Viscosity of Concentrated Peptide Solutions

Viscosity is the one bulk property of a peptide solution that changes character as you concentrate it. In dilute solution it reports mostly on the size and shape of the individual solute. In a crowded solution it reports on how the molecules interact with one another, and the two regimes can disagree about the same sample in the same buffer. The reference case in this literature is a concentrated monoclonal antibody: viscosity measured by capillary viscometer or cone-plate rheometer was highly dependent on protein concentration, pH and the ionic strength of buffer and charged excipients, and that antibody showed its highest viscosity near its pI at low ionic strength ^[1].

Peptides are not exempt, and at fixed length and fixed concentration the sequence can dominate. Two 12-residue self-assembling peptides — LDLKLDLKLDLK and the variant FDFKFDFKFDFK, in which leucine is replaced by phenylalanine to introduce aromatic interactions and promote π–π stacking-driven self-assembly — were compared at the same 1% w/v loading, corresponding to 6.8 mM. Fitting the flow curves with the Carreau model gave a zero-shear-rate viscosity of 1.0 Pa·s for the leucine peptide and 25.8 Pa·s for the phenylalanine variant ^[2]. Same concentration, same length, a twenty-five-fold difference in the fitted low-shear limit — though the authors add that a t test found no significant difference in the overall viscosity behaviour of the two peptides, so the contrast sits at the extremes of the fitted curves rather than across the whole flow curve ^[2]. The concentration on the tube label does not tell you which of those two solutions is in your hand.

Why the concentration term is not a straight line

Three things grow together as concentration rises: the excluded volume each molecule sweeps out, the frequency with which molecules encounter one another, and the lifetime of whatever transient contacts they form. Only the first has a counterpart in the dilute limit, and separating the three is the point of the semi-empirical Ross–Minton framework. Applied to four IgG1 molecules whose viscosity profiles were measured as a function of concentration at pH 6.0, a modified Ross–Minton analysis explicitly differentiated the effects of molecular shape, size, self-crowding and electrostatic intermolecular interactions on high-concentration viscosity ^[3]. Two of the four, designated MAb-H and MAb-A, showed significantly higher viscosities at high concentration than MAb-G and MAb-E; interaction parameters from dynamic light scattering indicated attractive intermolecular interactions for the two viscous molecules and repulsive interactions for the other two, and the solution storage modulus at high concentration was consistent with the same assignment ^[3].

The same study is a warning against the simplest explanation. All four molecules carried a net positive charge at pH 6.0, but the two most viscous molecules, MAb-H and MAb-A, were the ones with the lowest positive zeta potentials, and the authors concluded that a consistent interpretation of the impact of net charge was not possible and that electroviscous effects could not explain the differences ^[3]. What did track was the response to salt: the effect of salt addition on storage modulus and on the interaction parameter indicated that the interactions were primarily electrostatic in nature ^[3]. Net charge and charge-driven association are not the same observable.

Reversible self-association is not aggregation

The distinction matters because the two have opposite consequences for a stored sample. In the concentrated antibody described above, sedimentation equilibrium analysis suggested reversible self-association at high protein concentration; the association was quite weak and was not detectable by sedimentation velocity or size-exclusion chromatography at low protein concentration, and there were no significant differences in the amounts of non-dissociable soluble aggregates between low-viscosity and high-viscosity samples ^[1]. Reversible multivalent self-association mediated mainly by electrostatic interactions of charged residues was the assigned cause of the unusually high viscosity ^[1].

Read that operationally. A viscous stock is not, by itself, evidence of an aggregated stock, and the routine test you would reach for — dilute an aliquot and run SEC — is exactly the test that will miss the responsible species, because dilution dissolves the assembly you are trying to detect. Irreversible aggregation, which does survive dilution and does show up as new high-mass peaks, is the subject of the aggregation guide in this library. A peptide whose viscosity rise ends in a self-supporting network belongs to a third case, covered in the self-assembly guide: there the interesting quantity stops being viscosity at all and becomes the storage modulus.

Charge, pH and the isoelectric point

Across a panel of monoclonal antibodies studied over a wide range of solution conditions, all but one were more viscous at pH values closer to the molecular pI ^[4]. The mechanism given is worth stating precisely, because it is not simply "low solubility near the pI": at the pI the net charge is zero, so charge-induced repulsions are minimal while the charge distribution becomes most conspicuous, and the resulting dominance of non-specific attractive interactions increases self-association or aggregation behaviour and raises viscosity ^[4]. One antibody in that panel was an exception to the general behaviour, the interaction parameter could serve only as a qualitative screening tool, and the correlation with net charge was inconsistent, so direct quantitative assessment was not possible ^[4].

