Measuring the Persistence Length of Single-Stranded DNA Using a

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Measuring the Persistence Length of SingleStranded DNA Using a DNA Origami Structure Efrat Roth, Alex Glick Azaria, Olga Girshevitz, Arkady Bitler, and Yuval Garini Nano Lett., Just Accepted Manuscript • DOI: 10.1021/acs.nanolett.8b02093 • Publication Date (Web): 23 Oct 2018 Downloaded from http://pubs.acs.org on October 24, 2018

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Measuring the Persistence Length of SingleStranded DNA Using a DNA Origami Structure Efrat Roth*, Alex Glick Azaria, Olga Girshevitz, Arkady Bitler, and Yuval Garini*. Physics Department & Institute for Nanotechnology, Bar Ilan University, Ramat Gan 5290002, Israel KEYWORDS: DNA origami, single-stranded DNA (ssDNA), persistence length, polymer model, AFM

ABSTRACT

Measuring the mechanical properties of single-stranded DNA (ssDNA) is a challenge that has been addressed by different methods lately. The short persistence length, fragile structure, and the appearance of stem loops complicate the measurement, and this leads to a large variability in the measured values. Here we describe an innovative method based on DNA origami for studying the biophysical properties of ssDNA. By synthesizing a DNA origami structure that consists of two rigid rods with an ssDNA segment between them, we developed a method to characterize the effective persistence length of a random-sequence ssDNA while allowing the formation of stem loops. We imaged the structure with an atomic force microscope (AFM); the rigid rods provide a means for the exact identification of the ssDNA ends. This leads to an accurate determination of the end-to-end distance of each ssDNA segment and by fitting the


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measured distribution to the ideal chain polymer model, we measured an effective persistence length of 1.98±0.72 nm. This method enables one to measure short or long strands of ssDNA, and it can cope with the formation of stem loops that are often formed along ssDNA. We envision that this method can be used for measuring stem loops, for determining the effect of repetitive nucleotide sequences and environmental conditions on the mechanical properties of ssDNA, and the effect of interacting proteins with ssDNA. We further noted that the method can be extended to nano-probes, for measuring the interactions of specific DNA sequences, since the DNA origami rods (or similar structures) can hold multiple fluorescent probes that can be easily detected.

DNA origami was developed more than a decade ago1 and it has great potential for many scientific fields. The latest applications include structures for drug delivery2, calibration standards for super-resolution microscopy3, voltage sensing4, and designing complex logic in living cells5. Taking advantage of the high specificity of DNA sequences, DNA origami enables one to produce two- and three-dimensional structures with any desired architecture, static, and dynamic structures. The most common fabrication method is to mix a long ssDNA (scaffold) with many short single-stranded segments (staples) that are designed to fuse pairs of sequences along the DNA, providing a self-assembly mechanism that builds the structure bottom-up. DNA is the longest natural polymer6, 7, which can reach a length of half a meter in mammal chromosomes. It is also one of the most important structures in nature, since it encodes the whole genetic information for all species, and its structure, folding, and dynamic properties are an intrinsic part of the gene expression mechanisms8. Therefore, knowing the properties of DNA is


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extremely important, not only for efficiently constructing DNA origami structures, but primarily to better understand DNA’s complex genetic mechanisms. Here we present a unique use of DNA origami structures as a tool for characterizing the conformation and persistence length of ssDNA. ssDNA forms naturally in cells, it interacts with various proteins and other ssDNA strands, and it participates in crucial genetic mechanisms such as transcription and replication. It has a flexible and short persistence length and it tends to form stem-loops or hairpins9. ssDNA has been extensively studied before, but the main focus has been on the elastic properties of structures while preventing the interaction of nucleic acids and the formation of stem loops10, 11. Other theoretical works, which mainly focused on RNA folding, studied the conformation of the polymer based on free energy considerations and concluded that the end-to-end distance of the polymer approaches zero, independent of its length and sequence12. This is indeed the case for different RNA structures12, but to the best of our knowledge, it was not tested so far for ssDNA. When testing ssDNA in its natural form where loops can form, one can use known polymer models13, but the nominal polymer length should take into account the stem-loops formed along ssDNA. Previous measurements of the physical properties of ssDNA estimated a broad range of persistence lengths ranging from 0.7 to 6 nm. These methods included single-molecule stretching techniques such as optical13 or magnetic tweezers14, and dynamic force spectroscopy15. However, these methods are less relevant in a regime where the polymer is in its natural form and where stem-loops can form. Other measurement methods intentionally prevented the formation of stemloops. Murphy et al.16 and Chen et al.17 used fluorescence resonance energy transfer. They both used short ssDNA strands with specific sequences that prohibit the formation of loops16, 17 and


