Extended Experimental Procedures.
We selected residue 90, at the C-terminal end of the central hydrophobic NAC region of αS, as an appropriate position to incorporate the fluorophores. This residue is located at the periphery of the structure thought to be highly organized in the fibrillar form (Heise et al., 2005; Vilar et al., 2008
) (see B), and consequently no major changes in the nature of the fibrillar core are expected to result from the addition of fluorophores in this position.
A preliminary characterization to confirm the covalent attachment of the Alexa fluorescence dyes to the protein was performed. The efficiency of the labeling process was checked by mass spectrometry (Mass spectrometry facility, Department of Chemistry, University of Cambridge), resulting to be higher than 95% for both Alexa Fluor (AF) dyes. No cross-linked oligomer was observed by mass spectrometry and SDS-PAGE gel (NuPAGE Novex Bis-Tris Mini Gels, Invitrogen). The conditions used for the electrophoresis were constant voltage of 200 V, and the run time was 35 min using MES SDS running buffer (Invitrogen protocol) (this conditions were always used unless otherwise indicated). To check if the presence of the dyes could distort the conformational ensemble of the monomeric protein, dynamic light scattering was used to compare the hydrodynamic properties of the wild-type (WT) and the labeled A90C-αS. Due to the laser wavelength of the instrument, only AF488 labeled protein could be measured, although similar behavior is expected for the AF647 variant. Representative size distributions of 30 μM protein in Tris 25 mM, pH 7.4, 0.1 M NaCl were recorded at 25°C on the Zetasizer Nano ZS (Malvern Instruments Ltd.) instrument at 633nm. The samples were filtered through 0.2 μm filter and the scattered light was detected at an angle of 173°. The acquired data was analyzed by Zetasizer Nano software (Malvern Instruments Ltd.). The hydrodynamic diameter found for AF488-labeled A90C-αS was identical, within the error, to that of the unlabeled WT protein (6.07 ± 0.1 and 5.89 ± 0.18 nm, respectively; see C).
Incubations for bulk measurements were prepared exactly as for the single-molecule measurements by using 1mg/ml WT αS, AF488-labeled protein or equimolecular concentrations of AF488 and AF647-labeled protein (1 mg/ml total protein concentration) in Tris 25 mM, pH 7.4, 0.1 M NaCl, with 0.01% NaN3 to avoid bacterial growth during sample incubation. The samples were incubated in Eppendorf tubes at 37°C under constant shaking at 200 rpm. For WT αS 10 μl aliquots at different incubation times were analyzed for thioflavin T (ThT) fluorescence, after addition of 20 μM ThT, using a Cary Eclipse fluorescence spectrophotometer (Varian). At the same time, the amount of monomeric protein was quantified by quantitative size exclusion chromatography (SEC): aliquots of 100 μl of sample were loaded onto a superdex 75 10/300 (GE Healthcare) analytical column and the absorbance followed at 280 nm. For labeled αS, the increase in ThT signal upon amyloid fibril formation could not be followed due to interferences of the fluorescence dyes in the fluorescence properties of the ThT molecule. The kinetics of fibril formation in this case was quantified by quantitative SEC and SDS-PAGE gels using the fluorescence properties of the dyes. For SDS-PAGE analysis, 2 μl of aliquots were taken and the fluorescence quantification done on a Typhoon Trio scanner (Amersham Bioscience); AF488-labeled protein was excited at 488nm and emission collected at 526nm, while AF647-labeled protein was excited at 633nm and emission collected at 670nm. The image analysis was done with ImageQuant TL v2005 software (Amersham Bioscience). For quantitative SEC analysis, 50 μl of sample at different incubation times were injected onto a superdex 75 10/300 (GE Healthcare) and the absorbance followed by 280, 488 and 647 nm.
