in order to visualize -synuclein fibrils using dstorm , we prepared separate batches of covalently labeled 
 cysteine 
 variants ( n122c ) of the protein with alexa fluor 647 ( af647 ) and with 
 alexa fluor 568 ( af568 ) dyes ( invitrogen , carlsbad , ca , u.s.a . ) ( see 
 materials and methods in supporting information ) .
we verified that the dye labels do not interfere with the aggregation 
 process and that the fibril morphology and the kinetics of fibril 
 formation are indistinguishable from those of the unlabeled protein , 
 as revealed by afm and tht assays ( see supporting 
 information ) .
we chose to use direct covalent labeling of -synuclein 
 rather than immunofluorescence staining because of the very small 
 size of the alexa dye labels compared to antibody molecules , and because 
 of the high specificity of labeling afforded by use of covalent linkages , 
 both of which result in an increase in the resolution of the imaging 
 process .
we found the optimal labeling ratio for 
 two - color dstorm to be ca .
1:20 for the fraction 
 of labeled relative to unlabeled protein ; too high a labeling density 
 would compromise resolution ( by increasing the likelihood that proximate 
 fluorophores emit simultaneously and therefore cause mislocalization ) 
 and might potentially lead to steric interferences of the dye with 
 the amyloid protein .
figure 1a , c show the conventional , 
 diffraction limited fluorescence images of -synuclein fibrils ; 
 the corresponding dstorm images are shown in figure 1b , d . from the dstorm images , we 
 inferred an average fibril diameter of 18  2 nm , which shows 
 that the resolution achieved approaches that of techniques such as 
 afm .
comparison of conventional fluorescence 
 and super - resolution images 
 of directly labeled amyloid fibrils of -synuclein : ( a , c ) conventional 
 ( diffraction limited ) fluorescence images of the fibrils , labeled 
 with af647 and af568 , respectively ; ( b , d ) corresponding dstorm images , demonstrating the dramatic resolution enhancement obtainable 
 over conventional imaging .
having established that -synuclein fibrils can be 
 reliably 
 imaged using our super - resolution technique , we proceeded to perform 
 two - color dstorm experiments and to analyze the dynamics 
 of fibril growth .
we visualized the process of fibril elongation using 
 a seeded aggregation assay ; the starting point 
 was a solution of preformed fibrils of -synuclein with an average 
 length of 400 nm , labeled at 5% with af568 ( green ) ( see materials 
 and methods in supporting information for 
 details ) .
at the start of each such assay , a solution containing -synuclein 
 in its monomeric state with 5% of the protein molecules labeled with 
 af647 ( red ) was added to the initial sample at a 10-fold excess ( by 
 mass ) ; under these conditions the only relevant molecular process 
 is elongation , permitting the direct measurement 
 of the rates of this specific process .
the solution was left to incubate 
 for 24 h at 37 c and under quiescent conditions in which breakage 
 of fibrils is minimal . at different time points during the aggregation 
 reaction aliquots were taken from the solution and deposited onto 
 glass coverslip chambers containing photoswitching buffer , optimized 
 for two - color dstorm ( see materials and methods in supporting information ) .
the fibrils had therefore 
 been allowed to elongate in bulk solution in the absence of any sample - substrate 
 interactions that might have affected the growth kinetics .
figure 2 shows the elongation of the seed 
 fibrils as a function of time . in figure 2a , 
 the seed fibrils , labeled with green af568 , are shown before addition 
 of the monomeric protein . at the beginning of the experiment ( t = 0 h )
monomeric protein labeled with red af647 was added 
 and two - color super - resolution images were recorded at different time 
 points during 24 h of fibril growth , as shown in figure 2b  h . using two - color dstorm 

we are able to distinguish 
 between the seed fibrils initially present ( indicated by arrowheads 
 and rendered in green color ) and the freshly added protein ( indicated 
 by arrows and rendered in red color ) .
we can therefore monitor the 
 process of fibril elongation over hours or even days in the absence 
 of any destructive sample preparation steps such as drying or shaking , 
 which are known to induce breakage .
indeed , fibril breakage was observed 
 to be negligible in our experiments , as all fibrils we had imaged 
 contained either elements of both green fluorescence ( af568 from the 
 seed species ) and red fluorescence ( af647 , signifying the newly added 
 protein ) , or just green fluorescence ( af568 , the latter also indicating 
 that no detectable growth had taken place ) ; no fibrils were observed 
 that were solely labeled with red fluorophores , indicating that neither 
 monomer nucleation , nor fibril breakage were significant under the 
 experimental conditions reported here .
in contrast to conventional 
 tirf fluorescence imaging ( figure 2i ) , two - color dstorm ( figure 2h ) clearly distinguishes 
 between the original fibril seeds and the grown regions of the fibrils . 

