cells Article pH-Dependent Aggregation in Intrinsically Disordered Proteins Is Determined by Charge and Lipophilicity Jaime Santos 1,† , Valentín Iglesias 1,† , Juan Santos-Suárez 2 , Marco Mangiagalli 3 , Stefania Brocca 3 , Irantzu Pallarès 1 and Salvador Ventura 1, * 1 Institut de Biotecnologia i Biomedicina and Departament de Bioquímica i Biologia Molecular, Universitat Autònoma de Barcelona, 08193 Barcelona, Spain; jaime.santos@uab.es (J.S.); valentin.iglesias@uab.cat (V.I.); irantzu.pallares@uab.es (I.P.) 2 Galicia Supercomputing Center (CESGA), 15705 Santiago de Compostela, A Coruña, Spain; juansans98@gmail.com 3 Department of Biotechnology and Biosciences, University of Milano-Bicocca, 20126 Milano, Italy; marco.mangiagalli@unimib.it (M.M.); stefania.brocca@unimib.it (S.B.) * Correspondence: salvador.ventura@uab.es † These authors contributed equally to this work.  Received: 15 December 2019; Accepted: 6 January 2020; Published: 8 January 2020  Abstract: Protein aggregation is associated with an increasing number of human disorders and premature aging. Moreover, it is a central concern in the manufacturing of recombinant proteins for biotechnological and therapeutic applications. Nevertheless, the unique architecture of protein aggregates is also exploited by nature for functional purposes, from bacteria to humans. The relevance of this process in health and disease has boosted the interest in understanding and controlling aggregation, with the concomitant development of a myriad of algorithms aimed to predict aggregation propensities. However, most of these programs are blind to the protein environment and, in particular, to the influence of the pH. Here, we developed an empirical equation to model the pH-dependent aggregation of intrinsically disordered proteins (IDPs) based on the assumption that both the global protein charge and lipophilicity depend on the solution pH. Upon its parametrization with a model IDP, this simple phenomenological approach showed unprecedented accuracy in predicting the dependence of the aggregation of both pathogenic and functional amyloidogenic IDPs on the pH. The algorithm might be useful for diverse applications, from large-scale analysis of IDPs aggregation properties to the design of novel reversible nanofibrillar materials. Keywords: intrinsically disordered proteins; protein aggregation; protein solubility; amyloids; bioinformatics 1. Introduction Protein aggregation is an inherent feature of polypeptides that lies behind the onset of a wide range of human pathologies, including Alzheimer’s and Parkinson’s diseases or type II diabetes [1,2]. Moreover, aggregation often occurs during protein recombinant production and downstream processing, becoming a major bottleneck for the marketing of protein-based drugs [3,4]. Indeed, polypeptides are susceptible to suffering aggregation at every step during protein production, from recombinant expression and purification to formulation and storage [4]. This implies a constant monitorization and optimization of production conditions and processes, which is costly and time-consuming. However, protein aggregation is not always deleterious, and organisms exploit the particular properties of amyloid protein assemblies for beneficial purposes [5–7]. This evidence has inspired the use of Cells 2020, 9, 145; doi:10.3390/cells9010145 www.mdpi.com/journal/cells Cells 2020, 9, 145 2 of 14 aggregation-prone proteins and peptides to build up functionalized nanofibrils with applications in tissue engineering, drug delivery or as nanowires and nanosensors [8–11]. The development of in silico tools able to predict protein aggregation propensities has provided scientists with a versatile toolbox to assist and guide basic research and protein engineering processes [12]. These algorithms exploit the evidence that protein aggregation is driven by short and specific stretches, known as aggregation-prone regions (APRs), displaying unique physicochemical features: low net charge, high hydrophobicity and, frequently, a preference for β-sheet secondary structure [13]. AGGRESCAN, Amylpred, Amyloid Mutants, FoldAmyloid, MetAmyl, PASTA, Tango, Waltz and Zyggregator [14–23] are some examples of this kind of program. However, most of these prediction methods are blind to the protein environment, despite