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Mathematical model for bone mineralization.

Komarova SV, Safranek L, Gopalakrishnan J, Ou MJ, McKee MD, Murshed M, Rauch F, Zuhr E - Front Cell Dev Biol (2015)

Bottom Line: 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.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.

View Article: PubMed Central - PubMed

Affiliation: Faculty of Dentistry, McGill University Montreal, QC, Canada ; Shriners Hospital for Children-Canada Montreal, QC, Canada.

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.

No MeSH data available.


Related in: MedlinePlus

Changes in time in different players in the mineralization process in healthy bone. (A) The concentrations of naïve (x1, light green) and mature (x2, dark green) collagen matrix. (B) The concentration of the mineralization inhibitor (I, orange) and the nucleation centers (N, purple). (C) The concentration of mineral (y). Indicated are the mineralization lag time, measured as a time delay between time 0 and the onset of mineralization, and mineralization degree, measured as the amount of mineral at time = 100 days. For the simulation of healthy bone, the mineralization lag time is 10 days, and the mineralization degree is 1.
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Figure 2: Changes in time in different players in the mineralization process in healthy bone. (A) The concentrations of naïve (x1, light green) and mature (x2, dark green) collagen matrix. (B) The concentration of the mineralization inhibitor (I, orange) and the nucleation centers (N, purple). (C) The concentration of mineral (y). Indicated are the mineralization lag time, measured as a time delay between time 0 and the onset of mineralization, and mineralization degree, measured as the amount of mineral at time = 100 days. For the simulation of healthy bone, the mineralization lag time is 10 days, and the mineralization degree is 1.

Mentions: First, we examined the pattern of temporal changes in the five variables for the parameters representing bone mineralization in a healthy subject (Tables 1, 2). Naïve collagen, which initially constituted 100% of all collagen in the system, was gradually assembled into mature collagen, resulting in 80% conversion within 20 days, and in complete maturation within 40–60 days (Figure 2A). Inhibitors initially present in the naïve matrix were sustained for the first 10 days and rapidly degraded with the appearance of mature collagen (Figure 2B). Nucleating centers produced with the mature collagen reached the maximum at ~10 days, and were removed with the offset of the mineralization (Figure 2B). After a lag time of ~10 days, the mineralization first progressed rapidly followed by a continuous slow mineral formation (Figure 2C). The normalized mineralization degree of 1 (i.e., full mineralization) was reached ~100 days after the deposition of naïve collagen. Thus, the model describes the lag time required for matrix maturation, the rapid mineralization offset, and the continuous slow increase in mineralization with time (Roschger et al., 2008b).


Mathematical model for bone mineralization.

Komarova SV, Safranek L, Gopalakrishnan J, Ou MJ, McKee MD, Murshed M, Rauch F, Zuhr E - Front Cell Dev Biol (2015)

Changes in time in different players in the mineralization process in healthy bone. (A) The concentrations of naïve (x1, light green) and mature (x2, dark green) collagen matrix. (B) The concentration of the mineralization inhibitor (I, orange) and the nucleation centers (N, purple). (C) The concentration of mineral (y). Indicated are the mineralization lag time, measured as a time delay between time 0 and the onset of mineralization, and mineralization degree, measured as the amount of mineral at time = 100 days. For the simulation of healthy bone, the mineralization lag time is 10 days, and the mineralization degree is 1.
© Copyright Policy
Related In: Results  -  Collection

License
Show All Figures
getmorefigures.php?uid=PMC4544393&req=5

Figure 2: Changes in time in different players in the mineralization process in healthy bone. (A) The concentrations of naïve (x1, light green) and mature (x2, dark green) collagen matrix. (B) The concentration of the mineralization inhibitor (I, orange) and the nucleation centers (N, purple). (C) The concentration of mineral (y). Indicated are the mineralization lag time, measured as a time delay between time 0 and the onset of mineralization, and mineralization degree, measured as the amount of mineral at time = 100 days. For the simulation of healthy bone, the mineralization lag time is 10 days, and the mineralization degree is 1.
Mentions: First, we examined the pattern of temporal changes in the five variables for the parameters representing bone mineralization in a healthy subject (Tables 1, 2). Naïve collagen, which initially constituted 100% of all collagen in the system, was gradually assembled into mature collagen, resulting in 80% conversion within 20 days, and in complete maturation within 40–60 days (Figure 2A). Inhibitors initially present in the naïve matrix were sustained for the first 10 days and rapidly degraded with the appearance of mature collagen (Figure 2B). Nucleating centers produced with the mature collagen reached the maximum at ~10 days, and were removed with the offset of the mineralization (Figure 2B). After a lag time of ~10 days, the mineralization first progressed rapidly followed by a continuous slow mineral formation (Figure 2C). The normalized mineralization degree of 1 (i.e., full mineralization) was reached ~100 days after the deposition of naïve collagen. Thus, the model describes the lag time required for matrix maturation, the rapid mineralization offset, and the continuous slow increase in mineralization with time (Roschger et al., 2008b).

Bottom Line: 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.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.

View Article: PubMed Central - PubMed

Affiliation: Faculty of Dentistry, McGill University Montreal, QC, Canada ; Shriners Hospital for Children-Canada Montreal, QC, Canada.

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.

No MeSH data available.


Related in: MedlinePlus