Mathematical model for bone mineralization

Abstract

Defective bone mineralization has serious clinical manifestations, including deformities and fractures, but the regulation of this extracellular process is not fully understood. We have developed a mathematical model consisting of ordinary differential equations that describe collagen maturation, production and degradation of inhibitors, and mineral nucleation and growth. We examined the roles of individual processes in generating normal and abnormal mineralization patterns characterized using two outcome measures: mineralization lag time and degree of mineralization. Model parameters describing the formation of hydroxyapatite mineral on the nucleating centers most potently affected the degree of mineralization, while the parameters describing inhibitor homeostasis most effectively changed the mineralization lag time. Of interest, a parameter describing the rate of matrix maturation emerged as being capable of counter-intuitively increasing both the mineralization lag time and the degree of mineralization. We validated the accuracy of model predictions using known diseases of bone mineralization such as osteogenesis imperfecta and X-linked hypophosphatemia. The model successfully describes the highly nonlinear mineralization dynamics, which includes an initial lag phase when osteoid is present but no mineralization is evident, then fast primary mineralization, followed by secondary mineralization characterized by a continuous slow increase in bone mineral content. The developed model can potentially predict the function for a mutated protein based on the histology of pathologic bone samples from mineralization disorders of unknown etiology.

Predictive computational modeling to define effective treatment strategies for bone metastatic prostate cancer

“…In the context of prostate cancer, many elegant models have used biological parameters such as prostate specific antigen (PSA) to predict time to progression, and to model the effects of intermittent androgen therapy 8 . The tightly regulated process of normal bone remodeling lends itself well to modeling how key factors such as RANKL and TGFβ control the behavior and activity of bone stromal cells over time 39 40 41 42 43 . By extension, perturbing this balanced ecosystem with an invasive species such as cancer can also be modeled.…”

Cartilage canals in the distal intermediate ridge of the tibia of fetuses and foals are surrounded by different types of collagen

“…Also, maturation of collagen type I prior to mineralisation in bone formation is reported to take 10–14 days (Komarova et al. ). If the ring of collagen type I surrounding cartilage canals forms predominantly in response to gravitational force, it may therefore take up to 14 days from birth and the start of limb‐loading until fibrils have formed and become detectable in histological sections.…”

“…However, small amounts of collagen type I may be visible histologically immediately adjacent to fibroblasts after a few days (Oostendorp et al 2016), and become more abundant (Kumar et al 2003) and visible further away from the fibroblast (Oostendorp et al 2016) by week 2. Also, maturation of collagen type I prior to mineralisation in bone formation is reported to take 10-14 days (Komarova et al 2015). If the ring of collagen type I surrounding cartilage canals forms predominantly in response to gravitational force, it may therefore take up to 14 days from birth and the start of limb-loading until fibrils have formed and become detectable in histological sections.…”

Persistence of the ABCC6 genes and the emergence of the bony skeleton in vertebrates

“…Calcification is an essential physiological mechanism in the process of skeletal tissue formation, which is tightly controlled and restricted to specific body regions. Although the calcification process is incompletely understood, inhibitors and promoters are thought to act synergistically to maintain calcification of bone and dental tissue 19 . Calcification disorders occur when calcium is abnormally deposited in soft tissues causing ectopic calcification 20 .…”