Probing the occurrence of soluble oligomers through amyloid aggregation scaling laws

biomolecules A icle P obing he Occu ence o Soluble Oligome s h ough Amyloid Agg ega ion Scaling Laws Alexand a Sil a 1,2,† , Zsuzsa Sá kány 1,2,†,‡ , Joana S. F aga 1,2,3 , Pablo Taboada 4,5, Sand a Macedo-Ribei o 1,2 and Ped o M. Ma ins 1,2,3,* 1IBMC—Ins i u o de Biologia Molecula e Celula , Uni e sidade do Po o, 4200-135 Po o, Po ugal; [email p o ec ed] (A.S.); [email p o ec ed] (Z.S.); [email p o ec ed] (J.S.F.); [email p o ec ed] (S.M.-R.) 2Ins i u o de In es igação e Ino ação em Saúde, Uni e sidade do Po o, 4200-135 Po o, Po ugal 3ICBAS—Ins i u o de Ciências Biomédicas Abel Salaza , Uni e sidade do Po o, 4050-313 Po o, Po ugal 4Á ea de Física de la Ma e ia Condensada, Facul ad de Física, Uni e sidad de San iago de Compos ela, 15782 San iago de Compos ela, Spain; [email p o ec ed] 5Ins i u o de In es igación Sani a ia (IDIS), 15706 de San iago de Compos ela, Spain *Co espondence: [email p o ec ed]; Tel.: +351-220-408-800 † These au ho s con ibu ed equally o his wo k. ‡ P esen Add ess: LEPABE—Depa amen o de Engenha ia Química, Faculdade de Engenha ia da Uni e sidade do Po o. Recei ed: 4 Sep embe 2018; Accep ed: 1 Oc obe 2018; Published: 4 Oc obe 2018   Abs ac : D ug disco e y equen ly elies on he kine ic analysis o physicochemical eac ions ha a e a he o igin o he disease s a e. Amyloid ib il o ma ion has been ex ensi ely in es iga ed in ela ion o p e alen and a e neu odegene a i e diseases, bu hus a no he apeu ic solu ion has di ec ly a isen om his knowledge. O he agg ega ion pa hways p oducing smalle , ha d- o-de ec soluble oligome s a e inc easingly appoin ed as he main eason o cell oxici y and cell- o-cell ansmissibili y. He e we show ha amyloid ib illa ion kine ics can be used o un eil he p o ein oligome iza ion s a e. This is illus a ed o human insulin and a axin-3, wo model p o eins o which he amyloidogenic and oligome ic pa hways a e well cha ac e ized. Agg ega ion cu es measu ed by he s anda d hio la in-T (ThT) luo escence assay a e shown o e lec he ela i e composi ion o p o ein monome s and soluble oligome s measu ed by nuclea magne ic esonance (NMR) o human insulin, and by dynamic ligh sca e ing (DLS) o a axin-3. Uncon en ional scaling laws o kine ic measu ables we e explained using a single se o model pa ame e s consis ing o wo a e cons an s, and in he case o a axin-3, an addi ional o de -o - eac ion. The same i ed pa ame e s we e used in a disc e ized popula ion balance ha adequa ely desc ibes ime-cou se measu emen s o ib il size dis ibu ions. Ou esul s p o ide he oppo uni y o s udy oligome ic a ge s using simple, high- h oughpu compa ible, biophysical assays. Keywo ds: p o ein agg ega ion; amyloid; soluble oligome s; kine ic analysis; nuclea ion 1. In oduc ion The deposi ion o amyloid ib ils in he b ain is a pa hological hallma k o se e al di e en neu odegene a i e diso de s, ye he pa hogenic ole o hese insoluble agg ega es is no ully unde s ood [ 1 ]. On he o he hand, he e is now subs an ial in i o e idence o amyloidogenic p o eins also o ming small soluble oligome s ha sp ead o neighbo ing cells and induce downs eam p ocesses associa ed wi h neu odegene a ion [ 1 , 2 ]. Chemical kine ics, a classical co ne s one o d ug disco e y [ 3 ], is ha dly applicable o he s udy o his new and p e-eminen a ge [ 4 – 6 ], in pa due o he lack o s aigh o wa d me hods o moni o he o ma ion o a highly he e ogeneous g oup o Biomolecules 2018,8, 108; doi:10.3390/biom8040108 www.mdpi.com/jou nal/biomolecules Biomolecules 2018,8, 108 2 o 20 species anging om p o ein dime s o complex n-me s [ 7 , 8 ]. In con as , ex ensi e esea ch has been de o ed o p o ein agg ega ion kine ics based on he cha ac e is ic inc o ial p ope ies o amyloid ib ils [9]. An impo an s ep owa ds he kine ic quan i ica ion o o -pa hway agg ega ion was aken a e he obse a ion o p o ein p ecipi a ion occu ing in pa allel wi h he o ma ion o amyloid ib ils o lysozyme [ 10 ]. Be o e, kine ic analysis o amyloid agg ega ion o he isle amyloid polypep ide (IAPP) sugges ed he o ma ion o in e media e on- and o -pa hway phases du ing IAPP ib illogenesis [ 11 ]. The p esence o non-amyloidogenic species p oduces pe cep ible de ia ions om he ime e olu ion o he amyloid signal expec ed o he gene ic nuclea ion and g ow h p ocesses o he phase ansi ion: α=1−1 kb[exp(ka )−1]+1(1) whe e α is he no malized amyloid con e sion, and ka and kb a e combina ions o elemen a y a e cons an s [ 12 ]. One o he kine ic signa u es ound o be associa ed wi h o -pa hway agg ega ion was he unusually weak dependence o he lag phase du a ion on he ini ial concen a ion o lysozyme [ 10 ]. Simila beha io s obse ed wi h o he p o ein models ha e p o ided he basis o a ied in e p e a ions o he amyloid agg ega ion mechanism encompassing, o example, Michaelis-Men en-like sa u a ion o he elonga ion s ep [ 13 ], complex sub-s eps o nuclea ion and g ow h [ 14 ], s ochas ic luc ua ions in he nuclea ion ime [ 15 ], and he supp ession o ib il agmen a ion a high ib il concen a ions [ 16 ]. Unlike hese possible explana ions o he unde pe o ming scaling laws, o -pa hway agg ega ion can be di ec ly in es iga ed by analy ical and mic oscopic echniques such as hose used o iden i y insoluble agg ega es o lysozyme [ 10 ], and la e on, soluble oligome s o a axin-3 [17], and me as able oligome s o Aβ40 and Aβ42 pep ides [18,19]. Because he o ma ion o soluble and insoluble assemblies is ed by a common pool o p o