being well known that factors like temperature, ionic force or pH dramatically impact protein aggregation. Regarding pH, many protein products are purified, stored or formulated at pHs different from 7.0, the default pH in these algorithms. In particular, > 65% of antibodies, Fc fusion products and Fab conjugates are formulated at pH < 6.5 [24,25]. Therefore, it is surprising that, despite the vast experimental data supporting the modulation of intrinsic protein aggregative properties by the solution pH, such an effect has been essentially disregarded in computational approaches [26]. Among the different intrinsic protein properties that can contribute to protein aggregation, hydrophobicity plays a major role. Indeed, APRs usually comprise highly hydrophobic sequence stretches [27,28] and mutations of polar residues to nonpolar ones exacerbate aggregation [29], whereas changes in the opposite direction promote solubility. Therefore, it is not surprising that hydrophobicity is given a major weight, directly or indirectly, in the different equations implemented in sequence-based aggregation predictors [13,30]. Of note, all the aforementioned algorithms assume that the lipophilicity of the sequence is independent of the pH. However, it is well known that the partition coefficients of the neutral and charged species of ionizable amino acids, and therefore their hydrophobicity, depend on the pH of the solution [31,32]. Moreover, the electrostatic properties of proteins, i.e., their net charge in a given solution, are also connected to the solution pH, being important determinants of protein solubility [33,34]. To the best of our knowledge, we present here the first approach to predict how the relative aggregation propensity of a given protein changes with the solution pH. Towards this objective, we exploited a recently developed, pH-dependent lipophilicity scale of amino acids [35] and implemented a simple phenomenological equation that considers the effect of the pH on both the net charge and the lipophilicity of a protein sequence. We assayed the approach on top of intrinsically disordered proteins (IDPs), which lack defined secondary structure elements, to exclude any interference on calculations coming from structural constrains. Our approach accurately predicts the impact of the pH on the aggregation properties of well-known human disease-linked proteins like α-synuclein (α-S), Aβ-40, the islet amyloid polypeptide (IAPP) and the tau K19 variant, as well as in biologically relevant functional amyloids such as the melanosomal protein Pmel17, the B domain of the Bap protein and the corticotropin-releasing hormone, which indicates that it might find general application in the prediction of the pH-dependent aggregation properties of IDPs. 2. Materials and Methods 2.1. Generation of Lipophilicity Profiles The pH-dependent lipophilicity scale developed by Zamora and coworkers [35] using continuum solvation calculations was employed to infer the lipophilicity of each individual amino acid at the analyzed pH. Our algorithm employs a sliding window system, as previously described for the AGGRESCAN software, to generate the lipophilicity profile of any given protein [14]. Briefly, the program calculates the average lipophilicity of a sliding window and assigns this value to the amino acid in the center of the window. The size of the window is defined in relation with the protein length: 5 residues for proteins shorter than 75 amino acids, 7 for longer than 75 but shorter than 175, 9 for Cells 2020, 9, 145 3 of 14 longer than 175 but shorter than 300 and 11 for longer than 300. The resulting values can be employed to build/draw a lipophilicity profile along the protein sequence or to calculate a mean value of global protein lipophilicity. 