The formation of fibrils followed by ThT or the decrease in monomeric protein followed by either SDS-PAGE gel or SEC gave very similar results, and were individually analyzed using the empirical equation generally used to fit kinetics of fibrillization (Uversky et al., 2001
Incubations of equimolecular concentration of AF488- and AF647-labeled αS showed a slower rate of formation of amyloid fibrils than does the unmodified protein at the same conditions (the lag-time increased from 0.5 ± 0.2 days for the unmodified protein to 1.5 ± 0.2 days for the labeled proteins) and the quantity of fibrils formed was lower than with the unmodified protein (D and S1E). Interestingly, when only AF488-labeled protein was incubated, we found that the decrease rate of monomeric protein, as well as the final amount of monomeric protein at the end of the aggregation reaction showed intermediate values between those for the unlabeled protein and the mixture of labeled proteins (see E), suggesting that the addition of the fluorophores in position 90 in the protein sequence could influence the stability of the fibrils, and that the larger the fluoropore, the bigger is this effect. In fact, the labeled fibrils were found to incorporate both AF488- and AF647-labeled protein, but with a slight preference for AF488 (around 70% of AF488 and 30% AF647), according to SEC analysis, measured by following the amount of monomeric protein remaining in the soluble fraction during the incubation. However, we did not observe any preference for one color at the oligomeric level according to the analysis we performed during the aggregation of the protein by single-molecule fluorescence experiments using TCCD (Two Color Coincidence Detection), indicating that this preference for monomers labeled with AF488 only takes place at the fibrillar level. The fibrils formed with the mixture of labeled proteins were also morphologically indistinguishable by TEM from those derived from the unmodified protein (F), and showed similar proteinase K degradation profile (data not shown). In particular, there was no evidence for the formation of amorphous aggregation in either of the samples.
During the analysis of the aliquots at bulk conditions from the incubations of a mixture of AF488- and AF647-labeled protein, we observed another peak in the SEC chromatogram, apart of that of the monomeric protein, corresponding to oligomers eluting in the void volume of the column (G). The concentration of oligomers in mass as a function of incubation time was estimated from the area of the oligomeric peak in the chromatogram obtained at different incubation times (taking the area of the monomeric peak at time 0 as a reference), and resulted to be very small at all times (being the maximum ca. 2 μM, i.e., 3% of the total protein concentration; see D in main text). This result is in agreement with the SDS-PAGE analysis of the same aliquots, where no apparent differences were observed comparing the amount of soluble material before and after ultracentrifugation, after removing the fibrillar material.
Transmission Electron Microscopy
TEM images were obtained using a Philips CEM100 transmission electron microscope. The samples were applied on Formvar-carbon coated nickel grids and negatively stained with 2% (w/v) uranyl acetate. For the aliquots of early incubation times, the sample was applied directly onto the grids. For late incubation times, the sample was previously centrifuged for 10-15 min at 16,000 x g, and then the supernatant was applied to the grid and stained, while fibrillar material was applied to the grid, washed with ddH2O, and stained.
Calculation of the Association Coefficient in smFRET Experiments
After thresholding the raw data (see Experimental Procedures
in the main text), coincident events (due to oligomers exhibiting FRET) are identified and a list of all the fluorescent bursts from such events recorded during the measurement is obtained. From the number of oligomer and blue monomer events recorded per second (rC
, respectively), we obtain the association quotient, Q, for each aliquot, a measurement of the fraction of dual-labeled molecules within the sample, as previously reported (Orte et al., 2006
The ratio of the burst rate of coincident events to the burst rate of blue monomers is divided by two to account for the rate of red monomer bursts that cannot be measured but is assumed to be the same as that of the blue monomers. In addition, the monomer burst rate is assumed to be that of the total burst rate due to the very low frequency of oligomer events compared to monomer events detected in the single-molecule experiments. The Q value was further corrected for the efficiency of detection of coincidence fluorescence; in our experiments we determined this value to be 25%, using a sample containing only dual-labeled 40bp-dsDNA (Orte et al., 2006
), and for the fact that oligomeric species containing either only donor or only acceptor molecules are invisible in our approach (whose probability depends on the oligomer size according to Pascal's triangle).
