Polyglutamine peptide aggregation was monitored while varying both glutamine repeat length and concentration. Polyglutamine peptides including tracts of about 35 or more continuous glutamines demonstrate relatively rapid assembly into amyloid fibrils and likewise, tracts of greater than 35 glutamines in the huntingtin exon 1 lead to HD pathogenesis. Aggregation was initiated by TEV-mediated release of the polyQ peptide from the MBP-TEV-polyQ fusion complex for Q45, Q35, Q25, and Q15 (70 µM). Thioflavin T fluorescence and dynamic light scattering both confirmed this critical Q-length reporting almost complete fibril assembly in a 12 hour period for Q45 and Q35 while reporting no ThT binding or any shift in mean diffusion coefficient in the same period for Q25 and Q15 (). In ThT fluorescence was normalized to the mean fluorescence signal of mature Q45 fibrils. During this 12 hour period, both the TEV protease and the MBP complex were stable reporting no increase in ThT fluorescence, mean hydrodynamic radius, or time-averaged scattered intensity (figs. S1
Repeat length dependent polyQ aggregation.
The ThT growth curves for Q45 and Q35 are sigmoidal showing a dependence on time, which suggests that the assembly process is cooperative. Q35 demonstrates elongated lag and growth phases compared to Q45. Additionally, the fluorescent yield of ThT bound to mature Q35 fibrils is almost 70% of that recorded for Q45 indicating fewer β-sheet subunits in the total population. Growth kinetics reported by dynamic light scattering reveal the same Q-length dependence as expected but the growth curves take a slightly different shape than those measured with ThT (). Q35 in particular displayed a relatively long inactive lag phase before the growth of <Rh
> just after 100 minutes. Here mean hydrodynamic radius is calculated by use of the method of cumulants and normalized to the steady state Q45 values. Contributions to the amplitude of the static scattering signal from TEV protease and MBP-Q45 monomers are about 8×103
photons/sec and 104
photons/sec respectively. These magnitudes are 50 to 70 times smaller than the contributions from mature fibrils. As the polyQ peptides begin to aggregate the static, time-averaged scattering signal increases above the baseline scattering from these non-aggregating molecules (fig. S2
). The background dynamic light scattering signal from TEV and MBP complex contributes to a baseline size distribution which centers around 10 nm (fig. S3
). As aggregating polyQ peptide assemblies become larger than this 10 nm background, they become distinguishable with DLS (fig. S1B
In these dynamic light scattering measurements all particles in the scattering volume are approximated by spheres. Mature fibrils, in fact, often display a rod-like or fibrous morphology when imaged with electron microscopy () or atomic force microscopy and studies have used such techniques to measure fibril length or interpret DLS data 
. Here, since we are observing many species simultaneously, the spherical approximation is used to avoid bias in autocorrelation fitting caused by a priori
assumptions about particle shape. It should be noted however that in addition to this approximation the ability to accurately extract particle size with dynamic light scattering diminishes with increased aggregate size, conformational heterogeneity, and scattering fluctuations caused by increased rotational diffusion. Additionally, as large particles sediment within the scattering volume and cease to diffuse they become static scattering centers and contribute to noise in the DLS measurement.
Nucleated aggregation is a stochastic process and thus growth rates and lag times can vary up to 10 or 20 percent from experiment to experiment (). This intrinsic variation makes it difficult to compare results between different aggregation assays when they are performed on separate aggregation experiments. Using the combined system, the same aggregating sample can be examined with both DLS and ThT simultaneously. This approach ensures that discrepancies between the two measurement techniques are real and not caused by intrinsic variation in aggregation kinetics from one experiment to the next.
ThT binding and mean hydrodynamic radius evolution were measured simultaneously for Q35 and Q45 at three concentrations, 12 µM, 28 µM and 70 µM. The 12 µM reaction produced almost negligible increase in mean hydrodynamic radius for both Q45 and Q35 (not shown). compares aggregation measured by both ThT and DLS for 70 µM Q35, 70 µM Q45 and 28 µM Q45. At the same concentration, Q35 aggregates slower than Q45 as expected, but the lag phase of the growth curve of the 70 µM Q35 sample as measured by DLS is longer than that measured by ThT (). ThT binding seems to ensue almost immediately after TEV cleavage whereas <Rh> does not increase until just after 100 minutes. A similar disparity between DLS and ThT is observed in the more slowly aggregating 28 µM Q45 sample.
Simultaneous measurement of aggregation by DLS and ThT fluorescence.