2.2. Solubility Modelling The experimental data was obtained from Tedeschi et al. [33]. The pH-dependent experimental solubility of a model IDP was used as training set to parameterize a function that describes protein solubility as a function of pH. We selected two variables to model protein solubility: pH-dependent lipophilicity and net charge. pH-dependent lipophilicity was calculated as the average of the lipophilicity profile. Protein net charge was determined using the protein calculator v3.4 server [36] run at the selected pH. These theoretical values were parameterized against the solubility experimental data using Equation (1): Solubility = α × Lipophilicity + β × |Net Charge|2 + γ × |Net Charge| + δ, (1) For the parameterization we employed the non-linear least squares approach of the Scipy Python module, being able to define the α, β, γ and δ parameters in Equation (1). Different aggregation studies measure different parameters, from strict solubility to kinetic aggregation constants. To allow comparison between our predictions and the different experimental data, protein solubility is defined here as the inverse of the protein aggregation propensity in a given condition and not as a thermodynamic property of the protein solution. 2.3. Data Analysis and Fitting Kinetic constants for pH-dependent α-S aggregation at 37 ◦ C were obtained from Finke and Morris and Uverski and co-workers [37,38]. Fibrillation rates of IAPP at 25 ◦ C were previously reported by Alexandrescu and colleagues [39]. Tau K19 amyloid formation data at 37 ◦ C was extracted from Jeganathan and co-workers [40]. Data on Aβ40 solubility at 20 ◦ C and different pHs were obtained from Fändrich and co-workers [41]. Data on the effect of pH on functional amyloids were extracted from references [42–44]. Linear regression analysis was performed using Graphpad Prism 6. Tendency line and 95% confidence interval were plotted, and regression r-square was added to the graph. For linear regressions, a two-tailed p-value was calculated [45]. 3. Results 3.1. Rational Analysis of the Molecular Determinants behind pH-Associated Aggregation In order to develop a new theoretical model that can forecast the effect of pH on protein aggregation, we exploited our previous work on the N-terminus moiety of the measles virus phosphoprotein (PNT), an IDP model whose aggregation propensity was deeply analyzed in relation to pH and its net charge [33]. We engineered three PNT variants displaying different net charges and isoelectric points (pI) by reversing the sign of charged residues already present in the wild-type sequence, without mutating any other PNT residue (Figure 1A–D and Figure S1). In detail, the acidic PNT has a pI of 3.37 and includes 62 negatively charged residues while basic PNT has a pI of 9.61 and includes 37 positively charged and 23 negatively charged residues. Attempts to produce more basic PNTs, with further unbalanced composition, were unsuccessful. The solubility of each of these protein variants was assessed experimentally across a wide range of pH levels, thus generating an ideal dataset to parametrize a function intended to predict the pH-dependent aggregation propensity of protein sequences [33]. Although unmodified at their apolar residues, our PNT variants exhibit different lipophilicity at neutral pH, since they differ in the identity of the charged amino acids (Figure 1E). In addition, because the hydrophobicity of ionizable amino acids is dependent on the pH, the global protein lipophilicity (average lipophilicity score) in acidic or basic conditions might differ significantly from that calculated at pH 7.0 and this parameter should be taken into account together with the net charge Cells 2020, 9, 145 4 of 14 of the polypeptide when forecasting protein solubility. (A) (B) (C) Charged residues 1 13 25 37 49 61 73 85 97 9 131 143 155 7 9 191 203 5 7 9 251 3 1 13 25 37 49 61 73 85 97 129 1 3 5 167 9 1 3 215 7 9 1 3 1 13 25 37 49 61 73 85 97 9 1 3 155 7 9 1 3 5 7 9 1 3 10 12 16 18 21 22 24 10 13 14 15 18 19 20 22 24 25 10 12 13 14 16 18 19 20 21 22 24 25 Residue Residue Residue (D) (E) -0.35 wt-PNT Average lipophilicity score -0.30 Acidic-PNT -0.25 Basic-PNT -0.20 0 5 10 wt-PNT Acidic-PNT Basic-PNT Isoelectric point (pH) Figure 1. Figure Propertiesofof 1. Properties N-terminus N-terminus moiety moiety of the of the measles measles virus virus phosphoprotein phosphoprotein (PNT)(PNT) variants. variants. (A– (A–C) Scheme of charge distribution in wild-type PNT, acidic PNT and basic PNT. Positive C) Scheme of charge distribution in wild-type PNT, acidic PNT and basic PNT. Positive and negative and negative residues are represented in blue and red, respectively. (D) Isoelectric points of PNT residues are represented in red and blue, respectively. (D) Isoelectric points of PNT variants. (E) variants. (E) Average