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found a rather short persistence length of 1.5-2.2 nm. Chi et al.18 used dynamical mean-field theory and fluorescence correlation spectroscopy experimental data on ssDNA to prevent base pairing19, and found a persistence length of ~2.2 nm for an ion concentration of 300 mM. Tinland et al.20 used fluorescence recovery after photobleaching to measure the persistence length by estimating the gyration radius; however, a high concentration of 8M urea was used as a denaturant to prevent stem-loops. A persistence length of 4 nm was found at a salt concentration of 10 mM. Finally, ssDNA was also calculated by AFM by directly measuring the gyration radius21, but it necessitated analyzing the image of the whole molecule, a process limited to molecules that are not too condensed; a persistence length of 4.6 nm was calculated at a salt concentration of 10 mM. Overall, the previous experimental approaches that were used are not trivial and require either ssDNA that is prepared without loops or that is significantly noncondensed. The persistence length of ssDNA depends on the solution’s salt concentration. According to the Odijk-Skolnick-Fixman (OSF) theory22, 23, the persistence length of a polyelectrolyte such as DNA is described as l p  l0  lel , where l0 is the intrinsic part that depends on the microscopic polymer’s rigidity, and lel is the electrostatic part that varies with the solution’s salt concentration. This part was found to be proportional to the Debye screening length (inversely proportional to the square root of the salt concentration)24. It is negligible for high salt concentrations above ~1M and has a power law dependence at lower concentrations10, 17. In its simplest form, the ssDNA conformation can be modeled using the worm-like-chain (WLC)25 or the equivalent approximation of a freely jointed chain (FJC) model26 where the polymer is assumed to consist of N stiff rods with a fixed length, and the Kuhn length, b, which is connected through fully flexible joints (the persistence length, lp, is defined as half of the Kuhn


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length), resulting in L  Nb for a nominal polymer length L. This model, however, neglects the appearance of secondary structure stem-loops so as the excluded volume. In the frame of this model, the mean square end-to-end distance of the polymer is  r 2   Nb 2 and the probability distribution of r when the polymer is spread in two dimensions (2D) follows the Rayleigh distribution27, 28:

 3r 2  3  exp   P2D  r  dr    2 rdr ,  4 Ll p  4 Ll p   where r  x 2  y 2 . Although some works found good agreement for the persistence length of DNA, based on the WLC model25, other works indicated that the persistence length is not a well-defined quantity for ssDNA29. In order to take the secondary structure of stem-loops into account, we adopted a rather simple approximation and assumed an ideal chain polymer with an effective length, L* , described by a random walk, assuming that the self-avoidance and electrostatic repulsion effects are compensated by the polymer monomer interactions. We assumed that the effective length L* is equal to its nominal contour length minus the length of the loops formed along the polymer. Using the Mfold program, we calculated different efficiencies of loops formed along the ssDNA, according to the strength of these contacts30. To measure the conformation and persistence length of ssDNA using a DNA origami structure, we designed and fabricated a family of special structures composed of two rigid rods with a ssDNA segment in between (Figure 1). A similar principle of two rods connected by a doublestranded DNA (dsDNA) hinge was previously demonstrated as a method for structuring ‘superstructures’31.


