Abstract
The 20S proteasome is a core particle of the eukaryotic proteasome responsible for proteolysis and is composed of layered α and β hetero-heptameric rings. The α7 subunit, which is one of components of the α ring, is known to self-assemble into a double-ringed homo-tetradecamer composed of two layers of the α7 heptameric ring. The α7 tetradecamer is known to disassemble upon the addition of α6 subunit, producing a 1:7 hetero-octameric α6-α7 complex. However, the detailed disassembly mechanism remains unclear. Here, we applied high-speed atomic force microscopy (HS-AFM) to dissect the disassembly process of the α7 double ring caused by interaction with the α6. HS-AFM movies clearly demonstrated two different modes of interaction in which the α6 monomer initially cracks at the interface between the stacked two α7 single rings and the subsequent intercalation of the α6 monomer in the open pore of the α7 single ring blocks the re-association of the single rings into the double ring. This result provides a mechanistic insight about the disassembly process of non-native homo-oligomers formed by proteasome components which is crucial for the initial process for assembly of 20S proteasome.
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Introduction
The proteasome is the central enzyme responsible for regulated proteolysis mostly with ubiquitin-dependent manner in eukaryotic cells1,2. The eukaryotic 26S proteasome is a huge protein complex which can be divided into two primary parts, 20S and 19S. The 20S proteasome is a core particle functioning as the catalytic chamber while the 19S complex caps both or either ends of the 20S catalytic chamber and regulates proteolysis activity3. The 20S core particle is a barrel-shaped complex composed of two α and two β hetero-heptameric rings stacked of a layer in order of αββα4,5,6. The assembly of the 20S proteasome is initiated by the formation of a heptamer ring with seven homologous and distinct α subunits. The α subunits assemble into the ring form with the well-ordered manner of α1-α2-α3-α4-α5-α6-α7, which is promoted and stabilized by the help of assembly chaperones7,8. Subsequently the α-ring serves as a platform on assembly of the seven distinct β subunits in the order of rings β1-7 which is accomplished by the help of additional chaperones9,10. However, the detailed mechanism for creating a distinctively ordered assembly of the α and β rings and the consequent formation of the 20S proteasome remains elusive.
Among seven α-type subunits in human proteasome, the α7 subunit has a unique feature with which the α7s self-assemble into a double-ringed tetradecamer consisting of two stacked homo-heptameric rings11,12, similar to the α ring seen in archaea. Recent combination analysis of mass spectroscopy (MS) and sedimentation velocity analytical ultracentrifugation (SV-AUC) has revealed that the α7 double rings are disassembled into the single ring upon the addition of α6 monomers, resulting in a 1:7 hetero-octamer α6-α7 complex13. This implies that disassembly of non-native oligomeric forms of proteasome subunits existing as an assembly intermediate would be crucial toward the terminal 20S form. The following model has been proposed as for disassembly of the α7 double ring13: binding of an α6-monomer onto the outer face of an α7 double-ring tetradecamer allosterically induces conformational change of α7 at the interface between the two α7 single rings, which impairs the stacking interaction between the single rings. Nevertheless, the complex form of the α6 monomer and the α7 heptamer was not experimentally verified and further the disassembly mechanisms including validation of the proposed model remain unclear.
Here, we directly observed interaction between the α7 homo-tetradecamer and the α6 monomer by using high-speed atomic force microscopy (HS-AFM), which allows us to study various dynamic behavior of single proteins at work such as conformational change and binding/dissociation events14,15,16. The HS-AFM movies clearly show that the α6 monomer interacts with the open pore of the α7 heptamer ring corresponding to the stacked face of the double ring rather than the outer face. Further, stacking of the two α7-heptamer rings was quite wobbly, engendering a transient cleft between layered α7 single rings. This transient cleft is susceptible to the binding of the α6 monomer onto the α7 single ring’s open-pore site. These observations provide a straightforward view of the disassembly process of the α7 tetradecamer by which the α6 monomer works as a physical blocker against association of the α7 single rings into the double-ring form.