The cleanest demonstration that a dilute measurement can invert the answer comes from bovine serum albumin, whose effective isoelectric point was determined as pH 4.95 from electrophoretic mobility. In dilute solutions, at or below 40 mg/mL, viscosity was minimal at the pI; at high concentration, the pH 5.0 solutions were the most viscous ^[5]. The explanation offered is that in dilute solution the electroviscous effect due to net charge governs the behaviour, whereas at high concentration the viscosity cannot be justified on the basis of a single parameter and the net interplay of all intermolecular forces dictates it, with attraction giving higher viscosity ^[5]. A viscosity measured on a diluted aliquot licenses a statement about hydrodynamic size and net charge. It does not license a prediction of the concentrated behaviour, and it can rank your conditions backwards.

Whether the attraction is electrostatic or hydrophobic has to be decided per molecule rather than assumed. Five single-point mutants of an antibody that becomes unacceptably viscous at high concentration were built to disrupt either an aggregation-prone region that also participates in two hydrophobic surface patches, or a negatively charged surface patch in the variable region ^[6]. Mutation within the aggregation-prone region (V44K) and neutralisation of the charged patch (E59Y) both increased apparent solubility, but the viscosity profile of E59Y was considerably better than that of V44K, which the authors take as evidence that the intermolecular interactions in that antibody are electrostatically driven ^[6]. The same work records the cost of getting it wrong: an adjacent mutation in the same aggregation-prone region, L45K, destabilised the molecule and abolished antigen binding, and charge reversal at position 59 caused destabilisation and decreased solubility ^[6]. The general conclusion drawn was that neutralising negatively charged surface patches may be more beneficial for reducing viscosity than charge reversal or disruption of an aggregation-prone motif ^[6].

Ionic strength cuts both ways

For a solute whose crowded-state viscosity is driven by electrostatic attraction, added salt screens the attraction and the viscosity falls — that is the low-ionic-strength maximum recorded in the antibody work above. For a peptide designed to assemble, screening is the trigger rather than the remedy. Peptide amphiphiles self-assemble into gels of nanofibers after neutralisation or salt-mediated screening of the charged residues in their peptide segment, and the choice of counter-ion changes the network: calcium-mediated ionic bridges in CaCl₂-PA gels formed stronger intra- and interfibre cross-links than the hydrogen bonds formed by protonated carboxylic acid residues in HCl-PA gels, so the calcium gels withstood higher strains ^[7]. Recovery after deformation differed in the opposite direction — after sustained deformation at 100% strain the HCl gels recovered nearly 90% of their original stiffness within 10 minutes while the calcium gels recovered only 35% ^[7]. The salt addition that thins one sample can set another.

pH behaves the same way, and for peptides it can be self-shifting. A 13-residue peptide, Ac-KGSFSIQYTYHVD-CONH₂, derived from residues 37–49 of human semenogelin I, forms a pH-responsive hydrogel; pH monitoring during self-assembly recorded a gradual pH drift associated with modulation of the ionisable histidine side-chain pK_a as the peptide assembled into β-sheet fibrils and integrated into the network, and rheology showed a substantial increase in the elastic modulus as the pH shifted ^[8]. Under buffered conditions the same peptide formed hydrogels within the experimental dead time ^[8]. Two things follow for anyone preparing a concentrated peptide stock: the buffer has to hold the pH at the working concentration, not at the concentration where you titrated it, and a slow viscosity drift at constant composition is a real phenomenon rather than an instrument artefact.

Excipients that lower it

Nine amino acids or their salt forms, four salts and two chaotropic reagents were screened against two IgG1 formulations above 100 mg/mL. Significant viscosity decreases were obtained with the salts or with the amino acids in their salt forms — by up to 30–40% for one antibody and up to 50–80% for the other — which the authors read as evidence that charge–charge interaction dictates the high viscosity of those formulations ^[9]. Most of the viscosity-lowering excipients did not induce substantial aggregation or changes in secondary structure, as judged by size-exclusion HPLC, differential scanning calorimetry and FT-IR, even without sugars or surfactants present ^[9]. That last clause is the part to copy: an excipient screen that reports only viscosity is incomplete, because the cheapest way to lower a viscosity is to change the species you are measuring.

A single viscosity number is not a measurement

Report the shear rate or do not report the viscosity. Three IgG1 solutions differing only in their complementarity-determining regions were characterised by rotary and capillary rheometry: the two more viscous solutions were non-Newtonian at high shear, showing both shear thinning and appreciable normal stress differences over the shear-rate range 10 to 10⁴ s^-1, while the third remained Newtonian up to 6 × 10⁴ s^{-1 [10]}. Rheograms were retraced as shear rate was increased and then decreased, which suggests reversible self-associations under shear, and the critical shear stress marking the onset of the viscosity reduction increased rapidly with concentration above 100 mg/mL for the high-viscosity solutions ^[10]. Two samples that agree at low shear can therefore disagree completely in a syringe filter or a narrow-bore transfer line.

