A size-exclusion column separates by how much of the internal pore volume a molecule can reach. That is a hydrodynamic property, set by the volume a molecule sweeps out as it tumbles, and it is not the same quantity as mass. Two molecules of identical molar mass, one compact and one extended, leave the column at different times. One molecule can leave at two different times in two different mobile phases. Nothing in a retention time forces it to be a mass. The conversion is performed by a calibration curve built from standards, and the curve carries every one of the standards' assumptions with it.
Why a retention time is not a mass
Conventional size-exclusion molecular weight determination is a relative measurement. Standards of known mass are run, elution volume is fitted against log mass, and the sample is read off that fit. The fit is only valid for molecules that share the standards' shape and their absence of interaction with the stationary phase. In a direct comparison on recombinant human growth hormone and beta-lactoglobulin, in which the chromatographic system was calibrated with standard proteins and fitted by least squares to a third-order polynomial, the molecular weights returned by conventional size-exclusion chromatography with ultraviolet detection were higher than the reported values for both proteins. Light-scattering determinations on the same separation returned 23.1 plus or minus 0.57 kDa using a refractive index concentration detector and 21.2 plus or minus 0.80 kDa using ultraviolet, against a sequence mass of 22.1 kDa for growth hormone, values the authors judged to agree within experimental error [1].
The same study is a useful check on triumphalism. For beta-lactoglobulin the light-scattering values were themselves always higher than the 18.4 kDa figure supplied by the manufacturer: 22.5 plus or minus 0.55 kDa and 23.0 plus or minus 1.22 kDa, which is roughly 22 percent and 25 percent above the supplier's number, taking 18.4 kDa as the denominator [1]. The abstract does not assign a cause. The lesson is not that light scattering is always right. It is that the two approaches fail in different ways, and only one of them fails in a way you can see.
What multi-angle light scattering actually measures
A multi-angle light scattering detector measures the excess scattered intensity from each eluting slice at several angles. Combined with a concentration signal from the same slice, that yields a molar mass for the slice directly, with no reference to where the material came off the column. Because the calculation makes no assumption that the analyte is globular and needs no calibration standards, molar mass can be obtained for proteins of any shape, including intrinsically disordered proteins and aggregates [2]. In a separate evaluation across glycosylated and non-glycosylated proteins and antibodies, the author describes the determination of molecular weight as absolute, avoiding misleading results caused by molecular shape or by interactions with the column matrix, and notes that quantities and masses are obtained together from a single injection [3].
Two limits are worth stating plainly. The first is not a literature finding but a consequence of the physics. Scattering from particles much smaller than the laser wavelength is essentially isotropic, so the angular fit returns a mass but no meaningful radius of gyration. Small peptide oligomers sit well inside that regime, and expecting shape information from them is a category error. Separately, samples that absorb at the laser wavelength need correction; a published treatment of iron-sulfur cluster proteins applied various corrections to determine the absolute molar mass of both apo- and holo-forms, and for the [2Fe-2S]-containing holo-NEET proteins in particular the authors report that this allowed them to ascertain a change in oligomerization state upon cluster binding [2].
The refractive index increment is the number everything rests on
The reported mass is proportional to the scattering signal divided by the product of the slice concentration and the square of the refractive index increment, dn/dc. Where the concentration comes from matters, and the arithmetic is not intuitive. When concentration is taken from a refractive index detector, that concentration is itself the refractive index signal divided by dn/dc, so one power cancels and the reported mass varies inversely with dn/dc to the first power. A dn/dc value 10 percent too high then returns a mass about 9 percent below the true mass, and a value 10 percent too low returns a mass about 11 percent above it. When concentration instead comes from ultraviolet absorbance and an extinction coefficient, nothing cancels: the same two errors become roughly 17 percent low and 23 percent high. The denominator in all four figures is the true mass.
For an unmodified protein, dn/dc is commonly calculated from composition rather than measured directly. That is a convention of convenience, not a requirement, and it is the step at which an unexamined assumption most easily enters. The utility program SEDNTERP calculates the specific refractive increment of proteins from their composition, along with buffer density, viscosity and refractive index, and its author notes that new terms added to the partial specific volume calculation should improve accuracy particularly for smaller proteins and peptides [4]. Calculated values stop being safe once the buffer stops being simple. For lysozyme in solutions containing sodium chloride, arginine chloride, urea, sucrose or guanidine chloride, determination of the second osmotic virial coefficient required the refractive index increment measured at constant solvent chemical potential, and because that increment decreases as co-solvent composition rises, using a single constant value could lead to misinterpretation of the interaction trends deduced from the measurements [5].