Estimation of the Concentration of Oligomers at Bulk Conditions from smFRET Experiments
The concentration of oligomers (in number of species) at bulk conditions was estimated from the burst rate of oligomers detected in the smFRET experiments after correcting by the efficiency of detecting oligomers in our approach (see section above). The corrected burst rate was then transformed into concentration of oligomeric species at single-molecule conditions, using a reference to convert burst rates in concentration. As a reference, we use dual-labeled 40 base pair double-stranded DNA. The dsDNA is labeled with AF488 at the 5′-end of one strand and with AF647 at the 5′-end of the complementary strand, so the two fluorophores are far apart. For this 40bp-dsDNA model, the average molar burst rate in our setup, using the same scanning rate is 0.76 burst.s-1.pM-1. Finally, we can extrapolate the concentrations calculated at single-molecule conditions to bulk conditions by simply multiplying by the dilution factor (typically 105 for aggregation experiments, and 103 for disaggregation experiments). The stability of the oligomeric species upon dilution was checked and the effect of dilution on the number of oligomer detected was found to be very small, just 3 times higher for type A oligomers and 1.5 times higher for type B oligomers (data not shown). These values were used to correct the concentration of oligomers at bulk conditions from the smFRET analysis.
To estimate mass concentration of oligomers at bulk conditions, we used the same procedure explained above, but calculating the burst rate of protein aggregated (rC_mass) instead of the burst rate in number of oligomers.
This procedure of estimating the concentration of oligomers from the burst rate in smFRET experiments using a sample of dsDNA as a reference was further proved to be valid by an alternative procedure of estimating the concentration in the single-molecule sample, based on the burst rate of aggregated protein detected and the estimation of the scanned volume in the experiment. Assuming that the probe volume is spherical (ca. 4fL, although only 25% of that volume is functional (Orte et al., 2006
)), the scanned volume in the experiment can be then assumed to be cylindrical and it would depend on the scanning rate. In our experiments, the scanning rate is 200 μm.s-1
, which gives a scanned volume rate of 6.08 × 10−13
. This scanned volume rate multiplied by the burst rate of aggregated protein gives the number of oligomers per liter in the sample at single-molecule conditions. The concentration in number of oligomers per liter at bulk conditions can then be extrapolated by multiplying by the dilution factor. Both methods of calculating the concentration of oligomers at bulk conditions from smFRET measurements give rise to the same values within the experimental error.
Finally, we compared the mass concentrations of oligomeric species at bulk conditions derived from the smFRET experiments with the concentrations obtained by SEC analysis, at bulk conditions, at different incubation times during the aggregation reaction (see G). Both the concentrations of oligomers and the kinetic curves obtained by the two methods are very similar (D in main text), proving the validity of our smFRET approach.
Analysis of the Apparent Size- and FRET-Derived Oligomer Distribution
The apparent size and FRET efficiency for each individual oligomer can be estimated (see Experimental Procedures in the main text for a more detailed explanation). 2D histogram plots were generated, classifying each oligomer according to its apparent size and FRET efficiency value, using a bin size of 5 mers for the size histogram and a bin size of 0.05 for the FRET histogram. These values were chosen to get a statistically significant number of oligomers per bin and to account for the limit in size resolution due to the various possible combinations of AF488 and AF647 fluorophores in an oligomer and the different paths a molecule can take through the confocal volume. The data is robust to changes in the bin size used (data not shown). The oligomers were further classified in three classes according to their size: small (~2–5 mers), medium (~5–15 mers), and large (~15–150 mers) (we established 150 mers as a threshold in size for the analysis of soluble oligomers). The boundaries of the division in these three classes were chosen as to have the minimum number of classes whose FRET histograms showed the minimum number of Gaussian distributions. For each class of oligomers, the FRET efficiency histograms were globally analyzed for all incubation times recorded during the aggregation or fibril disaggregation experiment (see Figures C and B), and fitted to Gaussian distributions with constant center and width for all incubation time points. In the case of the medium size oligomers (~5–15 mers), two clear distinct FRET distributions were always observed in both aggregation and fibril disaggregation experiments, and two Gaussian distributions were needed for the fit.
