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Research Article

Nanomechanical properties of steric zipper globular structures

Neta Lester-Zer, Mnar Ghrayeb, and View ORCID ProfileLiraz Chai
  1. aInstitute of Chemistry, The Hebrew University of Jerusalem, 91904 Jerusalem, Israel;
  2. bThe Center for Nanoscience and Nanotechnology, The Hebrew University of Jerusalem, 91904 Jerusalem, Israel

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PNAS November 5, 2019 116 (45) 22478-22484; first published October 21, 2019; https://doi.org/10.1073/pnas.1908782116
Neta Lester-Zer
aInstitute of Chemistry, The Hebrew University of Jerusalem, 91904 Jerusalem, Israel;
bThe Center for Nanoscience and Nanotechnology, The Hebrew University of Jerusalem, 91904 Jerusalem, Israel
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Mnar Ghrayeb
aInstitute of Chemistry, The Hebrew University of Jerusalem, 91904 Jerusalem, Israel;
bThe Center for Nanoscience and Nanotechnology, The Hebrew University of Jerusalem, 91904 Jerusalem, Israel
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Liraz Chai
aInstitute of Chemistry, The Hebrew University of Jerusalem, 91904 Jerusalem, Israel;
bThe Center for Nanoscience and Nanotechnology, The Hebrew University of Jerusalem, 91904 Jerusalem, Israel
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  • ORCID record for Liraz Chai
  • For correspondence: liraz.chai@mail.huji.ac.il
  1. Edited by Ehud Gazit, Tel Aviv University, Tel Aviv, Israel, and accepted by Editorial Board Member Lia Addadi September 27, 2019 (received for review June 7, 2019)

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Significance

The increase in life expectancy has nowadays positioned neurodegenerative diseases as a leading cause of death. Neurodegeneration is related to early amyloid protein aggregation; however, in the lack of an aggregation mechanism, neurodegenerative diseases still remain neither cured nor prevented. In a fundamental study of amyloid early aggregation, we have characterized the nanomechanical properties of steric zippers, the shortest amyloid sequences that yet bear high propensity to form fibers. We have found that steric zippers form unprecedented globular structures on route to fiber formation that exhibit a characteristic nanomechanical fingerprint. Approaching amyloid fiber formation from a basic physical perspective, this study sheds light on the internal structure of amyloid precursor chains, providing insight into the design of antiamyloid drugs.

Abstract

The term amyloid defines a group of proteins that aggregate into plaques or fibers. Amyloid fibers gained their fame mostly due to their relation with neurodegenerative diseases in humans. However, secreted by lower organisms, such as bacteria and fungi, amyloid fibers play a functional role: for example, when they serve as cement in the extracellular matrix of biofilms. Originating either in humans or in microorganisms, the sequence of amyloid proteins is decorated with hexapeptides with high propensity to form fibers, known as steric zippers. We have found that steric zippers form globular structures on route to making fibers and exhibit a characteristic force–distance (F-D) fingerprint when pulled with an atomic force microscope (AFM) tip. Particularly, the F-D pulling curves showed force plateau steps, suggesting that the globular structures were composed of chains that were unwound like a yarn ball. Force plateau analysis showed that the F-D characteristic parameters were sequence sensitive, representing differences in the packing of the hexapeptides within the globules. These unprecedented findings show that steric zippers exhibit a characteristic nanomechanical signature in solution in addition to previously observed characteristic crystallographic structure. Getting to the fundamental interactions that govern the unzipping of full-length amyloid fibers may initiate the development of antiamyloid methods that target the physical in addition to the structural properties of steric zippers.

  • amyloid proteins
  • steric zippers
  • atomic force microscopy
  • single-molecule force spectroscopy

The amyloid fold of a protein is a “dead end” conformation that is adopted by proteins under specific conditions as they transition from monomers or oligomers into aggregates (1⇓–3). Aggregation of amyloid precursors involves intermolecular interactions between polypeptide chains that lead to the formation of higher hierarchy assemblies, often in the form of fibers. In humans, amyloid fibers are related to neurodegenerative diseases, such as Alzheimer’s and Parkinson’s (1⇓–3), whereas in lower organisms, they are mostly related to a functional role and therefore, classified as “functional amyloids” (4, 5). Surprising recent findings link between the human and the functional amyloid proteins, suggesting that gut microbes produce functional amyloid proteins that affect neurodegeneration in humans (6, 7). Whether they originate in humans or in microbes, in the lack of a mechanism of amyloid aggregation, neurodegenerative diseases remain neither cured nor prevented. An important lead in amyloid research has been provided by the discovery that amyloid precursors are responsible for neuronal toxicity (8⇓–10). This finding diverged the focus of amyloid research from mature fibers to early aggregation oligomers and precursors.

A common biophysical approach in amyloid research is to pull on amyloid fibers with an atomic force microscope (AFM) to elucidate their nanomechanical properties. To this end, a few pulling experiments have been reported with amyloid proteins in different aggregation stages. In particular, detachment of protofibrils from a surface (11) as well as unzipping of protofibrils or mature fibers bear a characteristic pulling force–distance (F-D) behavior (12⇓–14). Interestingly, despite the differences in protein sequences and the experimental conditions used in these studies, they all share a common characteristic: the appearance of force plateau steps in the F-D curves. In this study, instead of studying full-length sequences, we measured the nanomechanical characteristics of steric zippers, the shortest amyloid sequences known to form fibers. Steric zippers, first described by Eisenberg and coworkers (15), are self-complementing hexapeptides of a high propensity to form fibers. Their calculated interaction energy depends on parameters, such as shape complementarity and area of the interacting interface (16, 17), that are summed up to a threshold interaction energy for fiber formation. While their interaction energy has been calculated (18) and their cross–β-sheet structure has been determined (15, 19⇓–21), the direct interaction between such hexapeptides in solution has never been directly measured.

