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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

The effect of parameter affecting formation of hydroxyapatite crystals k3 on the mineralization outcome. (A) The effect of decreasing k3 3-fold. (B) Comparison of the mineralization lag time and degree following decrease in k3 to healthy mineralization. (C) The effect of increasing k3 3-fold. (D) Comparison of the mineralization lag time and degree following increase in k3 to healthy mineralization. The same color scheme is used as in Figure 2.
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Figure 3: The effect of parameter affecting formation of hydroxyapatite crystals k3 on the mineralization outcome. (A) The effect of decreasing k3 3-fold. (B) Comparison of the mineralization lag time and degree following decrease in k3 to healthy mineralization. (C) The effect of increasing k3 3-fold. (D) Comparison of the mineralization lag time and degree following increase in k3 to healthy mineralization. The same color scheme is used as in Figure 2.

Mentions: To model mineralization defects, we first examined the effect of the rate of hydroxyapatite formation k3 on the mineralization outcome (Figure 3). Changes in k3 predictably affected the rate of mineral formation, but also strongly and proportionally affected the degree of mineralization. A 3-fold decrease in the rate of hydroxyapatite formation k3 resulted in a 3-fold decrease in mineralization degree (Figures 3A,B), while a 3-fold increase in k3 led to a 3-fold increase in mineralization degree (Figures 3C,D). The robust effect of k3 on the degree of mineralization is due to the fact that the removal of nucleators from the model is regulated by two independent parameters—the rate of hydroxyapatite formation (directly affected by k3), and the efficiency of nucleator removal (r2), which remains high even when k3 is low. Therefore, when the rate of hydroxyapatite formation decreases, the time interval during which nucleators are present remains unchanged, resulting in a decrease in mineralization degree. Changes in k3 did not affect the dynamics of collagen maturation or turnover of its inhibitors.


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)

The effect of parameter affecting formation of hydroxyapatite crystals k3 on the mineralization outcome. (A) The effect of decreasing k3 3-fold. (B) Comparison of the mineralization lag time and degree following decrease in k3 to healthy mineralization. (C) The effect of increasing k3 3-fold. (D) Comparison of the mineralization lag time and degree following increase in k3 to healthy mineralization. The same color scheme is used as in Figure 2.
© Copyright Policy
Related In: Results  -  Collection

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

Figure 3: The effect of parameter affecting formation of hydroxyapatite crystals k3 on the mineralization outcome. (A) The effect of decreasing k3 3-fold. (B) Comparison of the mineralization lag time and degree following decrease in k3 to healthy mineralization. (C) The effect of increasing k3 3-fold. (D) Comparison of the mineralization lag time and degree following increase in k3 to healthy mineralization. The same color scheme is used as in Figure 2.
Mentions: To model mineralization defects, we first examined the effect of the rate of hydroxyapatite formation k3 on the mineralization outcome (Figure 3). Changes in k3 predictably affected the rate of mineral formation, but also strongly and proportionally affected the degree of mineralization. A 3-fold decrease in the rate of hydroxyapatite formation k3 resulted in a 3-fold decrease in mineralization degree (Figures 3A,B), while a 3-fold increase in k3 led to a 3-fold increase in mineralization degree (Figures 3C,D). The robust effect of k3 on the degree of mineralization is due to the fact that the removal of nucleators from the model is regulated by two independent parameters—the rate of hydroxyapatite formation (directly affected by k3), and the efficiency of nucleator removal (r2), which remains high even when k3 is low. Therefore, when the rate of hydroxyapatite formation decreases, the time interval during which nucleators are present remains unchanged, resulting in a decrease in mineralization degree. Changes in k3 did not affect the dynamics of collagen maturation or turnover of its inhibitors.

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