Multivariate Analyses of Amyloid-Beta Oligomer Populations Indicate a Connection between Pore Formation and Cytotoxicity

Aggregates of amyloid-beta (Aβ) peptides are thought to be involved in the development of Alzheimer’s disease because they can change synaptic plasticity and induce neuronal cell death by inflammation, oxidative damage, and transmembrane pore formation. Exactly which oligomeric species underlie these cytotoxic effects remains unclear. The work presented here established well-controlled aggregation conditions of Aβ 1–40 or Aβ1–42 peptides over a 20-day period and characterized these preparations with regard to their β-sheet content, degree of fibril formation, relative abundance of various oligomer sizes, and propensity to induce membrane pore formation and cytotoxicity. Using this multivariate data set, a systematic and inherently unbiased partial least squares (PLS) approach showed that for both peptides the abundance of oligomers in the tetramer to 13-mer range contributed positively to both pore formation and cytotoxicity, while monomers, dimers, trimers, and the largest oligomers (>210 kDa) were negatively correlated to both phenomena. Multivariate PLS analysis is ideally suited to handle complex data sets and interdependent variables such as relative oligomer concentrations, making it possible to elucidate structure function relationships in complex mixtures. This approach, therefore, introduces an enabling tool to the field of amyloid research, in which it is often difficult to interpret the activity of individual species within a complex mixture of bioactive species.

Pore formation by Ab is one plausible mechanism for toxicity and for antimicrobial peptide (AMP) activity [48], since oligomeric Ab binds to lipid membranes [49,50] and since Ab-induced pores could result in aberrant flux of Ca 2+ ions and cause cell death [6,22,[51][52][53][54][55]. For instance, Soscia et al. showed recently that Ab acts as an AMP against eight clinically relevant microorganisms and that brain homogenates of AD patients were significantly more antimicrobial than homogenates from age-matched control samples [48]. Various biochemical, biophysical, and computational techniques have indicated a range of aggregated Ab species that could potentially induce pores or form ion channel-like structures in artificial lipid bilayers and in neuronal membranes [54,[56][57][58][59]. For instance, Jang et al. performed molecular dynamics (MD) simulations and proposed that 16-to 24-mers of Ab arrange into pore-like structures [60], which are compatible with the dimensions and shape of putative Ab pore structures obtained from atomic force microscopy (AFM) [61,62]. In two separate MD studies, Strodel et al. identified tetramers or hexamers as the most stable structures that could form Ab pores [63], while Shafrir et al.
suggested that Ab pores contain assemblies of six hexamers (i.e. a 36-mer) [64]. Based on mass spectrometry, Pan et al. recently revealed b-barrels of tetrameric Ab 1-40 peptides arranged in antiparallel b-turn-b motifs [65]. Demuro et al. demonstrated on Xenopus oocytes that Ab 1-42 oligomers in the range from 5-to 40mers caused Ca 2+ flux that was independent of endogenous ion channels [44]. Schauerte et al. combined single molecule fluorescence microscopy with ion current recordings and reported that hexamers were the smallest oligomeric Ab structure that could permeabilize lipid membranes, while 12-to 14-mers resulted in pores with the largest conductivity for ions [66]. This work is particularly relevant since it was carried out with Ab concentrations in the nanomolar range and, therefore, close to the concentrations of Ab observed in human brains [67]. In addition, assays with liposomes showed dye leakage in the presence of Ab oligomers and reduced leakage in the presence of fibrils [49]. Laganowsky et al. showed recently that a segment of the amyloidforming protein ab crystallin can form cylindrical barrels with an open central channel from six antiparallel proteins and that this socalled cylindrin structure is compatible with a sequence element from Ab [68]b Lashuel et al. showed by electron microscopy that a mutant version of Ab that is associated with early-onset Alzheimer's disease, called Ab ARC , formed pore-like assemblies from 40 to 60 monomers [69], while recent X-ray diffraction and electron microscopy studies showed that these pore-like assemblies may be formed by 20-mers of Ab 1-42 with cross-b architecture [70].