We have found that steric zipper hexapeptides form globular structures on route to fiber formation, and we directly measured their nanomechanical properties and their interaction energy in an early aggregation stage. When we pulled the steric zipper globules with a complementary hexapeptide sequence attached to an AFM tip, plateau F-D rupture curves were observed similarly to the F-D signature previously observed with full-length sequences in the form of protofibrils or mature fibers (11⇓–13). Our study shows that, in addition to their ability to form amyloid fibers and their characteristic cross–β-sheet crystal structure, steric zippers also bear a characteristic nanomechanical signature in solution. Furthermore, this nanomechanical signature is independent of the genetic origin of the hexapeptides. Our results are important for understanding the fundamental mechanical properties of amyloid proteins as they transition from monomers to fibers, apparently through the formation of chains that collapse into prefibrillar globules.

Results and Discussion

Hexapeptide Steric Zippers Form Globular Structures on Route to Fiber Formation.

Steric zippers reside in proteins across the phylogenetic tree (19). As model hexapeptides, we chose 2 sequences from different genetic phyla, eukaryotic and bacterial, both of which have been identified by the Zipper database (ZipperDB) software (18, 22) to be of a high propensity to form fibers (relevant interaction parameters are in SI Appendix, Table S1). The hexapeptide, NNQQNY (henceforth referred to as NY6), is a classical amyloid eukaryotic hexapeptide of the yeast prion Sup35 that is commonly used as a model for amyloid fiber formation (23⇓⇓–26). NY6 forms cross–β-sheet crystals as confirmed by X-ray diffraction (15, 19, 27). By contrast and for comparison, we chose the hexapeptide, GVASAA (henceforth referred to as GA6), from the bacterial protein TasA, an extracellular matrix and fiber-forming protein (28⇓–30). The sequences of GA6 and NY6 are shown in Fig. 1 A and B, respectively. Unlike NY6, which is self-paired via hydrogen bonds between the side chains, the side chains in GA6 are mostly nonpolar and therefore, are potentially paired through van der Waals interactions.

Fig. 1.
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Fig. 1.

Early and late aggregation of the hexapeptides GA6 and NY6. The hexapeptides’ molecular structures are shown in (A) GA6 and (B) NY6. AFM topography images of the hexapeptides showed globular structures at early timescales (∼30 min). C and D correspond to GA6 and NY6, respectively. Hexapeptides formed fibers following a 3-d incubation (1 mg/mL with 10% acetic acid). E and F correspond to GA6 and NY6, respectively. (Scale bars: 200 nm.)

In order to probe the nanomechanical properties of the hexapeptide layers prior to fiber formation, we adsorbed the hexapeptide layers on a polyethylene glycol (PEG) layer (molecular weight = 2,000 Da). The PEG layer was covalently attached to a silicon surface through a short silane molecule (Materials and Methods has details) and used in order to minimize surface effects on the formation of the hexapeptide layers. AFM topography images of the surfaces following the different surface modification steps (prior to the hexapeptide adsorption) are shown in SI Appendix, Fig. S1. AFM images of the hexapeptide-modified surfaces (Fig. 1 C and D) show that, following a 30-min incubation, the hexapeptides formed globular structures of (20 ± 7)-nm diameter and (4 ± 1)-nm height (GA6) and (40 ± 15)-nm diameter and (4 ± 1)-nm height (NY6). The size of the globular structures remained unchanged with a 10- to 20-times dilution of the hexapeptide layer (SI Appendix, Fig. S2). Hexapeptide globular structures also formed directly on a silane monolayer, showing that the globule formation is intrinsic to the hexapeptides (SI Appendix, Fig. S3). Considering the volume of a single hexapeptide to be 0.6 nm3 (GA6) and 1 nm3 (NY6) (31), the globular structures constituted ∼725 GA6 hexapeptides and ∼940 NY6 hexapeptides. [The number of hexapeptides per globule was calculated from the ratio between the volume of the globule and the volume of a single hexapeptide. For the globule volume, we used the equation V(globule) = π/6 × h × (3c2 + h2), where h and c are the height and radius of the globule, respectively.] These globular structures remained unchanged for a few days following washing in a buffered solution. Repeating the adsorption protocol with a longer incubation of 1 mo yielded the formation of fibers (SI Appendix, Fig. S4), suggesting that indeed the hexapeptide globular structures were intermediate states on route to fiber formation. Fibers also formed following a 3-d incubation with acetic acid (Fig. 1 E and F). The fact that both hexapeptides formed globular structures (at the time point when we studied them), a geometry that minimizes their surface interaction with water, is suggestive of a self-preference of the hexapeptides over their interaction with water. This may be the initial driving force for the formation of fibers.

Pulling Hexapeptide Globular Structures Has a Characteristic Force Plateau Signature.

An AFM tip was modified with a covalently attached hexapeptide as is explicitly shown in the schematic in Fig. 2A. We measured the forces between the modified tip and the hexapeptide-modified surface on retraction from contact. The typical F-D curves, observed with both GA6 and NY6 hexapeptides, are shown in Fig. 2B. Curves I to III show nonspecific binding events owing to the interaction between the AFM tip and the substrate (curves I and III) or no binding events (curve II). Curve IV shows a worm-like chain (WLC) behavior observed when a PEG molecule, anchored to the substrate through the hexapeptide tail, is pulled away from the substrate with a parabolic restoring force (32⇓⇓⇓–36). Fitting a representative F-D curve with a WLC model is shown in SI Appendix, Fig. S5. In contrast to the F-D curves shown in curves I to IV, which have been previously observed in different experimental setups (37), particularly interesting curves are shown in curves V and VI, where steps of a constant force were observed. Curve V represents a single step, and curve VI represents multiple steps. In curve V (referred to here for simplicity), the plateau in the force region (marked by ** in curve V in Fig. 2B) was characterized by a certain distance, ΔL, and a rupture force, ΔF, as shown by an enlarged view into curve V (Fig. 2C). While the different curves shown in Fig. 2B were observed with both the GA6 and NY6 systems, the frequency of these events significantly differed in these 2 systems as outlined in the table in Fig. 2D. Specifically, in the GA6 system, more than 70% of the curves showed a step-like plateau in the force curve (curves V and VI). In comparison, less than 10% of the force curves in the NY6 system showed the step-like behavior, and the rest were distributed between curves I and IV, with a nonspecific adhesion F-D (curve I) dominating.