ein monome s, we p opose ha amyloid ib illa ion kine ics can be used o e eal he p esence o he pa allel oligome ic pa hway. To es his hypo hesis, we chose wo sys ems, human insulin and a axin-3, o which he ib illa ion kine ics ha e been measu ed unde condi ions o known oligome ic composi ion. Insulin is a p o ein ho mone exis ing in solu ion in a he modynamic equilib ium o monome s, dime s, e ame s, hexame s and highe -o de oligome s [ 20 , 21 ]. Changes in he p o ein molecula s uc u e induced by low pH, high empe a u e o he p esence o o ganic sol en s lead o he o ma ion o amyloid ib ils h ough he di ec associa ion o insulin monome s [ 20 ], o by he assembly o in e media e on-pa hway oligome s [ 22 ]. A axin-3 is a mul i-domain p o ein wi h a globula Josephin domain and a C- e minal lexible ail con aining a polyglu amine (polyQ) epea whose expansion ul ima ely causes Machado–Joseph disease. A axin-3 agg ega ion in ol es an ini ial s ep media ed by he Josephin domain, and a second s ep dependen on he expanded polyQ ac ha accele a es p o ein agg ega ion and p omo es he o ma ion o ma u e amyloid ibe s [ 23 , 24 ]. The analysis o he hio la in-T (ThT) binding assay un a di e en concen a ions o human insulin and a axin-3 unco e s mechanis ic aspec s o he oligome ic and ib illa pa hways. The dis inc agg ega ion mechanisms p edic ed o each p o ein a e expe imen ally alida ed by ime-cou se dynamic ligh sca e ing (DLS) measu emen s. 2. Ma e ials and Me hods 2.1. P o ein P epa a ion Human insulin pu chased om Sigma-Ald ich (Sain Louis, MO, USA) (I2643) was dissol ed wi hou u he pu i ica ion in 20% ace ic acid 0.5 M NaCl (pH 1.8) o a inal concen a ion o 5 mg/mL. Be o e incuba ion, samples we e il e ed wi h 0.22 µ m sy inge il e uni s (Millex-GV, Millipo e, Co k, I eland). Non-expanded a axin-3 was exp essed and pu i ied as p e iously desc ibed [17]. Biomolecules 2018,8, 108 3 o 20 2.2. T ansmission Elec on Mic oscopy T ansmission elec on mic oscopy (TEM) isualiza ion o insulin and a axin-3 ib ils was pe o med using a TEM JEM-1400 (JEOL, Tokyo, Japan) a an accele a ing ol age o 80 kV. 100 µ L samples o 5 mg/mL insulin we e incuba ed o 6 h a 45 ◦ C wi hou mechanical shaking in 1.5 mL eppendo ubes (DNA LoBind, Eppendo AG, Hambu g, Ge many). 700 µ L samples o 5 µ M (0.218 mg/mL) a axin-3 in 20 mM sodium phospha e pH 7.5, 150 mM NaCl, 1 mM di hio h ei ol (DTT) we e incuba ed in 1.5 mL eppendo ubes (DNA LoBind, Eppendo AG, Hambu g, Ge many) o 65 h a 37 ◦ C wi hou mechanical shaking. P o ein samples we e dilu ed in wa e (1:20 o insulin and 1:10 o a axin-3), adso bed o ca bon-coa ed 200 mesh nickel g ids (FCF300-NI, Elec on Mic oscopy Sciences, Ha ield, PA, USA), nega i ely s ained wi h 2% (w/ ) u anyl ace a e, d ied and obse ed a a magni ica ion o 80,000–100,000×. 2.3. Dynamic Ligh Sca e ing Dynamic ligh sca e ing measu emen s we e pe o med using an ALV/DLS/ SLS-5000F, SP-86 goniome e sys em (ALV-GmbH, Langen, Ge many) equipped wi h a CW diode-pumped Nd:YAG solid-s a e Compass-DPSS lase wi h a symme ize (Cohe en Inc., San a Cla a, CA, USA). The lase ope a es a 488 nm wi h an ou pu powe o 400 mW. The in ensi y scale was calib a ed agains sca e ing om oluene. 700 µ L samples o 5 mg/mL insulin we e incuba ed in glass cu e es a 45 ◦ C wi hou mechanical shaking and pe iodically analyzed a a sca e ing angle 90 ◦ o he inciden beam. Hyd odynamic adii o he pa icles in solu ion we e es ima ed om he di usion coe icien (s) deli e ed om CONTIN analysis [ 25 ]. Discon inuous au o-co ela ion unc ions we e no conside ed o CONTIN analysis. 3. Resul s and Discussion Fo he expe imen al condi ions adop ed in each model p o ein, human insulin and a axin-3 p oduce ib illa species wi h dis inc mo phologies (Figu e 1A,B) and a ma kedly di e en agg ega ion a es (Figu e 1C). Long, s aigh ilamen s o human insulin a e o med much as e han he small, wo m-like ib ils o a axin-3, he eby sugges ing ha phase ansi ion mechanisms a e di e en ly a ec ed by he ib il elonga ion s ep. Chemical kine ic analysis pinpoin s hese di e ences, and e eals how he p esence o soluble oligome s in luences each ype o p o ein agg ega ion cu es. The quan i a i e me hods p oposed he e a e expec ed o con ibu e o he iden i ica ion o mechanis ic changes p o oked, e.g., by he p esence o agg ega ion modula o s o by di e en condi ions o empe a u e, pH, ionic s eng h, e c. Figu e 1. Case s udy examples o human insulin and a axin-3 agg ega ion. T ansmission elec on mic oscopy (TEM) mic og aphs o nega i ely s ained ib ils o ( A ) 5 mg/mL human insulin and ( B ) 5 µ M (0.218 mg/mL) a axin-3 cap u ed a e 6 h and 65 h incuba ion, espec i ely (scale ba s, 100 nm). ( C ) Schema ic amyloid ib illa ion cu es ep esen ing he p og ess o no malized hio la in-T (ThT) luo escence ( F/FF ) du ing he agg ega ion o human insulin and a axin-3 in he ange o p o ein concen a ions s udied by Fode àe al. [ 26 ] and Sil a e al. [ 17 ], espec i ely. The hal -li e coo dina es 50 and 50 a e indica ed by he a ows and by he slopes o dashed lines, espec i ely. Biomolecules 2018,8, 108 4 o 20 3.1. Mechanis ic Analysis o Insulin Agg ega ion In he simpli ied mechanism ep esen ed in Figu e 2A, he elemen a y in e media e s eps pa icipa ing in he p ima y nuclea ion, seconda y nuclea ion and elonga ion o insulin ib ils a e summed up in o he o e all a e cons an s kn , k2 , and k+ , espec i ely [ 17 ]. The sigmoidal ( a he han hype bolic) p og ess cu e o insulin ib illa ion (Figu e 1C) poin s o low alues o he pa