A lyophilised peptide does not have a water content. It has an isotherm. The mass of water the solid holds is set by the relative humidity it last equilibrated with, and every number downstream of a weighing — the mass you dispensed, the molarity of the stock you reconstituted, the mass-normalised activity you report — inherits whatever point on that curve the powder occupied when the balance settled. The interactions of pharmaceutical peptides, proteins and their formulations with environmental water vapour have been reviewed with attention to the physical structure and chemical diversity of these molecules and to the influence of formulation processes and additives [1].
What the isotherm plots, and what it does not
The abscissa is water activity, conventionally the equilibrium relative humidity above the sample divided by 100; the ordinate is equilibrium water content, usually as a percentage of dry mass. Most globular proteins give a characteristic sigmoidal water adsorption isotherm at ambient conditions [2]. The shape is not decorative. A steep initial region, a shallow mid-range and a sharp upturn near saturation correspond to different populations of sorbed water, and a figure quoted from the middle says nothing about either end.
Water uptake as a function of relative humidity is measured routinely to characterise and monitor hygroscopicity, but the isotherm on its own does not establish a mechanism. Newman and colleagues argue explicitly for going beyond the measurement of water vapour sorption isotherms in order to establish the various mechanisms by which solids interact with water, and stress the role played by whether the solid is crystalline or amorphous [3]. That distinction is the first thing to settle for a synthetic peptide, because it decides whether you are watching adsorption confined largely to a crystal surface, absorption into the bulk of an amorphous matrix, hydrate formation, or a solid on its way to dissolving.
Dynamic vapour sorption and the equilibration criterion
Dynamic vapour sorption is the gravimetric implementation: a few milligrams on a microbalance in a stream of carrier gas at controlled humidity, with relative humidity stepped up and then back down while mass is logged continuously. The instrument cannot know when equilibrium has been reached; it applies a stop criterion, typically a threshold on dm/dt, and moves on. That criterion, not the balance, decides whether a point on your isotherm is a real equilibrium value.
How wrong a loose criterion can be has been quantified directly. Across twenty test cases on four cellulosic materials, the widely used 0.002% min-1 stop criterion produced errors in equilibrium moisture content as large as 1.2% MC with an average of 0.5% MC — much larger than the 0.1% MC error claimed in the literature — while a stricter criterion of 0.0003% min-1 evaluated over a two-hour window held errors below 0.75% MC with an average of 0.3% MC [4]. Those magnitudes come from wood and cellulose, not from peptide solids, and should not be transplanted. What does transfer is the structure of the problem: the errors for a given stop criterion were systematic and could be fairly well characterised by a simple linear regression, so a truncated isotherm is biased in a predictable direction rather than merely noisy [4].
The same weakness afflicts single-point hygroscopicity classifications. The compendial approach of equilibrating for 24 hours under a single humidity condition may not ensure complete equilibration, and neither it nor the older Callahan classification reports anything about solid-state changes occurring during the experiment [5]. If you intend to quote a hygroscopicity category, quote the equilibration criterion and the sample pre-treatment beside it: the choice of pre-treatment and the time allowed to reach an equilibrium state are the two experimental decisions that determine what the number means [3].
Hysteresis, and what it licenses you to conclude
Run the humidity back down and the desorption branch commonly sits above the sorption branch: at the same activity, the solid holds more water on the way down than it did on the way up. That loop is informative, but only after the trivial explanation has been excluded, which is that neither branch reached equilibrium and the separation is an artefact of the stop criterion [4].
Genuine hysteresis reports on structural change in the solid. In molecular dynamics simulations of amorphous protein matrices built from pheromone ER-23 and lysozyme, non-local disulfide linkages significantly restricted structural change during hydration and dehydration, and this in turn greatly reduced the extent of hysteresis between the adsorption and desorption branches; removing backbone connectivity by breaking all peptide bonds in lysozyme shifted the hysteresis towards the lower humidity regime and significantly enhanced water uptake capacity [2]. This is a simulation on protein matrices rather than a measurement on a synthetic peptide, so it sets an expectation rather than a calibration: a constrained, crosslinked solid should give a narrow loop and a loose one a wide loop. For a disulfide-bridged peptide, loop width is worth watching as a structural readout rather than a nuisance.