What SEC-MALS still inherits from the column
Light scattering fixes the mass axis. It does not fix the separation. Material that never elutes is not weighed, and material that dissociates on the column is weighed in whatever state survives to the detector.
The recovery problem has been shown directly. In an immunoglobulin study using mobile phases of 200 mM sodium phosphate at pH 7.0 with 0, 50, 100, 200 or 400 mM added sodium chloride, complete protein recovery from the column was attained only at 400 mM sodium chloride, a requirement the authors describe as surprising. Significant discrepancies against sedimentation velocity appeared at the lower salt concentrations, and the high molecular weight species that sedimentation velocity resolved eluted from the column as a single peak [6]. That is a result for those agitated and unagitated immunoglobulin samples and that series of mobile phases. It is not a salt concentration to copy into an unrelated method.
Dilution is the second inherited problem, and it needs no citation, only mass balance: an injected band spreads across the column bed, so a reversibly associating sample is continuously re-equilibrating at a falling concentration while it separates. A molar mass that drifts across a peak is the visible symptom, and it means either unresolved species or something the mass calculation is not modeling.
Sedimentation velocity: separation with no matrix at all
Sedimentation velocity analytical ultracentrifugation spins the sample fast enough that a boundary forms between depleted solvent and sedimenting solute, and an optical system records concentration against radius over time. There is no stationary phase, no mobile phase exchange and no injection dilution. The boundary spreads for two reasons: the sample is heterogeneous, and every species diffuses. Modeling the profiles as a combination of finite element Lamm equation solutions for a large number of discrete noninteracting species, with maximum entropy regularization, discriminates between the two, producing a relatively high-resolution sedimentation coefficient distribution c(s) from which, the author reports, more detail can be obtained than from van Holde-Weischet analysis [7]. That method uses estimates of the partial specific volume and the frictional ratio to calculate the diffusion coefficients [7], so c(s) is a distribution obtained under assumptions, not a raw observable.
From a sedimentation coefficient to a mass
The sedimentation coefficient is the mass times the buoyancy factor, divided by Avogadro's number and the frictional coefficient. Two of those terms are supplied rather than measured, and both amplify error.
The buoyancy factor is one minus the product of partial specific volume and solvent density. Take a partial specific volume of 0.73 mL/g in a buffer of density 1.00 g/mL: the factor is 0.27. If the partial specific volume is 1 percent too high, at 0.7373 mL/g, the factor falls to 0.2627, about 2.7 percent smaller, and because a derived mass is inversely proportional to that factor, the mass comes out roughly 2.8 percent too high. In denser buffers the factor is smaller still and the amplification worsens. This is algebra, not a finding, but it is why buffer composition is not a detail and why the partial specific volume of a short, unfolded peptide deserves more scrutiny than that of a folded protein.
The frictional term is the larger trap. The c(s) analysis approximates a single weight-average frictional coefficient for all particles, determined from the data, which scales diffusion to sedimentation consistently with the traditional relation in which s varies approximately as mass to the two-thirds power; the authors state this approximation is favored by several experimental factors and usually gives good results for macromolecules that are not too chemically dissimilar, such as mixtures of folded proteins, and they describe a two-dimensional extension, c(s,f_r), that determines average molar masses without the approximation of any scaling relationship between hydrodynamic and thermodynamic parameters [8]. The two-thirds power has a consequence people misread constantly. A dimer with the same partial specific volume and the same frictional ratio as its monomer sediments about 1.59 times as fast, because two raised to the two-thirds power is about 1.587. It does not sediment twice as fast. For the ratio to reach 2.0, the dimer's frictional ratio would have to be about 21 percent lower than the monomer's, taking the monomer's frictional ratio as the denominator, which folded proteins do not do.