From the parameters of the Gaussian distributions, the total number of oligomers at each time point and for each class of oligomers was estimated. Because the FRET efficiency histogram has a bin size of 0.05, to estimate the number of oligomers of each Gaussian distribution (which is a continuous function), each Gaussian distribution (obtained from several bins), was “transformed” into an equivalent bin of 0.05 with exactly the same area as that of the Gaussian distribution. The height of this bin corresponds to the total number of oligomers associated with the distribution. To compare the kinetics of the different oligomers with the kinetics of fibril formation obtained by SDS-PAGE gel analysis (determined then as the fraction in protein mass included in the fibrils), we need to estimate the fraction in mass of each oligomer class at bulk conditions. To do this, we first transformed the number of oligomers calculated from the analysis explained above into protein mass using an average size for each oligomer class: 4-mer for 2–5 mers, 10-mer for 5–15 mers, and 30-mer for 15–150 mer (corresponding to the approximate size at which half of the total oligomers of that class is smaller and half bigger). Then, we corrected these values for the different factors explained in the section above: the dilution factor, and the efficiency in detecting oligomers in our experiments, and the stoichiometries of the two fluorescent dyes that give FRET signal depending on the oligomer size, and the burst rate of protein aggregated for each oligomer class was calculated according to Eq.S2. This analysis was done for each oligomer class at each incubation time point, and the average values and associated standard errors for the 5 aggregation experiments performed were calculated. For the four oligomer classes (Asmall
, and Blarge
), the data was well fitted to single-exponential kinetics with a lag time:
corresponds to the final concentration of oligomers reached at the end of the kinetics, r
the apparent growth rate, and x0
the lag time before start of exponential kinetics. The kinetic parameters obtained for each oligomer class are shown in in the main text.
The possible effect of pipetting when the sample is diluted from bulk to single-molecule conditions on the number of oligomers detected was explored by comparing the number of coincident events and the oligomer distribution when the sample was pipetted using normal pipette tips and mixed by gently pipetting, with when the sample was obtained using pipette tips whose bottom part was cut (so the pipette had a bigger diameter to avoid fragmentation of large oligomers/fibrils) and the mixing was done by tube inverting. The differences in the number of coincident events and the size- and FRET-distributions were insignificant between these two methods.
Analysis of the Average Ratio of Donors and Acceptors in the Oligomeric Species by TCCD Experiments
Because we observed a slight preference of αS labeled with AF488 in the fibrils: ca. 70% of the protein incorporated in the fibrils contains AF488 and 30% AF647 according to SEC and SDS-PAGE analysis, we performed an analysis of the average ratio of number of donors and acceptor in the soluble oligomeric species detected in single-molecule experiments by Two Color Coincidence Detection (TCCD) method (Orte et al., 2006
) using the same instrument as that used for the smFRET experiments.
SmTCCD measurements of aliquots of an αS aggregating sample at different incubation times were performed in the same way as for the FRET measurements, and the data of 15 measurements corresponding to different incubation times and different αS aggregation experiments were independently analyzed. Grouping all the coincident events detected in all the experiments, the average ratio of brightness in the blue and the red channel obtained was 0.906. As the labeled fibrils seem to have a ratio between blue and red labeled monomers of 2.3, we also checked if there is a size-dependence of the ratio between brightness of oligomers detected in our experiments. For that, we calculated the size of each oligomer and we grouped all the oligomers detected in the 15 experiments by their size. The ratio between average brightness falls between 0.7 and 1.4 and without any dependence with the size of the oligomers, suggesting that the assumption of equal distribution of blue and red labeled proteins in the αS aggregates is valid at least for the soluble oligomeric species detected in our solution sm fluorescence approach. The preference for AF488-labeled molecules with respect to molecules containing AF647 is found to be then in large protein species inaccessible to our smFRET experiments, likely due to strong steric and electrostatic repulsions in fibrils composed by a high number of AF647 fluorophores, which is bigger and more negatively charged than AF488.
