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Revision as of 00:50, 28 October 2012
DNA origami structures are comprised of two basic components. The first, referred to as the scaffold, is M13mp18 bacteriophage E. Coli single stranded DNA (ssDNA), which has a known amino acid sequence, and hundreds of smaller single stranded pieces of DNA (30-50 base pairs in length), referred to as staples. The principles of Watson-Crick base pairing enable the precise design of staples that will bind with specific regions of the scaffold in a piece-wise fashion. The regions of the scaffold that are connected need not be adjacent in the sequence of the scaffold; however, after the staple binding these sequences will be spatially adjacent. In its most basic form, DNA origami is making use of DNA as a rope that knows how to tie itself in knots in order to form rigid shapes.
Triangles are a huge part of the world, as we know it. They can be found in high strength structures in the form of trusses, woven into spider webs, in the patchwork of a soccer ball, and even in the artwork of Matthew W. Moore. The versatility of triangles in nature inspired our group to explore their capabilities on the nano scale. The ultimate goal is to use triangles, combined into parallelograms, as the common factor in the construction of larger, more complex nano structures. Providing this framework allows for streamlining the formation of various triangle based objects as well as the future ability to shift between various objects via the parallelogram intermediate.
Previous DNA origami research has illustrated a wide array of 3D structures. Typically, folding multiple objects requires ordering a new set of DNA components for each desired structure. This project seeks to overcome this limitation by developing a hierarchical assembly framework where multiple 3D shapes can be constructed from a single base DNA origami structure. The basic shape is constructed by folding four equilateral triangles from a single DNA origami scaffold and then arranging them into a parallelogram. Schematics were created to fold these parallelograms into four nanoscale container-like shapes: a tetrahedron, an octahedron, an icosahedron, and a wheel. These final shapes are composed of triangles joined by double stranded DNA connections that can be disrupted utilizing DNA strand displacement to ultimately reconfigure a given shape into a different 3D shape (i.e. reconfigure an octahedron to an icosahedron). This project will enable an economic framework to fabrication of multiple DNA origami structures. Furthermore, this approach could be used to develop DNA structures that can reconfigure in response to a biological stimulus, for example cancer cell microenvironments, for drug delivery applications.
The ConceptClick Here to Close
DNA origami structures are time consuming and costly to build. Each structure requires a new design and thus represents an investment of many hours and as much as one thousand dollars. Our goal was to minimize the cost and time investment of designing a DNA origami structure by creating a single simple structure that has the ability to combine with other simple structures in various ways to make many devices of different sizes and shapes.
We designed a modular structure, a parallelogram composed of four equilateral triangles that can self-assemble into a variety of shapes depending on the addition of connecting staples. These connecting staples, hereafter called external staples, were used to connect different base shapes together to form larger shapes.
Figure 1: one version of the base shape
In figure 1, the numbers 1-12 correspond to potential locations for external staples. Connections can be made between any numbered side, within the same parallelogram or between two parallelograms, to form different shapes. The connections within the parallelogram are also modular. The form shown above is the form 2 parallelogram. The other forms are shown on the next page.
Figure 2: Possible parallelogram conformations, only form 2 and form 3 are used in the formation of other shapes
The parallelograms 2 and 3 are inverses of each other, meaning that the sides that are masked (used to make internal connections within the parallelogram shape) in form 2 are presented to solution in form 3 and vice versa. Additionally, the form 1 parallelogram was never physically manufactured. It merely serves as a useful visual intermediate in the folding of form 3.
Our design differs from traditional DNA origami in the use of “external staples.” Traditionally, staples are complementary to specific sequences of the scaffold. The scaffold-staple binding brings sequences of the scaffold together spatially and holds them there. In contrast, the external staples in our design never bind to the scaffold but instead bring together specific staples sequences that are external to other structures. These external staples are 18 base pairs in length. They are complementary to single-stranded DNA that hangs off the edge of sides of the equilateral triangles. These staples, hereafter called polymerization staples, are 10 base pairs in length and allow modularity in the design. Essentially, the hangover staples are unique sequences that provide attachment points between triangles or parallelograms. Our design incorporates 96 unique polymerization staples and over 400 external staples. External staples are unique in that they are complementary to specific polymerization staples. Each external staples is complementary to 9 base pairs from one polymerization staples and 9 base pairs from another polymerization staples (the polymerization staples are 10 base pairs each to allow some slack in the connection sites). When the external staples are put in solution they bind to the polymerization staples and draw the sides attached to the polymerization staples together in order to form the desired shape.