The particles observed by DLS during the lag phase of the slowly aggregating samples tend to have <Rh
> on the order of 10 nm (fig. S3
). In these experiments, the increase of ThT fluorescence which coincides with the apparent lag phase of the DLS aggregation curves implies that the dye is binding to some fibrilar structure during this period. This elongating fibrilar species must have a diffusion coefficient equivalent to or greater than a 10 nanometer particle, or else the elongation would be measured by light scattering as well. This indirectly suggests that the smallest ThT binding β-sheet unit has a hydrodynamic radius less than or equal to ten nanometers, a hypothesis supported by previous studies which conclude that the smallest ThT binding unit is cross β-sheet fibrils made of five or more β-strands 
This disparity between <Rh> and ThT binding does not occur in the rapidly aggregating 70 µM Q45 sample. Instead the two assays concomitantly report aggregation reaching a steady state plateau in both β-sheet content and <Rh> simultaneously (). ThT reveals higher steady-state fluorescence with increasing concentration (). Equally, DLS reports a slightly larger steady-state <Rh> in the 70 µM Q45 reaction than the 28 µM while the 12 µM sample displays almost no increase in <Rh> (not shown) confirming that fibril elongation is stunted at lower concentrations. ThT fluorescence alone only measures total β-sheet content, and is blind to the way in which β-sheets are distributed within fibrils. Thus without the complimentary DLS information it would be impossible to discern whether the lower relative ThT fluorescence measured in the less concentrated reactions was caused by shorter fibrils or fewer fibrils.
70 µM Q35 aggregates slower than the 70 µM Q45 as previously noted and like 28 µM Q45 reveals a discrepancy between ThT binding and <Rh
> evolution (). Features of the aggregation kinetics were quantified by fitting growth curves to the sigmoid function
and extracting the lag time, tlag
, and transition slope, k1/2
defined in . The Q-length and concentration dependence of polyQ fibril aggregation is corroborated by the observation that tlag
decreases and k1/2
increases as concentration and Q-length are increased (). This is observed by both ThT fluorescence and dynamic light scattering. The difference in shape between aggregation curves measured by DLS and ThT is summarized by the observation that in the slowly aggregating polyQ samples, specifically the 28 µM Q45 and 70 µM Q35, DLS reports a longer tlag
and a greater k1/2
than ThT. This can be interpreted to mean that ThT measures a faster nucleation rate, but a slower elongation rate than DLS.
This difference in shape must be caused by the fundamental difference between the species which ThT and DLS respectively observe. The magnitude of the ThT fluorescent signal reports the total number of minimal dye-binding β-sheet subunits. DLS measures the size distribution of diffusing particles and the signal is dominated by populations that exhibit the most scattering, specifically large or abundant species. In order to gain a more complete understanding of the species which DLS detects, CONTIN was used to solve equation (3
) for S(Γ)
and extract particle size distributions from the light scattering data from aggregating Q45 and Q35 at 70 µM and 28 µM (). CONTIN analysis revealed the evolution of multimodal distributions of scattering particles over the course of the aggregation reaction.
Size distribution evolution during aggregation.
As the shape of aggregate particles diverges from the spherical approximation, hydrodynamic radius becomes a less accurate description of the size of the aggregates. Instead it is useful to understand aggregate size in terms of Rh_apparent which is defined here as the hydrodynamic radius of a sphere with equal translational diffusion coefficient. Observation of the distribution of Rh_apparent in time reveals the emergence of a population of large diffusing particles () which coincides with the growth phase of <Rh> reported by cumulant analysis in . The magnitude of the light scattering signal from mature aggregates is in fact dominated by photons scattered from these larger species at about 5×105 photons/sec. This is apparent in the larger relative amplitudes of the peaks at the higher region of the particle size distributions in . The method of cumulants attempts to fit a single peak to the whole particle size distribution, including all species of scattering particles. The smaller species, while scattering fewer photons, still give a strong contribution to the decay rate of the autocorrelation function. Thus while the temporal features of the particle size distribution evolution measured by CONTIN track with the mean radius measured by the method of cumulants the particle size measurement in is only an average value. However CONTIN is also susceptible to noisy measurement caused by non-spherical fibrils which contain more complex diffusion characteristics including rotational diffusion and inter-fibrilar motion. Additionally at late time points during assembly, the static background scattering signal from sediment particles causes an ill-defined baseline in the measured autocorrelation functions. This is can be interpreted by CONTIN as contributions from slowly decaying time components of the autocorrelation function biasing the measurement towards larger radii. Nonetheless the CONTIN distributions offer insight into the polydispersity of various species measured by DLS. In accordance with the cumulant measurements, the emergence of the large species revealed by CONTIN analysis do not coincide with the rapid fibril growth measured by ThT fluorescence.