Limited Digestion of Protein Species with Proteinase K
The sensitivity of αS monomers, oligomers, and fibrils to proteinase K degradation was tested. To determine the sensitivity of monomers to proteinase K degradation, we used an equimolecular concentration of AF488- and AF647-labeled A90C αS of 70 μM in Tris 25 mM pH 7.4, 0.1 M NaCl; 2 μl of sample were diluted into 500 μl of buffer and 1 μl of proteinase K solution (Proteinase K from Tritirachium album, Sigma-Aldrich) was added to a final concentration of 0.01, 0.1, 0.4, 2, and 10 μg/ml (i.e., at protein:proteinase K ratios varying from 1:0.0025 to 1:2.5). The reaction sample was then incubated for 20 min at 37°C and the reactions stopped by addition of SDS-PAGE loading buffer and loaded in SDS-PAGE gels. The quantification of the level of proteinase K resistance was performed using the band in the gel corresponding to full-length monomeric αS (see B). The gel analysis was done as explained in the previous section (bulk experiments). An αS fibrillar sample with an estimated concentration of around 30 μM was incubated with the same proteinase K concentrations in the same way as for the monomeric sample, but in this case a serine-protease inhibitors cocktail (PMSF, Sigma-Aldrich) was added in 1200:1 ratio with respect to the proteinase K concentration to stop the degradation reaction. For quantification of the level of degradation of each sample, we dissolved the fibrils into monomers by adding guanidine thyocianate at a 2 M final concentration and incubated the sample for 1 hr at room temperature. This concentration of guanidine thyocianate was able to dissolve the fibrils without significantly increasing the ionic strength of the samples, allowing the normal running of the protein samples in SDS-PAGE gels for quantification (see B). High concentrations of either DMSO or urea were unable to dissolve the fibrils into monomers.
To quantify the stability of the oligomeric species, we incubated a sample of equimolar concentration AF488- and AF647-labeled A90C αS (70 μM of total concentration) in Tris 25 mM pH 7.4, 0.1 M NaCl in aggregating conditions, and after 5 days of incubation we took 2 μl aliquots, which were incubated with proteinase K exactly as was done for the monomeric and fibrillar samples. In this case, the reaction was stopped by diluting the sample 500 times in buffer, and the final sample was checked by single-molecule analysis (see A). In all cases the final proteinase K concentration is below its active concentration, and we did not observe any degradation during the single-molecule experiment.
Time-Resolved Fluorescence Measurements of the Labeled Proteins
Time-correlated single-photon counting was performed on a PicoQuant FluoTime 200, equipped with two pulsed diode lasers of 470 nm (LDH-P-C-470) and 635 nm (LDH-P-635), combined on a fiber coupling unit and controlled by a multichannel driver (‘Sepia’ PDL-808). The repetition rate was 20 MHz, giving a FWHM around 80 ps for both laser pulses. After a polarized set at the magic angle (54.7°), and an emission monochromator, a photomultiplier was used as detector. A TimeHarp 200 PC card is used to collect data in 1,320 channels. Photon histograms were recorded until they reached typically 2 × 104 counts at the maximum at four different emission wavelengths for each dye. Decay traces were analyzed by a least-squares based deconvolution method in terms of multi-exponential functions using FluoFit software. Decay traces at the different emission wavelengths were fitted globally with the decay times linked as shared parameters, whereas the pre-exponential factors were local adjustable parameters. The quality of each fit was judged by measuring the reduced χ2 value and the randomness in the distributions of weighted residuals and autocorrelation functions.
We measured the fluorescence decays of the labeled proteins in the soluble state and in the fibrillar state, using either 470 or 635 nm excitation to directly excite respectively the AF488 and AF647 fluorophores. The measured samples correspond to the final stage of aggregation of equimolar mixtures of AF488 and AF647-labeled synuclein. We collected fluorescence decays from both resuspended fibrils and the soluble protein (monomers and oligomers) in the supernatant of those samples.
