Polyphosphates Affect Biological Apatite Nucleation
Why this work is in the frame
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Bibliographic record
Abstract
While biological apatite (bone mineral) resorption is understood, from the perspective of crystallization theory, nucleation is not. The degree of saturation (Ω) describes the chemical driving force for mineral dissolution (Ω <1) or formation (Ω > 1). Ω is the ratio of the ion activity product (IAP) of free apatite (available for reaction) component ion concentrations (predominately [Ca<sup>2+</sup>] and [PO<sub>4</sub><sup>3–</sup>] for apatite) and its solubility product (K<sub>sp</sub>). Free ion concentrations can be less than total ion concentrations if the ions form complexes, or if the ion speciation changes. Within the acidic bone resorption pit, free [PO<sub>4</sub><sup>3–</sup>] is reduced due to speciation into H<sub>2</sub>PO<sub>4</sub><sup>_</sup>. This reduces IAP<sub>bio-Ap</sub>, and Ω<sub>bio-Ap</sub>; at Ω<sub>bio-Ap</sub> <1, apatite dissolves. Apatite nucleation requires Ω<sub>bio-Ap</sub> >1, and bioaccumulation of molar total [Ca<sup>2+</sup>] and [PO<sub>4</sub><sup>3–</sup>] to form the 60–70 weight percent mineral in bone tissue. This is possible with the polymerization of PO<sub>4</sub><sup>3–</sup> into polyphosphate [polyP: (PO<sub>3</sub><sup>–</sup>)<sub>n</sub>] which reduces free [PO<sub>4</sub><sup>3–</sup>] while leaving total [P] unchanged. polyP forms neutral complexes by chelation with Ca<sup>2+</sup>, which further reduces free [Ca<sup>2+</sup>] and Ω<sub>bio-Ap</sub>, yet total [Ca<sup>2+</sup>] is unchanged. In vitro experiments demonstrate reduction in free [Ca<sup>2+</sup>], free [PO<sub>4</sub><sup>3–</sup>], and Ω<sub>bio-Ap</sub> by Ca-polyP formation, while total [Ca<sup>2+</sup>] and total [P] are constant. polyP depolymerization restores free [Ca<sup>2+</sup>] and [PO<sub>4</sub><sup>3–</sup>] to total [Ca] and [P], and increases Ω<sub>bio-Ap</sub>, favouring apatite nucleation.
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Full frame distilled prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. Learned from the 10,348 direct Codex labels and 10,348 direct Gemma labels. Candidate is the union of thresholded teacher heads; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels or direct frontier model labels.
Codex and Gemma teacher scores by category
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.000 | 0.000 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.000 | 0.000 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.000 | 0.000 |
| Open science | 0.000 | 0.000 |
| Research integrity | 0.000 | 0.000 |
| Insufficient payload (model declined to judge) | 0.003 | 0.002 |
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 it