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Each rod is constructed of seven dsDNA segments and has a length of 100 nm. The different structures have different ssDNA length segments, with the number of nucleotides varying in range from 500 to 2000. As a scaffold, we used the M13mp18 plasmid, which contains 7249 nucleotides. Each rod is folded with 2096 bases and the remaining 3057 unpaired bases were divided differently between the edges of the structure and the segment in between the rods. When the structures are imaged with the AFM, the two origami rods precisely denote the edges of the ssDNA polymer; this allows one to measure its end-to-end distance with an accuracy of 4 nm. This therefore leads to a rather direct way of measuring the ssDNA conformation. In order to ascertain the environmental conditions for the experiments, all samples were prepared under similar conditions using TAEx1 and 14mM MgCl2.

A

B

Figure 1. A. Schematic drawing of the DNA origami structures. Each of the two rigid rods is composed of 7 dsDNA segments folded from a scaffold of 2096 bases. The green strand represents the scaffold and the colored strands represent the staples. Different structures have a different ssDNA length, varying from 500 to 2000 bases. B. AFM image of a folded structure with an ssDNA segment of 1019 nt length. M13mp18 is a circular plasmid and in order to convert it to a linear DNA, we used a restriction enzyme32 (PstI) before the folding (Supporting Information Note 1). Before adding the restriction


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enzyme, we added a complementary segment of DNA to the restriction site to make it doublestranded. Following the cutting reaction, a zymo-5 kit was used to remove the enzymes and the leftover primers, with a yield of about 60%. The cutting process was verified by gel electrophoresis (Supporting Information Note 2). The DNA origami structure was designed using caDNAno33,

34.

Because of the ‘parity

problem’ (the two strands emerging from each rod should exit from its two opposite ends); each rod was designed to consist of an odd number of seven dsDNA, and to fold at a specific site of the plasmid (Supporting Information Note 3). The linear plasmid and staples were mixed with TAEx1 buffer and 14mM MgCl2 and then incubated for about twenty hours at a gradient temperature. A detailed list of the staples and folding protocol is shown in supporting information note 4. Next, to confirm a proper assembly, the products were run on 2% agarose gels (0.5×TBE, 11 mM MgCl2) at 70 V for 2-3 h in ice (Supporting Information Note 5). After the folding process was completed, the solution containing the folded samples was deposited onto freshly cleaved mica treated with 5mM NiCl2 and washed with pure TAEx1 Mg+2 buffer (Supporting Information Note 6). It was previously shown35 that dsDNA deposited onto freshly cleaved mica can equilibrate on the surface as in an ideal two-dimensional solution, and numerous studies are performed this way36. Since the DNA origami rods also adhere to the surface, it is expected that the end-to-end distribution of ssDNA will not be affected by the rods themselves. This was also indicated in a previous work where DNA origami nanorods were connected by dsDNA31. The structures were imaged with a Bruker Bio-FastScan AFM (the Peak Force Tapping mode PFTm) using FastScan-C cantilevers with a force constant of 0.8 N/m. This mode has been used


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to acquire high-resolution images of the studied objects (DNA). In this mode, the AFM performs very fast ‘force-distance’ curves at each pixel of the imaged surface, following z-piezo oscillations at ~ 2kHz during the scan. The peak force of every curve is used as a feedback signal. PFTm provides higher resolution than other modes do because of the very small and controlled force that minimizes the deformation depth and consequently decreases the contact area between the tip and the sample. The images were typically captured in the retrace direction with a scan rate of 1.95 Hz and a resolution of 512 samples/line (for 2×2 µm2). Imaging was done in TAEx1 buffer with 14mM MgCl2 at room temperature. For image processing (height mapping) and assessment of the structure’s dimensions, Nanoscope Analysis Software was used. Before analyzing the height images, the “flatting” and “planefit” functions were applied to each image. The scans showed that the DNA origami structures were folded correctly according to their design (Figure 2). To verify that the DNA conformation on the mica substrate follows the expected theoretical predictions, we measured 927 nm long dsDNA in solution on mica. The sample (3 ng/µl DNA in 7.5 mM HEPES 50 mM Na+ buffer) was deposited onto freshly cleaved mica treated with 4 mM NiCl2. The DNA was imaged with a Bruker Bio-FastScan AFM (Tapping mode) using FastScanD cantilevers with a force constant of 0.25 N/m, and the end-to-end distance was located manually. The distribution follows the Rayleigh distribution with high accuracy (R2=0.92), as shown in supporting information note 7. By fitting it to an equilibrated polymer on the mica surface, we estimated a persistence length of 30±6 nm. Although this value is somewhat shorter than the commonly quoted value of 50 nm35, it is in good agreement with similar AFM measurements of dsDNA in solution37.