ame e kb=kn/ka , which gi es he ela i e weigh o p ima y nuclea ion o e he au oca aly ic s eps o seconda y nuclea ion and elonga ion ( ka=k2+k+ ) [ 10 ]. The as elonga ion a es sugges ed by he mo phology o insulin ib ils (Figu e 1A) a e con i med by he high alue o ka associa ed o he s eep bu s phase (and high 50 alue) in Figu e 1C. The speci ic weigh o seconda y nuclea ion and elonga ion in de e mining he alue o ka canno be dis inguished om single p og ess cu e analysis because hese s eps ollow simila a e laws [ 17 ]. Mo eo e , since ib il b eakage ( a e cons an k− ) does no change he o al mass o ThT-posi i e ilamen s bu only hei numbe [ 17 ], complemen a y measu emen s o ib il size dis ibu ions a e equi ed o di ec ly assess he ole o he b eakage s ep. P io knowledge o he p o ein oligome iza ion s a e is equi ed be o e we can mo e in o he deepe le els o he di e en agg ega ion pa hways [ 27 ]. The oligome iza ion equilib ium o human insulin (Figu e 2B) has been cha ac e ized by Bocian e al. [ 21 ] using 2D and pulsed ield g adien spin echo (PFGSE) nuclea magne ic esonance (NMR). I is, he e o e, possible o es ima e he a ailabili y o insulin monome s unde condi ions o o al p o ein concen a ion, p esence o zinc, and acidic pH ha a e simila o hose adop ed by Fode àe al. [ 26 ] while measu ing amyloid ib illa ion kine ics. Based on he knowledge o he alues o he monome concen a ion C1−me (Figu e 2C), peculia scaling laws o equilib ium (Figu e 2D) and kine ic (Figu e 2E,F) pa ame e s can be explained using a numbe o i ed pa ame e s commensu a e wi h he numbe o independen obse a ions. As an indica o o he amoun o amyloid ib ils p oduced, he inal ThT luo escence in ensi y ( FF ) (pink line in Figu e 2D) is no di ec ly de e mined by he o al p o ein a ailable (closed ci cles in Figu e 2D) o e en by he monome concen a ion alone. Since p o ein agg ega ion akes place un il he monome concen a ion C1−me equals he he modynamic solubili y C∗ , he alue o FF e lec s he di e ence (C1−me −C∗) o he wise known as supe sa u a ion ( ∆C ) [ 12 ]. This is illus a ed in Figu e 2D (blue line) wi h no o he i ing pa ame e s han he luo escence p opo ionali y cons an (in a bi a y uni s) and he insulin solubili y, which is a measu able quan i y. Besides con i ming amyloid ib illa ion as a phase ansi ion p ocess d i en by supe sa u a ion, he FF scaling law is consis en wi h a mechanism o monome addi ion admi ing no supplemen a y con ibu ion om p e-exis ing soluble oligome s o he inal ThT luo escence signal. Consequen ly, he amyloid pa hway (Figu e 2A) and he oligome ic equilib ium (Figu e 2B) a e ound o ake place o e dis inc imescales, wi h insulin monome s being consumed by he i s p ocess a much as e a es han hey a e p oduced by he second. Biomolecules 2018,8, 108 5 o 20 Figu e 2. Agg ega ion pa hways o human insulin in es iga ed h ough amyloid ib illa ion kine ics. ( A ) Reac ion s eps and co esponding a e cons an s pa icipa ing in he amyloid pa hway. G een glows ep esen an inc ease in he mass o ib ils. This a ia ion is de ec ed by amyloid binding assays and can be used o es ima e wo pa ame e s, ka and kb , consis ing o combina ions o he o he a e cons an s (see ex o de ails). ( B ) Oligome ic equilib ium o insulin as de e mined by Bocian e al. [ 21 ] using 2D and pulsed ield g adien spin echo (PFGSE) nuclea magne ic esonance (NMR) ( K12 = 4.9 × 10 5 , K24 = 5.0 × 10 4 , K46 = 2.7 × 10 3 and Kiso = 1.35 × 10 4 ). ( C ) Concen a ion o insulin monome s ( C1−me ) p edic ed by he oligome ic equilib ium ( B ) o he alues o o al p o ein concen a ion ( CT ) used in ( D – F ) (symbols). Pink line: polynomial i o he da a. ( D – F ) Reac ion scaling laws measu ed by Fode àe al. [ 26 ] (symbols) and p edic ed by he model equa ions shown in blue o he monome concen a ions es ima ed in ( C ) (solid blue lines). ( D ) The inal ThT luo escence ( FF ) is a di ec p opo ion o supe sa u a ion ∆C=C1−me −C∗ (p opo ionali y cons an cns = 1.95 × 10 5 ) o an in e ed solubili y alue o C∗= 0.029 mg/mL. Pink line: The polynomial i in ( C ) is used o es ima e FF wi hou he solubili y co ec ion ( cns = 1.15 × 10 5 and C∗= 0 ) . ( E ) Double-loga i hmic plo o hal -li e coo dina e 50 as a unc ion o CT . Red lines: Limi scaling exponen s |γ| o 1 (dashed line) and 0.5 (solid line) a e s ill oo high o ep esen he measu ed end. ( E , F ) Bo h ka and kb a e conside ed i s -o de dependen on ∆C ( i ed alues: ka= 1.34 × 10 2∆C h −1 and kb= 2.41 × 10 −7∆C ). Measu ed da a we e adap ed wi h pe mission om Fode àe al. [ 26 ]. Copy igh 2017 Ame ican Chemical Socie y. The sepa a ion o imescales simpli ies he applica ion o analy ic model equa ions ha we e o iginally de i ed by assuming he soluble p o ein ully dissocia ed [ 12 ]. Theo e ical cu es o 50 and 50 s. p o ein concen a ion can be compu ed using he equa ions in Figu e 2E,F (see Appendix A o de ails), a e exp essing ka and kb as a unc ion o ∆C (and o C1−me ). I , as i seems o be he case o insulin, ib il elonga ion p edomina es o e seconda y nuclea ion (i.e., ka≈k+ and kb≈kn/k+ ), hen bo h kaand kba e p opo ional o he ini ial supe sa u a ion (∝ ∆C) conside ing ha [10,12]: (k+∝ ∆C kn∝ ∆C2(2) Biomolecules 2018,8, 108 6 o 20 These simple p emises and wo model pa ame e s a e su icien o elucida e he uncon en ionally weak CT -dependence o 50 (Figu e 2E) as being he esul o he lowe mola ac ions o insulin monome obse ed o highe p o ein concen a ions (Figu e 2C). I he associa ed s a es o soluble insulin we e igno ed, he lowe limi s