Results and Discussion
HS-AFM observation of the human α7 homo-tetradecamer
Figure 1a shows a wide-view HS-AFM image of human-proteasome α7 homo-tetradecamers immobilized on a mica surface chemically treated with 3-aminopropyltriethoxysilane (APTES-mica). The HS-AFM image showed inhomogeneous particles with apparently different height. The diverse structures could be classified into three primary structures including disk (Fig. 1b), barrel-shaped (Fig. 1c) and ring (Fig. 1d) forms. The disk form obviously corresponds to the top surface of the double-ringed tetradecamer displaying the closed gate conformation. In fact, a simulated AFM image constructed by the crystal structure of α7 homo-tetradecamer (PDB code: 5DSV13) well reproduced the real HS-AFM image (Fig. 1e). The barrel-shaped form (Fig. 1c) seems to correspond to the side view of the α7 double ring, as is illustrated by a simulated AFM image (Fig. 1f). The third structure (Fig. 1d) showed a clear central pore with a diameter of about 3 nm. This ring-shaped structure appears to be significantly different from the tetradecamer (Fig. 1b). This configuration corresponds to the open-pore side of the α7 heptamer ring, which is turned inwards in the tetradecamer configuration. To illustrate this, a simulated AFM image of the open-pore side is shown in Fig. 1g. Furthermore, the height of the ring was about half of the double ring (Fig. 1h), indicating that the double-ringed tetradecamer was bisected into the single heptamer ring. Apparently, the diameters of the double ring and the bisected single ring are different (Fig. 1h). From the AFM images, the diameter of the double ring is found to be larger than that of the single ring. This is attributed to both the tip-shape convolution and a slight difference of the diameters at the topmost ring faces. The diameter of the taller double ring is affected by the finite and cone-shaped tip more than the single ring (Supplementary Fig. 1).
We assume that the double rings were disassembled into the two single rings during their adsorption onto APTES-mica. To confirm this, we observed adsorption process of the α7 double rings onto APTES-mica by adding the α7 double rings into the observation buffer during HS-AFM imaging (Fig. 1i and Supplementary Movie 1). The double ring was disassembled into two single rings within a single frame (1 s/frame) after the adsorption. This indicates that the strong affinity of the APTES-mica to the closed-pore side of α7 single ring overcomes the stacking interaction between two α7 heptamers. In relative numbers, the orientations of the oligomers were: 11% for the side view, 10% for the top view of the double ring and 79% for the single ring (determined by analyzing 263 oligomers). More than half of the double rings were disassembled by interacting with the substrate.
Structure of 1:7 hetero-octamer α6-α7 complex
We next examined a binding site of the α6 upon the α7 double ring by directly observing their interaction. Human-proteasome α6 subunits were added into the observation buffer to a final concentration of 1 μM during HS-AFM imaging of the α7 double ring on the APTES-mica. Within a few seconds after the addition of α6, bright spots appeared on the AFM images. Notably, bright spots were never observed on top of the α7 double ring structures, but only on the bisected single rings (Fig. 2a and Supplementary Movie 2). Since it has been addressed that the α6 primarily exits as a monomer form in the solution without forming any oligomer states13, the bright spots should correspond to the α6 monomer. Surprisingly, the α6 monomer was repeatedly bound to the open-pore side of the α7 single ring rather than the closed-pore side which is exposed to the solution in the double-ring form.
A magnified image displaying the trapped α6 at the open pore of the α7 single ring is shown in Fig. 2b. The resulting increase of the α7 heptamer’s height was about 2.5 nm. The α7 heptamer harboring the α6 monomer at the pore site should correspond to the 1:7 hetero-octamer α6-α7 complex found by a previous study13. The interaction between α6 monomers and α7 heptamers was dynamical with repeated binding and dissociation (Fig. 2c,d and Supplementary Movie 3). Time courses of α7 heptamers’ height increase due to binding of α6 are plotted in Fig. 2d. Interestingly, these plots show that the α6 dwell time is dependent on the time elapsed since the addition of α6. Histograms of the dwell time of α6 on the α7 single ring for an elapsed time of less than 15 min could be fitted well by a single exponential function (Supplementary Fig. 2a). The lifetime of the bound state increases linearly with the total elapsed time (Fig. 2e). When the time after the addition of α6 exceeds 20 min, the lifetime of the bound state becomes significantly longer (Fig. 2f and Supplementary Movie 4). Moreover, the histograms could not be fitted by a single exponential function (Supplementary Fig. 2e and f). The reason for this is that the dwell time for most of the α6 was longer than the maximum imaging frames (1000 frames, 100 s), hampering statistical analysis because of too few binding and dissociation events. Thus, the affinity between the α6 and the α7 single ring gradually changed depending on the time after α6 monomers were added and was nonlinearly boosted after 20 min. The affinity alteration took place only after the addition of α6. Even if α7 single rings were left for several tens of minutes after adsorption to the APTES-mica surface before α6 addition, the time-dependent affinity change between the α6 monomer and the α7 single ring was not affected. This implies that the affinity alteration stems from repeated binding and dissociation of the α6 to the α7 single ring.
