Bone is not just a structural scaffold — osteoblasts secrete osteocalcin into the bone matrix, and when osteoclasts resorb bone they release it into circulation. Inside the acidic resorption lacuna (pH ≈ 4–5, maintained by the osteoclast's vacuolar H⁺-ATPase) osteocalcin is non-enzymatically decarboxylated, stripping carboxyl groups from its Glu residues and converting it from the inert, matrix-bound carboxylated form (Gla-OC) into the active, circulating undercarboxylated form (ucOC).
Decarboxylated fraction: f(pH) = clamp((pH_lacuna_ref − pH) / 1.5, 0, 1)
Active hormone pool: d[ucOC]/dt = k_release · R(t) · f(pH) − k_clear · [ucOC]
Receptor occupancy: occ = [ucOC] / ([ucOC] + Kd) (GPRC6A on pancreatic β-cells)
Insulin secretion: d[Ins]/dt = Vmax · occ · S − k_decay · [Ins]
Blood glucose: d[G]/dt = k_diet − k_ins · [Ins], clamped to physiological range
R(t) is osteoclast resorption activity (left slider), S is receptor sensitivity, and Kd is the GPRC6A binding constant. Active ucOC binds GPRC6A on pancreatic β-cells and stimulates insulin secretion and β-cell proliferation; it also acts on muscle (energy expenditure), Leydig cells (testosterone), and crosses the blood-brain barrier to support memory — this simulator focuses on the best-characterised arm, the bone→pancreas insulin loop identified by Karsenty and colleagues.
With the feedback loop enabled, circulating insulin acts back on osteoblasts (via the insulin receptor, InsR) to increase osteocalcin production and suppress osteoprotegerin — closing a self-reinforcing bone-pancreas axis in which more bone turnover drives more insulin, and more insulin drives more bone turnover.
- Resorption rate — how actively osteoclasts (red, on the bone surface) excavate lacunae and release matrix-bound osteocalcin (yellow spheres).
- Lacunar pH — lower pH (more acidic) decarboxylates a larger fraction of released osteocalcin into its active form (particles turn bright green as they activate).
- Receptor sensitivity — how strongly the pancreatic islet (green organ, right) responds to a given concentration of circulating ucOC.
- Feedback toggle — switches the insulin→osteoblast arm of the loop on or off, showing the difference between an open-loop and closed-loop endocrine axis.