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Inverse Correlation Between Amyloid Stiffness and Size Roy Nassar, Eric Wong, Joerg Gsponer, and Guillaume Lamour J. Am. Chem. Soc., Just Accepted Manuscript • DOI: 10.1021/jacs.8b10142 • Publication Date (Web): 18 Dec 2018 Downloaded from http://pubs.acs.org on December 18, 2018
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Journal of the American Chemical Society
Inverse Correlation Between Amyloid Stiffness and Size. Roy Nassar,†,‡,§ Eric Wong, §,⊥ Jörg Gsponer,*, §,⊥ and Guillaume Lamour*,║ Laufer Center for Physical and Quantitative Biology, Stony Brook University, Stony Brook, NY 11794-5252; ‡ Department of Chemistry, Stony Brook University, Stony Brook, NY 11790-3400; § Michael Smith Laboratories, The University of British Colombia, Vancouver, BC Canada V6T 1Z4; ⊥ Department of Biochemistry & Molecular Biology, The University of British Colombia, Vancouver, BC Canada V6T 1Z3; ║ Laboratoire d’Analyse et Modélisation pour la Biologie et l’Environnement LAMBE-CNRS, UMR 8587, Université d’Evry, 91025 Evry, France †
Supporting Information Placeholder (N.A.) ABSTRACT: We reveal that the axial stiffness of amyloid fibrils is inversely correlated with their cross-sectional area. Since amyloid fibrils’ stiffness is determined by hydrogen bond (Hbond) density with a linear correlation, our finding implies that amyloid fibrils with larger radial sizes are generally softer and have lower density H-bond networks. In silico calculations show that the stiffness-size relationship of amyloid fibrils is, indeed, driven by the packing densities of residues and H-bonds. Our results suggest that polypeptide chains which form amyloid fibrils with narrow cross-sections can optimize packing densities in the fibrillar core structure, in contrast to those forming wide amyloid fibrils. Consequently, the density of residues and H-bonds that contribute to mechanical stability is higher in amyloid fibrils with narrow cross-sections. This size dependence of nanomechanics appears to be a global property of amyloid fibrils, just like the well-known cross- sheet topology.
Amyloid fibrils are involved in many diseases, including devastating neurodegenerative diseases such as Alzheimer’s and Creutzfeldt-Jakob diseases.1 Cross-β sheets running along the fibril axis are a defining trait of amyloids and are responsible for the characteristic X-ray diffraction pattern with ~4.7 Å and ~10 Å rings corresponding to interstrand and intersheet distances, respectively. This structural trait, common to all amyloid fibrils, is associated with a dense network of hydrogen bonds (H-bonds) that provides high intrinsic stiffness to fibrils.2 Interestingly, despite sharing a common structural trait, amyloid fibrils display a high level of polymorphism, which leads to diversity in their mechanical properties.3 Stiffness can vary significantly between amyloid fibrils because of differences in the density of “mechanical” H-bonds (i.e. β-strand connecting H-bonds contributing to amyloid mechanical properties, as opposed to internal H-bonds in α-helices). However, a key unanswered question is whether nanomechanics and H-bond density of amyloid fibrils depend on their size. Here we show that the axial stiffness of amyloid fibrils inversely scales with their radial size. Evidence for this finding is presented in Figure 1, where Young’s moduli of amyloid fibrils are plotted against their cross-sectional areas. The cross-sectional area quantifies the size of a fibril in the “radial” direction, that is, perpendicular to the fibril’s axis. Young’s modulus is a quantitative measurement of the stiffness of a material and reflects the strength of intermolecular forces that hold the material
together.4 Here, Young’s modulus is derived from measuring the persistence length (discussed later). Hence, it reflects the strength of intermolecular forces in the fibril axis direction. In addition to the amyloid fibrils that we generated in vitro and analyzed previously,3 the plot also includes all the experimental data that we were able to extract from the literature (see Table 1), resulting in Young’s moduli that span three orders of magnitude. The correlation coefficient between Young’s modulus and the crosssectional area is a remarkable 0.90.
Figure 1. Inverse correlation between Young’s modulus and the crosssectional area of amyloid fibrils. All the fibrils in this graph were previously generated in vitro and their morphological and mechanical properties experimentally measured.3,5-8 The dashed line is the result of standardized major axis (SMA) estimation9 using the SMATR R package.10 The scaling exponent β in Y = αCβ returned by SMA estimation is equal to: –2.2 ± 0.4. See second last paragraph and Table 1 for details about how the data points in this graph were generated and for full names of the samples.