usually admi ed o he absolu e scaling ac o |γ| would be oo high o ep oduce he measu ed end in Figu e 2E ( ed lines). Rema kably, he se o pa ame e s, ka and kb i ed o he lag- ime scaling da a in Figu e 2E a e he same as hose ha desc ibe he agg ega ion a e da a in Figu e 2F (Appendix B). In bo h cases, he used alue o C∗ is he one esul ing om he in e p e a ion o Figu e 2C. Fa om being edundan , he con i ma ion o kine ic p edic ions by di e en and independen measu emen s p o ides unequi ocal e idence ha he p esen heo e ical amewo k, wi h only wo model pa ame e s, is indeed alid. 3.2. Mechanis ic Analysis o A axin-3 Agg ega ion The s udy o a axin-3 agg ega ion ollows he same unde lying p inciple ha was adop ed o human insulin, and has a simila pu pose: o show how adi ional kine ics can be ma kedly dis o ed by he p esence o soluble oligome s. As in he case o o he polyQ- epea p o eins [ 28 ], he o ma ion o a axin-3 ib ils and he dissocia ion o a axin-3 oligome s occu simul aneously (Figu e 3A), and hus, imescale sepa a ion canno be assumed as a simpli ying hypo hesis. Suppo ed by DLS, size-exclusion ch oma og aphy and TEM da a, a de ailed accoun o he di e en s eps shown in Figu e 3A was ecen ly p o ided [ 17 ], including quan i a i e es ima ions o he a e cons an s κ1+ , κ1− , κn+ , κn− cha ac e izing he elemen a y s eps o a axin-3 oligome iza ion. The wo m-like ib ils shown in Figu e 1B a e p edominan ly o med by seconda y nuclea ion ( ka≈k2 ) and p ima y nuclea ion (kb≈kn/k2) , wi h mino con ibu ions om he ib il elonga ion ( k+≈ 0) and ib il b eakage (k−≈0) s eps [ 17 ]. The measu ed e ec o p o ein concen a ion on he ThT luo escence p og ess cu es (Figu e 3B, symbols) is no ully assessed i he oligome ic pa hway is no aken in o accoun ; on he whole, he black lines in Figu e 3B a e indica i e o good nume ical i s, ye hey a e based on Equa ion (1), which igno es he occu ence o he pa allel eac ions o soluble oligome o ma ion/dissocia ion. Rega dless o how elabo a ed he heo e ical model can be, he i ed pa ame e s a e, in his limi ed scena io, compa able o semi-empi ical coe icien s showing no e iden undamen al meaning. In he illus a i e case o Figu e 3B, he empi ically de e mined alues o ka and kb would ollow a p opo ional ela ionship wi h p o ein concen a ion, which is no econcilable wi h es ablished heo ies (Figu e S1). Biomolecules 2018,8, 108 7 o 20 Figu e 3. Agg ega ion pa hways o a axin-3 in es iga ed h ough amyloid ib illa ion kine ics. ( A ) The oligome ic and amyloid pa hways ake place simul aneously. The a e cons an s o oligome o ma ion/dissocia ion we e p e iously de e mined ( κ1+= 7.99 × 10 −4µ M −1 h −1 , κ1−= 9.73 h −1 , κn+= 0.167 µ M −1 h −1 , and κn−= 0.775 h −1 ) [ 17 ]. The s eps o amyloid ib il o ma ion a e he same as in Figu e 2A. The mass o amyloid ib ils is a unc ion o only ka and kb , whe eas he numbe o ilamen s is also in luenced by ib il b eakage and by he c i ical size o ib ils o med by p ima y and seconda y nuclea ion ( R∗ and R∗ 2 , espec i ely). ( B ) Symbols: ThT luo escence inc ease measu ed o a axin-3 concen a ions o ( om op o bo om) CT= 10 µ M, 7 µ M, 5 µ M, 4 µ M and 2 µ M [ 17 ]. Lines: indi idual (black) and global (blue) i ings o he expe imen al da a by Equa ions (1) and (S7), espec i ely. Fi ing s a is ics gi en in Figu e S1A. Global i ing: ka= 0.364 Cn2 T h −1 , kb= 2.91 × 10 −10C2−n2 T and n2= 0.160). ( C – E ) Reac ion scaling laws co esponding o he kine ic measu emen s (symbols) and global i ing (blue lines) shown in ( B ). ( C ) Double-loga i hmic plo . Red lines: Limi scaling exponen s |γ| o 1 (dashed line) and 0.5 (solid line) a e s ill oo high o ep esen he measu ed end. ( D ) Red-shadowed a ea: ypically, 50 is posi i ely co ela ed wi h CT (and wi h −1 50 ) [ 29 ]. Measu ed da a we e adap ed wi h pe mission om Sil a e al. [17]. Copy igh 2018 John Wiley and Sons. Ins ead o using he amyloid ib illa ion model in i s closed o m solu ion, he o iginal di e en ial equa ion, was sol ed simul aneously wi h he oligome iza ion a e equilib ium, Equa ions (A6) and (A7) (Appendix A), and hen i ed o he ThT luo escence p og ess cu es (Figu e 3B, blue lines). Al hough compu a ionally mo e demanding han he app oach ollowed wi h human insulin, he numbe o deg ees o eedom emains unusually low as ega ds o complex biophysical p oblems: h ee independen scaling laws o 50 (Figu e 3C), 50 (Figu e 3D) and FF (Figu e 3E) a e used o es ima e no o he unknowns bu he scaling cons an s associa ed o ka and kb . Unlike he case o insulin, he alue o a axin-3 solubili y is known be o ehand o be e y low ( C∗≈ 0) as e idenced by alues o monome concen a ion lowe han he de ec ion limi s unde equilib ium condi ions [ 17 ]. In con as , since he au oca aly ic a e cons an o a axin-3 is de e mined by he seconda y nuclea ion Biomolecules 2018,8, 108 8 o 20 s ep ( ka≈k2 ), a scaling exponen n2 is now in oduced o accoun o he poo ly unde s ood k2 s. ∆C ela ionship: (k2∝ ∆Cn2 kn∝ ∆C2(3) In p ac ice, di e en i ed pa ame e s a e p o ided by he indi idualized analysis o each p og ess cu e in Figu e 3B (black lines), whe eas he global i (blue lines) equi es a single se o a e cons an s ka and kb o model bo h he agg ega ion assay and i s scaling laws (Figu e 3C–E). The be e goodness-o - i s a is ics o he o me p ocedu e (Figu e S1) is no su p ising since, as in he case o o e pa ame e ized p oblems, he indi idual nume ical analysis is no c oss- alida ed and ends o o e i he expe imen al e o , he e o e, comp omising he