A dynamic light scattering instrument never sees a peptide. It sees a speckle pattern whose brightness flickers because the scatterers are diffusing, and it records how fast that flicker loses correlation with itself. Every number you write down afterwards — a radius, a polydispersity index, a claim that the preparation is monomeric — is inference stacked on one decay rate. DLS studies the diffusion behaviour of macromolecules in solution, and the diffusion coefficient, and hence the hydrodynamic radius calculated from it, depends on the size and shape of the macromolecule [1]. The second half of that sentence is the half that gets dropped.

From Brownian motion to a decay rate

Coherent light illuminates a small volume of solution. The scatterers move by Brownian motion, the relative phases of their contributions drift, and the detected intensity fluctuates on the timescale over which a scatterer diffuses a distance comparable to the inverse scattering vector. A correlator multiplies the intensity trace by a delayed copy of itself and averages, building the intensity autocorrelation function. For a dilute, monodisperse, non-interacting sample the underlying field correlation function decays as a single exponential whose rate is the diffusion coefficient times the squared scattering vector — the latter fixed by solvent refractive index, vacuum wavelength and detection angle. That framework is standard rather than a finding, and real samples break it: the data are properly described by a distribution of decay rates [5].

The step from diffusion coefficient to radius is the Stokes-Einstein relation: radius equals thermal energy divided by six pi times solvent viscosity times diffusion coefficient. Temperature and viscosity are typed in, usually from a water lookup table, and the radius scales inversely with the viscosity you declare. Measure in a glycerol-containing or high-denaturant buffer with the software still on water and the radius is wrong by exactly the ratio of the two viscosities.

The radius is apparent, and the model is yours

The hydrodynamic radius is the radius of the hard sphere that would diffuse at the rate you measured. Because diffusion depends on shape as well as size [1], any non-spherical object is reported as the sphere it is not, and the error scales with how far it departs from one.

Pulse field gradient NMR on native and non-native protein conformations gave two empirical relations between hydrodynamic radius and residue count: for native folded proteins the radius in angstroms is 4.75 times the residue count raised to the power 0.29, and for highly denatured states 2.21 times the residue count raised to the power 0.57, with predictions from those equations agreeing well with dynamic light scattering and small-angle X-ray or neutron scattering data reported for proteins from 58 to 760 residues [2]. Evaluate both at a hundred residues and you get roughly 18 angstroms compact against roughly 30 angstroms expanded — the same chain, a 1.7-fold spread, purely from conformation. A hundred residues sits inside the validated range; a twelve-residue peptide does not, so those expressions orient rather than answer.

Assembled peptides depart much further. Photon correlation spectroscopy on a self-assembling 24-residue peptide in 2-chloroethanol, from about 0.1 nM upward, found tapes behaving like semiflexible chains with persistence lengths of several hundred nanometres and much longer contour lengths, the polarised angle-dependent scattered intensity fitting a prolate object with major and minor axes of about 630 nm and about 40 nm [3]. A single hydrodynamic radius for that object is a summary statistic for something long and thin, and it is neither the 630 nm nor the 40 nm.

Radius also moves without mass moving, and can move the wrong way. A DLS study of calmodulin with eleven synthetic peptides comprising calmodulin-binding domains found that adding calcium to apo-calmodulin raised the hydrodynamic radius from 2.5 to 3.0 nm, and that the peptides induced a collapse of the elongated calcium-bound structure to a more globular form, decreasing its hydrodynamic radius by an average of 25 percent [4]. Those complexes carry the peptide's mass on top of the protein's, and the radius fell anyway. A hydrodynamic radius is not a proxy for mass.

Cumulants, the polydispersity index, and where they stop

The default fit is the method of cumulants, which expands the logarithm of the field correlation function so the first term gives a mean decay rate and the second its variance. The method provides information about the cumulants and moments of the decay-rate distribution, but it does not permit independent determination of the long-time baseline of the intensity correlation function and can lead to inconsistent results when different numbers of data points are included in the fit; reformulating it in terms of moments about the mean permits more robust and satisfactory fits, a comparison made on polydisperse vesicle samples [5]. That baseline problem means the answer depends on where you stopped fitting, so the fit range belongs in the record beside the result.

The polydispersity index most instruments report is the second cumulant over the square of the first — definitionally the squared relative width of the decay-rate distribution, not a count of species. Its useful range has been bounded. Analysing computer-generated correlation data with realistic noise by both linear and non-linear methods, the mean and variance of the distribution of diffusion constants were obtained quite accurately for distribution widths, defined as standard deviation over mean, up to about 0.6, but there appeared to be little prospect of obtaining meaningful higher moments [6]. Squaring that width puts the practical ceiling near a polydispersity index of about 0.36; above it the fit describes your fit range more than your sample.