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Table 1. Data used to calculate Young’s moduli and crosssectional areas displayed in Figure 1. Name
Persistence length (µm)
AFM height (nm)
TEM width (nm)
Refs
Prion23–231
6.0 ± 2.7
5.2 ± 2.1
26 ± 5.3
3
Prion89-231
2.7 ± 1.0
8.1 ± 2.7
19 ± 5.2
3
Insulin
3.0 ± 1.3
2.1 ± 0.8
7.3 ± 1.2
3
Lysozyme
4.0 ± 1.5
3.0 ± 1.0
9.5 ± 3.7
3
Sup35N
8.1 ± 3.5
2.6 ± 0.4
7.7 ± 1.4
3
Sup35NM
1.8 ± 0.7
4.7 ± 0.8
15 ± 2.7
3
HET-s
7.5 ± 2.8
2.1 ± 0.3
4.4 ± 0.7
3
RIP1/RIP3 complex
3.6 ± 1.3
1.8 ± 0.4
8.0 ± 1.0
3
TRIF
8.0 ± 3.7
2.7 ± 0.4
7.1 ± 1.3
3
κ-casein
2.4 ± 1.5a
3.5 ± 0.9a
11 ± 2.3a
5
β-casein
10 ± 4.9
4.8 ± 1.2
14 ± 1.9
5
β-lactoglobulin
4.6 ± 2.9a
2.8 ± 0.5a
9.5 ± 1.6a
5
SSSSFAFAC peptide – pH2
8.9 ± 0.7
3.8 ± 0.2
11 ± 4.2a
6
SSSSFAFAC peptide – pH7
0.72 ± 0.16
2.2 ± 0.2
18 ± 4.9a
6
α-synuclein “fibrils”
14 ± 3.3
6.4 ± 0.7
13 ± 2.0
7
α-synuclein “ribbons”
3.5 ± 1.0
5.1 ± 0.8
18 ± 1.5
7
Aβ1–40
3.2 ± 1.1a
6.0 ± 1.0
12 ± 2.7a
8
a
a
a
For all the cases in which the measurements were not explicitly mentioned by the authors, persistence lengths, AFM heights, and TEM widths were estimated from the images of fibrils published in the corresponding references. We applied the algorithm of the Easyworm software tool to estimate the persistence lengths.11 a
As a direct relationship between amyloid fibril stiffness and Hbond density has been established previously,3,12 our finding here suggests that H-bond density also decreases with increasing radial size of amyloid fibrils. We tested this hypothesis by comparing four models of amyloid fibrils that have different sizes and structures (Figure 2). The models vary according to the size of their cross-section from small (HET-s and Aβ)13,14 to large (IS2 and BH2).15-17 We estimated residue density by counting all the residues included in the fibril core and normalizing by the volume. From this analysis, we note that “small” amyloid fibrils have higher residue densities than “large” amyloid fibrils, with corresponding densities of 8–12 nm–3 and 5–8 nm–3, respectively (Figure 2B). Most importantly, the difference in packing densities of all residues also translates to a significant difference in the packing densities of mechanical residues (Figure 2C), i.e. residues that contribute to mechanical properties by making β-strand connecting H-bonds. Structural details explain why fibril models with overlapping residue densities (e.g. “Big” models IS2 and BH2) have clearly different mechanical residue densities (MRD) (Figure 2C, right panel). While IS2 is made predominantly of stacked β-sheets, only a small part of the sequence contributes to β-sheet formation in the BH2 model (Figure 2A). BH2 contains many α-helices that do not contribute to interlayer H-bonds, but instead increase the size of the fibril, and thereby decrease the MRD. Interestingly, Aβ has
a higher MRD than IS2, even though both are composed of stacked β-sheets. Further analysis reveals why these two fibril models (Aβ and IS2) that share similar stacked-sheet topologies have distinct MRDs. The fraction of residues contributing to mechanical stiffness, i.e. the ratio of mechanical residues to total number of residues, is very similar in these two models (Figure 2D, left panel), as is the number of mechanical H-bonds per mechanical residue (Figure 2D, right panel). However, looser global packing of residues in IS2 (Figure 2B), which has a larger cross-section, results in a lower MRD for this structure. Overall, these analyses on model fibrils show that, at least for the four structures considered here, the packing density of mechanical residues, just like that of all residues, tends to decrease when the radial size increases. It follows that H-bond density also decreases with increasing radial size of fibrils. These results are consistent with the inverse correlation between Young’s modulus and crosssectional area derived from experimental measurements (Figure 1). Note that the correlation between stiffness and size may not apply in some cases when the fibrils are either (i) “worm-like” or curvilinear, or (ii) crystal-like. Curvilinear fibrils have low persistence length. They have been made from various proteins including PrP,18 α-lactalbumin and αβ-crystallin.4 Curvilinear fibrils have characteristically low Young’s moduli, which suggest that packing densities are not as dense as