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The concavity: the shape of life
- Soluble, insoluble and geometric signals sculpt the architecture of mineralized tissues

There are several fundamental issues related to the reported biomimetic geometry or topography that displays specificity of expression of and binding affinity for selected osteogenic proteins of the TGF-β superfamily. The specific geometric configuration initiates spontaneous bone formation as a secondary response even when the biomimetic matrices are implanted in heterotopic sites and without the addition of exogenously applied osteogenic proteins of the TGF-β superfamily [40, 47].

A most important parameter for the spontaneous induction of bone formation is the geometric configuration of the biomimetic matrices in the form of specific concavities on the surface of the substratum that drive the morphogenetic cascade. The substratum may be either porous i.e. with a sequence of repetitive concavities embedded within the porous spaces or solid i.e. with concavities prepared on the outer surface of both planar surfaces, to enhance bone induction and hasten osteointegration when implanted in orthotopic sites.

Our research has shown that the concavities of our biomimetic biomaterial matrices are geometric regulators of growth endowed with shape memory, recapitulating events that occur in the normal course of embryonic development and appearing to act as gates, giving or withholding permission to growth and differentiation [40, 41, 47].

Our molecular, biochemical, histological and morphological data further show that the specific geometric configuration in the form of concavities is the driving micro-environment conducive and inducive to the sequence of events leading to bone formation by induction preceeded by angiogenesis and vascular invasion, mesenchymal cellular

attachment, orientation and aggregation to the biomimetic matrix of the smart concavity. Attached to the matrix and resident within the smart concavities, differentiating osteoblast-like cells express BMPs/OPs gene products as shown by Northern blot analyses and immunolocalization on tissue harvested from the concavities [2, 9–12, 40, 47].

The concavities are thus regulators of bone initiation and deposition during remodeling processes of the skeleton. Remodeling of the cortico-cancellous bones of the skeleton both of endochondral and membranous origins entails, at any given time along the trabeculae of bone, three fundamental biochemical and morphological processes that characterize the remodeling cycle of cancellous and cortical bone: 1) Resting, i.e. surfaces lined by resting lining cells; 2) Resorption, i.e. areas of trabeculae actively resorbed by osteoclasts, multinucleated bone cells that actively and specifically resorb bone. The bone resorption lacunae as formed by the osteoclastic activity are in the form of concavities; 3) Formation, i.e. the concavities formed by osteoclastic resorption reach dimensions similar if not equal to the concavities created in the above described biomimetic matrices. When these dimensions are reached, bone formation occurs as osteoblasts or bone forming cells are then recruited to the concavities, leading to bone formation until the resorption lacunae or concavities are filled with newly formed bone and the specific area reaches a resting status again.

There is a direct spatial and temporal relationship of morphological and molecular events that emphasize the similarity between the remodeling cycles of cancellous bone vs the geometric induction of bone formation, i.e. the induction of bone in smart concavities assembled in biomimetic matrices of highly crystalline hydroxyapatites. In the adult skeleton, the demand for osteoblasts is created by bone resorption [50, 51], i.e. by the concavities induced by osteoclastogenesis, whereas the demand for osteoclasts is governed by the purposes of bone remodeling [50].

The basic multicellular unit (BMU) of corticocancellous bone excavates a trench across the surface rather than a tunnel leaving in its wake (with some geometrical latitude) a hemiosteon rather than an osteon [50-52], i.e. a trench with cross-sectional geometric cues of concavities at different stages of osteoclastogenesis eventually leading to osteogenesis.

The morphogenetic and molecular mechanisms initiating the spontaneous induction of bone formation within concavities of the smart biomimetic matrices originates and progress with blood vessels arborizing within the mesenchymal tissue invading the concavities, i.e. capillary sprouting [40, 47].

Progression is sustained by the continued recruitment of mesenchymal cells eventually resting on the surface of the smart concavities and later targeted to differentiate into osteoblasts-like cells. Osteogenic proteins of the TGF-β superfamily are then expressed and secretion of the gene products is followed by the binding of the expressed gene products to the smart concavities of the biomimetic matrices. The necessary molecular signals initiating the cascade of bone formation by induction must originate from within the concavity itself and only deployed when osteoclastogenesis has created concavities of specific dimension. Reversal, i.e. osteoblastogenesis, is initiated after synthesis and expression of osteogenic proteins of the TGF-β superfamily are bound to the smart concavities of both the corticocancellous microarchitecture of the mammalian skeleton and intrinsically osteoinductive biomimetic matrices.

The concavities per se are regulators of growth, inducing specific tissue formation and bone induction as in the remodeling processes of bone and act as powerful geometric attractant for bone forming cells i.e. osteoblasts initiating bone formation. Soluble signals induce morphogenesis, physical forces imparted by the geometric topography of the insoluble signal or substratum dictate biological patterns, constructing the induction of bone and regulating the expression of selective messanger RNA of gene products as a function of the structure [2, 10, 12]. The specific geometric concavity being a geometrical and physical regulator of bone remodeling is of paramount importance in skeletal disorders such as systemic bone loss as in osteoporosis.

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