AF647 fluorescence decay was directly probed with 635 nm excitation. AF647 typically shows bi-exponential decays usually assigned to the cis-trans equilibrium of the cyanine bridge (White et al., 2006
). The average lifetime of AF647 for the soluble protein was 1.29 ± 0.01 ns, slightly higher than the reported value of 1 ns, which indicates the absence of quenching of the fluorophore upon tagging the protein. For the resuspended fibrils, another short lifetime appeared of 0.32 ± 0.01 ns that corresponded to self-quenching of the fluorophores in highly packed fibrillar material. Because this time only appears in the fibrils, we assumed negligible quenching of AF647 in the soluble oligomers.
AF488 fluorescence decay was probed with 470 nm excitation. For the soluble material, monomer and soluble oligomers, a single exponential decay was obtained, with a lifetime of 4.11 ± 0.01 ns, in good agreement with the free AF488 lifetime of 4.1 ns (Panchuk-Voloshina et al., 1999
). This supports that the fluorophore is not quenched in the protein either in the monomeric or oligomeric forms. The small population of the AF488-tagged proteins forming soluble oligomers should show a decreased lifetime caused by FRET toward the acceptor AF647 dyes. However, since this population is very small it is undetectable by an ensemble-averaged technique such as time-resolved fluorimetry. This emphasizes the power of the single-molecule fluorescence techniques to reveal very rare populations. In contrast, the AF488 dye in resuspended fibrils showed three different decay times: 4.12 ± 0.02 ns, 1.60 ± 0.10 ns, and 0.56 ± 0.02 ns. The longest lifetime corresponds to monomer and small soluble oligomers as it is very similar the lifetime from such species in the supernatant. The intermediate decay time can be attributed to bigger oligomers that show FRET from the AF488 to AF647-labeled subunits. The average FRET efficiency of this population is 0.61. The shortest lifetime corresponds to highly packed fibrils where the AF488 dyes are quenched by both FRET and self-quenching. The relative amplitudes of the three lifetimes were very variable depending on the manipulation of the sample since the resuspension and dilution of the fibrils produce breakage and fibril disaggregation.
Two-Color Total Internal Reflection Fluorescence Microscopy Measurements
Samples were prepared and diluted in the same manner as described for solution single-molecule FRET measurements, and allowed to adsorb to glass coverslips at 23°C for 5 min. The sample was illuminated through objective-type TIRF by sending the 488 nm output from a Kr/Ar laser (353-LDL-840-240, Melles Griot) through a high numerical aperture objective (60 × Plan Apo TIRF, NA 1.45, Nikon) mounted to an Nikon TE2000-U inverted microscope. A blue laser power of 1 mW was used to illuminate an area of 90 μm diameter, resulting in a good signal/noise ratio and low photobleaching. Green and red fluorescence was separated and filtered using dichroic and bandpass filters mounted within DualView optics, and imaged simultaneously on an Electron Multiplying Charge Couple Device (EMCCD; Cascade II: 512 Princeton Instruments, MA) operating at −70°C. Good image registration between the color channels was achieved as described previously (Chiou et al., 2009
). Videos of 10 frames of 33 ms were acquired in 50 separate locations for each experiment using IPLab 4.0.2 software (BDBiosciences, Rockville, MD).
Data analysis was carried out using custom written routines implemented in MATLAB (The Mathworks, Natick, MA). First, an average image of each 10 frame video was obtained for each color channel and the centroid position of fluorescent objects automatically identified, as described in a previous paper (Chiou et al., 2009
). In addition, the brightness of the object was calculated by summing pixels within a 7 pixel diameter circular window centered about the object.
After locating fluorescent objects, FRET species were identified using a nearest neighbor distance approach, similar to that described previously (Chiou et al., 2009
). Briefly, the user specified a distance increment d
, and calculated the number of red objects that were within a radius of d
nm of a blue object and vice versa. This calculation was repeated for multiples of d
up to a user specified maximum, Dmax
. For each object coincident at Dmax
, the red and blue brightnesses were recorded, and the FRET ratio calculated according to the same formula as for solution single-molecule experiments (Equation 3 in the main text), with the gamma-factor (γ) for this instrument calculated to be 0.273. In addition, the program recorded the brightnesses of objects which were not coincident at Dmax
. For this work it was found that true coincident objects could be identified at a distance of ~200 nm (data not shown).