Fig. 2.
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Fig. 2.

Representative F-D curves measured between a hexapeptide on an AFM tip and globular structures of the same hexapeptide on a PEG layer. A schematic of the experimental system shows the hexapeptide covalently attached to the AFM tip through a PEG linker that is bound to the AFM tip with (3-Aminopropyl) trimethoxysilane (APTMS) (A). Representative F-D curves are shown in B. Curves I to III represent nonspecific interactions between the AFM tip and the surface. Curve IV shows a WLC behavior. Curves V (single step) and VI (multiple steps; positions of steps in a curve are denoted by numbers) show the characteristic nanomechanical fingerprint of the hexapeptide globular structures. The enlarged view at curve V (C) highlights the characteristic step rupture force (ΔF) and step length (ΔL). Measurements between a GA6-modified AFM tip and surface and between an NY6-modified tip and surface showed similar F-D curves, but the frequency of the different F-D curve types varied between these experiments. The table in D depicts the percentage of each F-D curve type (I to VI in B) of the total number of analyzed F-D curves. N (number of F-D curves analyzed) = 5,760 to 9,212. We suggest that our pulling experiments are similar to pulling a macromolecular chain from a reservoir as described schematically in E. The asterisks in E correspond to different pulling stages along the F-D trace shown in curve V in B as marked with starts accordingly. Initially, the modified AFM tip detaches from the surface (* in curve V in B); then, the AFM tip is pulled with a constant force as the hexapeptide chains are being pulled from the (shrinking) globular reservoir (** in curve V in B) into the solution. A final rupture event occurs when dF/dX > K (spring constant) as the AFM tip detaches from the hexapeptide chain (*** in curve V in B).

We performed several control experiments in order to test whether the force plateau F-D curves were specific to the interaction between the hexapeptide modified tip and the hexapeptide globular structures on the surface. All of the control experiments have been performed with GA6 due to the higher percentage of force plateau events in the GA6 relative to the NY6 system. SI Appendix, Table S2 lists the different configurations that we tested in the control experiments as well as the percentage of the plateau F-D curves in each experiment. Similar force curves as those shown in Fig. 2B were also observed in the control experiments, but the F-D curves with a plateau force only dominated in setups where both the AFM tip and the surface were modified with the hexapeptide. We concluded that, for a pulling force plateau F-D curve to occur, the AFM tip had to be modified with a complementary sequence to that on the surface.

Interestingly, similar force plateau F-D curves have been observed on surface detachment of a polypeptide chain (38⇓–40) as well as α-synuclein protofibrils (11). By analogy, since the globular structures were larger than the size of a single hexapeptide, we suggest that during the force plateau events, we pulled on hexapeptide chains. The hexapeptide chains either preformed in the globular structures or they were shear induced, as they were pulled away from the globular structures by an AFM tip modified with a complementary hexapeptide. The force plateau (per step) implies a triangle potential for the chain-unwinding process, where the energy varies linearly with the distance as a chain is pulled from a globule (41⇓–43). From a molecular perspective, we suggest that the globules act as a reservoir of hexapeptide chains and that, following a nonspecific unbinding event (* in curve V in Fig. 2B), a constant force (** in curve V in Fig. 2B) is necessary to unwind the chains, possibly due to the equality between the chain-unwinding force and the restoring force of the chain. Then, the AFM tip desorbs from the chain, and a rupture event occurs (*** in curve V in Fig. 2B). Fig. 2E shows a schematic representation of our explanation of the force plateau curves (curve V in Fig. 2B). A similar F-D behavior has been observed when pulling a hydrophobic polymer from a globule into an aqueous media (44) or when pulling lipid tubes or tethers from membranes (45⇓⇓–48), suggesting a common origin to the plateau F-D curves.

We then performed a detailed statistical analysis of the characteristic parameters in force plateau curves, such as curves V and VI in Fig. 2B: the step rupture force, ΔF, and the length of the step, ΔL. Fig. 3 shows the distribution of these parameters (Fig. 3 A–D) calculated from all of the force plateau F-D curves with single and multiple steps. Gaussian fits to the distribution of the rupture force, ΔF, show similar values for both the GA6 and NY6 systems: ΔF = 90 ± 20 pN (GA6) and ΔF = 95 ± 20 pN (NY6) (Fig. 3 A and B). The single-peak distribution of the plateau rupture force, essentially lacking additional peaks of multiples of the rupture force, is suggestive of pulling a single chain (44, 49). Analysis of the distribution of ΔL and a Gaussian fit to the data yielded characteristic length for the GA6 system ΔL = (13 ± 2) nm and characteristic length for the NY6 system ΔL = (20 ± 10) nm (Fig. 3 C and D); both are of the order of the average diameter of the globular structures (∼20 nm for GA6, and ∼40 nm for NY6). Plotting the rupture force against the step length, ΔL (Fig. 3 E and F), shows that the rupture force is relatively constant over all of the step length ranges. The independence of ΔF on ΔL (as well as the lack of WLC events) is suggestive of a lack of an entropic stretching during the force plateau step event that is observed, for example, in pulling on a titin molecule (33, 34). This supports our suggestion that a chain was pulled from a reservoir rather than from a surface anchor.

