How Linear Tension Converts to Curvature: Geometric Control of Bone Tissue Growth

Abstract

This study investigated how substrate geometry influences in-vitro tissue formation at length scales much larger than a single cell. Two-millimetre thick hydroxyapatite plates containing circular pores and semi-circular channels of 0.5 mm radius, mimicking osteons and hemi-osteons respectively, were incubated with MC3T3-E1 cells for 4 weeks. The amount and shape of the tissue formed in the pores, as measured using phase contrast microscopy, depended on the substrate geometry. It was further demonstrated, using a simple geometric model, that the observed curvature-controlled growth can be derived from the assembly of tensile elements on a curved substrate. These tensile elements are cells anchored on distant points of the curved surface, thus creating an actin “chord” by generating tension between the adhesion sites. Such a chord model was used to link the shape of the substrate to cell organisation and tissue patterning. In a pore with a circular cross-section, tissue growth increases the average curvature of the surface, whereas a semi-circular channel tends to be flattened out. Thereby, a single mechanism could describe new tissue growth in both cortical and trabecular bone after resorption due to remodelling. These similarities between in-vitro and in-vivo patterns suggest geometry as an important signal for bone remodelling.

Surface Curvature Differentially Regulates Stem Cell Migration and Differentiation via Altered Attachment Morphology and Nuclear Deformation

“…In contrast, cells on convex structures adopt a snail‐like configuration with full contact to the substrate (Figure 3D). These observations are in accordance with the chord model presented by Bidan et al, that defines cells as tensile elements that are stretched upward between the focal adhesions on concave surfaces, while being pulled downward toward the surface on convex substrates 28. While the cell body on concave surfaces only partially adopted the curvature of the surface by lifting away from it, cells on convex surfaces had to bend and adopt their shape to the curvature of the surface (Figure 3D, and Movies S2 and S3, Supporting Information).…”

The enigmas of bone without osteocytes

“…The proposed hypothesis, 33 that osteoblasts are involved in mechanosensing in acellular bone, is supported by Kitamura et al's 76 demonstration in the (acellular and dermal) scales of goldfish of increased osteoblast but not osteoclast activity (via alkaline phosphatase (ALP) and tartarate resistant acid phosphatase (TRAP) staining, respectively) in response to increased swimming activity, and by in vitro studies of mammalian mesenchymal tissue-derived cells at various stages of differentiation showing response to their mechanical environment. [77][78][79][80][81] Lu et al's 55 illustration in vitro of higher mechanosensitivity in mammalian osteocytes than osteoblasts, however, suggests perhaps a different level of osteoblast mechanosensitivity in fish bone, starkly different loading demands, bone material properties in fishes and mammals, and/or recruitment of other mechanosensors in addition to Bone without osteocytes R Shahar and MN Dean osteoblasts. Further studies of osteoblast and osteoclast activity, through in vivo performance and selective staining studies, examination of signaling pathways, and in vitro cell culture and mechanostimulation work, will help to clarify the roles of these cells in fish bone mechanobiology.…”

The influence of curvature on three-dimensional mineralized matrix formation under static and perfused conditions: an in vitro bioreactor model

“…The total amount of tissue formed was dependent on the channel perimeter and was proportional to the local curvature. Other studies have also shown that the tissue growth rate was highly dependent on curvature [6,7,15]. Curvature sign was also found to be important, showing decreasing tissue growth from concave (negative curvature) to convex ( positive curvature) to flat (zero curvature) surfaces [6,[15][16][17].…”

“…Cells aim to reduce these forces by contracting their cytoskeleton, which subsequently leads to a flattening of the tissue surface. This has been attributed to the fact that cellular growth is not only controlled by biological signalling pathways but also by mechanical control mechanisms [6,7].…”