Correlating Topology, Geometry, and Mechanics in Tissue Monolayers
In disordered tilings in two dimensions, the distribution of neighbor numbers (topology) and sizes of the domains have been shown to correlate strongly, suggesting that such an analysis has diagnostic value in practical applications such as tissue samples for disease screening or morphogenetic studies. We have further demonstrated that the validity of the relation between cross-sectional area and topology known as Lewis’ Law is strongly dependent on the geometry of the individual domains, in particular their eccentricity. Seeking a deeper physical reason for the domain shapes, we show that a leading-order 2-D mechanical model containing only generic elasticity and adhesion terms for each domain can successfully link these topology and geometry properties to quantifiable mechanical properties of the disordered domain material. Changes in topological and domain shape statistics are thus understood as signatures of a rigidity transition in the tissue. Experimental results from epidermal plant tissue support these conclusions.
Bio
Sascha Hilgenfeldt obtained his diploma degree in physics from TU Munich and his PhD in physics from Marburg University. After a post-doctoral fellowship at Harvard University, he held faculty positions at University of Twente (The Netherlands) and Northwestern University before joining the University of Illinois at Urbana-Champaign, where he has appointments in Mechanical Science and Engineering as well as Physics. His research is concerned with the shape and dynamics of interfacial structures, ranging from oscillating micrometer-scale bubbles that drive novel microfluidic flows to the investigation of foams, biological cell shapes, the mechanical role of cell-cell adhesion, and the statistics of cells in tissues.