in “mature” fibrils (characterized by higher persistence lengths and higher Young’s moduli.4,18) In addition, atomic force microscope (AFM) and transmission electron microscope (TEM) sizes of these fibrils indicate that they are composed of single filaments with small cross-sectional areas.4,18 Consequently, curvilinear fibrils do not follow the power-law relationship of Figure 1 and would appear on the bottom-left corner of the graph instead. Conversely, certain short peptides have the ability to form crystal-like amyloids where a single “fibril” consists of much more than two or three filaments. Examples of peptides that can form crystal-like fibrils are the 11-residue peptide of TTR(105–115) and the GNNQQNY fragment of the yeast prion Sup35.4,19 Note that the amyloid fibrils that follow the stiffness-size relationship in Figure 1 are mostly composed of two or three filaments, as displayed in TEM images of the fibrils.3,5-8 A higher number of filaments does not imply higher axial Young’s modulus, because packing density of residues and H-bonds in the direction of the fibril axis is likely to remain similar as filaments attach to each other laterally. However, the cross-sectional area will increase together with the number of filaments and move data points to the right side of the graph in Figure 1. Our findings collectively hint that H-bond densities of amyloid fibrils, and thus their Young’s moduli, scale inversely with the cross-sectional size of the fibrils. By extension, this implies that if some proteins form amyloid fibrils that are very soft as characterized by low Young’s modulus, like PrP (see Figure 1), it is likely due to their sequences being unable to pack into dense cross-β-sheet structures. As a result, they can only form amyloid or amyloid-like fibrils with large cross-sectional areas that have rather low mechanical H-bond densities. We posit that the radial size dependence of nanomechanical properties is a general characteristic of amyloid fibrils that are neither crystal-like nor curvilinear. More studies are required to determine whether the ability or inability of certain sequences to form densely packed cross-β-sheet structures and, thus, fibrils with high Young’s modulus is related to different biological effects of amyloids within cells.2
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Figure 2. Comparison of packing densities among different models of amyloid fibrils. (A) VMD-generated and scaled schematics of amyloid structures (cross-sectional view from the top). Van der Waals surfaces are superimposed on secondary structure representations; yellow and purple indicate β-sheet and α-helix rich regions, respectively. (B) Overall residue density as a function of cross-sectional area showing how residue packing is affected as the fibril cross-section varies. (C) Mechanical residue density (MRD) as a function of cross-sectional area for the four fibril models. (D) Category plots of the fraction of mechanical residues out of the total number of residues (left), and number of mechanical H-bonds per mechanical residue (right).
Calculation of densities. Fibril models displaying a wide range of sizes and structures were selected for the calculation of residue and H-bond densities: the fungal prion HET-s(218–289) (PDB code 2KJ3),13 the Aβ(1–42) model (PDB code 2BEG),14 and two mouse prion (PrP) structures, IS2 and BH2. The IS2 fibril architecture consists of stacked parallel β-strands composed by residues 90–231.15 The BH2 fibril architecture is composed of a β-helix (residues 104-141) and α-helices (residues 142-231).16,17 Molecular dynamics simulations were used to equilibrate the structures, as described previously.3 The volumes of equilibrated structures were estimated by calculating the area, from van der Waals projections of fibril cross-sections,3 and by multiplying by the fibril length determined as the distance between centers of geometry of the top and bottom layers of each fibril. The disordered parts of each monomer, identified as the terminal segments with no secondary structure flanking the fibril core, were excluded from the analysis. VMD was used to compute Hbonds, using 3.5 Å and 30° cut-off values for donor-acceptor distance and donor-hydrogen-acceptor angle, respectively. As a control, we also used a cut-off value to 4.0 Å, which did not change the overall findings.