To estimate the average blue monomer brightness, the brightness of blue noncoincident events from a dilute late aggregation sample, where lots of monomers were detected (in contrast to the early disaggregation sample, where the majority of the objects detected were oligomers, in agreement with solution single-molecule experiments) was examined. Spots were detected at a threshold of 5 standard deviations above background (spot detection at this threshold was in agreement with detection by eye), and a histogram formed of blue noncoincident event brightnesses (which should mean that oligomers do not contribute). The result displays a log-normal distribution with a peak maximum at 151.5 counts- taken to be the monomer brightness.
Data acquired for early fibril disaggregation (FD) and late aggregation (LA) experiments were analyzed at a threshold of 10 standard deviations above the mean. At this threshold, a large fraction of detected species showed FRET: 0.66 (FD), 0.42 (LA). The larger fraction of aggregated species detected in the early fibril disaggregation sample compared to the late aggregation sample is in agreement with solution single-molecule results. An example of the data obtained for TIRF experiments is shown in D.
The results of FRET analysis are given in E. The histogram of FRET efficiencies normalized to the total number of objects detected (1888(FD) and 938(LA)) showed a strong peak at a FRET efficiency of approximately 0.7 for both fibril dissolution and late aggregation experiments. The distribution extended to lower FRET efficiencies for both samples, and this was particularly pronounced for the late aggregation sample, which showed a secondary peak around 0.4-0.5, in agreement with solution single-molecule experiments. Notice that in the early disaggregation sample only one FRET distribution at high-FRET efficiencies was detected, and at the same FRET values as the high-FRET oligomers observed in solution single-molecule experiments. Using the blue brightness values for coincident events in conjunction with the calculated monomer brightness, the apparent size distribution of oligomers could be calculated (F). This showed that larger aggregates were present in the early fibril disaggregation sample compared to late aggregation samples, as was also observed in solution smFRET experiments.
Preparation of Primary Rat Midbrain Neurons
For primary rat midbrain cultures, pups were culled by decapitation at postnatal day P2. The midbrain was removed and placed into sterile eppendorfs containing 1 ml of chilled Hanks buffered salt solution (HBSS). The HBSS was then replaced with 1 ml pre-warmed trypsin-EDTA solution and the midbrain was incubated for 5 min at 37°C. Cultures were pelleted by centrifugation at 2,000rpm for 5 min, the trypsin was gently aspirated and the cells were washed in pre-warmed HBSS, then in warm neurobasal medium containing 2% B27 supplement, 2mM glutamine, 100 I.U./ml penicillin and 100 I.U./ml streptomycin. The dissociated cells were resuspended in 1mL warm complete neurobasal medium and 3-4 drops of the cell solution were plated per well on poly-L-lysine coated coverslips in 6 well plates (6-8 coverslips per animal). The cultures were incubated in a humidified incubator at 37°C with 5% CO2 in air for 3-4 hr, then 2 ml pre-warmed neurobasal medium was added. Half the medium was replaced after 2 days, after which half the medium was replaced weekly. All live cell imaging experiments were performed between d12-d14 in culture.