importantly , our data establish unambiguously that -synuclein 
 fibril elongation under the conditions used here is a bidirectional 
 process , that is , that it proceeds from both ends of fibril seeds . 
 in previous experiments ,
both bidirectional and unidirectional growth of different amyloid fibrils such 
 as a , amylin , and -synuclein have been reported , although 
 issues such as substrate interference with fibril growth could not 
 be excluded , or the resolution from conventional techniques was limited . 
 here
, the elongation reaction occurs in an undisturbed environment 
 in bulk solution , and hence is unaffected by such interference .
furthermore , 
 the resolution achieved with two - color dstorm enables 
 to conclusively establish that fibril growth is bidirectional .
we performed additional control experiments using solutions containing 
 either seed fibrils in the absence of monomeric protein , or solutions 
 containing monomeric protein in the absence of seed fibrils .
incubation 
 of these samples for 24 h at 37 c resulted in no observable 
 fibril elongation or fibril formation ( see supporting 
 information figure 3 ) .
these results confirm that seed fibrils 
 are inert in the absence of monomeric protein and therefore do not , 
 for example , join together by mutual interaction of their free ends . 

also , de novo formation of -synuclein amyloid 
 fibrils via primary nucleation occurs at a negligible rate relative 
 to fibril growth , confirming elongation of seeds as the only significant 
 process during the aggregation reactions presented here .
in order to 
 investigate possible variations in growth kinetics for individual 
 fibrils , we analyzed multiple dstorm images of growing 
 fibrils , recorded at different time points during the aggregation 
 reaction and in different regions of the glass coverslips ( see materials 
 and methods in supporting information for 
 details ) ; we then studied the distribution of elongation values as 
 a function of time . in figure 3a , histograms 
 of the measured elongation lengths of individual fibrils are shown 
 ( dstorm , red channel ) for different time points up 
 to 24 h of the aggregation reaction . the width of the observed distributions 
 of fibril elongation values can be seen to increase significantly 
 with time ; for example , after t = 24 h , some fibrils 
 have reached lengths of up to 7 m , but others show either no , 
 or only a very small , increase in length . in figure 3b , we have plotted the histograms of the corresponding average 
 growth  velocities  ( calculated as the length increase 
 divided by the overall growth time ) at the same time points as depicted 
 in figure 3a .
these histograms show that the 
 variation in elongation rates remains approximately constant over 
 time , indicating that at each time point there is a range of fibrils 
 displaying distinct growth rates .
we further investigated the 
 two extreme elongation values ; namely the frequency of the occurrence 
 of seeds that show no detectable growth ( denoted by the absence of 
 any red regions that would indicate that fibril elongation had taken 
 place ) or that of species exhibiting very fast growth rates .
the most 
 striking feature of the data presented in figure 3c is that a significant proportion of seed fibrils ( 17% ) did 
 not exhibit any growth in the presence of monomeric protein and remained 
 at their initial length .
in contrast , 
 the majority of the fibrils ( 63% ) grew up to 10 times their initial 
 length in 24 h ; indeed , a small fraction of fibrils ( 20% ) grew more 
 than 10 times their initial length .
taking the average of all individual 
 rates observed , including data from fibrils that had not elongated , 
 we obtained a mean growth rate of 1.4 nm / min over 24 h , with a standard 
 deviation of 1 nm / min , which is in good agreement with the values 
 for average growth rates obtained using tht ensemble measurements .
clearly , the observed ensemble kinetics are 
 a consequence of a larger number of elementary reaction steps that 
 can not be resolved in ensemble measurements in which it is assumed 
 that the growth of all fibrils contributes equally to the observed 
 total increase in fibril mass .
of particular interest is the finding 
 that some seed fibrils remain inactive throughout the entire duration 
 of the experiment ( 24 h ) that suggests that individual seeds can have 
 very different elongation capacities .
two - color dstorm images 
 reveal details of the 
 elongation of -synuclein fibrils through addition of soluble 
 protein molecules , in vitro .
( a ) the initial sample 
 consists of -synuclein seed fibrils at 8 m concentration , 
 labeled with af568 ( green ) . at t = 0 h , monomeric 
 -synuclein at a total concentration of 80 m ( 76 m 
 wild type
, 4 m af647-labeled n122c ) ( red ) was added to the 
 solution .
( b  h ) aliquots were taken during the aggregation 
 reaction and imaged with two - color dstorm .
the images 
 show the overlay of the two channels ( green , af568 and red , af647 ) . 