What a polydispersity index licenses is a statement about width. Two well-separated populations, one genuinely broad population, and one clean population plus a trace of dust can all deliver the same second cumulant.

Distribution analysis is an inversion, and the inversion is ill-posed

Turning a correlation function into a size distribution means inverting a Laplace-type integral from noisy data, and particle size inversion of DLS data is a typically ill-posed problem addressed by regularisation; the classical inversion is constrained by the L2 norm, and the norm chosen determines the smoothness and stability of the result and so its accuracy [7]. In one systematic study, inversion errors fell overall as the norm order rose, and the L-infinity constraint showed lower sensitivity to noise and better peak resolution for bimodal particles [7]. The lesson is not that one norm wins, but that the peaks in a distribution plot are partly a property of the regulariser. The widely used CONTIN algorithm may, in some instances, produce non-physical results [8]. Never report a distribution without the algorithm and its settings, and never read peak area as stoichiometry.

The sixth power, and what it does to a trace of aggregate

The sixth-power relationship between scattered intensity and particle radius is simultaneously the technique's primary advantage and the thing that renders it sensitive to unwanted size fractions from unclean lab-ware, dust, and aggregated or dynamically aggregating sample [9]. The arithmetic: a scatterer of ten times the radius returns of order 106 times the intensity of a monomer, so a single such particle among a million monomers contributes roughly as much signal as the entire monomer population. That is why DLS is worth running on a peptide solution, and why its output is so easy to misread.

The bias has been quantified in one system. In lysozyme solutions containing dense liquid clusters of radius about 100 nm, comparison of DLS against Brownian microscopy showed that because of the sixth-power dependence of scattered intensity on scatterer size, DLS overestimates the mean cluster size by a factor that depends on the shape of the size distribution and was about 1.6-fold in that solution, with a related underestimate of cluster concentration of about tenfold; DLS yielded a reliable distribution width only when cluster concentration exceeded 109 per cubic centimetre and volume fraction exceeded 10-6, and returned a lower bound on cluster lifetime that may be orders of magnitude below the real one [8]. Those numbers belong to lysozyme clusters, not to your peptide; what transfers is the direction of each bias, which the weighting sets.

The same weighting explains the volume and number distributions the software offers: intensity goes as radius to the sixth, volume as radius cubed, number not at all. Converting intensity to volume divides out roughly a cube of the radius and converting to number roughly a sixth power, and the conversion is a model calculation assuming a particle shape and optical properties, not a re-measurement. It therefore amplifies precisely the small-size region the intensity fit constrains least. A number-weighted DLS distribution is not a count of objects and should never be quoted as one without the intensity distribution beside it.

Dust, filtration, and the sample you actually measured

Because of that weighting, sample preparation becomes iterative and time consuming, and it often requires data-filtering methods that leave an inaccurate estimate of the steady-state size fraction and may give the user no knowledge of the transient fractions that were removed [9]. Automatic dust rejection is not free: it discards data, and what it discarded was in your tube.

The bench consequences follow from the physics. Filter or centrifuge immediately before measurement, choosing a pore size above the species you intend to measure and below the debris you intend to lose — and record it, because a filter that removes dust also removes real aggregate, and the solution afterwards is not the solution you had. Filter the buffer by the same route and measure it alone: a blank with a low count rate and a flat correlation function is your only evidence that the peaks came from the peptide and not the cuvette.

Dilution is the other diagnostic: in a comparison of DLS with resonant mass measurement, it was evaluated as a technique to confirm and quantify the number of particles in solution [11]. Used as a control rather than a measurement it is cheap: a real scatterer population changes its contribution with dilution predictably, and a fitted artefact frequently does not.

Concentration cuts in both directions

DLS evolved as a fast, convenient tool for particle size analysis of non-interacting spherical colloids, with particle interaction, polydispersity, anisotropy and light absorption all bearing on the measured diffusion coefficient [12]. Both qualifiers in that phrase are conditions of validity, and a concentrated peptide solution satisfies neither.

The peptide tape system shows what happens when the first fails. At about 10-2 mM the tapes begin to overlap and form networks, and those semidilute solutions are characterised by one main relaxation mode associated with the cooperative diffusion of the entangled network plus a weaker, slower mode associated with gel cluster formation [3]. Once a network exists the fast decay rate reports a collective property, not the translation of one object, and feeding it into Stokes-Einstein produces a radius with no referent.