Fig. 3.
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Fig. 3.

Statistical analysis of F-D force plateau curves (curves V and VI in Fig. 2B). Distribution of the rupture force, ΔF, is shown for experiments with GA6 (A) and with NY6 (B). Distribution of step length, ΔL, is shown for experiments with GA6 (C) and with NY6 (D). A plot of the rupture force, ΔF, against the step length, ΔL, is shown in E for GA6, and in F for NY6. N = 250 to 1,400. Gaussian fits of the histogram distributions are shown in red together with the most probable ΔF and ΔL values.

We measured the F-D curves on retraction under different pulling speeds. We focused on the GA6 system because of its dominant force plateau behavior (as was done with the control experiments). The results, shown in SI Appendix, Fig. S6, show that the rupture force and step lengths are independent of the pulling speed, suggesting that, in the range of velocities tested, the system was in equilibrium with respect to molecular motion occurring during the pulling events. Similar behavior has been observed with a few other amyloid and polymer systems (13, 14, 50).

Pulling on surfaces covered with mature GA6 fibers, we observed multiple irregular F-D curves (a representative curve is shown in SI Appendix, Fig. S7). While the F-D curves showed steps occasionally, they were highly complex, and we could not easily classify them with the well-defined F-D curve types presented in Fig. 2B. The pulling events, sometimes extending to micrometers in length and nanonewtons in force (SI Appendix, Fig. S7), can be attributed to pulling on fibers with a more complex internal structure than the globular structures or to their surface detachment (11). In addition to the irregular F-D curves, we also observed nonbinding and nonspecific binding events. Since the fiber-coated layer itself was not as uniform and highly covered as that of the globules (Fig. 1E), these events can be attributed to the interaction of the modified tip with a bare surface. It can also be explained by the inaccessibility of the hexapeptide binding groups to the modified tip either due to them being buried inside the fibers or because they are more tightly packed (14).

The Characteristic F-D Curve Is Sequence Dependent.

Witnessing the differences between the GA6 and NY6 systems, we asked whether the F-D curves that we measured were sequence dependent. We studied the nanomechanical properties of shuffled hexapeptide sequences. The shuffled NY6, NNQYQN sequence (henceforth referred to as NY6S), and the shuffled GA6, VAAASG (henceforth referred to as GA6S), were used, because they both receive the lowest ZipperDB energy and composite score of all possible NY6 and GA6 shuffles (SI Appendix, Table S1). The shuffled hexapeptide NY6S (molecular structure is in Fig. 4A) also formed globular structures at the surface of a PEG layer (Fig. 4B) with an average diameter (30 ± 10 nm), which is between the diameters of GA6 (20 ± 10 nm) and NY6 (40 ± 15 nm). The F-D curves measured with NY6S exhibited a similar set of forces as that presented in Fig. 2B. However, shuffling the NY6 sequence resulted in ∼60% force plateau events of the total number of measured F-D curves relative to less than 10% measured with the NY6 system. Surprisingly, despite its low-ZipperDB score, the shuffled GA6 hexapeptide (molecular structure is in Fig. 4E) assembled into a mixture of globules and fibrils (Fig. 4F) under the conditions where GA6 formed only globules (Fig. 1C). Unlike the NY6S case where shuffling the sequence increased the frequency of force plateau events, with GA6S, only 3% of the F-D curves (relative to 70% with GA6) showed a force plateau behavior. This difference in step frequency suggests that NY6 and GA6S better pack in a globule, and thereby, they become less accessible to interaction with the hexapeptide-modified AFM tip. Analysis of the force plateau F-D curves measured with NY6S showed a step rupture force ΔF = 80 ± 20 pN (Fig. 4C) and a step length ΔL = 30 ± 20 nm (Fig. 4D). The shuffled GA6 structures that could be unzipped (3% of all of the F-D curves measured) showed a wide step length distribution (Fig. 4H), representing the large variety of the GA6S structures (the topography AFM image is in Fig. 4F). The distribution of step lengths of the GA6S system could not be fitted with a conventional statistical distribution function, but it included 3 dominant regions, peaking around 25 nm (corresponding to globular diameter) (SI Appendix, Fig. S8), ∼100 nm, and ∼170 nm (corresponding to fibrils’ lengths ranging between 50 and 250 nm). The step rupture force (70 ± 15 pN) (Fig. 4G) was single peaked, implying that we could not discriminate between globular structures and (young) fibril pulling in our experimental setup. Similarly to the unshuffled systems, the step rupture force was independent of the step length in the GA6S and NY6S systems (SI Appendix, Fig. S9).

Fig. 4.
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Fig. 4.

The effect of sequence on the F-D measurements. The molecular structure of NY6S and the shuffled sequence of the hexapeptide NY6 are shown in A, and the molecular structure of GA6S and the shuffled sequence of the hexapeptide GA6 are shown in E. NY6S forms globular structures at the surface of a PEG layer as shown by the AFM topography image in B, and GA6S forms a mixture of globules and fibrils (F). Analysis of the force plateau F-D curves measured between a hexapeptide-modified AFM tip and the hexapeptide layer yields the distribution of the step rupture force (ΔF) and the step length (ΔL) as shown for NY6S in C and D, respectively. The distributions of ΔF and ΔL are shown for GA6S in G and H, respectively. Gaussian fits of the histogram distributions are shown in red together with the most probable ΔF and ΔL values. The data in H could not be fitted with a standard statistical distribution function. (Scale bars: 200 nm.)

The Force Plateaus and Lengths Are Quantized.