Preparation of the data in Figure 1. To generate a homogeneous set of variables, values of Young’s moduli Y were all derived from calculations of the bending rigidities (B) and moments of inertia (I) of the fibrils, where Y = B/I. Bending rigidities were derived from persistence lengths P as B = P × kBT. The persistence length is itself calculated via a statistical mechanics technique that analyzes the fluctuations of fibril shape.11 Moments of inertia were computed from cross-sectional size and geometry, as described previously.3 All the crosssectional areas are estimates derived from measurements of AFM heights and TEM widths, assuming rectangular cross-sectional geometry. This assumption is justified because the TEM widths for all the fibrils are at least two times greater than their AFM heights. This difference is due to how filaments are connected in a lateral fashion in the mature fibril, giving rise to a flat “tape” structure.3 The proteins in Figure 1 are listed from top to bottom: [unless otherwise specified, data are taken from Reference (3)]: yeast prion HET-s(218–289) fragment, HET-s; RIP1/RIP3 complex, RIP13; Sup35N(1–123) fragment of the yeast prion sup35, sup35N; 54-residue fragment of Toll/interleukin-1 receptor (TIR)-domain-containing adaptor-inducing interferon-β, TRIF; 51-residue insulin, Ins; β-lactoglobulin,5 β-lac; 129-residue lysozyme, Lys; SSSSFAFAC peptide at pH2,6 S2; β-casein,5 βcas; κ-casein,5 κ-cas; α-synuclein “fibrils” polymorph,7 α-syn1; SSSSFAFAC peptide at pH7,6 S7; full-length (23–231) mouse prion protein, PrP; α-synuclein “ribbons” polymorph,7 α-syn2; Aβ(1–40) peptide,8 Aβ; Sup35NM(1–253) fragment of the yeast prion sup35, sup35NM; truncated (89-231) mouse prion protein, PrPt.
AUTHOR INFORMATION Corresponding Authors * (J.G.) E-mail:
[email protected] * (G.L.) E-mail:
[email protected] 3
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(9) Warton, D. I.; Wright, I. J.; Falster, D. S.; Westoby, M. Bivariate Line-Fitting Methods for Allometry. Biol. Rev. Camb. Philos. Soc. 2006, 81, 259-291. (10) Warton, D. I.; Duursma, R. A.; Falster, D. S.; Taskinen, S. SMATR 3-an R Package for Estimation and Inference About Allometric Lines. Methods Ecol. Evol. 2012, 3, 257-259. (11) Lamour, G.; Kirkegaard, J. B.; Li, H.; Knowles, T. P.; Gsponer, J. Easyworm: An Open-Source Software Tool to Determine the Mechanical Properties of Worm-Like Chains. Source Code Biol. Med. 2014, 9, 16. (12) Solar, M.; Buehler, M. J. Tensile Deformation and Failure of Amyloid and Amyloid-Like Protein Fibrils. Nanotechnology 2014, 25, 105703. (13) van Melckebeke, H.; Wasmer, C.; Lange, A.; AB, E.; Loquet, A.; Bockmann, A.; Meier, B. H. Atomic-Resolution Three-Dimensional Structure of HET-s(218-289) Amyloid Fibrils by Solid-State NMR Spectroscopy. J. Am. Chem. Soc. 2010, 132, 13765-13775. (14) Luhrs, T.; Ritter, C.; Adrian, M.; Riek-Loher, D.; Bohrmann, B.; Doeli, H.; Schubert, D.; Riek, R. 3D Structure of Alzheimer's Amyloid-β(1-42) Fibrils. Proc. Natl. Acad. Sci. U.S.A. 2005, 102, 1734217347. (15) Groveman, B. R.; Dolan, M. A.; Taubner, L. M.; Kraus, A.; Wickner, R. B.; Caughey, B. Parallel in-Register Intermolecular β-Sheet Architectures for Prion-Seeded Prion Protein (PrP) Amyloids. J. Biol. Chem. 2014, 289, 24129-24142. (16) Langedijk, J. P. M.; Fuentes, G.; Boshuizen, R.; Bonvin, A. M. J. J. Two-Rung Model of a Left-Handed β-Helix for Prions Explains Species Barrier and Strain Variation in Transmissible Spongiform Encephalopathies. J. Mol. Biol. 2006, 360, 907-920. (17) Shirai, T.; Saito, M.; Kobayashi, A.; Asano, M.; Hizume, M.; Ikeda, S.; Teruya, K.; Morita, M.; Kitamoto, T. Evaluating Prion Models Based on Comprehensive Mutation Data of Mouse PrP. Structure 2014, 22, 560-571. (18) Lamour, G.; Yip, C. K.; Li, H.; Gsponer, J. High Intrinsic Mechanical Flexibility of Mouse Prion Nanofibrils Revealed by Measurements of Axial and Radial Young's Moduli. ACS Nano 2014, 8, 3851-3861. (19) Nassar, R.; Wong, E.; Bui, J. M.; Yip, C. K.; Li, H.; Gsponer, J.; Lamour, G. Mechanical Anisotropy in GNNQQNY Amyloid Crystals. J. Phys. Chem. Lett. 2018, 4901-4909.
Notes The authors declare no competing financial interests.
ACKNOWLEDGMENT The authors acknowledge funding from: the SUNY Research Foundation, the Stony Brook Foundation, the National Science Foundation (NSF), the Natural Sciences and Engineering Research Council of Canada (NSERC), the Canadian Institutes of Health Research (CIHR), and from Genopole Biocluster at Evry (research associate fellowship to G.L.).
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