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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 collagen maturation on the mineralization outcome. (A–C) The effect of decreasing 3-fold (A) or increasing 3-fold (B) the amount of naïve collagen deposited by osteoblasts at time = 0 (x1(0)). (C) Comparison of the mineralization lag time and degree in conditions affecting x1(0) to healthy mineralization. (D–F) The effect of decreasing 3-fold (D) or increasing 3-fold (E) the rate of collagen maturation (k1). (F) Comparison of the mineralization lag and degree in conditions affecting k1 to healthy mineralization. The same color scheme is used as in Figure 2.
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Figure 6: The effect of parameters affecting collagen maturation on the mineralization outcome. (A–C) The effect of decreasing 3-fold (A) or increasing 3-fold (B) the amount of naïve collagen deposited by osteoblasts at time = 0 (x1(0)). (C) Comparison of the mineralization lag time and degree in conditions affecting x1(0) to healthy mineralization. (D–F) The effect of decreasing 3-fold (D) or increasing 3-fold (E) the rate of collagen maturation (k1). (F) Comparison of the mineralization lag and degree in conditions affecting k1 to healthy mineralization. The same color scheme is used as in Figure 2.

Mentions: Finally, we examined the effect of changing the parameters affecting initial collagen density x1(0) and maturation k1 on the mineralization outcome (Figure 6). Change in the initial density of naïve collagen x1(0) represents an altered ability of osteoblasts to produce collagen, or altered collagen packing. A 3-fold decrease in x1(0) resulted in a proportionally lower amount of mature collagen and the number of nucleators, leading to a 2-fold decrease in mineralization degree (Figures 6A,C). In addition, the inhibitor presence was sustained for a longer period of time leading to a 2-fold increase in mineralization lag time (Figure 6A). A 3-fold increase in x1(0) led to a 3-fold increase in the amount of mature collagen and in the number of nucleators, which however translated to only a 70-80% increase in mineralization degree (Figures 6B,C).


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 collagen maturation on the mineralization outcome. (A–C) The effect of decreasing 3-fold (A) or increasing 3-fold (B) the amount of naïve collagen deposited by osteoblasts at time = 0 (x1(0)). (C) Comparison of the mineralization lag time and degree in conditions affecting x1(0) to healthy mineralization. (D–F) The effect of decreasing 3-fold (D) or increasing 3-fold (E) the rate of collagen maturation (k1). (F) Comparison of the mineralization lag and degree in conditions affecting k1 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 6: The effect of parameters affecting collagen maturation on the mineralization outcome. (A–C) The effect of decreasing 3-fold (A) or increasing 3-fold (B) the amount of naïve collagen deposited by osteoblasts at time = 0 (x1(0)). (C) Comparison of the mineralization lag time and degree in conditions affecting x1(0) to healthy mineralization. (D–F) The effect of decreasing 3-fold (D) or increasing 3-fold (E) the rate of collagen maturation (k1). (F) Comparison of the mineralization lag and degree in conditions affecting k1 to healthy mineralization. The same color scheme is used as in Figure 2.
Mentions: Finally, we examined the effect of changing the parameters affecting initial collagen density x1(0) and maturation k1 on the mineralization outcome (Figure 6). Change in the initial density of naïve collagen x1(0) represents an altered ability of osteoblasts to produce collagen, or altered collagen packing. A 3-fold decrease in x1(0) resulted in a proportionally lower amount of mature collagen and the number of nucleators, leading to a 2-fold decrease in mineralization degree (Figures 6A,C). In addition, the inhibitor presence was sustained for a longer period of time leading to a 2-fold increase in mineralization lag time (Figure 6A). A 3-fold increase in x1(0) led to a 3-fold increase in the amount of mature collagen and in the number of nucleators, which however translated to only a 70-80% increase in mineralization degree (Figures 6B,C).

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