In our analysis of the force plateau curves, we thus far referred to the characteristic parameters ΔF and ΔL and their total distribution over all of the force curves disrespectfully of the number of the force plateau events per F-D curve (a representation of multiple steps in curve VI is in Fig. 2B). However, the number of steps observed per F-D curve is an additional characteristic of the force plateau curves, and it poses an important clue to the mechanism behind the force plateau steps. We propose that unwinding single-hexapeptide chains from globular structures during the force plateau events is similar to unwinding a yarn ball, where loops of equal length are being pulled from a reservoir with equal force (51). Using this analogy, we suggest that, in our system, multiple steps occur when unwinding hexapeptides loops from globular structures (schematic model is in Fig. 5I). Better packing of the chains within a globule will lead to a smaller number of steps (loops) and vice versa. Fig. 5 and SI Appendix, Fig. S10 show that pulling on different hexapeptide layers yielded a different number of steps in each F-D force plateau curve. Specifically, the number of steps in GA6S (2 steps) < NY6 (3 steps) < GA6 (4 steps) < NY6S (6 steps). The smaller number of steps of GA6S and NY6 together with the lower step frequency of GA6S (3%) and NY6 (8%) indicate that these hexapeptides pack better in a globule relative to the GA6 and NY6S globular structures.

Fig. 5.
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Fig. 5.

Comparison between the step rupture force (ΔF) and step length (ΔL) measured in different step positions. Step position 1 is the first rupture event as specified in curve VI in Fig. 2B. The step rupture force was measured with GA6 (A), GA6S (B), NY6 (C), and NY6S (D), and the step length, ΔL, was measured with GA6 (E), GA6S (F), NY6 (G), and NY6S (H). N = 232 to 812. Data are plotted on the same scale for clarity. We explain the multiple steps of equal ΔF and ΔL by analogy with unwinding a yarn ball as shown schematically in I (not drawn to scale). The globular structures are composed of hexapeptide chains (either preformed or shear induced) that are unwound loop by loop. The loops’ length matches the size of a step length, ΔL, and it is of the order of the globule’s diameter (both marked with an arrow). Unwinding the equally sized loops gives rise to multiple force plateau steps of equal force and length for each hexapeptide. The final loop is smaller than its preceding, resulting in smaller steps in the final rupture events. The rupture force measured in the final step was used to calculate the hexapeptide–hexapeptide interaction energy.

We compared the unwinding forces and step lengths between the different step positions in a force curve (curve VI in Fig. 2B shows the definition of the step position). Fig. 5 A–H shows that, in all of the hexapeptide layers, the unwinding lengths and forces are quantized (i.e., each unwinding event required the same amount of energy in agreement with the yarn ball model) (51). Interestingly, the characteristic step length of each hexapeptide globule, deduced from the F-D curves in Figs. 3 and 4—ΔL = 13 ± 2 (GA6), 20 ± 10 (NY6), 30 ± 20 (NY6S) nm—is of the order of the average globule diameter, deduced from the AFM images—20 ± 10 (GA6), 40 ± 15 (NY6), 30 ± 10 (NY6S) nm. We did not refer to GA6S in this comparison because it formed both globules and fibrils; however, here as well, the size of the globules measured by the AFM (20 ± 7 nm) was similar to ΔL ∼ 25 nm, as shown in SI Appendix, Fig. S8. Furthermore, the distribution of the step lengths correlates well with the distribution of the diameters of the globular structures (SI Appendix, Fig. S8). The correspondence between the measured step lengths and the size of the globules supports the suggestion that the force plateau steps represent unwinding of hexapeptide loops that are of the order of the diameter of the globular structure as illustrated in Fig. 5I. In the final step, before the AFM tip desorbs from the chain, the AFM probe is pulling the remaining part of the chain, and therefore, it is not necessarily similar in length to the “ΔL quanta.”

Last, we were intrigued to compare the Eisenberg hexapeptide–hexapeptide interaction energy with that calculated from the force needed to detach the hexapeptide-modified AFM tip from the hexapeptide chain. We used the equation ΔE = ΔF lengthhexapeptide to calculated the energy required to detach the hexapeptide-modified tip from the hexapeptide chain. Estimating the lengthhexapeptide to be the length of a single hexapeptide on which the detachment force acts (∼2 nm) and plugging in the rupture force values at the final step (ΔF [GA6] = 90 ±10 pN, ΔF [NY6] = 120 ±10 pN, ΔF [GA6S] = 70 ± 15 pN, ΔF [NY6S] = 80 ± 20 pN), we found that the hexapeptide–hexapeptide interaction was ΔE (NY6)= 35 ± 3 kcal/mol, ΔE (GA6) = 26 ± 3 kcal/mol, ΔE (NY6S)= 23 ± 2 kcal/mol, and ΔE (GA6S) = 20 ± 4 kcal/mol. Remarkably, all of these values stand well within the steric zipper unzipping energy calculated by Eisenberg and coworkers (18). However, while the calculation predicts that only the nonshuffled sequences form fibers (SI Appendix, Table S1), our results show that the differences in hexapeptide interaction energy are subtle, and indeed, eventually all of the hexapeptides formed fibers after a long time (Fig. 1 E and F and SI Appendix, Figs. S4 and S11). Considering all of the nanomechanical properties of hexapeptide structures that we measured and discussed, we conclude that it is the number of steps and their relative frequency in the F-D measurements and not their measured interaction energy that better probe the differences in the packing of these hexapeptide structures.