Here, we established a well-controlled and reproducible preparation method to form Ab aggregates over 0, 1, 2, 3, 10 and 20 days in water. We examined the ability of these populations to form ion pores in planar lipid bilayers and separately quantified their cytotoxic effects on a human neuroblastoma cell line. For each time point during the aggregation process, we quantified the relative abundance of different Ab oligomers and correlated individual oligomer levels with pore formation and toxicity data as well as with b-sheet content and degree of fibrillization. We carried out all assays with the same Ab preparation at each time point in order to enable a systematic study of cross-correlation of abundance of oligomer species in two Ab preparations (Ab 1-40 and Ab 1-42 ) with the propensity of the same preparations to form pores and cause cell death. To make this analysis quantitative, we adopted a partial least squares (PLS) approach and found that cytotoxicity and pore formation have identical dependencies on the oligomer distribution, supporting a causative relationship between these phenomena.

Results and Discussion
Probability of Pore Formation is Maximal after Incubating Ab Samples for 2-3 Days Figure 1 illustrates that both Ab 1-40 and Ab 1-42 caused channellike ion flux across planar lipid bilayers that could be inhibited by Zn 2+ ions, as reported previously [51,53,54,61,62,[71][72][73][74][75][76][77][78]. The conductance values of these recorded current modulations were not well defined and typically ranged from 80 pS to 0.8 nS, while their open pore lifetimes ranged from milliseconds to several minutes as reported previously [79]. These biophysical characteristics of Ab-induced transmembrane current flux suggest that Ab may either self-assemble to a transmembrane protein pore, reminiscent of ion channel proteins [71] or Ab may interact with lipid membranes [49,50,80] and induce defects in the membrane, reminiscent of certain antimicrobial peptides [48,54,67]. It is also possible that both mechanisms act in parallel. In the context of this work, we chose the terminology ''Ab-induced ion flux'' or ''pore formation'' in order to include both possibilities.
Since aggregation conditions affect the aggregation kinetics and potentially the morphology of Ab aggregates, we compared five different aggregation methods of Ab samples from various suppliers for their ability to form pores in planar lipid bilayers (Supporting Information, Table S1, Methods A-E and Figure S1, S2, and S3). Among these methods, we selected incubation of Ab samples in water for 0 to 20 days (Method A) because it made it possible to study the effects of Ab aggregation on pore formation over time while being compatible with assays for cytotoxicity, CD spectroscopy, and ThT fluorescence assays (see Supporting Information Section S2.2 for a comparison and discussion of these five methods for Ab aggregation). Fig. 2A shows that the probability of pore formation was highest when Ab samples were pre-incubated in water for 2-3 d in the case of Ab 1-40 or for 2 d in the case of Ab  . In contrast, pore formation was least likely when Ab samples were pre-incubated for 0 d or 20 d. With regard to the biophysical characteristics of Abinduced ion flux, we did not observe consistent differences in the conductance or lifetime of ion flux events among different aggregation methods (A-E, Table S1). In fact, the conductance and lifetime of Ab-induced pores varied significantly between experiments with the same preparation method or within the 30 min of one experiment. This variability suggests that Abinduced pores are dynamic structures with a range of conformations and sizes [79]. Control experiments without Ab revealed ion flux in one of eleven experiments; this activity was likely due to a sporadic instability of bilayers within the 30 min recording period; these instabilities can occur during bilayer recordings [81].
Cytotoxicity is Maximal after Aggregating Ab 1-40 for Three to Ten Days and Ab 1-42 for Two to Ten Days Samples of Ab resulted in maximal cytotoxicity in a human neuroblastoma cell line after incubating Ab 1-40 for three to ten days, while the toxicity of Ab 1-42 was highest between two and ten days (Fig. 2B). Wogulis et al. found a similar time-dependent trend of toxicity albeit under different conditions and therefore different kinetics [82]. For information on the toxicity of all Ab preparation methods explored here, see Table S1.