Each side of an equilateral triangle contains 8 polymerization staples. These polymerization staples are named uniquely. Each side is numbered 1-12. Each half of a trapezoid is labeled a-f. The outermost four connection points on each side are labeled “out” while the four inner connections are labeled “in.” Polymerization staples are paired and extend from the structure at adjacent loci. The staple that presents the 5’ end is therefore designated as 5’ while the polymerization staples that presents the 3’ end is designated 3’. This naming convention can be seen in the diagram below.
Figure 3: Naming convention for external and polymerization staples (4a out 5’ and 4b in 3’ are examples of how the naming convention works)
Figure 4: Layout of the design as seen in caDNAno in 2 dimensions. The 8 connections and labeling displayed in figure 3 are present in each of the 12 sides displayed above.
Figure 4 depicts the layout of the design as it is seen in caDNAno. The red lines represent scaffold routing at the pivot points that allow the formation of the 3 forms of the parallelograms that can be seen in figure 2. Each column of 3 “triangles” (note that the isosceles triangles in figure 4 above more closely resemble trapezoids) folds to form an equilateral triangle. A close up of the equilateral triangle scaffold routing can be seen below in figure 5.
Figure 5: The 5 rows mentioned above can be seen here. The nonlinear segments correspond to single stranded scaffold that joins the 5 rows. Note that each row of the trapezoid is separated only by the diameter of a DNA helix.
Detailed design descriptionClick Here to Close
The base shape consists of four equilateral triangles made out of a single scaffold 8064 base pairs in length. Each equilateral triangle consists of three identical trapezoids that are joined by ssDNA at the center and has a side length of 52.77 nm. The trapezoids are in turn composed of five parallel “rows” of DNA double helices. Each row is 24 base pairs shorter than the row above it: for example the top row contains 182 base pairs with 158 contributing to the structure (182 – 12*2) for a total length of 52.77 nm. The 24 base pair reduction between each row yields the 30ᵒ angle that is necessary to form the equilateral triangles when the trapezoids are joined together. This 30ᵒ angle and 12 base pair reduction between each row of the trapezoid necessitated 12 base pairs of ssDNA in order to form the junction without causing stress in the design.
Each equilateral triangle is attached to one or two other through single stranded scaffold. These connections are loose (8 singles stranded base pairs is approximately 5.6 nm) and would allow the triangles to move freely without the addition of more structural staples. These additional connections transform the loosely connected equilateral triangles into the parallelogram. These structural staples were provided in two forms. One form will be called internal bridge connections. These staples were “hardwired”, meaning that these connections could only be formed in one way. In other words these staples follow the traditional DNA origami method of complementarity with specific segments of DNA thereby drawing those segments together. The other form, designated as the external bridge design, relied on external staples to form the connections that would form the base shape.
Prestocks and Working StocksClick Here to Close
Working stocks and prestocks were used to simplify the folding processes. A prestock is a set of staples that have been combined because they are all used to create the same module of the design . For example, all staples used to create the internal connections of the parallelogram were added to the same prestock because they all serve the purpose of creating internal connections in the sub-triangle base shapes. This technique saved time and effort when working in the lab. When a structure is to be made and all of the internal connections needed to be added to a working stock, one needs to simply take from a single prestock instead of dozens of single oligos.
Working stocks are combinations of specific prestocks and additional staples in a single tube to bring together all staples required for a desired folding reaction. An example of a working stock would be the combination of the internal staples in the previously mentioned prestock with other prestocks of the equilateral triangles to create the base parallelogram shape. When preparing the sample for the folding reaction, a certain volume of working stock was used to produce the shape, while the remainder of the working stock was stored at 4° C to allow for future folding reactions.
Formation of parallelogram form 2 utilizing the internal bridge.
Formation of parallelogram form 2 utilizing the external bridge.
Formation of parallelogram form 3 utilizing the internal bridge. It was observed that this bridge method resulted in a lower yield.
Formation of parallelogram form 3 utilizing the external bridge. It was observed that this bridge method resulted in the lowest yield of the four parallelogram formations.
Step 1 in the formation of the octahedron with the use of parallelogram form 2 and the internal bridge. This working stock also contains the 10-12 external connection staples.
Step 1 in the formation of the octahedron with the use of parallelogram form 2 and the external bridge. This working stock also contains the 10-12 external connection staples.
Step 1 in the formation of the octahedron with the use of parallelogram form 3 and the internal bridge along with the addition of the 10-12 external connection staples.
