Stop-and-go kinetics in amyloid fibrillation
Jesper Fonslet, Christian Beyschau Andersen, Sandeep Krishna, Simone Pigolotti, Hisashi Yagi, Yuji Goto, Daniel Otzen, Mogens H. Jensen, Jesper Ferkinghoff-Borg
aa r X i v : . [ phy s i c s . b i o - ph ] O c t Stop-and-go kinetics in amyloid fibrillation
Jesper Fonslet , , Christian Beyschau Andersen , , Sandeep Krishna , Simone Pigolotti , HisashiYagi , , Yuji Goto , , Daniel Otzen , Mogens H. Jensen † and Jesper Ferkinghoff-Borg † Niels Bohr Institute, Blegdamsvej 17, DK-2100, Copenhagen, Denmark ∗ Herlev Hospital, Klinisk Fysiologisk Afd. Herlev Ringvej 75, DK-2730. Novo Nordisk A/S, Protein Structure and Biophysics, Novo Nordisk Park, DK-2750 M˚aløv, Denmark National Research Council, Institute of Biophysics, Via Ugo La Malfa, 153, I-90146 Palermo, Italy Osaka University, Institute for Protein Research, Yamadaoka 3-2, Suita, Osaka 565-0871, Japan CREST, Japan Science and Technology Agency, Saitama, Japan ˚Arhus University, Department of Molecular Biology,Gustav Wieds Vej 10 C, 8000 ˚Arhus C, Denmark and DTU · Elektro, Build. 349, Ørsteds Plads, Technical University of Denmark, 2800 Lyngby, Denmark † (Dated: October 28, 2018)Many human diseases are associated with protein aggregation and fibrillation. We present ex-periments on in vitro glucagon fibrillation using total internal reflection fluorescence microscopy,providing real-time measurements of single-fibril growth. We find that amyloid fibrils grow in anintermittent fashion, with periods of growth followed by long pauses. The observed exponentialdistributions of stop and growth times support a Markovian model, in which fibrils shift betweenthe two states with specific rates. Remarkably, the probability of being in the growing (stopping)state is very close to 1 / /
4) in all experiments, even if the rates vary considerably. This findingsuggests the presence of 4 independent conformations of the fibril tip; we discuss this possibility interms of the existing structural knowledge.
PACS numbers: 87.14.em 87.15.bk 82.39.-k
Protein fibrillation is the process by which misfoldedproteins tend to form large linear aggregates [1]. Its im-portance is related to the role played in many degenera-tive diseases, such as Parkinson’s, Alzheimer’s, Hunting-ton and prion diseases [2]. While our knowledge of thestructural properties of these fibrils improves at greatpace [3, 4, 5], the dynamics of their growth process isstill poorly understood. The formation of amyloid fibrilsinvolves at least two steps: the formation of growth cen-ters by primary nucleation, which is often a slow process,followed by elongation through addition of monomers [6].In many cases, a so-called secondary nucleation mecha-nism is also involved, whereby new growth centers areformed from existing fibrils [7, 8, 9, 10, 11]. Whereasthe process of secondary nucleation is known to entail anumber of different mechanisms [11], the primary elon-gation process has not been elucidated to the same levelof detail.In this letter, we present an experimental and theoret-ical study of the elongation process of glucacon fibrils.Glucagon is a small peptide hormone consisting of only29 amino acids produced in the pancreas. It has theopposite effect to that of insulin and therefore increasesblood glucose levels when released. As a model systemfor protein fibrillation, glucagon kinetics has provided in-sights into the early oligomerization stages of the process[12, 13, 14, 15], the interplay between growth and fibrilmorphology [16, 17] and amyloid branching [11]. Here,we focus on the properties of the late-stage elongationprocess.Experiments were performed on samples of glucagon monomers in solution. In order to detect the growtha specialized fluorescence microscopy technique was ap-plied, the so-called Total Internal Reflection FluorescenceMicroscopy (TIRFM). This technique utilizes total in-ternal reflection to create an evanescent electromagneticfield adjacent to the glass slide, thereby exclusively ex-citing fluorophores in only a very thin volume. The pen-etration depth, d , depends in a specific manner on thewavelength and the angle of the incident light, as wellas the refractive indices of the media [18]. In the setup,an argon laser was used along with a fused silica slidein contact with water, leading to a penetration depthof d = 150 nm. The TIRFM images of the fibrilla-tion process were obtained at initial glucagon concen-tration of ρ = 0 .
25 mg/ml in aqueous buffer (50 mMglycine HCl pH 2.5) with preformed seeds. Images of thegrowth are shown in Fig. 1 at three consecutive times t = 0 , ,
407 min. (see [11] for details on the experi-ment).Because the fibrils grow along the glass slide we areable to track each fibril length as function of time. Wemonitor 16 independent fibrils for each image frame inthe experiment. The time interval, ∆ t , between framesvaries from a minimum value of ∆ t min = 1 min. to amaximum value ∆ t max = 35 min., with a typical valueof ∆ t = 10 min.. The total duration of the experimentis t = 525 min. The combined results for the 16 fibrilsare shown in Fig. 2.A striking feature of the fibril dynamics is its discretenature, where long periods of growth are interrupted byextended periods of stasis (stop state). This prompted t = 216 min.t = 409 min.t = 0 min. FIG. 1: TIRFM images of glucacon fibril growth with initialglucagon concentration of ρ = 0 .