Microfluidic rheometry combined with static and dynamic light scattering pushes the same point into the mechanism. Monoclonal antibody solutions above 100 g/L are typically characterised by anomalously large viscosity and by shear thinning for strain rates at or above 10³ s^-1; comparing measured behaviour with predictions from the Baxter sticky hard-sphere model linked the observed shear thinning to the predicted percolation threshold, and the longest shear relaxation time was much larger than that of model sticky hard spheres in the same region of the phase diagram, which was attributed to the anisotropy of the interactions ^[11]. The conclusion drawn is that not only the strength but also the patchiness of short-range attractions has to be accounted for to predict shear-rate-dependent viscosity ^[11]. A peptide with one sticky face is not a small sphere with weak glue everywhere.

Where the network has actually formed, shear history joins shear rate. β-Hairpin peptide hydrogels shear-thin and flow under sufficient stress and recover immediately to a solid on removal of the stress; structural analysis during flow indicated fracture of the gel network into large hydrogel domains greater than 200 nm, which are immediately percolated once flow ceases ^[12]. Both the stiffness recovered immediately after flow and the ultimate stiffness after complete rehealing depended on the duration of shear and on the strain rate applied ^[12]. For such a sample the pre-shear and rest protocol is part of the result, and two laboratories quoting different numbers may both be right.

Sample volume constrains the method more than most peptide work admits. Cone-and-plate geometry and capillary viscometry both consume material, which is why probe-based alternatives exist: measuring the apparent hydrodynamic radius of polystyrene beads of known size by dynamic light scattering in a microplate reader returned glycerol viscosities in good agreement with literature values, and viscosities for two monoclonal antibody solutions that were comparable to cone-and-plate results ^[13]. The agreement was established for those analytes, not in general. If you adopt a probe method for a peptide that self-associates, the cross-check against a rotational or capillary measurement is the experiment, not a formality — a probe bead reports the resistance felt by an object of its own size, which need not match the bulk value when the solution has structure on a comparable scale.

Temperature is part of the result

Viscosity as a function of temperature was measured at a series of concentrations and formulation conditions for two monoclonal antibodies and a globular protein. The apparent intrinsic viscosity was independent of temperature for the globular protein and decreased slightly with increasing temperature for the antibodies; analysis with the Andrade–Eyring equation gave effective activation energies of viscous flow that differed between proteins but were independent of formulation conditions for a given protein ^[14]. Larger activation energies for protein–protein interactions corresponded to larger activation energies for viscosity, and those were predictive of the highest viscosities at higher concentrations ^[14]. The practical reading is that the temperature coefficient is a property of the molecule, so it can be measured once per analyte and then used to correct across conditions.

Cooling is not a neutral operation either. In the high-shear rheology study cited above, decreasing the temperature from 20 °C to 5 °C increased the viscosity at low shear rate but enhanced shear thinning, with its onset moving to a lower critical shear rate ^[10]. A stock held cold is more viscous at rest and begins to thin at a lower shear rate once you start pushing it, which is the worst combination for reproducible transfer. Equilibrate sample and geometry, and record the temperature alongside every viscosity you quote.

What high viscosity costs downstream

Filtration stops being linear well before the solution feels thick. Across solutions spanning 1.0 to 25.7 cP driven by a peristaltic pump at 10 to 120 rpm, flow rate increased linearly with pump speed in the 1.0 and 2.5 cP solutions, but at viscosities at or above 5 cP the relationship showed a linear region followed by a nonlinear decline beyond a critical inflection point, and that inflection shifted to lower pump speeds as viscosity increased; a consistent inflection point at approximately 19 psi was identified ^[15]. Those experiments used bovine serum albumin feeds rather than peptides, so treat the numbers as the shape of the problem rather than as your thresholds. The operational consequence transfers: past the inflection the relationship reverses, so turning the pump up no longer raises the flow rate and throughput has to come from somewhere other than pump speed.

Transfer is the other quiet loss. Default liquid-handling settings are not the ones that work here: multi-objective optimisation of aspiration and dispense rates enabled automated liquid handling platforms to transfer viscous liquids accurately ^[16]. Manual work has the same failure mode in a less visible form, since a slow-recovering meniscus and a film retained on the tip wall both bias the delivered volume low, and both errors scale with how fast you work. If a concentration determined by absorbance after several transfers disagrees with the value calculated from the weighed mass, suspect the transfers before the extinction coefficient.

What to record

A viscosity is reportable when it comes with concentration and the method used to establish it, buffer composition and ionic strength, pH with the measurement temperature, the shear rate and geometry, the sample temperature, and the shear and rest history if the sample has any structure. Without shear rate the number is unusable for a sample that shear-thins; without ionic strength and pH it cannot be compared with anyone else's; without temperature it carries an unquantified offset. Where the point of the measurement is to distinguish reversible self-association from irreversible aggregation, a dilution series with orthogonal sizing on each point does the work that a single high-concentration viscosity cannot.