Calcium, pH and electrolyte setpoints as loop attractors

A defended homeostatic setpoint is an Ornstein-Uhlenbeck attractor dx/dt=−k(x−x*)+load+noise; loop gain k sets the rejection error load/k, correction time 1/k, and variance σ²/2k. The node barrier γ²/4 supplies k, so the measured γ sets setpoint stability while the value stays cited.

A homeostatic setpoint, linearized about its target, is an Ornstein-Uhlenbeck process dx/dt = −k(x−x*) + load + noise. Its loop gain k sets disturbance-rejection error (load/k), correction time (1/k), and stationary variance (σ²/2k). The node barrier b=γ²/4 supplies k, so the measured γ sets setpoint stability.

The substrate sets loop stiffness, not the setpoint value

Each node is an R19 switch emerged from its measured master-gene γ. A deeper basin (larger barrier b=γ²/4) holds the controlled state more firmly, so γ contributes the disturbance-rejection stiffness k of the loop. The setpoint VALUE is biology (cited); the setpoint STABILITY is set by γ.

Demonstrated on the measured γ: barrier is monotone increasing in γ (True) and the peak displacement of a settled switch under a fixed perturbation is monotone decreasing (True) — a stiffer node resists perturbation more. Honest trade-off: the small-signal comparator slope ~1/γ moves oppositely, so γ tunes the sensitivity/stability balance.

The Ornstein-Uhlenbeck setpoint laws

Across a gain sweep the loop reproduces the control laws exactly: Var·2k/σ² ≈ 1 (True), step error × k ≈ 1 (True), and an integral arm drives the steady-state error to zero (True). Loop-gain loss therefore inflates variance and slows correction; k below a critical value is loss of regulation (attractor-shift).