To understand the nature of the discrepancy between ThT and DLS, we consider a simplified model of fibril growth 
in which there are only two species; polyQ monomers and a distribution of linear fibrils centered on a mean length of n
monomers. In this model nucleation ensues and fibrils begin to elongate by monomer addition after a lag phase associated with the fibril nucleation rate (). In such a case where the only aggregate growth mechanism – and thus the only cause for decrease in translational diffusion coefficient or an increase in Rh_apparent
– comes from fibril elongation via the formation of new β-sheet elements, CONTIN analysis would reveal a heterogeneous particle distribution peaked at an Rh_apparent
corresponding to the mean fibril length, and the mean of this distribution would track with the ThT fluorescence curve. This is observed during the rapid aggregation of 70 µM Q45 (). For cases of slower aggregation however, ThT fluorescence kinetics diverged from the kinetics of particle size distribution measured by DLS and thus implies another mechanism by which <Rh
> increases. If there were an abundant non-fibrilar intermediate state along the kinetic trajectory to fibril formation, DLS would report the presence of these species as an increased <Rh
> or an independent peak in the particle size distribution, preceding
ThT mediated fluorescent enhancement. Instead, in the more slowly aggregating samples, 28 µM Q45 and Q35 and 70 µM Q35, ThT reported fibrils that emerge first, and are then succeeded by a rapid increase in <Rh
>. The early ThT binding fibrils must be smaller than the 10 nm baseline in <Rh
> measurement and so in this case DLS only detects species with a larger Rh_apparent.
These data suggest that the large species reported by DLS require the presence of fibrils to form. It is therefore possible that these species are in fact a higher-order cluster of amyloid fibrils. It should be noted that the data does not rule out the possibility of non-fibrilar intermediate species which precede fibril formation. These proto-fibril intermediates however must then be smaller than the 10 nm baseline in the <Rh
Model for fibril and bundle formation.
Amyloid fibrils are often observed in tightly bunched plaques as seen in . It is possible that when individual fibrils reach a certain length, it becomes energetically favorable for fibrils to assemble into higher order structures. The formation kinetics of these large fibril bundles would thus be directly dependent on fibril nucleation and elongation rates.
A qualitative model is used to illustrate fibril bundling that is based on a classical single-step nucleation scheme (). Two critical parameters associated with the fibril bundle nucleation energy barrier are defined. The critical fibril length Lc, is defined as the mean fibril length that is required for fibril bunching. In other words it is energetically favorable for fibrils shorter than Lc to exist in an isolated state while fibrils longer than Lc have the potential to assemble into bundles. Fibrils of length L contain N polyQ monomers so Nc is the critical number of monomers in a fibril necessary for fibril bundling. A critical fibril number for bundling m* is also defined. m* defines the size of the critical nucleus for bundle formation and is analogous to the critical nucleus size for fibril nucleation n*. Fibril bundles made up of m<m* fibrils have a higher probability to disassociate into individual fibrils, whereas fibril bundles consisting of m >m* fibrils surmount the nucleation energy barrier and will recruit more fibrils for bundle growth. Thus the nucleation of fibril bundles is governed by two parameters, the rate that fibrils reach length L> Lc, and the rate that fibrils of L≥ Lc bundle together. This bundling rate is inherently dependent on the total number of fibrils with L> Lc.
In this qualitative model, nucleation and growth of fibril bundles is directly dependent on fibril elongation. In aggregating solutions of 28 µM Q45 and 70 µM Q35, fibril elongation proceeds slowly, so there is a lag time of about 100 minutes or more required before a sufficient population of fibrils reach Lc. Only then do we see fibril bundling reported by DLS. In this model it is necessary that bundling does not interfere with fibril elongation, thus the ThT binding curves coincide directly with fibril elongation which continues uninterrupted throughout the aggregation reaction.
In the case of 70 µM Q45, fibril elongation is so rapid, as confirmed by ThT fluorescence, that a large population of fibrils quickly reach the critical length Lc while other fibrils are still being formed and elongated. Additionally individual fibrils within the large fibril assemblies may still be undergoing elongation. This explains the simultaneous increase of ThT fluorescence and <Rh> in . Particle size distributions also reveal very heterogeneous populations after the initial increase in Rh_apparent, suggesting a spectrum of fibril structures ranging from single fibrils to the largest fibril assemblies (). The final population is a heterogeneous distribution of fibrils and fibril bundles, as demonstrated on the electron micrograph ().