substrate; and 2) oscillating waves of cellular motion arise spontaneously. Based on these observations, we propose a theory that connects forces and motions using two internal state variables, one of which generates an effective cellular polarization, and the other, through contractile forces, an effective cellular inertia. In agreement with theoretical predictions, drugs that inhibit contractility reduce both the cellular effective elastic modulus and the frequency of oscillations. Together, theory and experiment provide evidence suggesting that collective cellular motion is driven by at least two internal variables that serve to sustain waves and to polarize local cellular traction in a direction that deviates systematically from local cellular velocity.