Average lipophilicity lipophilicity of PNT of PNT variants variants at pH at pH 7.0.7.0. Due to the lack of a well-defined 3D structure, one can hypothesize that the physicochemical 3.2. Analysis and Validation of the Lipophilicity Scale as a Proxy for Aggregation Prediction determinants of pH-dependent aggregation of IDPs are directly encoded in their amino acid sequence. To explore We propose the relationship lipophilicity between amino (hydrophobicity) acid and net lipophilicity, charge pH, properties as the main and protein aggregation, accounting for we the exploited differentiala pH-dependent amino acid aggregation propensity lipophilicity of any scaleatrecently given protein derived different by Zamora pH levels. One canand co-workers argue that this [35]. We compared is a rather simplisticthe lipophilicity approach, score ofmethodologies but existing each amino acid at physiological only pHcharge consider the net (pH 7.4) with their contribution, in vivo-derived while they overlook experimental aggregation coefficient [15,46]. We observed a highly significant the role of lipophilicity. correlation Althoughbetween aggregation unmodified and at their lipophilicity apolar residues,(p-value our PNT < 0.00001) variants(Figure exhibit 2A). This lipophilicity different is expected, since hydrophobic side chains play a determinant role in aberrant protein self-assembly at neutral pH, since they differ in the identity of the charged amino acids (Figure 1E). In addition, [47]. Next, because wehydrophobicity the compared the lipophilicity of ionizableprofile aminoofacids threeiswell-characterized dependent on thedisease-related pH, the globalproteins protein (Aβ40, α-S (average lipophilicity and IAPP) at physiological lipophilicity pH with score) in acidic their or basic aggregation conditions mightprofile generated with differ significantly from AGGRESCAN [12]. AGGRESCAN is an in-house developed algorithm, which that calculated at pH 7.0 and this parameter should be taken into account together with the net charge implements the aforementioned of the polypeptide in when vivo derived aggregation forecasting propensity amino acid scale and stands as one of the protein solubility. most reliable algorithms to predict protein aggregation in close to in vivo conditions [48]. The 3.2. Analysis and lipophilicity and Validation aggregation of the Lipophilicity profiles Scale of all the as aproteins three Proxy forareAggregation Prediction (Figure 2B–D), in close agreement indicating that, atthe To explore constant pH, the relationship lipophilicity between aminocanacidbe lipophilicity, used as a proxy pH,ofand aggregation propensity. protein aggregation, Although other physicochemical determinants are certainly involved we exploited a pH-dependent amino acid lipophilicity scale recently derived by Zamora and in protein aggregation, we assume co-workershere[35]. that they have less the We compared impact than lipophilicity lipophilicity score of eachor charge aminoon pH-modulated acid at physiological protein pH aggregation. (pH 7.4) with their in vivo-derived experimental aggregation coefficient [15,46]. We observed a highly significant correlation between aggregation and lipophilicity (p-value < 0.00001) (Figure 2A). This is expected, since hydrophobic side chains play a determinant role in aberrant protein self-assembly [47]. Next, we compared the lipophilicity profile of three well-characterized disease-related proteins (Aβ40, α-S and IAPP) at physiological pH with their aggregation profile generated with AGGRESCAN [12]. AGGRESCAN is an in-house developed algorithm, which implements the aforementioned in vivo derived aggregation propensity amino acid scale and stands as one of the most reliable algorithms to predict protein aggregation in close to in vivo conditions [48]. The lipophilicity and aggregation profiles of all the three proteins are in close agreement (Figure 2B–D), indicating that, Cells 2020, 9, 145 5 of 14 at constant pH, the lipophilicity can be used as a proxy of aggregation propensity. Although other physicochemical determinants are certainly involved in protein aggregation, we assume here that they have Cells less 2020,impact 10, x than lipophilicity or charge on pH-modulated protein aggregation. 