Crystallography of Honey Bee Comb Construction

蜂巢是分布式架构的杰作。这种由蜡制成的储存结构对蜂群的生存至关重要，它以近乎最佳的方式建造，最大限度地减少了蜡与储存空间的比例，因为与蜡生产相关的能源成本很高。不管蜜蜂工作的表面是不规则的还是不平坦的，它们都能以惊人的精度构建蜂巢。然而，蜜蜂如何根据环境的限制（例如，树上预先存在的空穴）来调整它们的结构，人们对其机制知之甚少。这个项目的目标是通过将其作为一个图案形成过程来阐明梳子的构造过程，这使我们能够利用梳子结构与晶体和石墨烯等非生命材料结构之间的相似性。该项目结合了来自多个学科的工具，带来了来自动物行为和晶体学的见解。这项研究的结果是一个新颖的框架，用于模拟蜜蜂的集体行为，以及定量描述蜜蜂晶格的几何和拓扑结构。这个项目不仅将帮助我们理解蜜蜂的集体行为，而且还将帮助我们利用这种理解，在群体机器人、集体建筑和轻量级细胞结构领域创造生物启发的系统设计。该研究项目将解决三个具体问题：(1)蜂窝结构中的不规则性是考虑到远距离挫折源（例如，树洞的固体边界）的全局规划的结果，还是对给定细胞的直接环境的局部反应？(2)蜂窝状图案是否可以解释为能量最小化过程的结果，如果是这样，解决方案是否可以与几何挫折下各种自组织晶体系统（例如，胶体晶体或石墨烯）中一致发现的图案相媲美？(3)梳子构造几何问题的最优解在多大程度上受到环境的大规模变化（如工程边界、各种给定的单元尺寸或曲率）的调节？该项目的研究人员将使用3d打印来构建精确控制和量化的蜂窝基础，这可以用于在实验中引入系统和可重复的几何挫折源。最终的梳状结构将被成像和分析（计算机视觉技术，x射线显微镜），以精确表征单个细胞的几何形状和全局晶格的拓扑结构。这个丰富的信息集将用于开发和验证数据驱动的基于代理的模型，以探索集体梳子构建的可能潜在机制。该项目采用的方法超越了将集体行为视为耻辱的传统观点，即生物体对局部线索的反应很少或没有长期影响，以探索物理介导的远程相互作用的影响。该奖项反映了美国国家科学基金会的法定使命，并通过使用基金会的知识价值和更广泛的影响审查标准进行评估，被认为值得支持。

The honeybee comb is a masterpiece of distributed architecture. This wax-made storage structure, which is essential to the survival of the colony, is constructed in a near-optimal manner that minimizes the wax-to-storage space ratio, due to the high energy cost associated with wax production. Honeybees construct the comb with remarkable precision, regardless of irregular boundaries or unevenness of the surface on which they work. Yet the mechanisms by which honeybees adapt their construction to the constraints of the environment (e.g., a pre-existing cavity in a tree) are poorly understood. The goal of this project is to shed light on the process of comb construction by framing it as a pattern formation process, which allows us to leverage the similarities between comb structure and the structure of non-living materials such as crystals and graphene. This project bridges tools from multiple disciplines, bringing insights from animal behavior and crystallography. The outcome of this research is a novel framework for modeling the collective behavior of honeybees as well as quantitatively describing the geometry and topology of the honeybee lattices. This project will not only help us understand the collective behavior of bees, but will also help leverage that understanding to create bio-inspired system designs in the fields of swarm robotics, collective construction, and lightweight cellular structures. This research project will address three specific questions: (1) Are the irregularities in the honeycomb structure the result of global planning that accounts for distant frustration sources (e.g., solid boundaries of a tree cavity) or a local reaction to the immediate surroundings of a given cell? (2) Can the honeycomb pattern be explained as the result of an energy minimization process, and if so, are the solutions comparable to patterns consistently found in a diverse range of self-organized crystallographic systems under geometric frustration (e.g., colloidal crystals or graphene)? (3) To what extent is the optimality of the solution to the geometric problem of comb construction modulated by large-scale changes in the environment, such as engineered boundaries, various given cell sizes, or curvature? The investigators in this project will use 3D-printing to construct precisely controlled and quantified honeycomb foundations, which can be used to introduce systematic and repeatable sources of geometric frustration in the experiments. The final comb structures will be imaged and analyzed (computer vision techniques, x-ray microscopy) to precisely characterize the geometry of individual cells and the topology of the global lattice. This rich information set will be used to develop and validate data-driven agent-based models to explore possible underlying mechanisms of collective comb construction. The approach followed in this project goes beyond the traditional view of collective behavior as stigmergy -- wherein organisms respond to local cues with little or no long-range effects -- to explore the influence of long-range interactions that are physically mediated.This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.