Oligomer Levels during Aggregation
In order to correlate both pore formation and cytotoxicity with the aggregation state of Ab samples, we determined the relative abundance of monomeric and oligomeric species of Ab as a function of incubation time in water. Choosing among the available analytical methods, which all have their limitations [67], we selected SDS-PAGE separation of cross-linked Ab samples combined with Western blotting (Fig. 3) and densitometry for this quantification (i.e., analysis of grey levels from scanned images of Western blotted gels). This approach yielded the resolution of individual oligomer species or groups of oligomers as indicated in Fig. 3A (see Supporting Information, Section S2.4 and S2.5 for a discussion on using Western blot for this analysis). Figure 3B shows that the relative abundance of low molecular weight aggregates (i.e., monomers to trimers) decreased as a function of aggregation time, whereas the relative abundance of intermediate-sized oligomers (tetramers to 13-mers in the case of Ab 1-40 and tetramers to hexamers in the case of Ab 1-42 ) went through a maximum after approximately 2 to 3 days. We observed, as expected, that the relative abundance of high molecular weight oligomers (.18-mers) gradually increased over time.
Since the binding of anti-Ab antibodies to oligomers could be conformation dependent, we compared the results from densi- tometry analysis after Western blot with densitometry analysis after silver staining [83]. Results with Ab 1-40 showed that both detection techniques revealed similar trends for the change of relative abundance of small oligomer sizes but quantification of abundance for aggregates larger than hexamers was difficult with silver staining, as reported previously (see Supporting Information, Fig.  S4, and Fig. S5) [83,84]. Silver staining results suggested very low relative amounts of these larger aggregates despite results from TEM analysis, which showed the presence of a significant fraction of Ab protofibrils with lengths above 20 nm in three day samples and in samples with longer aggregation time (see Supporting Information, Figure S6 and Section S2.5). Therefore, we performed the quantitative analysis of oligomer abundance in this work based on Western blots. The time-dependent variations of the relative amounts of individual Ab species as determined by SDS-PAGE (Fig. 3) indicate that this Western-blot-based comparative analysis among differently-aged Ab preparations did indeed reveal information about the kinetics of aggregation. Possible artifacts by SDS-induced aggregation [67] or excess aggregation induced by chemical cross-linking [85], if present, were not sufficiently large to mask this time dependence. In fact, Ono et al. showed that purified samples of cross-linked Ab oligomers changed their composition by less than 15% during analysis by SDS-PAGE [23].

Characterization of Ab Aggregation by Thioflavin T Fluorescence and Circular Dichroism
We used thioflavin T (ThT) fluorescence as a surrogate to monitor fibrillization [23] and measured circular dichroism (CD) spectra to examine the extent of secondary structure in the samples of Ab 1-40 and Ab 1-42 in water after pre-incubation times of 0, 1, 2, 3, 10, and 20 d. The ThT signal from Ab 1-40 samples reached its half-maximal signal between one and two days (t Kmax = 1.6 d) and increased only slowly after the third day (Fig. 2C). In case of Ab 1-42 , the half-maximal ThT signal was reached in less than one day (t Kmax = 0.9 d). Data from CD spectroscopy revealed that the relative amount of b-sheet followed a similar trend as the ThT signal, i.e., a rapid increase during the first 1-2 days, followed by a slower increase as aggregation continued ( Fig. 2D and Supporting Information, Fig. S7 and Table S2). Together, these ensemble measurements suggested a good correlation between toxicity, ThT fluorescence, and b-sheet content, as reported   (right) preparations that had been incubated in water for 0, 1, 2, 3, 10, and 20 days (method A). All samples were cross-linked with 12 mM glutaraldehyde before electrophoresis through a 16.5% Tris-Tricine gel. Grouping of oligomers is indicated on the right. B) Average relative abundance of aggregated Ab 1-40 (red) and Ab 1-42 (blue) species of different size as a function of aggregation time. Each point represents the mean value of the relative abundance of each species from 4 to 6 gels; error bars represent the standard error of the mean. Red and blue curves are best curve fits of equation S1 to the data (see Supporting Information). doi:10.1371/journal.pone.0047261.g003 previously by Simmons et al [86], while pore formation correlated only during the first three days with ThT fluorescence and b-sheet content. The most pore-forming and most toxic Ab preparations were those whose ThT and CD signal transitioned from the initial fast increase to the phase of slow increase.