5 of 14 (A) (B) R2 = 0.78 5 Phe Trp 2 Lipohilicity pH 7.4 Arbitrary score Ile Pro Cys Leu Ala Met Tyr Val Gly 0 Thr Gln Asn Ser His Lys 0 Glu Asp Arg -5 -2 -2 -1 0 1 2 5 10 15 20 25 30 35 40 Relative experimental aggregation propensity Residue (C) (D) 1 2 Arbitrary score Arbitrary score 1 0 0 -1 -1 10 20 30 40 50 60 70 80 90 100 110 120 130 140 5 10 15 20 25 30 35 Residue Residue Figure2.2.Lipophilicity-based Figure Lipophilicity-basedprediction predictionaggregation aggregationpropensity propensityatatpHpH7.4 7.4against againsta astate-of-the-art state-of-the-art aggregation predictor. (A) Linear correlation between amino acids in vivo aggregation propensity,as aggregation predictor. (A) Linear correlation between amino acids in vivo aggregation propensity, asimplemented implementedininAGGRESCAN AGGRESCAN[15,46], [15,46], and and their their lipophilicity lipophilicity at at pH pH7.4. 7.4.(B–D) (B–D)Overlap Overlapbetween between AGGRESCAN-derived (dashed line) aggregation profiles and lipophilicity profiles (solid line) from AGGRESCAN-derived (dashed line) aggregation profiles and lipophilicity profiles (solid line) from Aβ40, α-S and IAPP, respectively. Aβ40, α-S and IAPP, respectively. 3.3. Modelling pH-Dependent Solubility usIng Lipophilicity and Net Charge 3.3. Modelling pH-Dependent Solubility usIng Lipophilicity and Net Charge We next sought to build a model to determine the role of lipophilicity and net charge on We next sought pH-dependent protein to build a model aggregation. to determine For each data pointthefrom roleour of lipophilicity previous study andwith net charge the PNTs,on wepH- dependent calculated theprotein proteinaggregation. net charge and Forthe each dataprotein overall point from our previous lipophilicity using astudy sliding with the PNTs, window system we calculated the protein net charge and the overall protein lipophilicity using a analogous to that in AGGRESCAN [14]. Therefore, each data point is defined by its lipophilicity, netsliding window system analogous charge to that in AGGRESCAN and experimental [14]. Therefore, solubility, allowing each data point their representation as is defined a 3-axis by itsplot. scatter lipophilicity, The visual net charge and inspection experimental of their solubility, reveals spatial distribution allowing their representation a dispersion that resemblesas a a3-axis scatter quadratic 3Dplot. The Since surface. visual inspection of their spatial distribution reveals a dispersion that resembles the distribution shows significant smoothness, we hypothesized that it could be modelled using a a quadratic 3D surface. Since theapproximated function distribution shows significant by a Taylor seriessmoothness, truncated at wesecond hypothesized order for that theit could be modelled net charge and at using first a function approximated by a Taylor series truncated at second order for order for the lipophilicity. Thus, we defined an empirical formula (Equation (1)) that describesthe net charge and at first a order for bivariate the lipophilicity. polynomial model withThus, we defined a quadratic an empirical component, formula suitable (Equation to address (1)) that regression a 3D-surface describes a inbivariate polynomial our dataset. Next, tomodel with a quadratic parameterize component, this equation, suitable we applied to addressleast a non-linear a 3D-surface regression squares approach. As a result of the fitting, we calculated parameters α, β, γ and δ (Table 1). The resultingapproach. in our dataset. Next, to parameterize this equation, we applied a non-linear least squares model, built using Equation (1), delineates a 3D surface, where the solubility is defined as a functionbuilt As a result of the fitting, we calculated parameters α, β, γ and δ (Table 1). The resulting model, of using net Equation charge (1), delineates and lipophilicity a 3D surface, (Figure where thethe 3A). Remarkably, solubility values is definedfrom derived as a the function of net equation charge show a and lipophilicity significant (Figure correlation with3A). the Remarkably, the values observed solubility dataderived (Figure from the equation 3B) (p-value show In < 0.00001). a significant contrast, correlation with the observed solubility data (Figure 3B) (p-value < 0.00001). In contrast, a mere a mere charge-dependent model, as the one implemented