Conclusions

We have shown that steric zippers form globular structures on route to fiber formation and that they exhibit characteristic force plateau F-D curves when pulled with an AFM tip of a complementary hexapeptide. Similar force plateau steps have been attributed to surface detachment of amyloid fibrils or other polypeptide chains (11, 38⇓–40, 52), but we attribute this behavior to pulling chains from a globule, in similarity to pulling a polymer from a reservior (38, 44⇓⇓⇓–48, 53). The hexapeptide chains either were preformed prior to the pulling or were shear induced and formed in response to the AFM pulling force. Our results were independent of the origin of the hexapeptide, as they were observed with eukaryotic and bacterial hexapeptide. The nanomechanical signature of early amyloid aggregates maps their internal structure, and therefore, it opens a different approach for drug design that is based on similarity between nanomechanical properties rather than on structural similarity. This approach is particularly relevant in early aggregation stages, where amyloid structures are not yet crystalline, and it becomes especially important in sequence independent systems/structures, such as the case of amyloid fibers. For these reasons, our study provides an additional insight into the design of drugs in the fight against neurodegenerative disease.

Materials and Methods

Detailed information on the experimental methods can be found in SI Appendix. Hexapeptides were purchased from GL Biochem (Shanghai). Silicon surfaces (TedPella Inc.) and AFM probes were modified with trimethoxy(propyl)silane:(3-Aminopropyl) trimethoxysilane (15:1) (Sigma) and N-Hydroxysuccinimide (NHS)-PEG-NHS (PG2-NS-2k; Nanocs). AFM topography images were taken in Peakforce QuantitativeNanomechanical (Peakforce QNM) mode, and force spectroscopy measurements were performed in force volume mode using a BioScope Resolve BioAFM (Bruker).

Acknowledgments

We thank Profs. Jay Feinberg, Daniel Strasser, and Uri Raviv for fruitful discussions and Shahar Dery and Yaelle Schilt for technical advice. This work was funded by Israeli Science Foundation (ISF) Grant 1150/14 (to L.C.).

Footnotes

  • ↵1To whom correspondence may be addressed. Email: liraz.chai{at}mail.huji.ac.il.
  • Author contributions: N.L.-Z. and L.C. designed research; N.L.-Z. and M.G. performed research; N.L.-Z., M.G., and L.C. analyzed data; and N.L.-Z., M.G., and L.C. wrote the paper.

  • The authors declare no competing interest.

  • This article is a PNAS Direct Submission. E.G. is a guest editor invited by the Editorial Board.

  • This article contains supporting information online at www.pnas.org/lookup/suppl/doi:10.1073/pnas.1908782116/-/DCSupplemental.

Published under the PNAS license.