A second class of loop is not hysteresis at all but an irreversible phase change caught mid-experiment. An amorphous solid that crystallises during a sorption run cannot accommodate the water it had taken up and expels it, so the mass trace rises and then falls within a single humidity step, and the desorption branch belongs to a different solid than the sorption branch did. Dynamic vapour sorption on amorphous trehalose resolved two uptake regimes below the crystallisation event — Type I Fickian diffusion predominating at 40% RH and below, and Type II behaviour described by the Peleg equation predominating at 50% RH and above — and the modelling was used to predict equilibrium sorption values and estimate recrystallisation onset times; the water content measured after recrystallisation exceeded the stoichiometric prediction [6]. Trehalose is a disaccharide, not a peptide, but amorphous lyophilisates containing sugars are exposed to exactly this failure mode, and the diagnostic is the same: mass falling at constant relative humidity.
Deliquescence: where the isotherm stops being a curve
For a water-soluble crystalline salt there is a humidity above which uptake ceases to be a gradual function of activity. Deliquescence is a first-order phase transition from solid to solution occurring at a relative humidity characteristic of the solid ingredient [7]. Below that threshold the crystal takes up very little; above it, uptake continues because the condensed phase is now a saturated solution that keeps diluting as more vapour condenses. The threshold is not an empirical accident: the deliquescence relative humidity of single components and of multicomponent crystal mixtures has been predicted from aqueous solubility data alone using PC-SAFT, with the model accounting for the temperature dependence and distinguishing hydrate from anhydrate formation [8].
Two consequences reach the bench. First, mixtures deliquesce lower than their components: in multi-component systems the transition occurs at lower relative humidity, so a blend can go wet under conditions at which each ingredient alone stays dry [7]. Second, whatever chemistry the solid is capable of accelerates once solution is present, because chemical reactions occur much more readily in solution [7]. That has been shown directly in crystalline powder blends: in single, binary, ternary and quaternary mixtures of thiamin hydrochloride, pyridoxine hydrochloride, sodium ascorbate and fructose stored between 43 and 98% relative humidity at 22 °C for up to 12 weeks, thiamin and ascorbate degradation was significantly promoted above the deliquescence point, while pyridoxine was least affected by storage relative humidity [9]. Those are small molecules, not peptides; the mechanism carries across, the rates do not. Moisture cycling across the threshold also drives repeated deliquescence and crystallisation, which promotes clumping and caking [7], and a caked salt cannot be subsampled representatively.
Water activity and Karl Fischer water content are different quantities
A Karl Fischer titration returns total water per unit mass of solid: an extensive quantity, everything the reagent can reach, with no distinction between water populations. Water activity is intensive. It describes the escaping tendency of that water, which is what governs whether the water will move into a reaction, into the headspace, or into a neighbouring excipient. The two are linked through composition rather than being interchangeable: water activity has been treated as the product of the water activity coefficient and the residual water content, making it a joint indicator of molecular interactions and of how much water is present [10]. Two lyophilisates returning identical Karl Fischer percentages can therefore sit at different water activities if their excipient systems differ.
In a study combining calculated water activity with glass transition temperature obtained from the Gordon–Taylor equation, formulations falling within a water activity range of 0.025 to 0.25 exhibited high long-term stability, and the design conclusion drawn was that favourable water activities can be achieved despite low residual moisture — and therefore high glass transition temperatures — through excipient choice and combination rather than through harder drying [10]. That work was performed on lyophilised monoclonal antibody formulations, not on peptides, and the numeric window should not be carried over to a peptide lot without re-measurement. The methodological point does carry over: a Karl Fischer percentage reported without the composition it belongs to under-determines the state of the solid, which is the limitation the companion Karl Fischer guide works through.
Where the titration earns its place is as the axis against which solid-state reactivity is calibrated. In insulin lyophiles prepared from pH 2–5 solutions and exposed to various relative humidities at 35 °C, water content within the powders was determined by Karl Fischer titration, and the degradation rate was observed to increase with water content at levels of hydration well below the suspected glass transition, approaching the rate in solution at or near the 20–50% water content required to induce a glass transition; the decomposition of insulin between pH 3 and 5 was described as a water-induced solid-state reaction accelerated by the plasticisation effect of sorbed water [11].
Sorbed water depresses the glass transition
That plasticisation is why a sorption isotherm is a storage document rather than a curiosity. Across a wide range of amorphous and partially amorphous pharmaceutical solids there is a rapid initial reduction in glass transition temperature from the dry state as water is absorbed, followed by a gradual levelling off of the response at higher water contents, and the effect could generally be described using a simplified form of the Gordon–Taylor/Kelley–Bueche relationships derived from polymer free volume theory [12]. Most of the systems considered showed nearly ideal volume additivity and negligible tendency to interact, consistent with water acting as a plasticiser in a way similar to other small molecules rather than through any specific or stoichiometric interaction [12]. The practical reading of that curve shape is that the steepest region sits at the dry end: the first fraction of a percent of sorbed water costs the most degrees.