in competing approaches, fail to predict charge-dependent model, as the one implemented in competing approaches, fail to predict the the experimental behavior of the dataset (p-value < 0.1) (Figure S2). Overall, these results reinforce experimental behavior of the dataset (p-value < 0.1) (Figure S2). Overall, these results reinforce the hypothesis that pH-induced lipophilicity fluctuations should be taken into consideration for an accurate prediction of protein aggregation. Cells 2020, 9, 145 6 of 14 the hypothesis that pH-induced lipophilicity fluctuations should be taken into consideration for an accurate prediction of protein aggregation. Table 1. Fitting parameters resulting from the non-linear least squares parametrization. Parameter α β γ δ Cells 2020, 10, x Values −97.82 −0.00747 0.8770 38.24 6 of 14 (A) (B) R2 = 0.70 100 Predicted solubility 50 0 0 50 100 Experimental solubility Figure 3. Modeling intrinsically disordered proteins (IDP) pH-dependent solubility based on Figure 3. Modeling intrinsically disordered proteins (IDP) pH-dependent solubility based on lipophilicity and net charge. (A) Experimental pH-dependent solubility modeled as a 3D surface lipophilicity and net charge. (A) Experimental pH-dependent solubility modeled as a 3D surface plot. plot. Experimental data from our previous work is represented as blue dots, and the 3D surface Experimental data from our previous work is represented as blue dots, and the 3D surface resultant resultant from modeling is colored as a heat map, according to the corresponding predicted solubility from modeling is colored as a heat map, according to the corresponding predicted solubility as as represented in the color bar. (B) Correlation between the experimental and predicted solubility. Solid represented in the color bar. (B) Correlation between the experimental and predicted solubility. Solid line corresponds to the fit of the data to a linear regression with a p-value < 0.00001. line corresponds to the fit of the data to a linear regression with a p-value < 0.00001. 3.4. pH-Dependent Aggregation Prediction in Disease-Linked Proteins Table 1. Fitting parameters resulting from the non-linear least squares parametrization. As a proof of principle of the predictive performance of the approach, we tested our charge Parameter and lipophilicity-dependent α model β in a set of well-characterized γ linked with conformational IDPs δ Values −97.82 −0.00747 0.8770 38.24 diseases. As discussed, IDPs represent an ideal test set for our model since they allow us to consider almost exclusively the contribution of primary structure on aggregation, excluding the folding and 3.4. pH-Dependent protein Aggregation Prediction stability contributions. in Disease-Linked The obtained pH-dependent Proteins aggregation profile for each protein was compared with available experimental data in the literature by As a proof of principle of the predictive performance of the assessing the we approach, linear regression tested between our charge and experimental and predicted solubility values. lipophilicity-dependent model in a set of well-characterized IDPs linked with conformational diseases. As discussed, IDPs represent an ideal test set for our model since they allow us to consider 3.4.1. α-Synuclein (α-S) almost exclusively the contribution of primary structure on aggregation, excluding the folding and Parkinson’s protein disease (PD) isThe stability contributions. theobtained second most prevalent neurodegenerative pH-dependent aggregation profiledisorder. Brains from for each protein was PD patients exhibit the recurrent presence of intracellular proteinaceous aggregates, compared with available experimental data in the literature by assessing the linear regression mainly composed by α-S. These between deposits,and experimental known as Lewy predicted bodies, represent solubility values. the main neuropathological hallmark of the disease and are responsible for eliciting cellular toxicity and causing neuronal death [49–51]. From a 3.4.1. α-Synuclein molecular (α-S) α-S is a 140-residues IDP, highly expressed in the synapses of dopaminergic perspective, neurons that has been Parkinson’s shown disease (PD)toisassemble in vitro the second mostinto amyloid prevalent fibrils under different neurodegenerative conditions