Steady state is not a metaphor — it is an arithmetic fact about exenatide

There is a specific and avoidable confusion at the centre of most discussions of dose timing. A once-weekly drug with a seven-day half-life does not produce a weekly peak-and-trough cycle of the kind a daily drug produces. At steady state the fluctuation between peak and trough is modest, and the practical consequence is that moving the injection from Sunday morning to Friday evening changes very little about total exposure and quite a lot about when the most noticeable effects land.

How you get seven days out of a two-minute peptide

Three engineering strategies account for essentially every long-acting agonist on the market. The first is substitution at the DPP-4 cleavage site: replacing the alanine at position 8 with a residue the enzyme cannot process removes the fastest route of degradation. The second is acylation with a fatty-acid chain, which promotes reversible binding to serum albumin; albumin-bound drug is protected from renal filtration and enzymatic attack, and dissociates slowly to provide a circulating depot. The third is fusion to a large carrier — an immunoglobulin Fc fragment, for instance — which raises the hydrodynamic radius above the glomerular filtration threshold.

Semaglutide uses the first two, with a C18 diacid linked through a spacer. Liraglutide uses a shorter C16 chain and achieves roughly thirteen hours rather than seven days, which is a useful demonstration of how much the chain contributes. Dulaglutide takes the fusion route. The strategies are not interchangeable and they produce different distribution and clearance behaviour, not merely different durations.¹

The accumulation arithmetic, worked

For a drug given at a fixed interval, the accumulation ratio at steady state is approximately 1 / (1 − e^−kτ), where τ is the dosing interval and k is the elimination rate constant, itself 0.693 divided by the half-life. For a once-weekly drug with a seven-day half-life, τ and the half-life are equal, e^−kτ is 0.5, and the accumulation ratio is 2. In plain terms: at an unchanged weekly dose, average concentration at steady state is roughly twice what it is after the first injection.

Time to steady state depends only on the half-life, not on the dose or the interval: about 94% of steady state after four half-lives, 97% after five. For a seven-day half-life that is four to five weeks. This is why a fixed four-week escalation step exists at all — it is approximately the time required for the previous dose to stop increasing — and why escalating faster than that means escalating onto a still-rising exposure curve.

These are approximations that assume linear kinetics and complete absorption. Both assumptions are reasonable for this class and neither is exact.

A missed dose, modelled

Because exposure declines with a seven-day half-life, a single missed weekly dose leaves roughly half the accumulated concentration in circulation at the point the next dose would have been due, and roughly a quarter a week after that. That is why product labelling for once-weekly agonists generally permits taking a missed dose within a defined window and otherwise skipping it, and why a single omission rarely produces a dramatic change.

An interruption of four weeks or more is a different situation. By then concentrations have fallen to a small fraction of steady state, tolerability has substantially reset, and resuming at the previous dose means presenting the receptor with an exposure step it has not seen for a month. The clinical convention — resume lower and re-escalate — follows directly from the pharmacokinetics rather than from caution alone.²

Injection timing: what the kinetics permit

At steady state on a seven-day half-life the peak-to-trough variation across the dosing interval is modest — on the order of tens of per cent rather than folds. Moving the injection by twelve hours, or from one day of the week to another, does not meaningfully change total exposure. It does change when the highest concentrations occur relative to a person’s week.

Time to maximum concentration after subcutaneous injection is on the order of one to three days for the long-acting agonists, so an injection on Friday evening produces its concentration peak somewhere in the weekend. Whether that is desirable is a question about a person’s schedule, not about pharmacology. What the pharmacology does say is that consistency of interval matters more than consistency of hour, because the interval is what determines the accumulation ratio.

Delayed gastric emptying is the mechanism, not the complication

Slowed gastric emptying is frequently described as a side effect. It is more accurately described as a mechanism that becomes an adverse effect at sufficient magnitude. Delayed emptying blunts the post-prandial glucose excursion, which is part of the glycaemic benefit, and it produces early satiety, which is part of the weight effect. Beyond a threshold it produces nausea, vomiting, reflux and the sensation of food sitting undigested.

Two properties of the effect matter clinically. It is dose-dependent, and it exhibits partial tachyphylaxis: the magnitude of delay attenuates over weeks of continued exposure at a fixed dose, which is the physiological basis for the observation that tolerability improves if a dose is held rather than escalated. The residual delay at steady state is real and is the reason pre-procedural fasting guidance for this class exists at all.³

None of this settles the question a reader most wants settled, which is what a given molecule will do to them. Receptor pharmacology is a description of average behaviour in a population of receptors, and a person is not a population. What it does provide is a way of telling a plausible claim from an implausible one — and in a market where the same four figures circulate for eighteen months attached to the wrong trials, that is not a small thing.