Why does deamidation accelerate at 37 °C rather than proceeding linearly?

The specifics, since they change the answer: deamidation · 37 °C.

I would like the mechanism, because I want to be able to reason about the cases nobody has written about.

I have tried to reason it out from first principles and got to two contradictory conclusions.

Can someone derive this rather than assert it?

The honest answer is that published stability data for these specific molecules in a research-grade presentation essentially does not exist, so what you get is extrapolation from the licensed formulations and from general peptide chemistry. That extrapolation is reasonable. It is still extrapolation.

Aggregation is the failure mode that reverse-phase HPLC is worst at detecting, because a large soluble aggregate may not elute at all and an insoluble one is filtered out during sample preparation. If your purity result comes back normal but the vial looks hazy, believe the vial. Size-exclusion chromatography is the method that sees this.

Specifically, light matters for specific residues rather than in general. Tryptophan and to a lesser extent tyrosine and methionine are photo-labile; a sequence without them is largely indifferent to ambient light over the timescales in question. Amber glass is cheap insurance rather than a requirement.

General guidance on lyophilised peptide storage from the major synthesis houses converges on minus twenty degrees for long-term storage of solids and refrigerated storage for solutions in use, with the explicit note that repeated freeze-thaw of solutions should be avoided. It is consistent advice precisely because it follows from the chemistry rather than from a study.

Minimise transitions rather than minimising temperature. One freeze and one thaw is fine; five is a different question.

A warm arrival is a reason to test, not automatically a reason to discard. Peptide degradation is kinetic — rate multiplied by time — and a few days at thirty degrees in the solid state is a small integral compared to weeks in solution.

For the solid state, residual moisture is the dominant variable. A cake at two per cent water is considerably more stable than the same cake at six per cent, because water is both a reactant in hydrolysis and a plasticiser that lowers the glass transition temperature. This is why a desiccant in the outer packaging is not theatre, and why opening a cold vial in a humid room is a genuine error — you condense water onto the cake.

The relevant detail is that freeze-concentration is the mechanism people miss. As ice forms, everything that is not water is excluded into a shrinking unfrozen fraction, so the local concentration of peptide, buffer salts and preservative rises sharply. If the buffer components crystallise at different rates, local pH can shift by more than a unit. That is why a phosphate-buffered solution can behave badly on freezing while an unbuffered one is fine.

The caveat is that "within specification" and "unchanged" are different claims. A vial can lose a few per cent of content and still be usable for its purpose while no longer matching its certificate.

If the material arrived warm and it was lyophilised, test it and proceed on the result. If it arrived warm and it was in solution, the result is more likely to be interesting than reassuring.

On the detail: start by separating chemical degradation from physical degradation, because they fail differently and they are detected differently. Chemical degradation changes the molecule and shows up as new peaks on a chromatogram. Physical degradation aggregates the molecule and often shows up as nothing at all on reverse-phase HPLC, because the aggregate never makes it onto the column.

Practical thermal arithmetic for a shipment: a single 250 g phase-change pack in a thin-walled polystyrene box holds sub-ten-degrees for roughly 24 to 48 hours in a 25 °C ambient, and considerably less at 35 °C. Any lane taking eight to fourteen days is therefore not temperature-controlled for most of its duration regardless of what was in the box, which is the argument for shipping the material lyophilised.

The Arrhenius relationship underpinning accelerated stability testing is the basis of ICH Q1A, which is why accelerated studies at 40 °C and 75 per cent relative humidity are used to predict shelf life at 25 °C. The same relationship lets you reason about a warm transit lane, with the same caveats about extrapolation.

The practical rule is that time and temperature multiply, so shorten whichever one you control.

Put another way, freeze-thaw damage happens at the moving ice front, not at the storage temperature. Once the sample is frozen solid and cold, very little is happening. The damage is done during freezing and thawing, which is why the number of cycles matters and the duration of the hold mostly does not.

On re-freezing something that thawed in transit: if it arrived as a lyophilised solid that warmed but never got wet, re-freezing costs you nothing except the thermal cycle. If it arrived as a solution that thawed, re-freezing adds a second transition and therefore a second dose of ice-front shear. The asymmetry is worth internalising.

Where community-submitted samples with known thermal excursions have been tested at Janoshik or Medutest, the recurring finding is that lyophilised material tolerates warm transit far better than intuition suggests, while reconstituted material shipped warm does not. The asymmetry is consistent enough to plan around.

The single highest-value change most people can make is buying a cheap logging thermometer, because it converts an assumption about their storage into a record.