References

  1. ↵
    1. T. Eichner,
    2. S. E. Radford
    , A diversity of assembly mechanisms of a generic amyloid fold. Mol. Cell 43, 8–18 (2011).
    OpenUrlCrossRefPubMed
  2. ↵
    1. D. Eisenberg,
    2. M. Jucker
    , The amyloid state of proteins in human diseases. Cell 148, 1188–1203 (2012).
    OpenUrlCrossRefPubMed
  3. ↵
    1. F. Chiti,
    2. C. M. Dobson
    , Protein misfolding, amyloid formation, and human disease: A summary of progress over the last decade. Annu. Rev. Biochem. 86, 27–68 (2017).
    OpenUrlCrossRefPubMed
  4. ↵
    1. D. M. Fowler,
    2. A. V. Koulov,
    3. W. E. Balch,
    4. J. W. Kelly
    , Functional amyloid–From bacteria to humans. Trends Biochem. Sci. 32, 217–224 (2007).
    OpenUrlCrossRefPubMed
  5. ↵
    1. L. P. Blanco,
    2. M. L. Evans,
    3. D. R. Smith,
    4. M. P. Badtke,
    5. M. R. Chapman
    , Diversity, biogenesis and function of microbial amyloids. Trends Microbiol. 20, 66–73 (2012).
    OpenUrlCrossRefPubMed
  6. ↵
    1. R. P. Friedland,
    2. M. R. Chapman
    , The role of microbial amyloid in neurodegeneration. PLoS Pathog. 13, e1006654 (2017).
    OpenUrlCrossRef
  7. ↵
    1. S. G. Chen et al
    ., Exposure to the functional bacterial amyloid protein curli enhances alpha-synuclein aggregation in aged fischer 344 rats and Caenorhabditis elegans. Sci. Rep. 6, 34477 (2016).
    OpenUrlCrossRefPubMed
  8. ↵
    1. R. Kayed,
    2. C. A. Lasagna-Reeves
    , Molecular mechanisms of amyloid oligomers toxicity. J. Alzheimers Dis. 33 (suppl. 1), S67–S78 (2013).
    OpenUrlCrossRefPubMed
  9. ↵
    1. C. G. Glabe
    , Structural classification of toxic amyloid oligomers. J. Biol. Chem. 283, 29639–29643 (2008).
    OpenUrlAbstract/FREE Full Text
  10. ↵
    1. D. P. Hong,
    2. S. Han,
    3. A. L. Fink,
    4. V. N. Uversky
    , Characterization of the non-fibrillar α-synuclein oligomers. Protein Pept. Lett. 18, 230–240 (2011).
    OpenUrlPubMed
  11. ↵
    1. F. S. Ruggeri et al
    ., Identification and nanomechanical characterization of the fundamental single-strand protofilaments of amyloid α-synuclein fibrils. Proc. Natl. Acad. Sci. U.S.A. 115, 7230–7235 (2018).
    OpenUrlAbstract/FREE Full Text
  12. ↵
    1. A. Karsai et al
    ., Mechanical manipulation of Alzheimer’s amyloid β1-42 fibrils. J. Struct. Biol. 155, 316–326 (2006).
    OpenUrlCrossRefPubMed
  13. ↵
    1. M. S. Z. Kellermayer et al
    ., Reversible mechanical unzipping of amyloid β-fibrils. J. Biol. Chem. 280, 8464–8470 (2005).
    OpenUrlAbstract/FREE Full Text
  14. ↵
    1. D. Alsteens,
    2. C. B. Ramsook,
    3. P. N. Lipke,
    4. Y. F. Dufrêne
    , Unzipping a functional microbial amyloid. ACS Nano 6, 7703–7711 (2012).
    OpenUrlCrossRefPubMed
  15. ↵
    1. R. Nelson et al
    ., Structure of the cross-beta spine of amyloid-like fibrils. Nature 435, 773–778 (2005).
    OpenUrlCrossRefPubMed
  16. ↵
    1. M. C. Lawrence,
    2. P. M. Colman
    , Shape complementarity at protein/protein interfaces. J. Mol. Biol. 234, 946–950 (1993).
    OpenUrlCrossRefPubMed
  17. ↵
    1. S. A. Combs et al
    ., Small-molecule ligand docking into comparative models with Rosetta. Nat. Protoc. 8, 1277–1298 (2013).
    OpenUrlCrossRefPubMed
  18. ↵
    1. L. Goldschmidt,
    2. P. K. Teng,
    3. R. Riek,
    4. D. Eisenberg
    , Identifying the amylome, proteins capable of forming amyloid-like fibrils. Proc. Natl. Acad. Sci. U.S.A. 107, 3487–3492 (2010).
    OpenUrlAbstract/FREE Full Text
  19. ↵
    1. M. R. Sawaya et al
    ., Atomic structures of amyloid cross-beta spines reveal varied steric zippers. Nature 447, 453–457 (2007).
    OpenUrlCrossRefPubMed
  20. ↵
    1. A. Schmidt,
    2. K. Annamalai,
    3. M. Schmidt,
    4. N. Grigorieff,
    5. M. Fändrich
    , Cryo-EM reveals the steric zipper structure of a light chain-derived amyloid fibril. Proc. Natl. Acad. Sci. U.S.A. 113, 6200–6205 (2016).
    OpenUrlAbstract/FREE Full Text
  21. ↵
    1. A. W. P. Fitzpatrick et al
    ., Atomic structure and hierarchical assembly of a cross-β amyloid fibril. Proc. Natl. Acad. Sci. U.S.A. 110, 5468–5473 (2013).
    OpenUrlAbstract/FREE Full Text
  22. ↵
    1. M. J. Thompson et al
    ., The 3D profile method for identifying fibril-forming segments of proteins. Proc. Natl. Acad. Sci. U.S.A. 103, 4074–4078 (2006).
    OpenUrlAbstract/FREE Full Text
  23. ↵
    1. E. Gazit
    , A possible role for π-stacking in the self-assembly of amyloid fibrils. FASEB J. 16, 77–83 (2002).
    OpenUrlCrossRefPubMed
  24. ↵
    1. I. G. Cuesta,
    2. A. M. J. Sánchez de Merás
    , Energy interactions in amyloid-like fibrils from NNQQNY. Phys. Chem. Chem. Phys. 16, 4369–4377 (2014).
    OpenUrl
  25. ↵
    1. O. S. Makin,
    2. L. C. Serpell
    , Structures for amyloid fibrils. FEBS J. 272, 5950–5961 (2005).
    OpenUrlCrossRefPubMed
  26. ↵
    1. P. C. A. van der Wel,
    2. J. R. Lewandowski,
    3. R. G. Griffin
    , Solid-state NMR study of amyloid nanocrystals and fibrils formed by the peptide GNNQQNY from yeast prion protein Sup35p. J. Am. Chem. Soc. 129, 5117–5130 (2007).
    OpenUrlCrossRefPubMed
  27. ↵
    1. M. Balbirnie,
    2. R. Grothe,
    3. D. S. Eisenberg
    , An amyloid-forming peptide from the yeast prion Sup35 reveals a dehydrated beta-sheet structure for amyloid. Proc. Natl. Acad. Sci. U.S.A. 98, 2375–2380 (2001).
    OpenUrlAbstract/FREE Full Text
  28. ↵
    1. D. Romero,
    2. C. Aguilar,
    3. R. Losick,
    4. R. Kolter
    , Amyloid fibers provide structural integrity to Bacillus subtilis biofilms. Proc. Natl. Acad. Sci. U.S.A. 107, 2230–2234 (2010).
    OpenUrlAbstract/FREE Full Text
  29. ↵
    1. L. Chai et al
    ., Isolation, characterization, and aggregation of a structured bacterial matrix precursor. J. Biol. Chem. 288, 17559–17568 (2013).