model’s p edic i e powe [17,30–32] . The global i ing con i ms ha p e-de e mined oligome iza ion cons an s can be in eg a ed in agg ega ion eac ion ne wo ks o explain highly peculia kine ics, such as he e y weak CT -dependence o 50 (Figu e 3C), and no ably, he nega i e CT -dependence o 50 (Figu e 3D). Al hough a mo e con en ional esul in he absence o quenching phenomena [ 33 , 34 ], he linea scaling law o he end-poin ThT luo escence (Figu e 3E) is explained by he dissocia ion o a axin-3 oligome s occu ing in he same ime scale as amyloid ib illa ion. The obse ed s aigh line c ossing he o igin also indica es ha he soluble p o ein was con e ed in o amyloid-like ib ils wi hou he occu ence o signi ican monome deg ada ion du ing incuba ion [ 17 ]. The complex, ye sel -consis en beha io s o hal -li e and end-poin eadings c oss- alida e he molecula -le el implica ions a ising om he de ini ion o he seconda y nuclea ion a e cons an ( k2 ), and pa icula ly, om he ob ained alue o he scaling exponen n2 close o 0. A di ec compa ison wi h he ib il elonga ion s ep would sugges a i s -o de dependence o k2 on he ini ial supe sa u a ion ∆C since bo h a es linea ly inc ease wi h he ins an aneous alues o supe sa u a ion and ib il mass [ 10 , 17 ]. Howe e , mo e han jus a collisional a e coe icien , k2 is an o e all a e cons an accoun ing o he a e-limi ing s eps leading o he o ma ion o seconda y nuclei [ 35 ]. Acco ding o classical nuclea ion heo y [ 36 ], he nuclea ion p omo ing e ec elici ed by highe supe sa u a ion le els (and lowe ene ge ic ba ie s o phase ansi ion) can be, in pa , coun e ac ed by he concomi an dec ease in he c i ical sizes o he p ima y ( n∗ 1 ) and seconda y ( n∗ 2 ) nucleus. This ex a con ibu ion, which is no e iden o p ima y nuclea ion o amyloid ib ils [ 12 ], seems ele an o he seconda y nuclea ion o a axin-3. Somewha unde alued in ega d o induc ion ime measu emen s, hal -li e agg ega ion a es 50 (o , equi alen ly, maximum agg ega ion a es) o e he oppo uni y o iden i y he p edominan au oca aly ic p ocess. Whils he scaling o 50 is g ea ly in luenced by p ima y nuclea ion, he scaling o 50 is de e mined by he balance be ween elonga ion and seconda y nuclea ion a es, wi h he e ec o CT ge ing weake as seconda y nuclea ion becomes mo e impo an . The e o e, and simila ly o wha was concluded o insulin, he measu ed scaling laws o a axin-3 agg ega ion a e de e mined by he ib illa ion mechanism i sel and by he p esence o he modynamically s able, soluble agg ega es ha u he deple e he concen a ion o ee monome in solu ion. 3.3. Model P edic ions A e Fu he Con i med by Size Dis ibu ion Analysis o Insulin Agg ega ion The p e ious models p esen a de ailed pic u e o he di e en s eps a ec ing he o ma ion o he insoluble ilamen s ha can be u he es ed using DLS measu emen s o pa icle size dis ibu ions (PSDs). Con a y o wha was obse ed o a axin-3 [ 17 ], he size o insulin ib ils ends o inc ease o e ime un il eaching hyd odynamic adii ( Rh ) abo e he mic ome e scale—Figu e 4A–D (insulin) and Figu e 4E (a axin-3). This is no su p ising aking in o accoun he TEM images ob ained a he end o each agg ega ion assay (Figu e 1A,B), and he negligible ole o he elonga ion s ep du ing a axin-3 ib illa ion. Ano he ob ious di e ence o a axin-3 is he pe sis ing dominance o he le -side peak ( Rh< 10 nm) up o he end o he agg ega ion eac ion (Figu e 4A–C). To a ce ain ex en , his is explained by he alue o p o ein solubili y ( C∗ ), which as al eady discussed, is much highe in he case o human insulin. While he inal concen a ion o soluble a axin-3 was oo low o be Biomolecules 2018,8, 108 9 o 20 de ec ed by DLS [ 17 ], he C∗ alue o insulin is esponsible o he popula ion o soluble p o ein o con inue p edomina ing, e en a e la ge insoluble agg ega es a e o med (Figu e 4C). Ano he eason explaining he modes inc ease in he in ensi y o sca e ed ligh o la ge pa icles is associa ed wi h he dispe sion o sizes and consequen ial b oadening o PSDs p o oked by he con inuous elonga ion o old and newly- o med insulin ib ils, as opposed o he o ma ion o a axin-3 ilamen s wi h he cons an dimension cha ac e is ic o he a axin-3 seconda y nucleus. In common wi h a axin-3, ib il b eakage has a mino ole in de e mining he ime a ia ion o he PSD in quiescen insulin solu ions: in he case o a axin-3, he shape o hese dis ibu ions did no change signi ican ly du ing he bu s and pla eau phases o agg ega ion despi e he inc eased ela i e impo ance o he popula ion o a axin-3 ib ils [ 17 ]. In he case o insulin, he elonga ion-domina ed mechanism can be disce ned om he expec ed ib il size inc ease du ing he bu s phase (Figu e 4A,B,D), whe eas, a e ∼ 4.5 h incuba ion, he mean agg ega e size s abilizes a a cons an alue o Rh≈ 1100 nm wi hou any isible signs o ib il agmen a ion (Figu e 4C,D). Figu e 4. Time-cou se DLS analysis o human insulin agg ega ion—di e ences and common aspec s wi h a axin-3. ( A – C ) Symbols connec ed by lines: in ensi y-based size dis ibu ions measu ed a di e en ime poin s as indica ed by he colo ba in ( A ). La ge symbols: alues o he hyd odynamic adius ( Rh ) used as es ima es o he mean size ( Rh ) o insulin ib ils. Ve ical dashed lines: isual e e ence o he i s Rh alue o each panel. (D) Measu ed (symbols) and simula ed (lines) ime e olu ion o Rh. Biomolecules 2018,8, 108 16 o 20 n∞= 9 × 10 6 monome s was adop ed as he maximum dimension o soluble a axin-3 oligome s, and he condi ion dCn/d = 0 was imposed o n≥n∞ . The ini ial condi ions we e se assuming no ib illa agg ega es p esen in solu ion ( M(0)= 0) and ha he ac ional composi ions o monome s and n -me s co espond o hose ex ac ed om DLS measu emen s [ 17 ]. Since he p edominan au oca aly ic s ep du ing a axin-3 ib illa ion is seconda y nuclea ion, ka≈k2 and kb≈kn/k2 . Owing o he low solubili y o a axin-3 ( C∗≈ 0), he ini ial supe sa u a ion is a di ec p opo ion o CT and he CLM pa ame e s a e gi en as ka=k0 aCn2 T and kb=k0 bC2−n2 T . The p opo ionali y cons an s k0 2 and k0 n , and he o de -o - eac ion n2 we e es ima ed by minimizing he absolu e e o be ween p edic ed and measu ed ThT luo escence ( F ) p og ess cu es using he expe imen ally de e mined calib a ion cu e F(a.u.)