Dependence of Pore Formation and Cytotoxicity on the Oligomer Populations
In order to develop a model that describes the effect of oligomer populations on pore formation and cytotoxicity, we adopted a multivariate regression approach. This approach is particularly well suited here since we had observations at six time points over twenty days that included the measured levels of pore formation, cytotoxicity, b-sheet content, and ThT fluorescence, as well as the relative abundance of nine different oligomer species for two Ab peptides. A multiple linear regression approach might seem logical in this case, but was not appropriate given the relative uncertainties in the explanatory variables (oligomer levels) and response variables (pore formation, cytotoxicity, ThT fluorescence, and b-sheet content) as well as the significant correlations in the oligomer population. Instead, we used a partial least squares (PLS) formalism since it is suited for limited data sets and correlated predictor variables, and has been shown to work well for similar problems ranging from pharmaceutics to neuroimaging [87][88][89]. Further, PLS regression does not require any assumptions about the relationship between the observations and the predictor variables, and is ideal for mixtures of species whose predictor variables (i.e., the relative abundance of each oligomer class) contain uncertainty and are interdependent (i.e., tetramer levels depend on trimer and pentamer levels and on the levels of all other oligomer classes in the preparation).
We performed PLS regression using the oligomer abundance as predictor variables and simultaneously carried out regression for all four observables: pore formation, cytotoxicity, b-sheet content, and ThT fluorescence. We carried out this analysis twice by treating data from Ab 1-40 and Ab 1-42 independently and found for each case that a model with two components or latent variables [87] was sufficient to explain 92-95% of the variance of the four observables (see Fig. S8). Interestingly, the component vectors that were obtained for Ab 1-40 and Ab 1-42 are nearly identical, suggesting that the dependence of pore formation, cytotoxicity, b-sheet content, and ThT signal on the underlying oligomer distributions must be similar for both peptides. Figure 4 shows the PLS regression coefficients for all four observables for Ab 1-40 and Ab 1-42 peptides. In this plot, positive or negative coefficients indicate a positive or negative effect on the given observation, and the asterisks indicate the statistical significance of a given coefficient based on jackknife test [90]. Again we found that both peptides had a nearly identical dependence on the distribution of oligomeric species. In terms of specific observations, cytotoxicity and pore formation had highly correlated dependencies: both had a significant negative contribution from small oligomers (monomers to trimers), significant positive contributions from tetramers to hexamers as well as the 7to 13-mer group, and then again negative contributions from large oligomers, particularly the .210 kDa class of protofibrils.