Modeling the Data
The kinetics of the early stages of amyloid fibril formation observed in our single-molecule fluorescence experiments may be quantified in terms of a general kinetic model, shown in A of the main text, where two classes of structures are considered explicitly. These are type B oligomers, with structural characteristics closer to amyloid fibrils, and type A oligomers, which are structurally distinct from the former species. Both types of aggregates can grow through monomer addition, and also undergo the inverse process of monomer dissociation. Furthermore, the equilibrium between monomers and aggregates is established primarily through the type A structures and no direct nucleation of type B structures from monomer occurs. The type A and type B structures of a given aggregation number can, moreover, inter-convert, with the effective nucleation of a type B species occurring via the conversion of a type A to a type B species. These considerations lead to the description of the system in terms of the master equation:
represent the (number) concentrations of type A and type B oligomers respectively, with polymerization number j
at the time t
. The free monomer concentration is given by
. The first term in Eq.S4,
represents the increase in the number of oligomers of type A of length j
through the growth of oligomers of length j-1
and the second term
describes the respective decrease through the growth of polymers of length j
to a length j+1
. The next two terms proportional to
describe the inverse process, namely monomer dissociation, and the term
accounts for the creation of type A oligomers from monomers through direct primary nucleation as a reaction of the order
. Similar terms are present in Eq.S5 for type B species. The rate constants
govern the inter-conversion of type A species into type B species. Finally, the rate
accounts for the possible presence of a sink from type B oligomers to larger fibrillar species that form after the bulk lag-time for amyloid fibril formation. In the most general case, the conversion rates may depend on the concentration of monomer; here we subsume these dependencies into the rate constants and note that the values obtained for the conversion rate constants are, therefore, upper bounds for those that would be observed at lower total protein concentrations. Related to this, the conversion steps may involve a change in oligomer polymerization number, but the strategy outlined below, which considers the total number of oligomers of each type, is unaffected by changes in this detail of the mechanism.
The master equations in the form of the Eqs.S4 and S5 are an infinite set of coupled non-linear differential equations and do not in general admit an exact solution but may be solved numerically.
In order to analyze our experimental data in the context of the master equation Eqs.S4 and S5, we consider the zeroeth moments of the distributions f
, which are the observables directly measured in single-molecule fluorescence experiments: the number-concentrations
. We consider the system before the bulk lag-time for fibril formation,
, before which the free monomer concentration has not been significantly depleted and is approximately constant at its initial value,
(see E). In this regime, many of the processes in Eqs.S4 and S5 do not have a significant effect on the number-concentrations of oligomers. In particular, in the early stages of the reaction, the reverse conversion rate can be neglected in front of the forward conversion rate,
, and the destruction of oligomers through depolymerization can be neglected in front of primary nucleation of new oligomers,
. In addition, since type B oligomers are heavily populated before the bulk lag-time, it must be that
With these observations, we can obtain the principal moments in closed form under the assumption that many of the rate constants in the master equation that apply to the smaller species, populated before the lag-time and observed in our experiments, are approximately independent of the polymerization number, i.e.,
for all j
populated during the time period t
. The resulting rate constants represent averaged values over the oligomer size distributions, and allow representative timescales to be obtained from experimental data for each process. These simplifications allow the sums for the polymer number concentrations to be written out in closed form, with the terms in the elongation and depolymerization rates forming telescopic sums that vanish, leaving the (ordinary) differential equation system:
These equations may be solved analytically to yield:
where the initial conditions corresponding to a purely monomeric system, Q(0) = P(0) = 0
, have been used. The leading order dependencies for
for the number-concentrations Q
and P can be obtained as:
It is also interesting to note that in the absence of monomer depletion, Q
tends to the limit
Prior to significant depletion of the free monomer, the primary nucleation reaction order,
, does not influence the observables and we may define an effective nucleation rate with the same dimensions as the conversion rate,
. Interestingly, the results Eqs.S10 and S11 show that the effect of the kinetic parameters
can be robustly decoupled at early times. The initial gradient of Q
is determined predominantly by
, and once this is fitted it allows
to be determined from the early time form of P
The results derived in Eqs. S4–S11
allow the constants
to be determined from the number concentrations of type A and type B oligomers prior to the bulk lag-time for fibril formation. Using the analytical results Eqs.S8 and S9 we are able to fit the single-molecule fluorescence experimental data up to the lag-time and obtain good fits using the two kinetic parameters
. The fit, shown in B of the main text, determines the microscopic kinetic rate constants as
. We note that for early times the rate of primary nucleation is faster than the rate of conversion of type A to type B oligomers,
In order to understand the time course of the reaction beyond the bulk lag-time for fibril formation, we observe that the terms from the master equation Eqs.S4 and S5 that are not significant at early times can become important. In particular, the reverse conversion of type B to type A oligomers, the destruction of oligomers by depolymerization, and the formation of large fibrillar species observed in bulk experiments become significant at later times.