= 0.70 ×M(µM) and he known oligome iza ion a e cons an s κ1+= 7.99 × 10 −4µ M −1 h −1 , κ1−=9.73 h−1,κn+=0.167 µM−1h−1, and κn−=0.775 h−1[17]. To simula e he 50 and 50 scaling laws in Figu e 6, Equa ions (A6) and (A7) we e nume ically sol ed as desc ibed o a axin-3 using illus a i e alues o C∗= 0, ka= 0.4 Cn2 T h −1 and kb= 5 × 10 −4(CT/5)2−n2 . Two limi si ua ions co esponding o p edominan elonga ion s ep ( n2= 1) o p edominan seconda y nuclea ion ( n2= 0) p ocesses we e conside ed. Soluble p o ein was admi ed o occu ei he as a monome o as a dime ( κn+= 0 and κn−= 0) wi h he dis ibu ion o ini ial species gi en by he exempla unc ion C1= 10 ×1−e−CT/10 o CT alues comp ised be ween 0 and 20 in a bi a y concen a ion uni s. The ela i e weigh o he oligome dissocia ion a e was in es iga ed by changing he alue o κ1− be ween 0 and 5 h −1 while keeping a ixed alue o κ1+= 0. The no malized amyloid signal ( M/MF ) was compu ed o e ime and he co esponding hal -li e coo dina es, 50 and 50 we e ep esen ed as a unc ion o CT(Figu e 6). Appendix B.2. Disc e ized Popula ion Balance The ime e olu ion o he size dis ibu ion o insulin ib ils was simula ed using he disc e e popula ion balance de i ed o gene al phase ansi ion p ocesses comp ising he s eps o p ima y nuclea ion, seconda y nuclea ion, g ow h/elonga ion and b eakage [ 12 , 17 ]. As p e iously desc ibed o a axin-3, he concen a ion o ilamen s composed by jmonome s ( j) is gi en as [17]: d j d =1 jhkn(1−α)2M∞δj,n∗+k2(1−α)αM∞δj,n∗ 2i+ +k+(1−α)(j−1) j−1−k+(1−α)j j+ +1 j"−k− j(j−n∗ 2)H(j−2n∗−1)+ ∞ ∑ i=j+1 k− iH(i−2n∗−1)#(A8) The K onecke del a unc ions in Equa ion (A8) se he sizes o he p ima y and seconda y nuclei o ixed alues o n∗ and n∗ 2 , espec i ely, wi h he la e being adop ed as he smalles possible ilamen size ( j≥n∗ 2 ). The Hea iside unc ion es ablishes a minimum ib il size o 2 n∗+ 1 molecules abo e which agmen a ion s a s o occu [ 46 ]. In he case o insulin, his equa ion is simpli ied since seconda y nuclea ion and ib il b eakage ake place o a negligible ex en ( k2≈ 0 and k−≈ 0). The p e ious Equa ion (A2) can be ob ained om Equa ion (A8) by ex ending he sum o j×d j/d o all ilamen s [17]: dM d = ∞ ∑ j=n∗ 2 jd j d (A9) A popula ion o p e-exis ing clus e s wi h hyd odynamic adii Rh> 100 nm was iden i ied in he analyzed insulin solu ions (Figu e S2). The DLS in ensi y-peak co esponding o his popula ion g adually anished om he measu ed size dis ibu ions as ib il elonga ion ook place (Figu e 4A–D). To simula e his beha io , a simple pa icle adhesion mechanism is p oposed in which p e-exis ing clus e s composed by k monome s a e conside ed o join o he a ailable j -me ib ils and o m he e ogeneous agglome a es composed by l=k+j monome s. Du ing he ini ial phases o he eac ion, a numbe o p e-exis ing clus e s emains isola ed because he e a e ewe ib ils han clus e s. Biomolecules 2018,8, 108 17 o 20 This scena io is hen e e sed as newly o med ib ils ou numbe he ini ial clus e s. The e o e, he less abundan species a e he ones dic a ing he numbe o agg ega es ha will pa icipa e in he adhesion p ocess (Pa): Pa=min P= ∞ ∑ j j,Pc(0)= ∞ ∑ k k(0)!(A10) whe e P is he concen a ion o insulin ib ils, Pc(0)≈ 5.5 × 10 −16 M is he o al concen a ion o clus e s and k(0) is he concen a ion o k -me clus e s— Pc(0) and k(0) a e es ima ed om he ini ial DLS measu emen s. A a gi en ins an , he numbe o k -me clus e s joining o j -me ib ils is a unc ion o he ela i e amoun s o each ype o agg ega es, k→j=Pa× j P× k(0) Pc(0), (A11) meaning ha he concen a ions o isola ed ib ils ( 0 j) and isola ed clus e s ( 0 k) a e 0 j= j− ∞ ∑ k k→j, (A12) 0 k= k(0)− ∞ ∑ j k→j, (A13) and ha he concen a ion o he e ogeneous agglome a es composed by a o al lmonome s ( 1 l) is 1 l= ∞ ∑ k ∞ ∑ j k→jδk+j,l. (A14) He e, he K onecke del a unc ion is used o limi he sum e ms o he possible adhesion con ac s p oducing l-me agglome a es. Finally, he concen a ion o all l-me agg ega es ( l) is gi en as: l= 0 j=l+ 0 k=l+ 1 l, (A15) which can be used o compu e he heo e ical size dis ibu ions. I ollows om he p oposed one- o-one adhesion mechanism ha Pa= ∞ ∑ l 1 l, (A16) and ha he o al numbe o sca e ing pa icles co esponds o he concen a ion o he mos abundan species: ∞ ∑ l l=max(P,Pc(0)). (A17) The ollowing addi ional app oxima ions we e adop ed du ing he de i a ion o his model: (i) ib il elonga ion is una ec ed by he p esence o joined clus e s, (ii) complex adhesion pa hways a e no conside ed and (iii) he p esence o isola ed ib ils and isola ed clus e s is a necessa y and su icien condi ion o p oduc i e adhesion. O he mechanisms explaining he obse ed decline o he clus e popula ion a e admissible, e.g., by admi ing p og essi e clus e dissocia ion. The goal o desc ibing he expe imen al esul s in Figu e 4A–D could, howe e , be achie ed using p e iously