Osteocytes as a record of bone formation dynamics: A mathematical model of osteocyte generation in bone matrix

Abstract

The formation of new bone involves both the deposition of bone matrix, and the formation of a network of cells embedded within the bone matrix, called osteocytes. Osteocytes derive from bone-synthesising cells (osteoblasts) that become buried in bone matrix during bone deposition. The generation of osteocytes is a complex process that remains incompletely understood. Whilst osteoblast burial determines the density of osteocytes, the expanding network of osteocytes regulates in turn osteoblast activity and osteoblast burial. In this paper, a spatiotemporal continuous model is proposed to investigate the osteoblast-to-osteocyte transition. The aims of the model are (i) to link dynamic properties of osteocyte generation with properties of the osteocyte network imprinted in bone, and (ii) to investigate Marotti׳s hypothesis that osteocytes prompt the burial of osteoblasts when they become covered with sufficient bone matrix. Osteocyte density is assumed in the model to be generated at the moving bone surface by a combination of osteoblast density, matrix secretory rate, rate of entrapment, and curvature of the bone substrate, but is found to be determined solely by the ratio of the instantaneous burial rate and matrix secretory rate. Osteocyte density does not explicitly depend on osteoblast density nor curvature. Osteocyte apoptosis is also included to distinguish between the density of osteocyte lacuna and the density of live osteocytes. Experimental measurements of osteocyte lacuna densities are used to estimate the rate of burial of osteoblasts in bone matrix. These results suggest that: (i) burial rate decreases during osteonal infilling, and (ii) the control of osteoblast burial by osteocytes is likely to emanate as a collective signal from a large group of osteocytes, rather than from the osteocytes closest to the bone deposition front.

Quantifying the osteocyte network in the human skeleton

“…At this stage, imaging modalities in the hard tissue of bone have not yet allowed specific location of these interactions, exchange of soluble factors, or juxtacrine signalling specifically at the site of dendrite tip to tip contact. However, the efficiency of cell-contactdependent wire transmission through the dendritic network may also depend on absolute number of cells within the network given the possibility of distant neighbour connections and of direct connections to the vascular pore surface [22,49].…”

“…This extensive level of replenishment suggests that therapeutic approaches that change the nature of new osteocytes being deposited (such as gene therapy approaches that target the osteoblast) may allow rapid incorporation of modified osteocytes within the skeleton. It also indicates that a large number of bone surface osteoblasts are incorporated into the matrix, in a manner dependent on signals from within the extensive osteocytic network [49]. Although these proportions are unclear, it has been suggested that 19-29% of the osteoblast population is incorporated into the bone matrix [25,28], suggesting that the number of osteoblasts produced per day in the skeleton ranges from 1.14 × 10 11 -1.7 × 10 11 .…”

“…Continuing work to identify whether the extent of the network varies across species, including extinct species, may also provide insights into how this network complexity has evolved [68][69][70][71]. Finally, as mathematical models of the biomechanical regulation of the skeleton become more comprehensive [49,[72][73][74][75][76][77][78][79][80][81], valid quantifications of the osteocyte network from the cellular to the whole organ scale will allow realistic predictions of this complex dynamic system and its emergent behaviours [82,83]. High-resolution 3D imaging of bone is improving, thus revealing new understandings of the function of the osteocyte network.…”

Chronic stress and body composition disorders: implications for health and disease

“…In bone remodeling, osteoclasts dissolve/resorb old bone tissue and osteoblasts produce osteocytes, actively renewing bone tissue. Bone tissue participates in numerous functions: it maintains blood pH levels, acts as calcium and phosphate storage, provides protection of vital organs and support for muscles, organs, and soft tissues, helps with leverage and movement, and, lastly, participates indirectly in the formation of blood cells in the bone marrow interspersed within the spongy bones [73].…”

Melorheostotic Bone Lesions Caused by Somatic Mutations in MAP2K1 Have Deteriorated Microarchitecture and Periosteal Reaction

“…The osteocyte lacunar density, evaluated by 2D analysis of qBEI, was increased by nearly 40%, which is possibly related to enhanced cell proliferation and/or altered cell differentiation, as observed in cell cultures from affected bone . It has been speculated indeed, that the quantity of osteocytes generated during bone formation depends, on the one hand, on the number of preexisting osteoblasts and, on the other hand, on their matrix synthesis activity . Thus, in melorheostotic bone, more osteocytes might be encased in the matrix because a larger osteoblastic pool is present and/or because less matrix is synthesized at the single‐cell level, which would be in line with a reduced COL1A1 expression observed in affected osteoblasts .…”