There are several reports of proteins that undergo a time-dependent conformational change due to ligand bindings. The interconversion between two different conformational states of such proteins sometimes shows a time scale of several tens of minutes17,18,19. Furthermore, it has been found that fibrinogen gradually changes by immobilization onto the solid substrate, resulting in an enhanced affinity to the substrate20. Therefore, we speculate that the origin of the affinity change is caused by time-dependent conformational changes in either the α7 subunits of the heptamer or the α6 monomer, which is induced by their dynamic interaction.
In summary, α6 monomers predominantly interact with the open pore of the α7 single ring but have very little affinity to other sides. Interaction between the α6 monomer and the α7 single ring was dynamical at the onset but the affinity was gradually reinforced, possibly by conformational changes on either the α6 or the α7, which could be elicited by repeated binding and dissociation. Binding of the α6 monomer onto the α7 single ring was eventually strengthened, which would block re-stacking of the α7 single rings.
Interaction between α6 and the α7 double ring
The fact that α6 interacts with the open-pore side of an α7 single ring implies spontaneous disassembly of the α7 double ring, which raised the question as to how the stacking interaction is fragile. To investigate this issue, we used a bare mica as a substrate with a lower affinity to the α7 double ring than the APTES-mica. The amount of the double rings on the bare mica was increased to 67% from 21% on APTES-mica. However most of them appeared as the barrel shape, indicating the dominant interaction site of the α7 double ring to mica surface was the sidewall of the double ring.
The HS-AFM images revealed an unanticipated wobbling motion of the stacked α7 single rings for ~60% of the α7 double ring forms (Fig. 3a and Supplementary Movie 5), while ~40% of them showed the tightly packed interface as shown in Fig. 1c. A similar wobbling motion was observed for the α7 tetradecamer adsorbed on mica in a different orientation (Supplementary Fig. 3a). The interface between the two rings was perpendicular to the scanning direction of AFM tip. This suggests that the gap formation between the rings is not induced by the scanning of the tip. Center-to-center distance between two single rings (Dcc) for the wobbling double ring, which corresponds to a distance between two dashed lines drawn on the images at 9.9 s and 18.6 s in Fig. 3a, was fitted by a Gaussian distribution with the center value of about 8 nm and the width of ±0.9 nm (Fig. 3b, upper panel). Furthermore, the α7 double rings sometimes completely dissociated into single rings and then reassembled (Supplementary Movie 6 and Supplementary Fig. 3b). This reassembly of two α7 single rings after the complete dissociation presumably occurs only when the rings are constrained to the surface and, thus, the diffusion is limited to a two-dimensional surface. If the molecules are in a solution, dissociated rings would be shuffled and then associate with a different partner ring. On the other hand, a small-angle neutron scattering (SANS) analysis has revealed no exchange of α7 single rings between double rings in the absence of α612,21. This suggests that the complete dissociation of the double ring is caused by the tip disturbance and the dissociation of the single rings is transient.