The optics fail separately. Characterisation of colloidal suspensions by DLS is in general limited to systems with negligible contributions from multiple scattering, and for larger particle sizes with high scattering contrast this immediately limits the technique to very low concentrations; a 3D cross-correlation experiment built to suppress multiple scattering was able to measure the dynamic structure factor in concentrated polydisperse latex suspensions without resorting to high dilution [13]. That ceiling belongs to the single-scattering geometry of a conventional instrument, not to light scattering in principle — but if yours is conventional, the ceiling is yours.

Interaction, multiple scattering and genuine concentration-dependent association are told apart only by a concentration series. A radius that drifts monotonically with dilution says one thing; a radius flat across a decade says another. One measurement at one concentration says neither.

Concentration is a chemical variable for the analyte as well. Quasi-elastic light scattering on synthetic amyloid beta-protein (1-40) in 0.1 M HCl tracked hydrodynamic radii through the entire process of fibril nucleation and growth, finding that above a peptide concentration of approximately 0.1 mM the initial elongation rate and the final fibril size were independent of concentration, whereas below 0.1 mM the initial elongation rate was proportional to peptide concentration and the resulting fibrils were significantly longer [14]. That threshold belongs to that peptide in that acid and carries to no other sequence or buffer. What generalises is that a concentration chosen for optical convenience may have selected the assembly pathway you then measured.

What DLS cannot resolve

Close populations are the hard case. In a four-platform comparison using monodisperse polystyrene particles of nominal modal size 220, 330 and 410 nm, only the tunable resistive pulse sensor and the disc centrifuge resolved all three populations in the mixed sample; the DLS system detected a single population, corresponding to the smallest, 220 nm particles [10]. Measured separately, every platform returned a mean within 10 percent of the electron microscopy reference, yet the breadth of the measured distributions deviated greatly, with coefficients of variation two- to sixfold larger than the microscopy values across all four platforms, while all four gave under 5 percent variance in shape descriptors over replicates [10]. Precision is not accuracy.

Resolution is also a function of relative abundance. Using polystyrene standards from 20 to 1000 nm, and binary mixtures holding 20 nm particles at a fixed 1014 particles per millilitre against various concentrations of one larger size, DLS resolved two species in a manner dependent on both concentration and particle size, the working range of the method depending on both [11]. Whether two populations separate is a property of the specific pair and their ratio, not a fixed instrument specification.

Set that against what a peptide question usually asks. If a monomer and a dimer were both compact spheres of equal density, their radii would differ by the cube root of two, about 1.26-fold — far below the near twofold separation that went unresolved in the bead mixture above. No regulariser has been shown to recover a separation that small.

Oligomeric state is a mass question

The literature contains a clean illustration of the correct verb. After dissolution in 0.1 M Tris-HCl at pH 7.4 and removal of pre-existent seeds, amyloid beta-protein chromatographed almost exclusively as a single peak, and the molecules composing that peak had average hydrodynamic radii of 1.8 plus or minus 0.2 nm, consistent with the predicted size of a dimer [15]. Consistent with. The radius was compared against an expectation computed from a model; it did not count subunits, and could not have.

Mass is measured directly by a different experiment. SEC-MALS determines the absolute molar mass of macromolecules in solution by detecting their light scattering intensity, and because it does not rely on an assumption about the globular state of the analyte or on calibration with standards, the molar mass can be obtained for proteins of any shape as well as for intrinsically disordered proteins and aggregates; in the study cited, absolute molar mass allowed the authors to ascertain a change in oligomerisation state upon iron-sulfur cluster binding, with corrections needed for samples that absorb at the MALS laser wavelength [16]. The companion guide on SEC-MALS and analytical ultracentrifugation covers that route in full.

The division of labour is clean. DLS answers whether anything large is present, whether it is appearing over time, and whether a solution is homogeneous enough to be worth a slower method. It does not answer how many chains are in the particle.

What to report

  • Temperature and the viscosity and refractive index values the software used, not just the buffer name.
  • Concentration, whether a series was run, the filtration route, and the buffer blank's count rate and correlation function.
  • Scattering count rate and attenuator position, showing whether signal was adequate or saturating.
  • The fit: cumulants or regularised distribution, the algorithm, its settings and the fit range; polydispersity index with that range, and no higher cumulants [5, 6, 7].
  • The weighting shown — intensity, volume or number — and, if not intensity, the intensity distribution alongside it.
  • Number of independent runs and the spread across them, kept separate from the fitted distribution width [10].

Reported that way, a DLS measurement is a defensible statement about the diffusion of whatever was in the cuvette. Reported as a size, it is a sphere that does not exist.