the time points after the initiation of aggregation are ( b ) t = 1 h , ( c ) t = 2 h , ( d ) t = 3 h , ( e ) t = 5 h , ( f ) t = 6 
 h , and ( g , h ) t = 24 h. each fibril consists of the 
 initial seed ( green , indicated by an arrowhead ) and the extended region 
 formed through addition of monomeric protein ( red , indicated by an 
 arrow ) . the lengths of the fibrils reach several micrometers with 
 the initial seed fibril being extended from both ends .
( h ) two - color dstorm image of a fibril at t = 24 h and 
 ( i ) conventional fluorescence image in tirf of the same fibril as 
 in ( h ) , showing that the increase in resolution achieved by dstorm enables the original and the newly formed section 
 of the fibril to be clearly distinguished .
to gain insights into possible molecular mechanisms underlying the 
 observed variations in elongation rates we carried out a more detailed 
 analysis of rate distributions and studied the results in the context 
 of different models of fibril elongation . for a random ( stochastic ) 
 process involving discrete events , such as the addition of monomeric 
 protein molecules to fibril ends ,
the probability of a certain number 
 of these events occurring in a given time is governed by poisson statistics . 
 in each histogram of figure 3a , we have therefore 
 overlaid curves depicting the corresponding poisson distributions 
 for the number of attached monomers , based on the averages of the 
 elongation values obtained from the histograms and assuming that addition 
 of a single monomer of -synuclein leads to a fibril length 
 increase of 0.5 nm .
the data indicate 
 that the measured distributions are not at all represented by poisson 
 distributions and that much larger variations in elongation rates 
 are observed than predicted by this analysis , again indicating rapid 
 growth of certain fibrils whereas others exhibit imperceptible growth , 
 as schematically depicted in figure 4 .
a different model to account for inhomogenous growth kinetics invokes 
 the so - called  stop - and - go 
mechanism , which has been 
 discussed for amyloid fibrils of a2535 and glucagon . in 
 these studies
, it was proposed that the origin of the observed switching 
 between active (  go  ) and inactive (  stop  ) 
 states lies in the occasional incorrect addition of a monomer onto 
 a fibril end , such that the templating effect is lost until this monomer 
 detaches or rearranges into the correctly folded state .
the consistency of this hypothesis with the 
 reported in these studies data can , however , be probed by a simple 
 argument ; the free energy barrier for the dissociation of a correctly 
 incorporated monomer from a fibril end must represent an upper bound 
 for the energy barrier of dissociation , or for the rearrangement of 
 improperly attached monomers , given that the correctly incorporated 
 monomer is likely to represent the minimum in the free energy landscape .
the data presented in ref ( 14 ) allowed the elongation 
 rate constants during the growth phases , k+ , to be determined as 10 m s and the critical concentration , ccrit to be 10 m . at equilibrium , the fluxes 
 of growth and dissociation are equal , and therefore the equilibrium 
 constant is k = 1/ccrit = k+/koff , where koff is the rate constant of 
 dissociation . from this analysis we estimate koff  10 s , which represents a rate 
 more than 2 orders of magnitude faster than that of switching between 
 the growth - incompetent and the growth - competent states reported in 
 ref ( 14 ) ( 0.03 
 s ) .
it therefore seems likely that additional 
 factors determine the duration of the inactive periods in the experiments 
 reported ; one possibility is interactions with the surfaces on which 
 the fibrils grow . in the present study ,
the seed fibrils grow in solution 
 and are only deposited onto a surface for imaging , therefore minimizing 
 such additional interactions .
histograms of the distributions of elongation 
 lengths ( corresponding 
 to the newly formed ( red ) regions ) of seed fibrils .
the histograms 
 in panel ( a ) show the relative frequency of different elongation lengths 
 obtained at 1 , 3 , 6 , and 24 h. a curve depicting the poisson distribution 
 for the number of attached monomers with the same average value as 
 the average elongation value obtained from the histogram is overlaid 
 at each time point .
the x - axis label , k , corresponds to the number of attached monomers divided by 2 , assuming 
 that each monomer has a length of 0.5 nm .
( c ) 
 diagram summarizing the distribution of the elongation values of fibrils 
 at the end of the incubation process ( t = 24 h ) . 