When the α6 was added to the observation buffer, the α6 was bound to the cleft at the interface between the two α7 single rings but not to either end of the double ring (Fig. 3c and Supplementary Movie 7). This indicates that α6 favors to interact with the transient cleft at the interface between the two single rings and probably dives into the cleft where the stacking is loose. Here, the question was raised whether α6 can interact with the interface site even if two rings were tightly stacked or not. To investigate this, we prepared chemically cross-linked α7 tetradecamers using the S96C variant and bis(maleimide)ethane. The S96 is placed near the interface and therefore chemical cross-linking through the Cys residues is assumed to stabilize the double ring (Supplementary Fig. 4a). The HS-AFM images of the double ring of the cross-linked S96C variants showed stable double ring forms for all molecules observed even on APTES-mica (Supplementary Fig. 4b). The Dcc was about 4 nm which was almost half of that of the WT. Also the width of the distribution with ±0.3 nm was smaller than that of the WT. These values confirm that the double ring was tightly packed with the chemical cross-linking (Fig. 3b, lower panel). In the presence of α6 in the solution, binding of α6 to the interface at the double ring was never observed within the frame time of 0.1 s (Supplementary Movie 8). This suggests that loose interaction with concomitant cleft formation is crucial for the interaction between the α6 monomer and the α7 tetradecamer.
A mass spectroscopy study revealed that the α7 double ring form survived even in the presence of an excess amount of α6, indicating that the homo-tetradecameric and hetero-octameric forms are in equivalent state13. This could originate from the populations of the double rings with a tightly or loosely packed interface.
In summary, our HS-AFM results capturing single-molecule dynamics clearly demonstrate the interaction between the self-assembled α7 oligomer and the α6 subunit which are parts of the human 20S proteasome. Based on the HS-AFM imaging, we propose a model for a two-step disassembly mechanism which illustrates a comprehensive view of the disassembly of the α7 homo-tetradecamer induced by the α6 monomer and consequent α6-α7 hetero-octamer (Fig. 4). The stacking interaction of the α7 tetradecamer is inherently unsteady and thus the interface between two α7 single rings creates a transient cleft. When the interface has sufficient clearance, an α6 monomer initially encounters the cleft and breaks open the gap due to a strong affinity to the open-pore side of the α7 single ring, resulting in bisection of the double ring and transient interaction between α6 and the open-pore of the α7 single ring. Then, as the second step, subsequent affinity reinforcement induces tight binding of α6 at the central pore of the single ring. The final formation of the octamer complex impedes the re-assembly of α7 subunits to tetradecamers (Supplementary Movie 9).
Disassembly of homo-oligomers of proteasome α subunits could be essential as the initial stage of the formation of 20S proteasome because distinct seven α subunits may self-assemble into oligomers in a cell. Similar molecular mechanism found in this study would be involved in disassembly homo-oligomer composed of other α subunits. In this context, our study provides the implication of the initial process for assembly of the 20S proteasome. To unveil the full view of the formation process of a proteasome, further comprehensive investigation requires extended to initial disassembly processes of both α and β homo-oligomers and following their assembly to hetero-heptamers with assistance of assembly chaperones. Combination of HS-AFM with other technique such as MS, SV-AUC and SANS should be powerful analytical strategy to this purpose.
Methods
Purification of wild-type α7 DR, mutant DRS96C and α6
Human proteasome α6 short isoform and α7 subunits were produced in Escherichia coli and purified as previously described12,13,21. Briefly, cell lysates were subjected to anion-exchange chromatography (DEAE Sepharose, GE Healthcare) after sonication and centrifugation. The resultant proteins were further purified using anion-exchange and size-exclusion columns with RESOURCE Q and Superdex 200 pg resins (GE Healthcare), respectively.
The S96C mutant was purified the same way as the wild-type α7. For the chemical cross-linking, 500 μl of the purified 0.2 mM S96C-α7 dissolved in 20 mM Tris-HCl (pH 8.0) and 150 mM NaCl was incubated with 10 μl of 10 mM bis(maleimido)ethane (BMOE, Thermo Scientific) at 4 °C for 1 h. To quench and remove the unreacted BMOE, 1 mM DTT was added and subsequently size-exclusion chromatography (Superdex 200 increase, GE Healthcare) was performed.
Purified samples (wild-type α6 and α7 and cross-linked α7 S96C variant) were confirmed to show expected molecular masses by SDS-PAGE (Supplementary Fig. 5).