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B

C

D

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Figure 2. Folding of the DNA origami structure (1019 nt between the rods). A. AFM image of the folded structures in liquid (TAEx1, 14mM MgCl2). The bar equals 480 nm. B. Zoom in of two structures; the length of each rod provides an exact scale of 102 nm. C. Histogram of the rods' length as calculated from all measured structures (n=689), yielding a length of 102±10 nm. D. Traversal cross section profile of a single rod. The red curve shows the best Gaussian fit with a FWHM of 10.3 nm.

Figure 2A, B shows pairs of rods with different angles in between and different end-to-end distances of ssDNA in between them. ssDNA is also observed at the edges of the rods (Figure


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1B), as planned. The measured length of the rods is 102±10 nm (Figure 2C), the height of the rods is ~4.5 nm, as expected, and the FWHM, which was found to be 10.3 nm, is in agreement with the expected DNA origami width (Figure 2D), which should be in the range of 4-8 nm, after being convoluted with the tip width. Figure 2A, B shows images measured from the structure with an ssDNA length of 1019 nucleotides. Since the length of each nucleotide is 0.676 nm18, the total ssDNA length is 688.84 nm. We also measured the angles between each of the two rods and found them to be approximately uniformly distributed, which confirms the fact that the adherence of the structures to the mica surface is not biased by the structure’s shape (Supporting Information Note 8). All measurements were performed with the Matlab script that we wrote; however, the edges of the rods were located manually from structures that are far apart from each other to prevent errors (overlapping structures were not measured). We also measured only structures where ssDNA was clearly identified in between the rods’ edges so that it is clear which sides of the rod are those that are connected to ssDNA. For all structures that we synthesized, we found many structures in the frames measured by AFM. Nevertheless, to fulfill all the conditions described above, we selected from every frame only a few structures (Supporting Information Note 9). In order to collect enough structures, we captured many frames with a typical area of 2  2  m 2 and measured only 1-6 structures from each frame. The histogram’s distribution of the end-to-end distances of the 1019 nucleotide structure is shown in Figure 3 (n=91), together with the best Rayleigh fit (solid line). The fit shows small residuals distribution (Figure 3, bottom, R2=0.9) and has only one single free parameter, σ, which was found to be 24.21±2.65 nm.


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Figure 3. Histogram of the end-to-end distance of the 1019 nt ssDNA between two rods in the DNA origami structure. Ninety-one structures were measured by picking their edges manually and the distances were calculated from the known AFM image pixel size. The solid line shows the best fit to the Rayleigh distribution with a single parameter and the residuals are rather small (R2=0.9). We first noted that the distribution we measured for all the structures does not reflect a zero end-to-end distance, as suggested and found for RNA12, and that a significant Rayleigh-like distribution was found with a mean value of ~25-40 nm. It may result from the DNA origami folding process through a slow temperature gradient. Such a process may result in the preferred selection of short-range DNA loops that eventually do not allow long-distant loops to form. It may also result from the difference between the nucleotide bond energy of ssDNA and RNA, with which most calculations were performed. In order to extract the persistence length, the number of nucleotides that form loops has to be determined, since it effectively shortens the nominal polymer length. Although it may be possible to identify some of the loops from the AFM images, in most cases it is still below the