    OpenUrlAbstract/FREE Full Text
  30. ↵
    1. A. Diehl et al
    ., Structural changes of TasA in biofilm formation of Bacillus subtilis. Proc. Natl. Acad. Sci. U.S.A. 115, 3237–3242 (2018).
    OpenUrlAbstract/FREE Full Text
  31. ↵
    1. A. Chazan
    , Peptide Property Calculator. http://biotools.nubic.northwestern.edu/proteincalc.html. Accessed 20 May 2019.
  32. ↵
    1. M. Carrion-Vazquez,
    2. P. E. Marszalek,
    3. A. F. Oberhauser,
    4. J. M. Fernandez
    , Atomic force microscopy captures length phenotypes in single proteins. Proc. Natl. Acad. Sci. U.S.A. 96, 11288–11292 (1999).
    OpenUrlAbstract/FREE Full Text
  33. ↵
    1. M. Carrion-Vazquez et al
    ., Mechanical and chemical unfolding of a single protein: A comparison. Proc. Natl. Acad. Sci. U.S.A. 96, 3694–3699 (1999).
    OpenUrlAbstract/FREE Full Text
  34. ↵
    1. R. Berkovich,
    2. V. I. Fernandez,
    3. G. Stirnemann,
    4. J. Valle-Orero,
    5. J. M. Fernández
    , Segmentation and the entropic elasticity of modular proteins. J. Phys. Chem. Lett. 9, 4707–4713 (2018).
    OpenUrlCrossRef
  35. ↵
    1. J. E. Bemis,
    2. B. B. Akhremitchev,
    3. G. C. Walker
    , Single polymer chain elongation by atomic force microscopy. Langmuir 15, 2799–2805 (1999).
    OpenUrlCrossRef
  36. ↵
    1. M. Rief,
    2. M. Gautel,
    3. F. Oesterhelt,
    4. J. M. Fernandez,
    5. H. E. Gaub
    , Reversible unfolding of individual titin immunoglobulin domains by AFM. Science 276, 1109–1112 (1997).
    OpenUrlAbstract/FREE Full Text
  37. ↵
    1. J. Zlatanova,
    2. S. M. Lindsay,
    3. S. H. Leuba
    , Single molecule force spectroscopy in biology using the atomic force microscope. Prog. Biophys. Mol. Biol. 74, 37–61 (2000).
    OpenUrlCrossRefPubMed
  38. ↵
    1. S. Krysiak,
    2. S. Liese,
    3. R. R. Netz,
    4. T. Hugel
    , Peptide desorption kinetics from single molecule force spectroscopy studies. J. Am. Chem. Soc. 136, 688–697 (2014).
    OpenUrl
  39. ↵
    1. D. Horinek et al
    ., Peptide adsorption on a hydrophobic surface results from an interplay of solvation, surface, and intrapeptide forces. Proc. Natl. Acad. Sci. U.S.A. 105, 2842–2847 (2008).
    OpenUrlAbstract/FREE Full Text
  40. ↵
    1. C. Friedsam,
    2. H. E. Gaub,
    3. R. R. Netz
    , Probing surfaces with single-polymer atomic force microscope experiments. Biointerphases 1, MR1–MR21 (2006).
    OpenUrlPubMed
  41. ↵
    1. L. Dai,
    2. P. S. Doyle
    , Trapping a knot into tight conformations by intra-chain repulsions. Polymers (Basel) 9, E57 (2017).
    OpenUrl
  42. ↵
    1. L. Dai,
    2. P. S. Doyle
    , Effects of intrachain interactions on the knot size of a polymer. Macromolecules 49, 7581–7587 (2016).
    OpenUrl
  43. ↵
    1. J. N. Israelachvili
    1. J. N. Israelachvili
    , “Nonequilibrium and time-dependent interactions” in Intermolecular and Surface Forces, J. N. Israelachvili, Ed. (Academic Press, Boston, MA, ed. 3, 2011), pp. 169–188.
  44. ↵
    1. J. Mondal et al
    ., How osmolytes influence hydrophobic polymer conformations: A unified view from experiment and theory. Proc. Natl. Acad. Sci. U.S.A. 112, 9270–9275 (2015).
    OpenUrlAbstract/FREE Full Text
  45. ↵
    1. V. M. Laurent,
    2. A. Duperray,
    3. V. Sundar Rajan,
    4. C. Verdier
    , Atomic force microscopy reveals a role for endothelial cell ICAM-1 expression in bladder cancer cell adherence. PLoS One 9, e98034 (2014).
    OpenUrlCrossRefPubMed
  46. ↵
    1. B. Gumí-Audenis et al
    ., Pulling lipid tubes from supported bilayers unveils the underlying substrate contribution to the membrane mechanics. Nanoscale 10, 14763–14770 (2018).
    OpenUrl
  47. ↵
    1. D. Raucher,
    2. M. P. Sheetz
    , Characteristics of a membrane reservoir buffering membrane tension. Biophys. J. 77, 1992–2002 (1999).
    OpenUrlCrossRefPubMed
  48. ↵
    1. M. Sun et al
    ., Multiple membrane tethers probed by atomic force microscopy. Biophys. J. 89, 4320–4329 (2005).
    OpenUrlCrossRefPubMed
  49. ↵
    1. A. Sarkar,
    2. S. Caamano,
    3. J. M. Fernandez
    , The mechanical fingerprint of a parallel polyprotein dimer. Biophys. J. 92, L36–L38 (2007).
    OpenUrlCrossRefPubMed
  50. ↵
    1. S. Kienle,
    2. T. Pirzer,
    3. S. Krysiak,
    4. M. Geisler,
    5. T. Hugel
    , Measuring the interaction between ions, biopolymers and interfaces–one polymer at a time. Faraday Discuss. 160, 329–340 (2013).
    OpenUrl
  51. ↵
    1. D. G. Padfield
    , The motion and tension of an unwinding thread. I. Proc. R. Soc. Lond. A Math. Phys. Sci. 245, 382–407 (1958).
    OpenUrl
  52. ↵
    1. P. Delparastan,
    2. K. G. Malollari,
    3. H. Lee,
    4. P. B. Messersmith
    , Direct evidence for the polymeric nature of polydopamine. Angew. Chem. Int. Ed. Engl. 58, 1077–1082 (2019).
    OpenUrl
  53. ↵
    1. A. Scherer,
    2. C. Zhou,
    3. J. Michaelis,
    4. C. Brauchle,
    5. A. Zumbusch
    , Intermolecular interactions of polymer molecules determined by single-molecule force spectroscopy. Macromolecules 38, 9821–9825 (2005).
    OpenUrlCrossRef
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Nanomechanical properties of steric zipper globular structures
Neta Lester-Zer, Mnar Ghrayeb, Liraz Chai
Proceedings of the National Academy of Sciences Nov 2019, 116 (45) 22478-22484; DOI: 10.1073/pnas.1908782116

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Nanomechanical properties of steric zipper globular structures
Neta Lester-Zer, Mnar Ghrayeb, Liraz Chai
Proceedings of the National Academy of Sciences Nov 2019, 116 (45) 22478-22484; DOI: 10.1073/pnas.1908782116
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