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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 parameters affecting nucleator production and removal on the mineralization outcome. (A–C) The effect of decreasing 3-fold (A) or increasing 3-fold (B) the number of nucleators per crosslinked collagen (k2). (C) Comparison of the mineralization lag time and degree in conditions affecting k2 to healthy mineralization. (D–F) The effect of decreasing 3-fold (D) or increasing 3-fold (E) the rate of use of nucleators by mineralized bone (r2). (F) Comparison of the mineralization lag time and degree in conditions affecting r2 to healthy mineralization. The same color scheme is used as in Figure 2.
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Figure 4: The effect of parameters affecting nucleator production and removal on the mineralization outcome. (A–C) The effect of decreasing 3-fold (A) or increasing 3-fold (B) the number of nucleators per crosslinked collagen (k2). (C) Comparison of the mineralization lag time and degree in conditions affecting k2 to healthy mineralization. (D–F) The effect of decreasing 3-fold (D) or increasing 3-fold (E) the rate of use of nucleators by mineralized bone (r2). (F) Comparison of the mineralization lag time and degree in conditions affecting r2 to healthy mineralization. The same color scheme is used as in Figure 2.

Mentions: Next we examined the role of parameters affecting the nucleators, the number of nucleators per mature collagen k2, and rate of removal of nucleators caused by hydroxyapatite formation r2 (Figure 4). Mineralization lag time was not affected by changes in k2 and r2, since the dynamics of collagen and inhibitors does not depend on these parameters (Figures 4C,F). A 3-fold decrease in the number of nucleators per mature collagen k2 resulted in a 40% decrease in mineralization degree (Figures 4A,C), while a 3-fold increase in k2 led to a 60% increase in the mineralization degree (Figures 4B,C). A 3-fold decrease in the rate of nucleator removal caused by hydroxyapatite formation r2 resulted in an almost 2-fold increase in mineralization degree (Figures 4D,F), while a 3-fold increase in r2 resulted in 40% decrease in mineralization degree (Figures 4E,F).


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 parameters affecting nucleator production and removal on the mineralization outcome. (A–C) The effect of decreasing 3-fold (A) or increasing 3-fold (B) the number of nucleators per crosslinked collagen (k2). (C) Comparison of the mineralization lag time and degree in conditions affecting k2 to healthy mineralization. (D–F) The effect of decreasing 3-fold (D) or increasing 3-fold (E) the rate of use of nucleators by mineralized bone (r2). (F) Comparison of the mineralization lag time and degree in conditions affecting r2 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 4: The effect of parameters affecting nucleator production and removal on the mineralization outcome. (A–C) The effect of decreasing 3-fold (A) or increasing 3-fold (B) the number of nucleators per crosslinked collagen (k2). (C) Comparison of the mineralization lag time and degree in conditions affecting k2 to healthy mineralization. (D–F) The effect of decreasing 3-fold (D) or increasing 3-fold (E) the rate of use of nucleators by mineralized bone (r2). (F) Comparison of the mineralization lag time and degree in conditions affecting r2 to healthy mineralization. The same color scheme is used as in Figure 2.
Mentions: Next we examined the role of parameters affecting the nucleators, the number of nucleators per mature collagen k2, and rate of removal of nucleators caused by hydroxyapatite formation r2 (Figure 4). Mineralization lag time was not affected by changes in k2 and r2, since the dynamics of collagen and inhibitors does not depend on these parameters (Figures 4C,F). A 3-fold decrease in the number of nucleators per mature collagen k2 resulted in a 40% decrease in mineralization degree (Figures 4A,C), while a 3-fold increase in k2 led to a 60% increase in the mineralization degree (Figures 4B,C). A 3-fold decrease in the rate of nucleator removal caused by hydroxyapatite formation r2 resulted in an almost 2-fold increase in mineralization degree (Figures 4D,F), while a 3-fold increase in r2 resulted in 40% decrease in mineralization degree (Figures 4E,F).

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