black bar : percentage of fibrils that exhibit zero growth ( no detectable 
 red regions ) .
blue bar : percentage of fibrils that have grown to a 
 size ranging from the lowest detectable length to up to 10 times the 
 length of the initial seed .
violet bar : percentage of fibrils that 
 have elongated by more than 10 times the length of the initial seed 
 fibril .
schematic diagram of the elongation of -synuclein 
 seed fibrils , 
 depicting the different mechanisms that influence fibril growth .
the 
 green cylinders correspond to fibrillar seeds labeled with alexa fluor 
 568 and the red spheres correspond to the monomeric protein labeled 
 with alexa fluor 647 .
we next explored whether or not the heterogeneous growth 
 kinetics 
 for individual fibrils observed in our experiments are compatible 
 with a 
looking at the histograms 
 in figure 3 it is apparent that some fibrils 
 have inactive periods of several hours . assuming that a fibril will 
 become active again
when an incorrectly folded monomer becomes detached 
 at its end we can estimate using similar arguments as above whether 
 this time scale is compatible with such a hypothesis : using a critical 
 concentration of -synuclein of 2 m , and the determined average growth rate of k+  10  375 m s ( this work and ref ( 31 ) ) we obtain an estimate for the lower bound for 
 the average dissociation rate , koff  
 ( 2.0  0.8 )  10 s. although this value may deviate from that for individual fibrils , 
 it can not account for the observation that some fibrils are inactive 
 for the entire duration of the experiment , that is , for at least 24 
 h. additionally , since this process should affect fibrils of all lengths 
 equally , it is unlikely to provide an explanation of the observed 
 heterogeneity in fibril elongation rates
. therefore we suggest the 
 following alternative explanations : ( 1 ) certain amyloid templates / seeds 
 are not efficient in recruiting 
 monomeric protein , leading to different fibril morphologies and growth 
 rates ( fibril polymorphism ) .
this mechanism 
 has been proposed for several proteins such as the yeast prion sup35 , glucagon , a , tau , and -synuclein .
( 2 ) the spatial arrangement of fibrils , for example , because 
 of 
 assembly into higher order structures or variations in protofilament organization , may block the access needed for monomers to attach to fibril 
 ends . additionally , the ends of seed fibrils may become damaged during 
 production , although this is unlikely here , because neither sample 
 drying nor harsh fragmentation methods , such as sonication , were used . in conclusion , we have demonstrated the development and application 
 of two - color dstorm as a powerful tool for the visualization 
 of -synuclein fibril growth from seed templates and have carried 
 out a quantitative analysis of the kinetics of this process . with 
 this technique , we are able to distinguish de novo growth of fibrils from the original seed and to follow elongation 
 at nanometer resolution .
our method proves conclusively that -synuclein 
 fibril elongation , under the conditions used here , is a bidirectional 
 process .
in addition , no end - to - end association of seed fibrils was 
 observed to occur and elongation of seeds was evident only in the 
 presence of monomeric protein .
the kinetics of fibril growth are not 
 adequately described by a single elongation rate parameter ; rather , 
 a large variation in growth rates was found to exist .
type 
 mechanism in which misfolded species at the fibril end need to be 
 removed before growth can resume , nor with the notion that monomer 
 addition is a diffusion controlled , stochastic process , for which 
 variations in growth rates would be much smaller .
we therefore suggest 
 two alternative mechanisms that can be explored in future studies . 
 furthermore
, the methodology described here can be readily extended 
 to in situ applications in biological samples , for 
 example , to monitor aggregation within cells and to elucidate the 
 various parameters that affect fibril growth .
it could also be used 
 to identify different fibril strains , which may arise in vivo , and to investigate their role in the production and spreading of 
 amyloidogenic species in disease .
 the 
 self - assembly of normally soluble proteins into fibrillar amyloid 
 structures is associated with a range of neurodegenerative disorders , 
 such as parkinson s and alzheimer s diseases . in the 
 present study 
 , we show that specific events in the kinetics of the 
 complex , multistep aggregation process of one such protein , -synuclein , 
 whose aggregation is a characteristic hallmark of parkinson s 
 disease , can be followed at the molecular level using optical super - resolution 
 microscopy . 
 we have explored in particular the elongation of preformed -synuclein 
 fibrils ; using two - color single - molecule localization microscopy we 
 are able to provide conclusive evidence that the elongation proceeds 
 from both ends of the fibril seeds . 
 furthermore , the technique reveals 
 a large heterogeneity in the growth rates of individual fibrils ; some 
 fibrils exhibit no detectable growth , whereas others extend to more 
 than ten times their original length within hours . 
 these large variations 
 in the growth kinetics can be attributed to fibril structural polymorphism . 
 
 our technique offers new capabilities in the study of amyloid growth 
 dynamics at the molecular level and is readily translated to the study 
 of the self - assembly of other nanostructures . 
Amyloid Growth from Seed Fibrils Is a Bidirectional
Process
Analysis of Fibril
Elongation Kinetics Reveals Inhomogeneous
Growth Rates and Distinct Fibril Populations
The Mechanism of -Synuclein Fibril Elongation Deviates
from a Purely Stochastic Process Involving Random Growth