de e mined alues o ka and kb (Figu e S3A–C) and adop ing he physical limi o pa icle de ec ion ( l> 1.6 × 10 −23 M) as he only adjus able pa ame e se o minimize he di e ences be ween he measu ed DLS da a and he heo e ical size dis ibu ions. Ma hwo ks ® MATLAB R2013b was used o nume ically sol ed Equa ion (A8) and Equa ions (A10)–(A15) o a cu -o size o isola ed insulin ib ils o n= 1 × 10 13 monome s. The ob ained l( ) p o iles we e con e ed in o in ensi y-based size Biomolecules 2018,8, 108 18 o 20 dis ibu ions ollowing he Rayleigh law o ligh sca e ing [ 17 ]. Impo an ly, he inal size dis ibu ions we e no signi ican ly a ec ed by he p esence o ini ial clus e s as indica ed by he simula ed esul s o Pc(0)=0 (Figu e S3D–F). Re e ences 1. Da id, B.; Haye -Ha l, M.; Ha l, F.U. In Vi o Aspec s o P o ein Folding and Quali y Con ol. Science 2016 , 353, aac4354. 2. Selkoe, D.J.; Ha dy, J. The Amyloid Hypo hesis o Alzheime ’s Disease a 25 yea s. EMBO Mol. Med. 2016 ,8, 595–608. [C ossRe ] [PubMed] 3. Wienke s, L.C.; Hea h, T.G. P edic ing In Vi o D ug In e ac ions om In Vi o D ug Disco e y Da a. Na . Re . D ug Disco . 2005,4, 825–833. [C ossRe ] [PubMed] 4. Kundel, F.; Tosa o, L.; Whi en, D.R.; Wi hensohn, D.C.; Ho ocks, M.H.; Klene man, D. Shedding Ligh on Abe an In e ac ions: A Re iew o Mode n Tools o S udying P o ein Agg ega es. FEBS J. 2018 . [C ossRe ] [PubMed] 5. B eydo, L.; U e sky, V.N. U e sky. S uc u al, Mo phological, and Func ional Di e si y o Amyloid Oligome s. FEBS Le . 2015,589, 2640–2648. [C ossRe ] [PubMed] 6. Young, L.M.; Ashc o , A.E.; Rad o d, S.E. Small Molecule P obes o P o ein Agg ega ion. Cu . Opin. Chem. Biol. 2017,39, 90–99. [C ossRe ] [PubMed] 7. Benilo a, I.; Ka an, E.; De S oope , B. The Toxic A β Oligome and Alzheime ’s Disease: An Empe o in Need o Clo hes. Na . Neu osci. 2012,15, 349–357. [C ossRe ] [PubMed] 8. Lee, S.J.; Nam, E.; Lee, H.J.; Sa elie , M.G.; Lim, M.H. Towa ds an Unde s anding o Amyloid- β Oligome s: Cha ac e iza ion, Toxici y Mechanisms, and Inhibi o s. Chem. Soc. Re . 2017 ,46, 310–323. [C ossRe ] [PubMed] 9. A osio, P.; Vend uscolo, M.; Dobson, C.M.; Knowles, T.P. Chemical Kine ics o D ug Disco e y o Comba P o ein Agg ega ion Diseases. T ends Pha macol. Sci. 2014,35, 127–135. [C ossRe ] [PubMed] 10. C espo, R.; Villa -Al a ez, E.; Taboada, P.; Rocha, F.A.; Damas, A.M.; Ma ins, P.M. Wha Can he Kine ics o Amyloid Fib il Fo ma ion Tell abou O -Pa hway Agg ega ion? J. Biol. Chem. 2016 ,291, 2018–2032. [C ossRe ] [PubMed] 11. Pad ick, S.B.; Mi anke , A.D. Isle Amyloid: Phase Pa i ioning and Seconda y Nuclea ion A e Cen al o he Mechanism o Fib illogenesis. Biochemis y 2002,41, 4694–4703. [C ossRe ] [PubMed] 12. C espo, R.; Rocha, F.A.; Damas, A.M.; Ma ins, P.M. A Gene ic C ys alliza ion-Like Model Tha Desc ibes he Kine ics o Amyloid Fib il Fo ma ion. J. Biol. Chem. 2012,287, 30585–30594. [C ossRe ] [PubMed] 13. Meisl, G.; Yang, X.; Hells and, E.; F ohm, B.; Ki kegaa d, J.B.; Cohen, S.I.; Dobson, C.M.; Linse, S.; Knowles, T.P. Di e ences in Nuclea ion Beha io Unde lie he Con as ing Agg ega ion Kine ics o he A β 40 and Aβ42 Pep ides. P oc. Na l. Acad. Sci. USA 2014,111, 9384–9389. [C ossRe ] [PubMed] 14. Meisl, G.; Ki kegaa d, J.B.; A osio, P.; Michaels, T.C.; Vend uscolo, M.; Dobson, C.M.; Linse, S.; Knowles, T.P. Molecula Mechanisms o P o ein Agg ega ion om Global Fi ing o Kine ic Models. Na . P o oc. 2016 ,11, 252–272. [C ossRe ] [PubMed] 15. Eden, K.; Mo is, R.; Gillam, J.; MacPhee, C.E.; Allen, R.J. Compe i ion be ween P ima y Nuclea ion and Au oca alysis in Amyloid Fib il Sel -Assembly. Biophys. J. 2015,108, 632–643. [C ossRe ] [PubMed] 16. Mo is, R.J.; Eden, K.; Ya wood, R.; Jou dain, L.; Allen, R.J.; MacPhee, C.E. Mechanis ic and En i onmen al Con ol o he P e alence and Li e ime o Amyloid Oligome s. Na . Commun. 2013 ,4, 1891. [C ossRe ] [PubMed] 17. Sil a, A.; Almeida, B.; F aga, J.S.; Taboada, P.; Ma ins, P.M.; Macedo-Ribei o, S. Dis ibu ion o Amyloid-Like and Oligome ic Species om P o ein Agg ega ion Kine ics. Angew. Chem. In . Ed. 2017 ,56, 14042–14045. [C ossRe ] [PubMed] 18. Finkels ein, A.V.; Do idchenko, N.V.; Galzi skaya, O.V. Wha is Responsible o A ypical Dependence o he Ra e o Amyloid Fo ma ion on P o ein Concen a ion: Fib il-Ca alyzed Ini ia ion o New Fib ils o Compe i ion wi h Oligome s? J. Phys. Chem. Le . 2018,9, 1002–1006. [C ossRe ] [PubMed] 19. Bane jee, S.; Sun, Z.; Hayden, E.Y.; Teplow, D.B.; Lyubchenko, Y.L. Nanoscale Dynamics o Amyloid β -42 Oligome s as Re ealed by High-Speed A omic Fo ce Mic oscopy. ACS Nano 2017 ,11, 12202–12209. [C ossRe ] [PubMed] Biomolecules 2018,8, 108 19 o 20 20. Nielsen, L.; F okjae , S.; B ange, J.; U e sky, V.N.; Fink, A.L. P obing he Mechanism o Insulin Fib il Fo ma ion wi h Insulin Mu an s. Biochemis y 2001,40, 8397–8409. [C ossRe ] [PubMed] 21. Bocian, W.; Si kowski, J.; Ta nowska, A.; Bedna ek, E.; Kaw e¸ cki, R.; Ko´zmi´nski, W.; Koze ski, L. Di ec Insigh in o Insulin Agg ega ion by 2D NMR Complemen ed by PFGSE NMR. P o eins S uc . Func . Bioin . 