These results agree well with previous observations, in particular that the smallest oligomers may in fact be protective rather than pathologic [24,55,91,92], and that oligomers in the tetramer to 13mer range exert the most significant effect on Ab-induced pore formation and toxicity [26,39,44,49,58,[61][62][63][64][65][66]. For instance, Lin et al showed that at least three monomers are required to form Abinduced pores [93], while Pan et al. specifically identified a porinlike, tetrameric b-barrel oligomer in solution and proposed that it may form ion pores in membranes [65]. Moreover, a recent single molecule microscopy study showed that the dimer to tetramer range of Ab 1-40 constitutes the majority of species binding to neuronal cells at physiological Abconcentration and that these binding events were associated with sporadic Ca 2+ leakage [94]. Bernstein et al. found by ion mobility coupled with mass spectrometry that Ab 1-40 forms stable annular tetramers, while Ab 1-42 forms quasiplanar, annular hexamers as well as dodecamers (from stacking two such hexamers) [39]. Annular oligomers were proposed before as possible pore-forming Ab structures [61,68,69,95]. Schauerte et al. combined bilayer experiments with single molecule fluorescence studies and reported that hexamers to 14-mers of Ab formed pores [66], while Demuro et al. showed by Ca 2+ -imaging that 5-to 40-mers of Ab induced pores for Ca 2+ in plasma membranes [44]. It is surprising and revealing that PLS analysis on the results from planar lipid bilayer experiments carried out here under significantly different experimental conditions identified the same range of oligomer sizes as poreforming as those identified by single molecule studies on live cells [44,94]. This agreement between different techniques suggests that similar Ab pore structures can form in artificial lipid bilayers and in cellular membranes. Evidence from electrophysiological [44,51,54,96], electron microscopic [69,70], X-ray diffraction [70], NMR [97,98], AFM [56,61], mass spectrometry [39,65], and molecular dynamics experiments [97,99,100] suggests that these Ab pore structures are formed by an annular arrangement of several monomers.
In order to further examine the plausibility for the formation of these proposed Ab pore structures, we applied a simple barrelstave model of such an Ab pore to estimate the numbers of monomers per pore from single channel recordings of Ab-induced ion flux (Fig. 1) and compared these numbers with the results from PLS analysis. This analysis revealed that the theoretically expected single channel conductance values through the lumen of Ab pores that form by assembly of four to thirteen Ab monomers to a regular polygon of transmembrane cylinders range from 47 pS to 1.2 nS (Fig. S9, Supporting Information). This range is in excellent agreement with the experimentally measured range of 80 pS to 0.8 nS and illustrates that annular arrangements of four to thirteen Ab monomers could indeed form ion pores in a size range that is consistent with experimentally measured values of single channel conductance (Fig. S9). In contrast, trimeric assemblies as well as assemblies of more than thirteen Ab monomers would have predicted conductance values that are outside of the majority of experimentally measured values according to this simple model (Fig. S9).
The size range from dimers to 8-mers constitutes the predominant Ab oligomer fraction in the brain [15] and includes the range of oligomer sizes suspected to be the most clinically relevant in the context of Alzheimer's disease [23]. Injection of purified 9and 12-mers into the ventricle of pre-trained rats, for instance, had acute effects on special memory performance [15]. Finally, Ono et al. reported toxicity studies with cross-linked and purified Ab oligomer species [23]. These studies showed the following rank order of increasing and additive toxicity: Ab monomers , dimers , trimers , tetramers (larger aggregates were not examined).
Unlike the tetramer to 13-mer range of oligomers, the monomer, dimer, and trimer species were anticorrelated with both pore formation and cytotoxicity (Fig. 4). These findings agree with observations by Schauerte et al. that dimers do not permeabilize membranes and with previous observations that at least three peptides are required to form a pore [66,79,93]. These results deviate, however, from reports that Ab dimers are the most toxic species [28][29][30][31][32][33][34]. Belinova et al. recently reviewed these findings and concluded that the identified dimers may aggregate to larger oligomers during toxicity assays and that the observed toxicity may have originated from these larger species [67]. In fact, O'Nuallain confirmed rapid aggregation of these dimers to metastable protofibrils [31].
The observation that large oligomers (.210 kDa) are anticorrelated with pore formation and toxicity, rather than making no contribution, may be explained by recent findings that monomers bind to and dissociate from Ab oligomers and fibrils in a dynamic process [23,101,102]. Therefore, fibrils (and, presumably, large oligomers) can act as non-toxic scavengers of pore-forming and toxic Ab species [67] that may otherwise be free to form small toxic oligomers [27,103]. Several recent reports showed that Ab fibrils are not toxic [13,23,58,[103][104][105]. This close correlationboth, negative and positive -between pore formation and cytotoxicity over the entire size range of both Ab peptides implies a close mechanistic connection and is consistent with recent findings by Diaz et al. that blockers of Ab ''ion channels'' protected cells from Ab-induced toxicity [106].
