Disordered hyperuniformity in biological systems: organization, function, and design principles.

Disordered hyperuniform systems are characterized by a complete suppression of normalized infinite-wavelength density fluctuations as in perfect crystals, yet they possess no conventional long-range order or broken symmetry like glasses. This unique form of organization endows such systems with certain superior structural and physical properties, including enhanced isotropy, robustness against defects, nearly optimal transport characteristics and mechanical behaviors. Originally studied in the context of condensed matter and soft materials, disordered hyperuniformity has recently been identified across a wide range of biological systems. Notable examples include avian photoreceptor mosaics, epithelial cell packings, looped leaf vein networks, and vegetation patterns in arid and semi-arid ecosystems, to name but a few. Despite vast differences in scale and function, these systems exhibit convergent hyperuniform organization, suggesting a possible unifying principle underlying biological pattern formation. In this review, we synthesize these developments and examine biological hyperuniformity through the lens of functionality optimization under intrinsic constraints, where evolutionary selection acts as a driving force toward near-optimal spatial organization. We discuss the physical mechanisms that can give rise to hyperuniform states in living systems, including interactions, growth dynamics, and environmental feedback. Finally, we highlight how these insights can inform the design of bio-inspired materials with tunable hyperuniformity and superior performance characteristics.