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resolution limit. Therefore, we used Mfold, a program that calculates the possible loops for a specific sequence as a function of the solution temperature and salt concentration. According to the end-to-end distribution that we found (which is not zero), we limited the maximum distance between the edges of each loop to be 50 nucleotides at 25ºC. It is also expected, especially during the temperature gradient process, that in an ideal chain model, the probability of two sites at a distance of N nucleotides along the polymer to be found next to each other is  N 3/ 2 . Furthermore, if we do not limit this distance, Mfold indeed finds a conformation where all the nucleotides of ssDNA take part in the formation of stem loops and the end-to-end distance approaches zero, a situation that we know does not occur (Supporting Information Note 10). To test different possible loops, as explained above, we started by taking all the loops that are supposedly formed from Mfold. For most of the structures, Mfold produced a single possible stem-loops combination. For the 500nt ssDNA structure, however, three possible secondary structures were found, but they only differed slightly regarding the number of nucleotides participating in the loops (318, 324, and 339 nt) and we took the average number (327 nt). Then, we assumed three different loop formation efficiencies of 0%, 50%, and 100%, which represent the actual percentage of loops formed from all possible ones. We next fit the distribution to a Gaussian chain model and extracted an effective persistence length for our experimental conditions of 2 mM NaCl. For each percentage we obtained a * different effective nominal length, L , and when we substituted it for the standard deviation

value found from the Rayleigh distribution fit, we found the effective persistence length according to   2l p L / 3 . For example, for the 1019 nt structure with no loops at all, we obtained 1.28±0.28 nm. Similar calculations were performed for all the structures (Table 1) for different effective loop formation percentages (Figure 4 and Supporting Information Note 11).


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Table 1. Parameters of the different structures assuming no loops Sample number

nt

L [nm]

σ [nm]

R2

lp [nm]

lp [nm] 95% confidence

1

500

338

21.18

0.96

1.99

1.72-2.28

2

1019

689

24.21

0.9

1.28

1.01-1.57

3

1481

1001

23.63

0.91

0.83

0.62-1.09

4

2000

1352

34.71

0.96

1.33

1.12-1.58

Summary of the parameters of the four different structures, assuming no loops. nt is the number of nucleotides in the ssDNA segment, L is the ssDNA segment length, σ is the fitted mode parameter of the Rayleigh function (a single parameter fit), and lp is the calculated persistence length. The last column shows the range of lp values in the 95% confidence interval.

Figure 4. Calculated persistence length for the different DNA origami structures with different nucleotide lengths. The calculation is repeated for the case of no loops at all (red squares) along the ssDNA, 50% folding of the possible loops (green circles), and folding of all possible loops (blue triangles).


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The calculated persistence length values of most of the structures are in good agreement, except for the sample with 500 nucleotides (Figures 4 and 5). Taken together, the average persistence length from all structures and the possible loop formation efficiencies was found to be 2.35±1.35 nm. We believe, however, that a more accurate value can be obtained if we consider that only 50% of the loops are closed. This is a reasonable assumption especially because most of stem-loops contain 4-14 nucleotide pairs and the single-base free energy is ~0.20.9 Kcal/mol, which is in the same range as the thermodynamic temperature energy at room temperature (0.6 Kcal/mol)38. Therefore, it is statistically likely that only part of the loops are closed at any given moment. In this case, the persistence length was found to be 1.98±0.72 nm. This value is in agreement with most of the values published so far, which are in the range of 1.5-3 nm16, 18, although other works published much larger values, in the range of 5-9 nm21.

Figure 5. Possible loops formed along the 500nt ssDNA at 25ºC. All possible loops with a maximal distance of 50 nt between their edges are shown as calculated by Mfold30.