High-speed AFM observation
All HS-AFM images shown in the article were taken by a laboratory-built HS-AFM. As an operation mode of AFM, tapping mode was used to minimize disturbance of molecular phenomena by the AFM probe22,23. A small cantilever with a length of 7 µm, a width of 2 µm, and a thickness of 90 nm was used. Nominal spring constant, mechanical resonant frequency and quality factor in a solution are ~0.2 N/m, ~800 kHz and ~2, respectively. An amorphous carbon pillar was grown on the original bird-beak tip of the small cantilever by using electron beam deposition (EBD) with the spot mode of a scanning electron microscope24. The EBD tip was further sharpened to be less than 4 nm in diameter by plasma etching under argon environment24. For HS-AFM imaging, the free oscillation amplitude was set to be ~2 nm and the set-point amplitude for the feedback control to keep the cantilever amplitude constant was ~90% of the free oscillation amplitude, resulting in a few tens of pico-Newton for the tapping force.
As a solid substrate to adsorb α7 tetradecamers, either bare mica or chemically functionalized mica with 3-aminopropyltriethoxy silane (APTES-mica) was used. The APTES-mica was prepared by placing a droplet (3 μl) of 0.01% APTES on a fleshly cleaved mica surface. After 5 min incubation, the APTES solution was thoroughly washed with pure water. A sample droplet (3–5 μl) including α7 tetradecamers was placed on the substrate and incubated for 3 min. Then residual proteins were washed out with the observation buffer (20 mM Tris-HCl (pH 8.0), 150 mM NaCl). After that, the sample stage was immersed into the observation buffer with 70 μl and the HS-AFM imaging was carried out. In some experiments, a solution of α6 monomer was added to the observation buffer so that the final concentration was 1 μM.
Simulation of AFM Image
Simulated AFM images of an α7 tetradecamer or a heptamer were generated by a simple hard sphere model using the crystal structure (PDB code: 5DSV). For the α7 single ring, one single ring was deleted from the PDB file by using PyMol. An AFM probe was modeled by a cone shape with a radius of 1 nm and half cone angle of 10°. The simulated AFM images were then smoothed by a frequency filter with a cut-off spatial frequency of 3 nm.
Dwell time Analysis
To estimate binding lifetime (τ) of α6 on the α7 single ring, the bound-state dwell times were measured for successive HS-AFM images. The binding and dissociation events of α6 were determined visually, namely if a bright spot appeared or disappeared between two successive AFM images.
Analysis of center-center distance between two α7 single rings
On the side–view image of the double ring form, the middle lines at each single ring were drawn as shown in Fig. 3a (images at 9.9 s and 18.6 s). These middle lines were positioned to coincide with the highest points of each ring. The distance between the middle points of the lines was measured.
References
Pickart, C. M. Mechanisms underlying ubiquitination. Annu Rev Biochem 70, 503–33 (2001).
Glickman, M. H. & Ciechanover, A. The ubiquitin-proteasome proteolytic pathway: destruction for the sake of construction. Physiol Rev 82, 373–428 (2002).
Baumeister, W., Walz, J., Zuhl, F. & Seemuller, E. The proteasome: paradigm of a self-compartmentalizing protease. Cell 92, 367–80 (1998).
Groll, M. et al. Structure of 20S proteasome from yeast at 2.4 A resolution. Nature 386, 463–71 (1997).
Unno, M. et al. The structure of the mammalian 20S proteasome at 2.75 A resolution. Structure 10, 609–18 (2002).
Osmulski, P. A., Hochstrasser, M. & Gaczynska, M. A Tetrahedral Transition State at the Active Sites of the 20S Proteasome Is Coupled to Opening of the alpha-Ring Channel. Structure 17, 1137–1147 (2009).
Yashiroda, H. et al. Crystal structure of a chaperone complex that contributes to the assembly of yeast 20S proteasomes. Nat Struct & Mol Biol 15, 228–236 (2008).
Kusmierczyk, A. R., Kunjappu, M. J., Funakoshi, M. & Hochstrasser, M. A multimeric assembly factor controls the formation of alternative 20S proteasomes. Nat Struct & Mol Biol 15, 237–244 (2008).
Hirano, Y. et al. Dissecting beta-ring assembly pathway of the mammalian 20S proteasome. EMBO J 27, 2204–13 (2008).
