Limits...
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 inhibitor production and degradation on the mineralization outcome. (A–C) The effect of decreasing 10-fold (A) or increasing 10-fold (B) the rate of inhibitor production (v1). (C) Comparison of the mineralization lag time and degree in conditions affecting v1to healthy mineralization. (D–F) The effect of decreasing 3-fold (D) or increasing 3-fold (E) the rate of inhibitor degradation (r1). (F) Comparison of the mineralization lag and degree in conditions affecting r1 to healthy mineralization. The same color scheme is used as in Figure 2.
© Copyright Policy
Related In: Results  -  Collection

License
getmorefigures.php?uid=PMC4544393&req=5

Figure 5: The effect of parameters affecting inhibitor production and degradation on the mineralization outcome. (A–C) The effect of decreasing 10-fold (A) or increasing 10-fold (B) the rate of inhibitor production (v1). (C) Comparison of the mineralization lag time and degree in conditions affecting v1to healthy mineralization. (D–F) The effect of decreasing 3-fold (D) or increasing 3-fold (E) the rate of inhibitor degradation (r1). (F) Comparison of the mineralization lag and degree in conditions affecting r1 to healthy mineralization. The same color scheme is used as in Figure 2.

Mentions: To examine the effect of parameters affecting the homeostasis of inhibitors on the mineralization outcome, we changed the rates of inhibitor production v1 and degradation r1 (Figure 5). Since Equations (1a) and (1b) are not affected by these parameters, no change in the degree or timing of collagen maturation was evident following changes in v1 and r1. The rate of inhibitor production v1 was changed 10-fold since smaller changes only resulted in slight differences in the mineralization. A 10-fold decrease in the rate of inhibitor production v1 resulted in a ~20% decrease in mineralization lag time and a similar 20% increase in mineralization degree (Figures 5A,C). A 10-fold increase in the rate of inhibitor production v1 led to a 3-fold increase in mineralization lag time and a 40% decrease in mineralization degree (Figures 5B,C). The effect of changing the rate of inhibitor degradation r1 on mineralization mirrored the effects of changing the rate of inhibitor production v1, however, smaller, 3-fold alterations of r1 were required to obtain noticeable effects on mineralization. A 3-fold decrease in r1 resulted in a sustained inhibitor presence, a 2-fold increase in mineralization lag time and 40% decrease in mineralization degree (Figures 5D,F). A 3-fold increase in the rate of inhibitor degradation r1 resulted in a 2-fold decrease in the mineralization lag time and 20% increase in mineralization degree (Figures 5E,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 inhibitor production and degradation on the mineralization outcome. (A–C) The effect of decreasing 10-fold (A) or increasing 10-fold (B) the rate of inhibitor production (v1). (C) Comparison of the mineralization lag time and degree in conditions affecting v1to healthy mineralization. (D–F) The effect of decreasing 3-fold (D) or increasing 3-fold (E) the rate of inhibitor degradation (r1). (F) Comparison of the mineralization lag and degree in conditions affecting r1 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 5: The effect of parameters affecting inhibitor production and degradation on the mineralization outcome. (A–C) The effect of decreasing 10-fold (A) or increasing 10-fold (B) the rate of inhibitor production (v1). (C) Comparison of the mineralization lag time and degree in conditions affecting v1to healthy mineralization. (D–F) The effect of decreasing 3-fold (D) or increasing 3-fold (E) the rate of inhibitor degradation (r1). (F) Comparison of the mineralization lag and degree in conditions affecting r1 to healthy mineralization. The same color scheme is used as in Figure 2.
Mentions: To examine the effect of parameters affecting the homeostasis of inhibitors on the mineralization outcome, we changed the rates of inhibitor production v1 and degradation r1 (Figure 5). Since Equations (1a) and (1b) are not affected by these parameters, no change in the degree or timing of collagen maturation was evident following changes in v1 and r1. The rate of inhibitor production v1 was changed 10-fold since smaller changes only resulted in slight differences in the mineralization. A 10-fold decrease in the rate of inhibitor production v1 resulted in a ~20% decrease in mineralization lag time and a similar 20% increase in mineralization degree (Figures 5A,C). A 10-fold increase in the rate of inhibitor production v1 led to a 3-fold increase in mineralization lag time and a 40% decrease in mineralization degree (Figures 5B,C). The effect of changing the rate of inhibitor degradation r1 on mineralization mirrored the effects of changing the rate of inhibitor production v1, however, smaller, 3-fold alterations of r1 were required to obtain noticeable effects on mineralization. A 3-fold decrease in r1 resulted in a sustained inhibitor presence, a 2-fold increase in mineralization lag time and 40% decrease in mineralization degree (Figures 5D,F). A 3-fold increase in the rate of inhibitor degradation r1 resulted in a 2-fold decrease in the mineralization lag time and 20% increase in mineralization degree (Figures 5E,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