Both ThT fluorescence and b-sheet content have little contribution from small and intermediate oligomers in these ensemble measurements -all the coefficients are relatively small and only a few are significant, however, in the case of Ab 1-40 , both of these observables have strong, positive contributions from the 78-210 kDa and .210 kDa oligomer classes. As one might expect, the b-sheet and ThT signals from these large oligomers are largely correlated, however both observables are anticorrelated with pore formation and cytotoxicity. This result is important since it demonstrates that fibrillization, b-sheet content, pore formation, and toxicity can depend differently on various oligomer species (Fig. 4), although ensemble measurements on mixtures of Ab species suggest the misleading result that all four observables are correlated with each other (Fig. 2).

Conclusions
One of the proposed mechanisms of Ab-induced neurotoxicity is pore formation [69,71,107]. Studies from different research groups using various techniques [51][52][53][54]56,[58][59][60][61][62][63][64]66,108] have indicated that aggregated forms of Ab with a broad range of sizes can induce ion flux through artificial and cellular lipid membranes. One of the big challenges for revealing the pathogenic mechanisms of Ab is that measurements are performed on a dynamic and distributed ensemble of oligomers [12,109,110]. In fact, it is intrinsically difficult or impossible to perform assays on individual Ab species because even cross-linked and purified Ab dimers were reported to form a small fraction of tetramers [23] or larger oligomers during the course of experiments [67,109,110]. Moreover, assays performed on these complex mixtures of Ab oligomers are usually limited to bulk measurements whose readouts such as cytotoxicity, extent of fibrillization, or b-sheet content may appear to be correlated (Fig. 2), while the biophysical basis for these phenomena may depend on different oligomer species in the mixture (Fig. 4) [67,80]. In order to tackle these complications, we used a PLS formalism that reduced the dimensionality from ten oligomer classes to two component vectors, and made it possible to analyze four observables at six time points simultaneously over a 20 day period. This analysis showed that measures of structure such as b-sheet content or degree of fibrillization depended on different Ab oligomer species than pore formation and toxicity. Interestingly, pore formation and toxicity showed nearly identical dependence on different species in the oligomer distribution. Moreover, the close connection between pore formation and  [90]. Coefficients less than 0.25 were considered insignificant and values that were at least one or two standard deviations from zero are marked as significant (*) or highly significant (**) respectively. doi:10.1371/journal.pone.0047261.g004 toxicity was observed independently for Ab 1-40 and Ab 1-42 despite differences in aggregation kinetics (Fig. 2) and relative amounts of aggregated Ab species of different size at any given time point (Fig. 3) in these two amyloid preparations [39].
Based on this analysis, we found tetramers to 13-mers contributed positively to pore formation and toxicity and within this range, the tetramer to hexamer populations showed the highest statistical significance for both peptides. This size range is in excellent agreement with previously identified size ranges of Ab oligomers as determined by biophysical, computational, and structural studies on pore formation as well as with in-vitro and in-vivo studies of neurotoxicity.
Multivariate PLS analysis also revealed that the smallest (monomer to trimer) and largest Ab species (.210 kDa) contributed negatively to pore formation and cytotoxicity and may therefore act as inert sinks that scavenge toxic oligomers [67]. Taken together, these results provide evidence that -under the experimental conditions explored in this work -pore formation was a significant component of cytotoxicity. The tetrameric to hexameric oligomers that we identified as the most pore-forming and toxic oligomers, have been found in the brain of AD patients and it is plausible that they could cause sporadic leaks of calcium ions into neurons [44,94]. These insults, over years of exposure, may contribute to cumulative neuronal damage in Alzheimer's disease.