Pulling that transition down towards the storage temperature returns molecular mobility to the solid, and the chemistry which mobility permits has been characterised directly in a lyophilised peptide powder. Lyophilised insulin exposed to elevated temperature and moisture undergoes both covalent and non-covalent aggregation; the covalent process was elucidated as intermolecular thiol-catalysed disulfide interchange following β-elimination of an intact disulfide bridge, accelerated by increasing the temperature and the water content of the powder, and the water sorption isotherm for insulin revealed that the extent of aggregation correlates directly with water uptake by the lyophilised powder [13].
That correlation is not a general law, and the limit is worth knowing before an isotherm is used predictively. Human insulin held for six months at 1%, 33% and 75% relative humidity degraded chiefly by deamidation and covalent aggregation, and the humidity effect proved temperature-dependent: moisture-induced degradation was minimal at 25 °C and 40 °C but an important factor at 60 °C, with dynamic vapour sorption showing clear differences in insulin moisture sorption characteristics at 60 °C relative to the lower temperatures. The authors concluded that the effect of moisture on deamidation and covalent aggregation rates was not a function of water content but of the nature of the insulin–moisture interaction [14]. One isotherm measured at 25 °C therefore does not license a statement about behaviour at an elevated storage temperature; if the storage condition matters, the isotherm has to be measured at that temperature.
The counter-ion is part of the solid
Peptides made by solid-phase synthesis are obtained, for cationic sequences, mainly as trifluoroacetate salts, because trifluoroacetic acid is used at cleavage and in purification; the counter-ion is tightly bound, and the classical removal route of repeated freeze-drying in the presence of excess hydrochloric acid means working below pH 1, which can induce peptide degradation [15]. On the dicationic octapeptide lanreotide, reverse-phase HPLC and an ion-exchange resin gave partial to almost complete exchange of trifluoroacetate for an ion from a weaker acid such as acetic acid, while a deprotonation/reprotonation cycle of the amino groups permitted complete removal; the procedures were compared by 19F NMR, 1H NMR and attenuated total reflectance FT-IR, and ATR-IR can be used to monitor the removal [15].
For sorption work the consequence is that a trifluoroacetate salt and the acetate salt of the same sequence are different solids, and because the deliquescence relative humidity of a crystalline component is set by its aqueous solubility [8], the two forms cannot be assumed to share a threshold. An isotherm measured on one form does not transfer to the other, and a hygroscopicity category assigned to a sequence without naming the salt form is under-specified. Nor can counter-ion content be inferred from the synthesis route, because the lyophilisation step itself alters it: in lyophilised formulations of the caveolin-1 scaffolding domain peptide CSP7, volatile counter-ions sublimate during the process, the pH-modifier excipient had the greatest impact on counter-ion loss, higher chamber pressure lowered the sublimation rate, and the counter-ion-to-peptide molar ratio had to be measured from 1H and 19F NMR peak areas; losing the volatile component shifted the pH of the reconstituted solution and caused peptide aggregation [16]. The lyophilisation formulation guide treats the process variables; the point here is that the salt stoichiometry of the lot in front of you is a measured quantity, not an inherited one.
Weighing a solid that gains mass while you weigh it
All of this converges on a mundane problem. If the isotherm shows meaningful uptake between the dry state and ambient activity, a dry powder exposed to room air moves along that curve during the weighing itself, and a balance reading that creeps upward and will not settle is the isotherm asserting itself in real time. Waiting for stability makes the reading worse, not better, because the endpoint you are waiting for is equilibrium with the room.
The workable responses all consist of fixing the position on the curve rather than fighting the drift. Equilibrate the whole lot to a defined relative humidity before subdividing, so that every aliquot sits at the same known point and the mass correction is the same for all of them; this is the same pre-treatment logic that governs the isotherm measurement itself [3]. Where that is impractical, weigh by difference into a tared, closed vessel and record the elapsed time, or bypass dry mass entirely by weighing solvent into the vial and determining concentration on the reconstituted solution by a method that does not depend on the powder mass. Bring vials to room temperature before opening, since a cold surface exposed to laboratory air is a condensation site rather than a sorption site, and the mass gained that way is not on any isotherm.
Finally, choose the storage humidity from the curve rather than by habit. For a crystalline salt form, that means staying below the deliquescence threshold with margin, and applying the mixture-lowering caveat above to any multi-component solid [7]. For an amorphous lyophilisate it means choosing a humidity whose corresponding water content leaves the glass transition comfortably above the storage temperature [12], and recording the water content by titration so the mass can be corrected later. An isotherm measured once on a representative lot converts all of these from guesswork into arithmetic; it does not, on its own, tell you what the water is doing chemically, which is why the sorption run and the stability study answer different questions.