Surface curvature both emerges from, and influences the behavior of, living objects at length scales ranging from cell membranes to single cells to tissues and organs. The relevance of surface curvature in biology is supported by numerous experimental and theoretical investigations in recent years. In this review, first, a brief introduction to the key ideas of surface curvature in the context of biological systems is given and the challenges that arise when measuring surface curvature are discussed. Giving an overview of the emergence of curvature in biological systems, its significance at different length scales becomes apparent. On the other hand, summarizing current findings also shows that both single cells and entire cell sheets, tissues or organisms respond to curvature by modulating their shape and their migration behavior. Finally, the interplay between the distribution of morphogens or micro‐organisms and the emergence of curvature across length scales is addressed with examples demonstrating these key mechanistic principles of morphogenesis. Overall, this review highlights that curved interfaces are not merely a passive by‐product of the chemical, biological, and mechanical processes but that curvature acts also as a signal that co‐determines these processes.

Significance: The explanation of how bone senses and adapts to mechanical stimulation still relies on hypotheses. The fluid flow hypothesis claims that a load-induced fluid flow through the lacunocanalicular network can be sensed by osteocytes, which reside within the network structure. We show that considering the network architecture results in a better prediction of bone remodeling than mechanical strain alone. This was done by calculating the fluid flow through the lacunocanalicular network in bone volumes covering the complete cross-sections of mouse tibiae, which underwent controlled in vivo loading. The established relationship between mechanosensitivity and network architecture in individual animals implies possibilities for patient-specific therapies. A new connectomics approach to analyze lacunocanalicular network properties is necessary to understand skeletal mechanobiology.

A popular hypothesis explains the mechanosensitivity of bone due to osteocytes sensing the load-induced flow of interstitial fluid squeezed through the lacunocanalicular network (LCN). However, the way in which the intricate structure of the LCN influences fluid flow through the network is largely unexplored. We therefore aimed to quantify fluid flow through real LCNs from human osteons using a combination of experimental and computational techniques. Bone samples were stained with rhodamine to image the LCN with 3D confocal microscopy. Image analysis was then performed to convert image stacks into mathematical network structures, in order to estimate the intrinsic permeability of the osteons as well as the load-induced fluid flow using hydraulic circuit theory. Fluid flow was studied in both ordinary osteons with a rather homogeneous LCN as well as a frequent subtype of osteons—so-called osteon-in-osteons—which are characterized by a ring-like zone of low network connectivity between the inner and the outer parts of these osteons. We analyzed 8 ordinary osteons and 9 osteon-in-osteons from the femur midshaft of a 57-year-old woman without any known disease. While the intrinsic permeability was 2.7 times smaller in osteon-in-osteons compared to ordinary osteons, the load-induced fluid velocity was 2.3 times higher. This increased fluid velocity in osteon-in-osteons can be explained by the longer path length, needed to cross the osteon from the cement line to the Haversian canal, including more fluid-filled lacunae and canaliculi. This explanation was corroborated by the observation that a purely structural parameter—the mean path length to the Haversian canal—is an excellent predictor for the average fluid flow velocity. We conclude that osteon-in-osteons may be particularly significant contributors to the mechanosensitivity of cortical bone, due to the higher fluid flow in this type of osteons.

During bone remodeling, osteoblasts are known to deposit unmineralized collagenous tissue (osteoid), which mineralizes after some time lag. Some of the osteoblasts differentiate into osteocytes, forming a cell network within the lacunocanalicular network (LCN) of bone. To get more insight into the potential role of osteocytes in the mineralization process of osteoid, sites of bone formation are three‐dimensionally imaged in nine forming human osteons using focused ion beam‐scanning electron microscopy (FIB‐SEM). In agreement with previous observations, the mineral concentration is found to gradually increase from the central Haversian canal toward pre‐existing mineralized bone. Most interestingly, a similar feature is discovered on a length scale more than 100‐times smaller, whereby mineral concentration increases from the LCN, leaving around the canaliculi a zone virtually free of mineral, the size of which decreases with progressing mineralization. This suggests that the LCN controls mineral formation but not just by diffusion of mineralization precursors, which would lead to a continuous decrease of mineral concentration from the LCN. The observation is, however, compatible with the codiffusion and reaction of precursors and inhibitors from the LCN into the bone matrix.

The osteocyte lacunar-canalicular network (LCN) penetrates bone and houses the osteocytes and their processes. Despite its rather low volume fraction, the LCN represents an outstanding large surface that is possibly used by the osteocytes to interact with the surrounding mineralized bone matrix thereby contributing to mineral homeostasis. The aim of this study was to quantitatively describe such contributions by spatially correlating the local density of the LCN with the mineral content at the same location in micrometer-sized volume elements in human osteons. For this purpose, 65 osteons from the femur midshaft from healthy adults (n = 4) and children (n = 2) were structurally characterized with two different techniques. The 3D structure of the LCN in the osteons was imaged with confocal laser scanning microscopy after staining the bone samples with rhodamine. Subsequent image analysis provided the canalicular length density, i.e. the total length of the canaliculi per unit volume (μm/μm3). Quantitative information on the mineral content (wt%Ca) from the identical regions was obtained using quantitative backscattered electron imaging. As the LCN-porosity lowers the mineral content, a negative correlation between Ca content and network density was expected. Calculations predict a reduction of around -0.97 fmol Ca per μm of network. However, the experiment revealed for 62 out of 65 osteons a positive correlation resulting in an average additional Ca loading of +1.15 fmol per μm of canalicular network, i.e. an accumulation of mineral has occurred at dense network regions. We hypothesize that this accumulation happens in the close vicinity of canaliculi forming mineral reservoirs that can be utilized by osteocytes. Significant differences found between individuals indicate that the extent of mineral loading of the reservoir zone reflects an important parameter for mineral homeostasis.