disorder. [52–54]. Brains from Owing to the connection between α-S and PD, there is a great interest to PD patients exhibit the recurrent presence of intracellular proteinaceous aggregates, mainly explore the determinants of α-S aggregation. composed by α-S.In that context, These Uversky deposits, and co-workers known described as Lewy bodies, the effect represent theofmain pH onneuropathological α-S solubility [38]; later on, Finke and Morris fitted the data into formal aggregation kinetic hallmark of the disease and are responsible for eliciting cellular toxicity and causing neuronalequations [37]. To assess death whether [49–51]. From a molecular perspective, α-S is a 140-residues IDP, highly expressed in the synapsesthe the effect of pH on α-S aggregation could be anticipated by our equation, we compared of predicted dopaminergic α-S solubility withhas neurons that the been experimental shown to aggregation assemble in kinetic vitro data parameters into amyloid across fibrils a wide under range different of pHs. We[52–54]. conditions found an excellent Owing to thecorrelation connection between between ourα-Spredicted and PD,solubility there is a and greatboth the elongation interest to explore the determinants of α-S aggregation. In that context, Uversky and co-workers described the charged constants and latency times of the reaction (Figure 4). Remarkably, in α-S the majority of the effect of residues pH on α-S aresolubility segregated[38];inlater the C-terminal on, Finke and of the protein, Morris fittedwhile the into the data hydrophobicity is clustered formal aggregation in kinetic equations [37]. To assess whether the effect of pH on α-S aggregation could be anticipated by our equation, we compared the predicted α-S solubility with the experimental aggregation kinetic data parameters across a wide range of pHs. We found an excellent correlation between our predicted solubility and both the elongation constants and latency times of the reaction (Figure 4). Remarkably, in α-S the majority of the charged residues are segregated in the C-terminal of the protein, while the Cells 2020, 9, 145 7 of 14 Cells 2020, 10, x 7 of 14 its central NAC domain; such dual distribution does not seem to compromise the performance of Cellsapproach. the 2020, 10, x 7 of 14 (A) (B) 80 80 (A) R2 = 0.82 (B) R2 = 0.87 80 80 70 70 7.23 R2 = 0.82 R2 =7.23 0.87 5.82 5.82 Predicted solubility Predicted solubility 70 70 8.52 60 8.52 60 7.23 7.23 5.82 5.82 Predicted solubility Predicted solubility 8.52 60 8.52 60 50 50 2.79 2.79 4.08 4.08 1.92 1.92 50 50 40 2.79 40 2.79 4.08 4.08 1.92 1.92 40 40 30 30 0.0 0.5 1.0 0 10 20 30 Kapp (h-1) Latency time (h) 30 30 0.0 0.5 1.0 0 10 20 30 Figure 4. Prediction of experimental Kapp (h-1) α-synuclein (α-S) aggregation kinetic constants. Latency time (h) Correlation between the elongation constant Kapp (A) and latency time (B) and the predicted protein solubility Figure 4. 4. Prediction Predictionofofexperimental experimental α-synuclein (α-S)(α-S) α-synuclein aggregation kinetickinetic aggregation constants. Correlation constants. between Correlation at different pH (1.92, 2.79, 4.08, 5.82, 7.23, 8.52). Experimental data were extracted from Morris and the elongation between constant Kapp the elongation constant(A) and Kapplatency timelatency (A) and (B) andtime the predicted protein (B) and the solubility predicted at different protein pH solubility Finke’s work [37]. Each point represents an experimental datum labelled with its corresponding pH. (1.92, 2.79, 4.08, 5.82, 7.23, 8.52). Experimental data were extracted from Morris and at different pH (1.92, 2.79, 4.08, 5.82, 7.23, 8.52). Experimental data were extracted from Morris and Finke’s work [37]. A linear regression (solid line) and its 95% confidence interval (dashed line) were applied to fit the Each Finke’spoint work represents [37]. Eachanpoint experimental represents datum labelled withdatum an experimental its corresponding labelled withpH. A linear regression its corresponding pH. data with a p-value < 0.05 for Kapp and < 0.01 for latency time. (solid line) A linear and its 95% regression confidence (solid line) and interval (dashed its 95% line) were confidence applied interval to fit the (dashed data line) werewith a p-value applied < 0.05 to fit the for dataKapp withand < 0.01