The calcium setpoint loop

Serum calcium is a loop quantity, defended by a negative-feedback loop: CaSR senses calcium, PTH is the fast effector, vitamin-D the slow arm, bone the reservoir, kidney the integrator. A load or deficit is corrected back to the cited setpoint (ionized ~1.2 mM); the loop mechanism is reproduced.

Serum calcium is defended near its setpoint by the PTH↔vitamin-D↔bone↔kidney↔gut loop. CaSR is the comparator; PTH the fast effector; vitamin-D the slow arm; bone the reservoir. A Ca load and a Ca deficit are both corrected to setpoint.

The four-parameter PTH-calcium comparator

PTH follows the Brown inverse sigmoid of calcium, with the set-point at the calcium giving half-maximal PTH and a Hill slope (~3) set by the calcium-sensing receptor. In simulation PTH is suppressed by a calcium load (True) and raised by a deficit (True).

Disturbance rejection

A calcium load drives serum Ca to a transient peak (2.128, normalized) and a deficit to a nadir (-0.043); the loop returns serum Ca to setpoint (final 1.0003). The value held is biology (ionized ~1.2 mM, total ~2.4 mM, cited); the correction is the reproduced mechanism.