Tomko, R. J. Jr. & Hochstrasser, M. Molecular architecture and assembly of the eukaryotic proteasome. Annu Rev Biochem 82, 415–45 (2013).
Gerards, W. L. et al. The human alpha-type proteasomal subunit HsC8 forms a double ringlike structure, but does not assemble into proteasome-like particles with the beta-type subunits HsDelta or HsBPROS26. J Biol Chem 272, 10080–6 (1997).
Sugiyama, M. et al. SANS simulation of aggregated protein in aqueous solution. Nucl Instr Meth Phys Rev A 600, 272–274 (2009).
Ishii, K. et al. Disassembly of the self-assembled, double-ring structure of proteasome alpha 7 homo-tetradecamer by alpha 6. Sci Rep 5, 18167 (2015).
Ando, T., Uchihashi, T. & Scheuring, S. Filming biomolecular processes by high-speed atomic force microscopy. Chem Rev 114, 3120–88 (2014).
Kodera, N., Yamamoto, D., Ishikawa, R. & Ando, T. Video imaging of walking myosin V by high-speed atomic force microscopy. Nature 468, 72–6 (2010).
Uchihashi, T., Iino, R., Ando, T. & Noji, H. High-speed atomic force microscopy reveals rotary catalysis of rotorless F1-ATPase. Science 333, 755–8 (2011).
Charest, P. G., Terrillon, S. & Bouvier, M. Monitoring agonist-promoted conformational changes of beta-arrestin in living cells by intramolecular BRET. Embo Reports 6, 334–340 (2005).
Lin, S. X. & Neet, K. E. Demonstration of a Slow Conformational Change in Liver Glucokinase by Fluorescence Spectroscopy. Journal of Biological Chemistry 265, 9670–9675 (1990).
Oshima, G. T.-D. C. Change of Thrombin Molecules Induced by Sulfated Polysaccharides. Chemical & Pharmaceutical Bulletin 37, 1324–1328 (1989).
Agnihotri, A. & Siedlecki, C. A. Time-dependent conformational changes in fibrinogen measured by atomic force microscopy. Langmuir 20, 8846–52 (2004).
Sugiyama, M. et al. Kinetic asymmetry of subunit exchange of homooligomeric protein as revealed by deuteration-assisted small-angle neutron scattering. Biophys J 101, 2037–42 (2011).
Hansma, P. K. et al. Tapping mode atomic-force microscopy in liquids. Appl Phys Lett 64, 1738–1740 (1994).
Putman, C. A. J., Vanderwerf, K. O., Degrooth, B. G., Vanhulst, N. F. & Greve, J. Tapping mode atomic force-microscopy in liquid. Appl Phys Lett 64, 2454–2456 (1994).
Uchihashi, T., Kodera, N. & Ando, T. Guide to video recording of structure dynamics and dynamic processes of proteins by high-speed atomic force microscopy. Nature Protoc 7, 1193–1206 (2012).
Acknowledgements
We thank Kiyomi Senda and Kumiko Hattori for their help in the preparation of the recombinant proteins and Dr. Christian Ganser for critical reading and the English language improvement of the manuscript. This work was supported in part by JSPS KAKENHI Grant Numbers JP15H03540 (to T.U.), MEXT KAKENHI Grant Numbers JP16H00830 and JP16H00758 (to T.U.), JP17H05890 (to H.Y.), and JP15H02491 and JP25102008 (to K.K.), and CREST/JST (to T.U.).
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T. Satoh, T.U. and K.K. conceived and designed research; T. Satoh, T. Sekiguchi and H.Y. prepared sample. T. K. and T.U. performed HS-AFM imaging and analysed the data. T.K., T.U., T. Satoh, H.Y. and K.K. wrote the paper.
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Kozai, T., Sekiguchi, T., Satoh, T. et al. Two-step process for disassembly mechanism of proteasome α7 homo-tetradecamer by α6 revealed by high-speed atomic force microscopy. Sci Rep 7, 15373 (2017). https://doi.org/10.1038/s41598-017-15708-8
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DOI: https://doi.org/10.1038/s41598-017-15708-8
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