25 mg/ml in aqueous buffer(50 mM glycine HCl pH 2.5) at three consecutive times afterthe initiation of the aggregation. Red lines in the last picturemark examples of fibrils which are tracked during the growthprocess. us to collect the statistics of time spent in the growth(g) and the stop (s) state, f g ( t ) and f s ( t ) respectively,for all 16 fibrils. In Fig. 3, these distributions are shownon semi-logarithmic plots. Note that the finite samplingrate implies that actual time spent in given state canonly be estimated in terms of upper and lower bounds[19]. The upper estimates are shown by the dashed bluecurves and the lower estimates are shown by the full bluecurves. As seen in the figure, the difference between F i b r il Leng t h [ µ m ] FIG. 2: Length as a function of time for 16 fibrils trackedfrom the images shown in Fig 1. Note the long plateaus, cor-responding to the stop states, followed by shorter (on average)growing periods. The average growth is indicated with a dot-ted blue line. The sampling time between each image can beseen from the time separation between each point. the distributions for the upper and lower estimates ofboth f g and f s are marginal. All distributions are verywell fitted by exponential functions, f g ( t ) ∼ exp( − k − t )and f s ( t ) ∼ exp( − k + t ), as shown by the yellow curves(here, the dashed yellow curve is the fit to the upper es-timates and the full yellow curve is the fit of the lowerestimates). The fits are of excellent quality over almosttwo decades, as signified by high R values ( R > . k + = 9 . · − min − and k − = 2 . · − min − . A series of four independentexperiments A − D have been performed with the sameglucagon monomer concentration (0.25 mg/ml) and pH(2.5) with differences in the seed concentrations ( ∼ g and one in which it cannot grow. The intrinsic transi-tion rates between the two states is then identified withthe observed transition rates k + (stop → growth) and k − (growth → stop), see Fig. 4.The Markovian nature of the model implies, that thetime spent in each state is exponentially distributedwhich is indeed consistent with the results from the data-analysis, Fig.(3), leading to estimates of k + and k − . De-noting the total rate k = k + + k − , one can calculate theprobability of being in the growing state, p + = k + /k andin the stopped state, p − = k − /k . Table I presents a sum-mary of the parameters in 4 different experiments. Bycomparing the four different series, we observe that the Time [min] R e c o r ded E v en t s (a) − −1 (a) k = 0.0278 min Time [min] R e c o r ded E v en t s (b) + −1 (b) k = 0.0090 min FIG. 3: Growth f g ( t ) (a) and stop f s ( t ) (b) times distribu-tions on semi-logarithmic scales. Blue lines are data and yel-low straight lines are the exponential fit. Both for data andfits, continuous lines are the lower estimates and dashed linesare the upper estimates (see text). All fits are of extremelygood quality as indicated by the large R-value, R > . k + k + k − k − ... g g Growth stateStop state
FIG. 4: The simplest two-state model of fibril growth. Thefibril is assumed to be in one of two states with intrinsic tran-sition rates of k + and k − . In the growing state, monomerattachment occurs with the rate g . rates k + and k − vary quite significantly, up to a factor3. A possible explanation for this could be the variationin sampling frequency (as is indicated in Table I), dueto heating of the sample by the laser. Indeed, the de-pendency of the fibril growth on both the laser intensityas well as the illumination time has been observed un-der similar experimental conditions for β -microglobulinkinetics [21].The striking result is that, even though both transition rates vary among experiments, they combine in such away that the probabilities of growing and stopping, p + and p − , do not change appreciably in different exper-iments. In particular, p + is always very close to 1 / p − is very close to 3 /
4. Notice that,if the difference between the growing and the stoppedstate would have been due to an energy gap, one wouldhave expected the population ratio of the two states to bemuch more sensitive to variations in the individual tran-sition rates, k ± . Conversely, the constancy of this ratiosuggests that the energy difference between the growingand the stopped states to be irrelevant. This ratio couldthen reflect the presence of three stopped configurationsfor each growing one, all of them being isoenergetic.One may wonder whether the observed ’1 / /
4’ lawis really independent of the monomer concentration, asin the model. Due to experimental limitations, this hasnot been directly tested. However, the observed averagegrowth rate, g , displays more than a two-fold variationfrom Exp. A to Exp. D, suggesting notable differences inthe local monomer concentration of the growing fibrils.If the state probabilities were sensitive to changes in theconcentration, we would have expected a correlation be-tween p ± and g . We further tried to test the pertinenceof the state probabilities by dividing the data sets intotwo parts, one corresponding to the first half of the ex-periment and the other to the second half, and measuring p + and p − separately in the two parts. Unfortunately,the statistical noise increased significantly when consid-ering sub-parts of the data series and neither added tonor altered our conclusions.To conclude, we have presented a stop-go model forglucagon fibril elongation. In fact, similar kinetic behav-ior has recently been reported for the fibril elongationof Aβ -peptides [22, 23] as well as for α -synuclein [24],although the timescales involved are 1-2 orders of mag-nitude faster. This suggests that the observed stop-gokinetics reflects the presence of some kind of structuralchange at the fibril ends, which is not necessarily spe-cific to glucagon. In this picture, the protein propertieswould affect the barrier height, and thus the timescale ofthe process, only.If our hypothesis about the existence of approximatelyisoenergetic states holds up to scrutiny, it suggests thatthere may be an additional dimension in the fibrillationenergy landscape that cannot easily be identified by con-ventional techniques. Glucagon is known to adopt a num-ber of different conformations depending on the fibrilla-tion conditions, but these conformations differ consider-ably in energy and are unlikely to co-exist to an equalextent [25] . Rather, it is possible that we have a num-ber of closely related states with different propagationproperties which are separated by high local activationbarriers within a relatively flat ground state level. Fur-ther experimental studies are required to establish thevalidity of this suggestion. Parameters
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