Mathematical model capturing physicochemical and biological regulation of bone mineralization
Bibliographic record
Abstract
Bone mineralization is a complex process tightly regulated by both biological factors such as collagen maturation as well as physicochemical factors such as pH. A previous model of biological mineralization captured the biological regulation of bone mineralization dynamics, but not the impact of bone microenvironment such as ion availabilities which may be altered in hypo or hyperphosphatemia. To build an integrated model of bone mineralization, we utilized two previously developed models which addressed a distinct aspect of bone mineralization. The first model described the processes of the extracellular matrix formation and maturation, inhibitor and nucleator formation and removal and their combined action in regulating bone mineralization. The second model simulated the bone interstitial fluid (BIF) permissive to precipitation of hydroxyapatite and described the physicochemical process of hydroxyapatite precipitation. The resulting bone mineralization model accounts for biological and physicochemical aspects of the process. The integrated model was analyzed for the impact of physicochemical factors (pH, levels of calcium and phosphate) on the mineralization dynamics. Model predictions were compared to experimental findings using two outcomes characterizing mineralization dynamics: mineralization delay that corresponds to histomorphometry measures of osteoid volume or thickness, and mineralization degree that corresponds to bone mineral density distribution. We identified the limitation of the previously developed model in predicting the mineralization delay observed in the situations of hypophosphatemia and hypocalcemia and proposed a model adaptation that predicts these outcomes. The resulting mathematical model can be used for in silico testing of hypotheses regarding the role of different physicochemical, molecular, or cellular factors in causing a specific disruption in mineralization dynamics.
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How this classification was reachedexpand
Full frame machine prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. The Gemma side is a direct model label for every work in the frame, read from the title-only record. The Codex side is a classifier learned from the 10,348 direct Codex labels and calibrated to design-weighted sample rates; fields without enough sample support carry no Codex call. Candidate is the union of the two sides; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels.
Distilled classifier scores by category (both heads)
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.001 | 0.002 |
| Meta-epidemiology (narrow) | 0.001 | 0.001 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.001 | 0.001 |
| Science and technology studies | 0.001 | 0.001 |
| Scholarly communication | 0.002 | 0.001 |
| Open science | 0.002 | 0.001 |
| Research integrity | 0.003 | 0.001 |
| Insufficient payload (model declined to judge) | 0.003 | 0.001 |
Machine scores (provisional)
The two teacher heads of the student model, read on this work. A score orders the frame for review; it never asserts a category, and the validation status ships verbatim with every row.
Baseline scores from an immature model (maturity gate not passed, 7 training rounds). Scores rank; they never assert a category.
score_only:v0-immature-baseline · verbatim from the scoring run: score_only means the number may rank works, and no category label ships from itClassification
machine, unvalidatedMachine predicted; a candidate call from one source (direct Gemma or distilled Codex), not a consensus.
How this classification was reached, model by model and score by score, is at the end of the page under "How this classification was reached".