Configurational entropy as a driver of tissue structural heterogeneityVasudha Srivastava, Jennifer L. Hu, Sundus F. Shalabi, James C. Garbe, Boris Veytsman, Martha R.Stampfer, Matt Thomson, Greg Huber, Mark A. LaBarge, ZevJ. Gartner

A hallmark of tissues is the ability of their multiple cell types to form and maintain complex structures by self-organization. While tissues have an identifiable average structure, tissues remain spatially and temporally heterogeneous, where the local arrangement of cells can deviate significantly from the population average. The fundamental sources of this heterogeneity remain unknown. We therefore reconstituted primary human mammary epithelial cells into organoids with carefully controlled composition, geometry and microenvironment as models to study the emergence of tissue heterogeneity during self-organization. At the steady state these organoids closely mimic in vivo tissue architecture, excluding luminal cells from the tissue edge while maintaining a highly heterogeneous ensemble structure centered around a reproducible mean. We demonstrate that the observed structural ensemble follows Boltzmann statistics, corresponding to the maximum entropy distribution subject to the energetic constraints derived from interfacial mechanics. We directly measure the relative entropy and mechanical energy of different tissue configurations and use a statistical mechanical framework to systematically engineer organoid ensembles by either perturbing their mechanical potential, entropy, or activity (the active "temperature" of the tissue). These experiments reveal that the configurational entropy of cell arrangements imposes a theoretical limit to structural order at the tissue level.