This study introduces an unbiased, systematic approach to deduce statistical correlations between the size distribution of Ab oligomers and pore formation, toxicity, b-sheet content and extent of fibrillization. This multivariate approach is different from previous studies on Ab-induced toxicity and pore formation, nonetheless its results agree with many previous findings on Abinduced pore formation or cytotoxicity. This approach therefore supports the idea that Ab-induced pore formation may be a significant mechanism of its toxicity. Similar multivariate PLS analyses might be valuable for other amyloidogenic diseases in which standard ensemble measurements often mask the cytotoxic contributions of individual aggregate species in complex and dynamic mixtures of amyloids.

Materials and Methods
Please refer to the Supporting Information for details on chemicals, materials and methods such as formation of lipid bilayers, current recordings, preparation of AAb samples, toxicity assays, Western blotting, silver staining, densitometry analysis, ThT fluorescence assays, CD spectrometry, transmission electron microscopy, statistical analysis, partial least squares analysis as well as for Supplementary Results, Tables, and Figures.  Figure S9 Comparison of experimentally measured single channel conductance values of Ab1-40 pores with theoretically predicted values. These box plots were constructed from the amplitude of single-step current jumps in current versus time traces such as those shown in Fig. 1 of the main text. The first six box plots (Ab 40-0d to Ab 40-20d) represent the distribution of single channel conductance values from Ab preparations that had been pre-incubated for 0 to 20 days prior to planar lipid bilayer recordings under the same conditions as in Fig 1 of the main text. The last box plot (dark yellow) represents the theoretical estimate of single channel conductance values of a model of Ab pores that assumes an annular assembly of Ab monomers to a regular polygon with an internal pore lumen. In this model, each Ab monomer is represented by a transmembrane cylinder with a diameter, d, of 1 nm (approximate diameter of a transmembrane peptide) [112] and a length, l, of 3.5 nm (approximate thickness of a lipid bilayer). The centers of the crosssection of each cylinder are located at the corners of the regular polygon and the lengths of the polygon sides are equal to d. The theoretically predicted box plot was constructed from estimated single channel conductance values of eleven possible regular polygons ranging from the smallest one (assembly of three monomers to a triangle) to a regular polygon of 13 monomers. We estimated the single channel conductance as a function of the number of Ab monomers, N, in these assemblies by calculating the area of the lumen A L (N) in such a pore. We obtained this area by calculating the area of a regular polygon with N sides, A RP (N) and subtracting the area of circle sectors, A CS (N), that overlap with the polygon area. The area of a regular polygon is given by: A RP (N) = d 2 6 N/[4 6tan(180u/N)] and the area of circle sectors depends on the angle, a, between the sides of a regular polygon -which is given by a (N) = 180u (N -2)/N -in the following way: A CS (N) = a (N) 6p 6d 2 /(4 6360u). Therefore, the area of the lumen is given by: A L (N) = A RP (N) -N 6A CS (N) = (d 2 /4) 6[N/tan(180u/N) -(p/2) 6 (N -2)]. With A L (N), we calculated the area equivalent radius of a circle as a function of the number of monomers, r(N), i.e. r(N) = (A L (N)/p) 0 . 5 , which we then used to calculate the single channel conductance,c(N), through a pore with radius r(N) and length l in an electrolyte with resistivity r using the relationship c(N) = [(l + p 6 r(N)/2) 6r/[p 6 r 2 (N)]] 21 [113]. Since we used a lipid bilayer with 50 mol% negatively-charged lipid head groups, we estimated the local resistivity near the membrane from work by Apell et al [114] and found r = 0.313 V m for the experimental conditions used in Fig. 1 of the main text. The predicted box plot (dark yellow) was then obtained from the c(N) values of oligomers with 3 to 13 monomers, weighed by the relative abundance of each of these oligomers as shown in Fig. 3B of the main text. In these plots, the box encloses the 25 th to 75 th percentile, the whiskers enclose the 5 th to 95 th percentile, the crosses enclose the 1 st to 99 th percentile, the hyphens indicate the minimum and maximum single channel conductance value, while the horizontal line in the box indicates the median and the open square symbol indicates the mean single channel conductance value. (TIF)