Receptor box: pulsed versus continuous stimulation

The same mean dose, delivered in pulses or continuously. When receptors desensitise under continuous exposure, pulsing can keep the response up. Change the parameters and watch both.

16 scenarios: IR × cc × a1 × FF. Every other parameter comes from the left. A dot marks the current gc in the panel whose four values match.

(r) R RL (x) (d) D DL (y) kr k−r kd k−d k−1 k1 k−2 k2
The four-state receptor box (after Segel et al. 1986). Both receptor states, R and D, bind the ligand L. RL → DL is ligand-induced desensitization; D → R is resensitization of the free receptor. (r), (x), (d), (y) are the fractions in each state. With fast binding the four collapse to one variable, the active fraction r + x, which this app calls r.

Why pulses?

Many hormones, insulin among them, are released in pulses. Many receptors lose sensitivity (they are phosphorylated or taken into the cell) when the stimulus stays on. Between pulses they recover. A continuous signal with the same mean wears them down.

One line of reasoning about type 2 diabetes runs like this: a large body smooths out the insulin pulses in the blood, so muscle and liver cells see insulin all the time. Their receptors desensitise and respond less (insulin resistance), glucose uptake slows, the pancreas secretes more insulin, and the loop tightens. This app shows the receptor part of that argument.

The model

Four receptor states (R, RL, D, DL) with fast ligand binding collapse to one variable, the active fraction r:

  • dr/dt = v − (u + v) r
  • u = (k1 + k2 g) / (1 + g): desensitisation; v = (k₋1 + k₋2 g cc) / (1 + g cc): recovery
  • k1 = k₋1 / (L1 IR), k2 = FF k₋1, k₋2 = k2 L2 / IR
  • activity A = a r + b (1 − r), with a, b set by a1 to a4

The stimulus is a block pulse with period TT, on/off ratio beta and off level g0. The on level is raised so the time-average stays gc, so every comparison is at the same mean dose. Because r is linear with piecewise-constant coefficients, both the time course and the periodic steady state have exact solutions. No numerical solver is used.

M_c is the activity under continuous stimulation at gc. M_p is the mean activity over one period at periodic steady state. G_p = M_p / M_c is the gain from pulsing. A_IR is the irreversible-binding limit, gc / (1 + gc)².

Where it comes from

From my 1997 PhD thesis on pulsatile signalling of peptide hormones and receptor desensitization, Université Libre de Bruxelles.