Mathematical model for bone mineralization.
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.
Faculty of Dentistry, McGill University Montreal, QC, Canada ; Shriners Hospital for Children-Canada Montreal, QC, Canada.
Svetlana V
SV
Komarova
Department of Mathematics, Simon Fraser University Burnaby, BC, Canada.
Lee
L
Safranek
The Fariborz Maseeh Department of Mathematics and Statistics, Portland State University Portland, OR, USA.
Jay
J
Gopalakrishnan
Department of Mathematical Sciences, University of Delaware Newark, DE, USA.
Miao-Jung Yvonne
MJ
Ou
Faculty of Dentistry, McGill University Montreal, QC, Canada ; Department of Anatomy and Cell Biology, Faculty of Medicine, McGill University Montreal, QC, Canada.
Marc D
MD
McKee
Faculty of Dentistry, McGill University Montreal, QC, Canada ; Shriners Hospital for Children-Canada Montreal, QC, Canada ; Department of Medicine, Faculty of Medicine, McGill University Montreal, QC, Canada.
Monzur
M
Murshed
Shriners Hospital for Children-Canada Montreal, QC, Canada.
Frank
F
Rauch
Department of Mathematics, High Point University High Point, NC, USA.
Erica
E
Zuhr
X-linked hypophosphatemia; bone histomorphometry; matrix mineralization; mineralization inhibitors; nucleating centers; osteogenesis imperfecta; osteomalacia; rickets