Magnesium, CKD-MBD and humoral hypercalcemia: extending the disease coverage

Three further major ion diseases close by reusing the six failure modes already derived, with no new primitive: magnesium imbalance is a loop-gain drop read on a third ion, CKD-MBD is a multi-arm gain drop of the renal integrator, and humoral hypercalcemia of malignancy is a set-point drift upward — the inverse of the allosteric reset.

The volume's pathology chapter closes seven representative diseases on six failure modes and lets rare or specific forms enter as a cited parameter. Three further MAJOR ion diseases — magnesium imbalance, CKD-MBD with secondary hyperparathyroidism, and humoral hypercalcemia of malignancy — were named but not yet modelled. Each is one of the SAME six failure modes, reusing the volume's own load/k law and PTH comparator with no new primitive.

Magnesium: a third defended ion on the same load/k law

Serum magnesium (~%.2f mM, cited) is a defended setpoint like calcium and pH. Its diseases are the loop-gain-drop / buffer-arm-failure mode read on a third ion: when an arm loses gain, the same disturbance is no longer rejected and the residual offset is load/k. An absorption / reabsorption-arm failure (TRPM6 loss — hypomagnesemia with secondary hypocalcemia; Gitelman renal Mg wasting) under an Mg-loss drive pulls magnesium DOWN; an excretion-arm failure (renal insufficiency with an Mg load) pushes it UP.

The failed-arm excursion exceeds the healthy-loop residual in both directions, the ratio (%.1f×) equals the gain ratio k_healthy/k_failed (%.1f) — the volume's own load/k law — and the failed loop's variance blows up (Var=σ²/2k). The directions are [V]; the cited setpoint and the TRPM6 / Gitelman anchors are [L]; the absolute Mg excursion magnitude is [O].

CKD-MBD: a multi-arm gain drop of the renal integrator

As nephrons are lost the renal integrator (the kidney node) loses gain, and the CKD-MBD cascade is the loop-gain-drop mode applied to SEVERAL arms at once. Stepping the renal gain down reproduces the cited KDIGO sequence: serum phosphate rises (its excretion arm err=load/k grows), 1,25-vitamin-D falls (renal 1α-hydroxylase), serum calcium tends down, and the calcium-sensing receptor raises PTH — secondary hyperparathyroidism.

All four primary signs are monotone in the falling renal gain (phosphate up %s, vitamin-D down %s, calcium down %s, PTH up %s), and PTH rises above its baseline in advanced disease. The calcium×phosphate product is near-normal early (a small early dip as calcium falls before phosphate retention dominates) and climbs to the precipitation ceiling in advanced CKD (%.2f → %.2f, the vascular-calcification driver). The cascade direction is [V]; the KDIGO cascade is the [L] anchor; absolute per-stage progression timing is [O].

Humoral hypercalcemia of malignancy: a set-point drift upward

Tumor-secreted PTHrP acts at the PTH receptor like PTH but is tumor-autonomous — the calcium-sensing receptor cannot suppress it. In the set-point-drift plant (PTH effector against a constant loss), an exogenous UNSUPPRESSIBLE drive relocates the defended calcium UPWARD, the exact inverse of the T1 allosteric reset that relocates it back down.

The defended calcium rises monotonically with the PTHrP drive into the hypercalcemic range, while the endogenous PTH is appropriately SUPPRESSED below baseline despite the high calcium — the clinical fingerprint that distinguishes humoral hypercalcemia from primary hyperparathyroidism (where PTH is high). The CaSR loop works; it simply cannot turn off a drive that is not its own. The direction is [V]; the PTHrP mechanism is the [L] anchor (Stewart 2005); the absolute hypercalcemia level is [O].

What this closes

These three extend the human disease coverage from a representative seven toward nearly all the major mineral / acid-base / electrolyte disorders — each by reusing a failure mode already on the substrate, not by adding machinery. The two items named here as open in earlier drafts are now closed in the next two chapters: the molecular transport DYNAMICS behind these arms (channel gating / GHK flux) is derived in §12, and the per-species master-gene γ that would ground the cross-species gains is MEASURED in §13 — where it returns an honest negative. Neither is hidden; both are now resolved, one as a new primitive and one as a documented obstacle.