How many weeks does it actually take to reach steady state?

The receptor pharmacology I can follow; the in vivo translation is where I lose the thread.

Please show the division. I want to check my own against yours.

I would like the general form as well as the specific number, so I can apply it again.

Where is my error, and what is the correct working?

Specifically, the receptor is also expressed in the heart, kidney and vasculature, which is the plausible route for effects that are not obviously metabolic.

Glucose-dependence arises because the insulinotropic signal amplifies glucose-stimulated secretion rather than initiating secretion. With no glucose signal to amplify, there is little to amplify.

Biased agonism — differential recruitment of beta-arrestin versus G-protein signalling — is an active research area and is one hypothesis for why agents with similar receptor affinity have different tolerability.

The incretin effect itself was established by comparing the insulin response to oral and intravenous glucose loads matched for plasma glucose; the difference is what the gut hormones contribute.

Nothing here is medical advice; this is pharmacology.

Mechanism is a good guide to what to expect and a poor guide to how much.

Stated carefully, the glucose-dependence is the key property. Below about four millimoles per litre the insulinotropic effect largely disappears, which is why monotherapy hypoglycaemia is uncommon.

Central effects reach the arcuate nucleus and the area postrema, regions with an incomplete blood-brain barrier. That anatomy is why a large peptide can act centrally at all, and it also explains the nausea, since the area postrema is the chemoreceptor trigger zone.

Receptor density and downstream coupling differ between tissues, so the dose-response curves for glycaemia, weight and nausea are not the same curve. That is the pharmacological basis for titration.

Area postrema involvement in nausea from this class is supported by lesion studies in animals and by the anatomy of the circumventricular organs.

A receptor being expressed in a tissue does not establish that activating it there matters at therapeutic exposures.

Tissue distribution first, then signalling. Nearly every question in this tag resolves at the first step.

The short version: glucose-dependent insulinotropic action, glucagon suppression, delayed gastric emptying and central appetite effects, from one receptor in four places.

Native GLP-1 has a circulating half-life of one to two minutes because dipeptidyl peptidase-4 cleaves the two N-terminal residues. Substituting the position-8 alanine, as the long-acting analogues do, blocks that cleavage and is the single most consequential modification in the class.

The position-8 substitution conferring DPP-4 resistance appears in essentially every long-acting agent in the class, which is about as strong a piece of convergent evidence as medicinal chemistry offers.

Research-use material is not approved for human use, and mechanism is not a safety argument.

The half-life problem and the albumin-binding solution are the whole story of the class chemically.

Answering this needs the distinction between the native hormone and the pharmacological agents, whose half-lives differ by three orders of magnitude and whose effects therefore differ in kind.

Gastric emptying delay attenuates with continued exposure for long-acting agents through receptor desensitisation, which is why the early nausea usually settles while the appetite effect persists.

The caveat is that mechanism predicts direction and rarely predicts magnitude in an individual, and people reason from mechanism to dose far too confidently.

Nausea and appetite share an anatomy, which is why they are hard to separate by dose.