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Self-tuning—the ability of disordered systems to develop desired collective behaviors by tuning internal couplings in response to feedback—has recently emerged as a powerful framework for understanding adaptation in amorphous solids, mechanical metamaterials, and electrical networks. These systems can learn desired responses, encode memory, and robustly reorganize under repeated stimuli, much like artificial neural networks but without requiring processors to adjust their weights. Here, we extend this paradigm to morphogenesis and show that it is useful to view the epithelium as tunable matter and epithelial convergent extension (CE) as a self-tuning process. Using a vertex model with active interfacial tensions, we systematically compare distinct tension-update processes, including externally imposed shear, global gradient descent optimization, and decentralized local feedback rules. We find that while all methods can generate tissue elongation, only a local orientation- and length-sensitive rule reproduces key experimental features of CE with reasonable fidelity. These features include supracellular actomyosin pattern formation, cell shape changes, and junctional alignment. In contrast, global optimization produces homogeneous, nearly isotropic tension patterns and tissue states that are less robust to force perturbations. By interpreting CE through the lens of tuning, our framework bridges the physics of tunable matter with developmental biology, revealing how simple, local rules enable tissues to efficiently orchestrate complex morphogenetic outcomes through decentralized mechanical feedback and adaptation. 

Rigidity is an emergent property of materials—it is not a feature of individual components that compose the structure, but instead arises from interactions between many constituent parts. It has been recognized that floppy–rigid or fluid–solid transitions are harnessed by biological systems at all scales to drive form and function. This review focuses on the different mechanisms that can drive emergent rigidity transitions in biomechanical networks and describes how they arise in mathematical formalisms and how they are observed in practice in experiments. The goal is to aid researchers in identifying mechanisms governing rigidity in their biological systems of interest, highlight mechanical features that are universal across different systems, and help drive new scientific hypotheses for observed mechanical phenomena in biology. Looking forward, we also discuss how biological systems might tune themselves toward or away from such transitions over developmental or evolutionary timescales. 

Abstract Stratified epithelial tissues such as the skin epidermis maintain barrier integrity during development and homeostasis through the coordinated action of cell proliferation, differentiation, delamination, and tissue-scale mechanical forces. During development, the orientation of cell division within the basal layer plays a pivotal role in tissue stratification; however, the mechanical principles linking the orientation of the division plane to these processes across developmental stages remain poorly understood. Here, we expand a recently developed three-dimensional vertex model for stratified epithelia, composed of the basement membrane, basal, and suprabasal layers, to study the mechanical and structural impact of cell divisions with a wider range of orientations. The model integrates developmental stage via specific changes in heterotypic interfacial tensions (arising from actomyosin cortical contractility and adhesion molecules at the basal–suprabasal interface) and tissue stiffness that have been quantified previously in experiments. By systematically varying background mechanical parameters, we investigate how heterotypic tension, division orientation, and tissue fluidity collectively influence the outcome of cell division. Our goal is to uncover the strategies that the embryo may employ to generate stratified phenotypes at different developmental stages, recognizing that these strategies might evolve over time. Although our focus is on the embryonic developmental stages of the epidermis, this framework may also be extended to investigate transformed cells, such as in cancer, to explore how altered division orientation contributes to precancerous or transformed phenotypes. 

Cells, tissues, and organs must change shape in precise ways during embryonic development to execute their functions. Multiple mechanisms including biochemical signaling pathways and biophysical forces help drive these morphology changes, but it has been difficult to tease apart their contributions, especially from tissue-scale dynamic forces that are typically ignored. We use a combination of mathematical models and in vivo experiments to study a simple organ in the zebrafish embryo called Kupffer’s vesicle (KV). Modeling indicates that dynamic forces generated by tissue movements in the embryo produce shape changes in KV that are observed during development. Laser ablations in the zebrafish embryo that alter these forces result in altered organ shapes matching model predictions. These results demonstrate that dynamic forces sculpt cell and organ shape during embryo development. 

Spontaneous phase separation, or demixing, is important in biological phenomena such as cellsorting. In particle-based models, an open question is whether differences in diffusivity can drive such demixing. While di erential-di usivity-induced phase separation occurs in mixtures with a packing fraction up to 0:7 [Weber et. al, Phys Rev Lett 2016], here we investigate whether demixing persists at even higher densities relevant for cells. For particle packing fractions between 0.7 and 1.0 the system demixes, but at packing fractions above unity the system remains mixed, exposing re-entrant behavior in the phase diagram that occurs when phase separation can no longer drive a change in entropy production at high densities. We also  find that a confluent Voronoi model for tissues does not phase separate, consistent with particle-based simulations. 

Flocking behavior is observed in biological systems from the cellular to superorganismal length scales, and the mechanisms and purposes of this behavior are objects of intense interest. In this paper, we study the collective dynamics of bovine sperm cells in a viscoelastic fluid. These cells appear not to spontaneously flock, but transition into a long-lived flocking phase after being exposed to a transient ordering pulse of fluid flow. Surprisingly, this induced flocking phase has many qualitative similarities with the spontaneous polar flocking phases predicted by Toner-Tu theory, such as anisotropic giant number fluctuations and nontrivial transverse density correlations, despite the induced nature of the phase and the clearly important role of momentum conservation between the swimmers and the surrounding fluid in these experiments. We also find a self-organized global vortex state of the sperm cells, and map out an experimental phase diagram of states of collective motion as a function of cell density and motility statistics. We compare our experiments with a parameter-matched computational model of persistently turning active particles and find that the experimental order-disorder phase boundary as a function of cell density and persistence time can be approximately predicted from measures of single-cell properties. Our results may have implications for the evaluation of sample fertility by studying the collective phase behavior of dense groups of swimming sperm.