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Our approach for extracting the effective persistence length assumes that the free part of ssDNA (which does not participate in the formation of stem loops) behaves like an ideal chain. A possible explanation for the differences in the persistence length of the 500 nt sample is based on the fact that the rigidity of ssDNA also depends on the specific sequence of nucleotides along the strand39, which is not the same in the structures that we fabricated. Previous experiments showed that the interactions of self-stacking poly(dT) are much weaker than those of poly(dC), poly(dG), and poly(dA), which means that poly(dT) is more flexible than the other molecules39-41 and as a result, the flexibility of the chain will grow with the number of dTs. The percentages of all the kinds of repetitive nucleotides in the structures we measured are presented in Table 2. As one can see, the 500nt ssDNA has the lowest percentage of dTs and a more detailed examination shows that this structure has significantly fewer dTs in a row. Therefore, this structure should be more rigid than the other structures that we found, which may explain our result.

Table 2. Poly(dN) percentage in the different structures. 500nt

1019nt

1481nt

2000nt

Poly(dA) [%]

11.8

11.4

12.4

12.0

Poly(dC) [%]

6.2

6.8

7.7

8.0

Poly(dG) [%]

19.4

12.9

13.9

12.1

Poly(dT) [%]

11.8

21.1

15.7

19.4

The table represents the percentage of poly(dN), from the whole sequence, which participate in repetitive sequences such as TT, TTT, and others.


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In summary, we present an innovative use of DNA origami for studying the biophysical properties of ssDNA. We developed a method to measure and characterize the conformation and persistence length of ssDNA by using a DNA origami structure that consists of two rigid rods with an ssDNA segment between them. In contrast to previous methods, this method does not enforce any restrictions on the measured ssDNA, not regarding its length nor its sequence, and therefore serves as an important experimental method for further studies. The rods provide a means of exact location recognition of the ssDNA ends, which leads to accurate determination of the end-to-end distance for each ssDNA segment. By using this precise recognition capability on structures with various ssDNA segment lengths, we found an end-to-end Rayleigh distribution with an average value of 25-40 nm. This value is not consistent with theoretical predictions of a zero end-to-end distance for RNA, which was validated experimentally12. As mentioned, this difference may result from the different binding affinity of ssDNA versus RNA, or result from the DNA origami folding process, which prefers short-range loop formation. This demonstrates the capability of this method for studying ssDNA. Finally, by fitting the measured distribution to the ideal chain polymer model (Gaussian chain), we measured an effective persistence length in a range of 1.98±0.72 nm. In the future, this method can be used for measuring stem loops, the influence of repetitive nucleotide sequences and environmental conditions on the mechanical properties of ssDNA, as well as the interaction of proteins with ssDNA. It can be further extended to nano-probes for measuring the interactions of specific DNA sequences, since the DNA origami rods (or similar structures) can handle multiple fluorescent probes that can be easily detected. ASSOCIATED CONTENT Supporting Information


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The following files are available free of charge. Protocols, Electrophoresis gel, DNA origami sequences, and distribution histograms. (PDF)

AUTHOR INFORMATION Corresponding Author *E-mail: [email protected]. *E-mail: [email protected]. Author Contributions The manuscript was written through contributions of all authors. All authors have given approval to the final version of the manuscript. Notes The authors declare no competing financial interest. ACKNOWLEDGMENTS We would like to thank Uri Sivan and Kfir Kuchuk from the Technion for their advice and help with the AFM measurements. In addition, we wish to thank Yitzhak Rabin (Bar Ilan University) and Avinoam Ben-Shaul (Hebrew University, Jerusalem, Israel) for their insightful comments. The authors would like to acknowledge financial support from the Israel Science Foundation (ISF) grants 1902/12 and 1219/17 and from the S. Grosskopf grant for ‘Generalized dynamic measurements in live cells’. ABBREVIATIONS


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Nano Letters

ssDNA, single-stranded DNA; AFM, atomic force microscope; dsDNA, double-stranded DNA; WLC, worm-like-chain; FJC, freely jointed chain; Lp, persistence length.

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Measuring the Persistence Length of Single-Stranded DNA Using a

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