Precision has its own hierarchy. In a study of a monoclonal antibody monomer and dimer system, alignment of the sample cells to the center of rotation was the most significant contributing factor to overall variability, ahead of the other factors examined, which included temperature equilibration, time-invariant noise and meniscus misplacement [9]. There is also no single mandated protocol. A multi-author paper distills the experimental and analysis procedures used by its authors into a series of best-practices considerations, with the stated goal of helping harmonize aggregate quantitation approaches across the biopharmaceutical industry [10]. Harmonizing is what a field does when practice has diverged, which is a fair description of where the convention stands.
Detecting reversible self-association
A stable oligomer travels as one species at every concentration. A reversibly associating one does not: it re-equilibrates continuously, so its apparent size depends on the concentration at which you looked. The workhorse diagnostic is a concentration series, and both techniques support one.
In sedimentation velocity, integrating a differential sedimentation coefficient distribution gives a thermodynamically well-defined isotherm of weight-average s against concentration, provided that distribution is a good model for the sedimentation profiles. Deconvoluting diffusion in c(s) can be advantageous for identifying species that do not participate in the association; the large number of scans that can be analyzed makes the resulting weight-average values very precise, allowing the isotherm to be extended to very low concentrations; corrections are derived for the slowing of the boundaries caused by radial dilution; and direct global modeling of several experiments with Lamm equation solutions exploits the shape of the profiles, permitting identification of the association scheme from fewer experiments [11]. Whether exchange is fast or slow relative to the duration of the run governs whether resolved peaks or one shifting boundary appear; that is standard transport theory rather than a result, but it decides how the data can legitimately be read.
Static light scattering under a composition gradient answers the same question without a rotor. For zinc-free insulin, the dependence of scattering intensity on total concentration up to 1.5 mg/mL at pH 3.0 to 8.0 may, the authors write, be quantitatively accounted for by a simple isodesmic association scheme requiring only a single association constant for addition of monomer to monomer or to any oligomer; at pH 10 the constant for monomer adding to monomer was smaller than the constant for monomer adding to all higher oligomers by a factor of approximately five; and the same isodesmic scheme accounted for the concentration dependence of weight-average molecular weight derived from previously published sedimentation equilibrium measurements at pH 7.0, with the authors reporting excellent agreement between the stepwise constants obtained by the two techniques [12]. That paper also carries a caution worth more than the model: at nearly the same low pH, insulin was found to be monomeric in acetic acid at pH 1.95 and dimeric in hydrochloric acid at pH 1.85 [12]. The acid, and not the pH alone, set the state.
For peptides that self-associate readily, orthogonality is not optional. In a solution-state characterization of amyloid beta-derived diffusible ligand preparations, analytical ultracentrifugation together with size-exclusion chromatography coupled to multi-angle laser light scattering indicated that the solutions existed primarily as a binary mixture of monomeric peptide and high-molecular-mass oligomers, and the authors concluded that the low-molecular-mass oligomers identified by gel electrophoresis likely represent artifacts induced by the peptide's interaction with detergent [13]. An assay that adds detergent to a self-associating peptide is not a neutral observer of it.
What these methods do not settle
Neither technique gives a structure. An oligomeric state is a stoichiometry plus a hydrodynamic description; it says nothing about which surfaces are in contact.
A mass from a light-scattering slice is a weight average over whatever co-elutes. When two species overlap, the returned number is arithmetically correct and corresponds to no species actually present. A flat mass across a peak is evidence of homogeneity within that peak; a sloping one is evidence of a problem, and neither identifies what is hiding.
In sedimentation velocity, the high hydrodynamic resolution of c(s) rests on approximating one weight-average frictional ratio for every particle present, an approximation the authors qualify as usually giving good results for macromolecules that are not too chemically dissimilar [8]. Relaxing it with a two-dimensional size-and-shape distribution asks more of the same data. Whether a small feature in a distribution is a genuine minor species or a consequence of the regularization is a judgment the analyst makes, not the software.
There is a general limit neither method escapes. Both report on the sample as it exists in that buffer, at that temperature and concentration, with that handling history. A monomer measured at low concentration after twenty minutes on a column and a monomer measured at ten times that concentration in a stationary cell are two measurements, not one. When they disagree, the first hypothesis is that the association is concentration-dependent, not that an instrument is broken.