Supplementary material Investigation o α-synuclein Amyloid Firils Using the Fluorescent Proe Thiolavin T Anna I. Sulatskaya, Natalia P. Rodina, Maksim I. Sulatsky, Olga I. Povarova, Iuliia A. Antieeva, Irina M. Kuznetsova, Konstantin K. Turoverov,2,* Laoratory o Structural dynamics, staility and olding o proteins, Institute o Cytology o the Russian Academy o Science, St. Petersurg, Tikhoretsky ave. 4, 94064, Russia 2 Institute o Physics, Nanotechnology and Telecommunications, Peter the Great St.- Petersurg Polytechnic University, St. Petersurg, Polytechnicheskaya 29, 9525, Russia * Corresponding author: K.K. Turoverov e-mail: kkt@incras.ru Tel.: +7 82 297 9 57 Fax: +7 82 297 35 4
. Pitalls o the total ThT concentration (C0) using instead concentration o ree dye (C ) or determination o the dye inding parameters to amyloid irils ThT α-synuclein inding constants actually were determined earlier. For example, in the work [] it was shown the existence o the one ThT α-synuclein indihg mode with Kd value equal to 588 nm (K =.7*0 6 M - ). Thus, the value o the inding constant otained in this work has the same order o magnitude as the inding constant, which we determined or the second mode o dye-iril inding. However the asolute values o these parameters are signiicantly dierent. It should e noted that in work [], as in most papers aimed to this prolem, or dissociation constant determination the dependence o the dye luorescence intensity on its total concentration was used. In order to show the incorrectness o such approach application, it is necessary to write an equation or determining the inding constant. I all the ThT inding sites in amyloid iril are identical and independent rom each other, then the inding constant o the dye to amyloid iril (K) is determined as: K = C. ( nc p C ) C where C is the concentrations o ree ligand, C is the concentration o the dye ound to irils, i.e. the concentration o occupied inding sites, Cp is the concentration o the protein that orms iril, n is the numer o sites o ThT inding to amyloid iril per protein molecule. Thus nсp is the total concentration o the inding sites and (nсp - C) is the concentration o ree inding sites. This means that the dependence o the ound dye concentration on the ree dye concentration in solution ollows a saturation curve: C nc pc =. K + C d This equation can e rewriten as (Klots plot): C = nc p K d + nc p C Thus, or the "direct" determination o the dissociation constant, the values o C and C must e calculated. However, the determination o these values is a nontrivial task, since a solution o ThT with irils is always an equilirium system o ree and ound dye molecules. In this regard, in most works aimed at ThT-amyloid irils inding constants determination (including, in work []), the ollowing equations were used: F = F max d + K X, X K d = +, F F F X max max
in which the total concentration o ThT (С0) as the X value was used instead o the concentration o the ree (non-amyloid-associated) dye. Experiments ased on luorescence intensity measurement, in principle, cannot provide inormation aout the concentration o ree dye. However the replacement o the concentration o ree dye with the concentration o total dye contradicts to the physical meaning o the current task. In this paper we showed how this prolem can e solved using the samples otained y the equilirium microdialysis. It should e noted that in most cases o the inding parameters determination, the authors do not take into account the inluence o the primary inner ilter eect on the recorded luorescence intensity values. Even experienced researchers, who do not specialize in luorescence techniques, do not take into account the act that a plateau o the dependence o luorescence intensity on the concentration o a luorescent sustance could not point to the saturation o inding centers, since such a character o the dependence is its general property. Furthermore, the recorded luorescence intensity could even decrease with an increase in the content o the luorescent sustance which is also a general property o such dependences. Thus, in order to determine the correct inding parameters values, it is necessary to correct the recorded luorescence intensity or the primary inner ilter eect. In this paper, we showed how this correction can e perormed using a coeicient (W) that depends only on the total optical density o the solution. Finally, another important prolem aced y researchers using the F(С0) dependence to determine ThT-amyloid irils inding parameters is that this approach can e applied only or the case o the one inding type existence. And in itsel, this approach does not provide an opportunity to estimate the numer o inding modes. In this paper, we showed that this prolem can e solved using two approaches - y determining C(C) using asorption spectroscopy o solutions otained y the equilirium microdialysis or F(C) using luorescence spectroscopy o the same solutions. 2. The reasons o the nonlinearity o the dependence o the luorescence intensity on concentration and luorescence intensity correction or the primary inner ilter eect The nonlinearity o the concentration dependence o the luorescence intensity is caused y the so-called primary inner ilter eect. The reasons or this eect include oth the attenuation o the excitation light lux on its path through an asoring solution (Beer Lamert law) and the dierence etween the area that is illuminated y the excitation light and the working area rom which the luorescence light is gathered. It is generally accepted that or low concentration solutions (low asorance), the luorescence intensity is proportional to the concentration o the luorescence sustance, and primary inner ilter eects are negligile; however, this assumption is not valid [2]. In reality, the total luorescence intensity is only proportional to the asorance (A) at one point, where A = 0. Even at A = 0., the deviation rom linearity is 2%, and at A = 0.3, the deviation is 38% [2] In an ideal case when the area illuminated y the excitation light coincides with the working area rom which the luorescence light is gathered, the recorded total luorescence intensity F( ex) is proportional to the raction o the excitation light that is asored y the solution ( 0 A ). I only one sustance is responsile or the asorption and luorescence o a solution, then:
Here, ( ) ' A ( ) 0 ( ) ( 0 ) A ( 0 ) F = k I q = k A q ( ) ex ex ex FL A I is the intensity o the excitation light at ex, k' is a proportionality actor, 0 ex ex ex is the spectral width o the slits o the monochromator in the excitation pathway and k = k I is a normalization actor determined using a standard (a luorescent ( ) ' 0 ex ex sustance with known luorescence quantum yield) at the same experimental conditions (i.e., slits widths, photomultiplier voltage, and other actors) used in the experiment with this sample. The coeicient k is chosen in a such way that the total luorescence intensity o the standard and the sample give physical meaning to the product o asorance and the luorescence quantum yield: ( ) ( ) F = F W = A q ( 2 ) 0 ex ex FL Here, W is a correction actor that is determined y the total asorance o the solution at ex: W A 0 = FL. ( 3 ) A FL I there are several components in the solution that asor A FL, i and luoresce with a luorescence quantum yield asorance AABS, then: ( ) ( ) 0 ex ex FL, i i q i, ut others only asor the excitation light with total F = F W = A q ( 4 ) 0 A where W = and A AFL, i AABS A = +. It should e noted that in most spectroluorimeters, the detected luorescence intensity is not proportional to the raction o light that is asored y the solution. Thus, the correction actor cannot e calculated according to Eq. 4; instead, it must e determined experimentally [3]. Moreover, ecause the luorescence intensity measured y these spectroluorimeters decreases as the asorance o the investigated solutions increases, the luorescence o solutions with high asorance (A > 5.0 or most spectroluorimeters with a cell with an optical path length o cm) cannot e recorded at all. We showed experimentally [2] that the Cary Eclipse spectroluorimeter (Agilent Technologies, Australia) enales recordings o luorescent solutions with very high asorance; in contrast to all known spectroluorimeters, this spectroluorimeter has horizontal slits (Fig. S), [4] that allows recording the luorescence o solutions in a much wider range o asorance. The unique eature o this spectroluorimeter is that the area illuminated y the excitation light coincides with the working area rom which the
luorescence light is gathered (Fig. S). Thus, in Cary Eclipse spectroluorimeter, the detected luorescence intensity is proportional to the raction o the light asored y the luorescent solution. In this connection, in the present work the correction actor W was calculated using only the solution asorance according to Eq. 4 or all investigated solutions o ThT with α-synuclein amyloid irils prepared y equilirium microdialysis. Figure S. Schematic representation o the light lux in the spectroluorimeters with vertical (standard) and horizontal slits geometries [2] 3. The procedure or otaining o the spectral characteristics o ThT ound to α-synuclein amyloid irils y the use o equilirium microdialysis Figure S2. The use o equilirium microdialysis or examination o ThT-αsynuclein amyloid irils interaction. (A) () - asorption spectra o ThT in chamer #2 (ree ThT at concentration C); (2) - asorption spectra o ThT in chamer # (superposition o the asorption spectra o ree ThT in concentration C, ThT ound to irils in concentration C, and the apparent asorption caused y the light scattering) ater the equilirium; (3) - optical density determined y the iril light scattering as calculated y the equation Ascat=aλ -m. Coeicients a and m were determined rom the linear part o the curve 2 (where there is no active dye asorption) plotted in logarithmic coordinates lg(ascat)=(lg(λ)) (see Insert, curve 3). (4) - total asorption o ree and ound dye ater light
scattering sutraction (A(λ)#2 Ascat); (5) - asorption spectrum otained y measuring the dierence spectrum etween the spectra o solutions rom chamers # and #2 (superposition o the asorption spectra o ound to irils ThT and the apparent asorption caused y the light scattering). (B) Asorption spectra o ThT incorporated into α-synuclein amyloid irils (6) - evaluated as A( )=A(λ)#2 A(λ)scat A(λ)# (the dierence etween the spectra (4) and ()) and (7) - otained rom spectrum (5) ater light scattering sutraction (calculation procedure is shown in the Insert). (C) - () corrected on the primary inner ilter eect luorescence spectra o ThT in chamer #2 (ree ThT); (2) - corrected on the primary inner ilter eect luorescence spectra o ThT in chamer # (superposition o the luorescence spectra o ree and ound to irils ThT); (3) - luorescence spectrum o ThT incorporated into α-synuclein amyloid irils (the dierence etween the spectra (2) and ()). Asorption spectra (6) and (7) were averaged. Otained asorption and luorescence spectra o ree and ound to irils ThT were smoothed and normalized to unity at the spectra maximum and presented at the Figure 3. 4. Statistical analysis o the experimental data approximation y the models o one and two modes (types) o ThT inding to α-synuclein amyloid irils A statistical analysis o the results otained under the assumption o existence o one and two inding modes was perormed. inding mode 2 inding modes Ā, % ρ F-statistics R 2 d 36 0.72 50. 0.85 0.5 4 0.95 52.2 0.89 2. We showed that the approximation under the assumption o two onding modes has etter values o the model characteristics compared with approximation under the assumption o one inding mode: a smaller average error o approximation Ā (which indicates etter mathematical accuracy); a larger correlation index ρ (which indicates a stronger nonlinear coupling); a larger calculated value o the Fisher's F-test (which indicates a more adequate description o the experimental data and the statistical signiicance o the approximation); a larger adjusted coeicient o determination R2 (which indicates a etter agreement etween the experimental data and the approximating curve). A comparison o the models residuals was made and it was shown that the residuals o the two inding modes model are much smaller than the residuals o the model o one inding mode (P < 5 0-5 ). The models ias (t-test) was estimated and it was shown that the model o one inding mode is iased, and the model o two inding modes is uniased. In addition, using the Durin-Watson statistics (d) or a model o one inding mode (in contrast to the model o two inding modes) positive residuals autocorrelation was shown, which indicates the unsatisactory nature o this approximation. Thus, using careul statistical analysis the etter it y the two-site inding model approximation was proved.
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