2008,71, 1057–1065. [C ossRe ] [PubMed] 22. Ves e gaa d, B.; G oenning, M.; Roessle, M.; Kas up, J.S.; Van De Wee , M.; Flink, J.M.; F okjae , S.; Gajhede, M.; S e gun, D.I. A Helical S uc u al Nucleus is he P ima y Elonga ing Uni o Insulin Amyloid Fib ils. PLoS Biol. 2007,5, e134. [C ossRe ] [PubMed] 23. Sca , C.A.; Almeida, B.; F aga, J.; Macedo-Ribei o, S.; Rad o d, S.E.; Ashc o , A.E. Examina ion o A axin-3 (A x-3) Agg ega ion by S uc u al Mass Spec ome y Techniques: A Ra ionale o Expedi ed Agg ega ion Upon Polyglu amine (polyQ) Expansion. Mol. Cell. P o eom. 2015,14, 1241–1253. [C ossRe ] [PubMed] 24. Ellisdon, A.M.; Thomas, B.; Bo omley, S.P. The Two-S age Pa hway o A axin-3 Fib illogenesis In ol es a Polyglu amine-Independen S ep. J. Biol. Chem. 2006,281, 16888–16896. [C ossRe ] [PubMed] 25. P o enche , S.W. A Cons ained Regula iza ion Me hod o In e ing Da a Rep esen ed by Linea Algeb aic o In eg al Equa ions. Compu . Phys. Comm. 1982,27, 213–227. [C ossRe ] 26. Fode a, V.; Lib izzi, F.; G oenning, M.; Van De Wee , M.; Leone, M. Seconda y Nuclea ion and Accessible Su ace in Insulin Amyloid Fib il Fo ma ion. J. Phys. Chem. B 2008,112, 3853–3858. [C ossRe ] [PubMed] 27. Se ano, A.L.; Lomon , J.P.; Tu, L.H.; Raleigh, D.P.; Zanni, M.T. A F ee Ene gy Ba ie Caused by he Re olding o an Oligome ic In e media e Con ols he Lag Time o Amyloid Fo ma ion by hIAPP. J. Am. Chem. Soc. 2017,139, 16748–16758. [C ossRe ] [PubMed] 28. Jaya aman, M.; Kodali, R.; Sahoo, B.; Thaku , A.K.; Mayasunda i, A.; Mish a, R.; Pe e son, C.B.; We zel, R. Slow Amyloid Nuclea ion Via α -Helix-Rich Oligome ic In e media es in Sho Polyglu amine-Con aining Hun ing in F agmen s. J. Mol. Biol. 2012,415, 881–899. [C ossRe ] [PubMed] 29. Knowles, T.P.; Waudby, C.A.; De lin, G.L.; Cohen, S.I.; Aguzzi, A.; Vend uscolo, M.; Te en je , E.M.; Welland, M.E.; Dobson, C.M. An Analy ical Solu ion o he Kine ics o B eakable Filamen Assembly. Science 2009,326, 1533–1537. [C ossRe ] [PubMed] 30. Be nacki, J.P.; Mu phy, R.M. Model Disc imina ion and Mechanis ic In e p e a ion o Kine ic Da a in P o ein Agg ega ion S udies. Biophys. J. 2009,96, 2871–2887. [C ossRe ] [PubMed] 31. Di le , J.A.; Maye , B.J.; Loew, L.M. The e Is Mo e Than One Way o Model an Elephan . Expe imen -D i en Modeling o he Ac in Cy oskele on. Biophys. J. 2013,104, 520–532. [C ossRe ] [PubMed] 32. Wang, G.; Fe sh , A.R. Mechanism o Ini ia ion o Agg ega ion o P53 Re ealed by Φ -Value Analysis. P oc. Na l. Acad. Sci. USA 2015,112, 2437–2442. [C ossRe ] [PubMed] 33. Lindbe g, D.J.; Wenge , A.; Sundin, E.; Wesén, E.; Wes e lund, F.; Esbjö ne , E.K. Binding o Thio la in-T o Amyloid Fib ils Leads o Fluo escence Sel -Quenching and Fib il Compac ion. Biochemis y 2017 ,56, 2170–2174. [C ossRe ] [PubMed] 34. Xue, C.; Lin, T.Y.; Chang, D.; Guo, Z. Thio la in-T as an Amyloid Dye: Fib il Quan i ica ion, Op imal Concen a ion and E ec on Agg ega ion. R. Soc. Open Sci. 2017,4, 160696. [C ossRe ] [PubMed] 35. Jeong, J.S.; Ansaloni, A.; Mezzenga, R.; Lashuel, H.A.; Die le , G. No el Mechanis ic Insigh in o he Molecula Basis o Amyloid Polymo phism and Seconda y Nuclea ion Du ing Amyloid Fo ma ion. J. Mol. Biol. 2013 , 425, 1765–1781. [C ossRe ] [PubMed] 36. Aga wal, V.; Pe e s, B. Solu e P ecipi a e Nuclea ion: A Re iew o Theo y and Simula ion Ad ances. In Ad ances in Chemical Physics: Volume 155; John Wiley & Sons, Inc.: Hoboken, NJ, USA, 2014; pp. 97–160. 37. Lomakin, A.; Chung, D.S.; Benedek, G.B.; Ki schne , D.A.; Teplow, D.B. On he Nuclea ion and G ow h o Amyloid Be a-P o ein Fib ils: De ec ion o Nuclei and Quan i a ion o Ra e Cons an s. P oc. Na l. Acad. Sci. USA 1996,93, 1125–1129. [C ossRe ] [PubMed] 38. Pa ma , A.S.; Go schall, P.E.; Muschol, M. P e-Assembled Clus e s Dis o C ys al Nuclea ion Kine ics in Supe sa u a ed Lysozyme Solu ions. Biophys. Chem. 2007,129, 224–234. [C ossRe ] [PubMed] 39. Fe ei a, C.; Ba bosa, S.; Taboada, P.; Rocha, F.A.; Damas, A.M.; Ma ins, P.M. The Nuclea ion o P o ein C ys als as a Race agains Time wi h On- and O -Pa hways. J. Appl. C ys . 2017,50, 1056–1065. [C ossRe ] 40. Yan, L.M.; Velko a, A.; Ta a ek-Nossol, M.; Rammes, G.; Sibae , A.; And ee o, E.; K acklaue , M.; Bakou, M.; Malideli, E.; Göke, B.; e al. Selec i ely N-Me hyla ed Soluble IAPP Mimics as Po en IAPP Recep o Agonis s and Nanomola Inhibi o s o Cy o oxic Sel -Assembly o Bo h IAPP and Aβ40. Angew. Chem. In . Ed. 2013, 52, 10378–10383. [C ossRe ] [PubMed] Biomolecules 2018,8, 108 20 o 20 41. Bi ol, M.; Kuma , S.; Rhoades, E.; Mi anke , A.D. Con o ma ional Swi ching wi hin Dynamic Oligome s Unde pins Toxic Gain-o -Func ion by Diabe es-Associa ed Amyloid. Na . Commun. 2018 ,9, 1312. [C ossRe ] [PubMed] 42. Ke, P.C.; Sani, M.A.; Ding, F.; Kakinen, A.; Ja ed, I.; Sepa o ic, F.; Da is, T.P.; Mezzenga, R. Implica ions o Pep ide Assemblies in Amyloid Diseases. Chem. Soc. Re . 2017,46, 6492–6531. [C ossRe ] [PubMed] 43. Se igny, J.; Chiao, P.; Bussiè e, T.; Wein eb, P.H.; Williams, L.; Maie , M.; Duns an, R.; Salloway, S.; Chen, T.; Ling, Y.; e al. The An ibody Aducanumab Reduces A β Plaques in Alzheime ’s Disease. Na u e 2016 ,537, 50–56. [C ossRe ] [PubMed] 44. Schenk, D.B.; Kolle , M.; Ness, D.K.; G i i h, S.G.; G undman, M.; Zago, W.; So o, J.; A iee, G.; Os owi zki, S.; Kinney, G.G. Fi s -in-Human Assessmen o PRX002, an An i— α -Synuclein Monoclonal An ibody, in Heal hy Volun ee s. Mo . Diso d. 2017,32, 211–218. [C ossRe ] [PubMed] 45. Ma ins, P.M. T ue and Appa en Inhibi ion o Amyloid Fib il Fo ma ion. P ion 2013 ,7, 136–139. [C ossRe ] [PubMed] 46. Collins, S.R.; Douglass, A.; Vale, R.D.; Weissman, J.S. Mechanism o P ion P opaga ion: Amyloid G ow h Occu s by Monome Addi ion. PLoS Biol. 2004,2, e321. [C ossRe ] [PubMed] © 2018 by he au ho s. Licensee MDPI, Basel, Swi ze land. This a icle is an open access a icle dis ibu ed unde he e ms and condi ions o he C ea i e Commons A ibu ion (CC BY) license (h p://c ea i ecommons.o g/licenses/by/4.0/).