Step 1 in the formation of the octahedron with the use of parallelogram form 3 and the external bridge along with the addition of the 10-12 external connection staples.
Formation of the tetrahedron with the use of parallelogram form 2 and the internal bridge along with the addition of all external connections staples.
Formation of the tetrahedron with the use of parallelogram form 2 and the external bridge along with the addition of all external connection staples.
Formation of the wheel with the use of parallelogram form 2 and the internal bridge along with the addition of all external connection staples. It was discovered that this concerted process of formation was not successful; therefore the formation of the wheel was separated into three steps. This is described in detail in shape formation.
Formation of the wheel with the use of parallelogram form 2 and the external bridge along with the addition of all external staples. It was discovered that this concerted process of formation was not successful; therefore the formation of the wheel was separated into three steps. This is described in detail in shape formation.
Polymerization and External StaplesClick Here to Close
The 96 polymerization staples need to be unique sequences. Additionally, the design incorporates 60 single-stranded scaffold components to form the connections between the rows within a trapezoid. In order to avoid difficulties with unwanted binding between polymerization staples or external staples, the 96 polymerization staples needed to each be different from the 60 single-stranded scaffold sequences and from the reverse complement of each of these 60 sequences. Moreover, each polymerization staple adds additional restrictions. The problem is further complicated by the fact that multiple complementary base pairs will weakly bind to each other locally even if the entire strand is not complementary. We therefore limited our strands to have less than 5 consecutive complementary base pairs out of 10 base pair external staples sequences. 4n different sequences can be created for a sequence with n base pairs. In our case where the external staples contain 10 base pairs, 1,048,576 sequences are possible. However, out of more than a million options fewer than 400 met the specifications for our external staples. These staples were produced using the program displayed below, written by Andrew Krieger. This program first generated all possible sequences starting with 10 consecutive A’s and then created sequences after comparing them to a list of the 60 single-stranded scaffold sequences. Each staple created was stored and then added to the list of disallowed sequences. It is worth noting that the sequences produced differ when the initial input is changed.
Additionally, the relationship between the number of acceptable staples and the parameters (staple length and number of consecutive complementary base pairs allowed) for a given set of parameters is complex. For 4 consecutive complementary staples allowed for strands of 6 base pairs 46 external staples were generated by the program. However, for 4 consecutive complementary staples allowed for strands of 7 base pairs only 36 external staples were generated. We suspect that this decrease in number of staples despite the increase in the strand size is due to the fact that adding a staple adds a four-fold increase the number of possible staples but also adds many more restrictions by increasing the chances that a staple is complementary with one of the disallowed sequences.
Figure 3: Part 1 of the Program that generated the external staples, written by Andrew Krieger
Figure 3: Part 2 of the Program that generated the external staples, written by Andrew Krieger
Shape FormationClick Here to Close
Working stocks 9 and 10 (described in Working Stocks and Prestocks LINK) form the tetrahedron with the use of parallelogram form 2 in two different versions; one utilizing the internal bridge and the other the external bridge. The formation occurred in one concerted thermal ramp cycle followed by an agarose gel electrophoreses purification. A schematic for the tetrahedron is shown below.
Step 1: Formation of both forms of the parallelogram with 10-12 external connection staples, which will allow the complementary form to bind. This step creates working stocks 5 through 8, varying in parallelogram form and bridge form. These working stocks were purified through agarose gel electrophoresis prior step 2.
Step 1 – formation of parallelograms: Parallelogram form 2 with internal bridge (working stock 1) as well as parallelogram form 3 with external bridge (working stock 3) were folded. These folded parallelograms then underwent gel electrophoreses.
Step 2 – connection of the top two parallelograms: A dilution of 8-12 external staples was formed and combined with working stocks 1 and 3. This was then incubated over night at 37°C and 400rpm.
Step 3 – connection of the bottom two parallelograms: A dilution of 2-6 external staples was formed and combined with working stocks 1 and 3. The combined parallelograms and staples were then gel purified.
Step 4 – addition of the middle parallelogram to the top two parallelograms: A dilution of 6-6 external staples was formed and combined with icosahedron step 2. This was then again gel purified.
Step 5 – combination of top three parallelograms to the bottom two parallelograms: A dilution was formed of 12-12 external staples and combined with the purified icosahedron steps 3 and 4. This was then incubated over night at 37°C and 400rpm.
Step 6 – linkage of side-to-side connections: A dilution was formed of the external staples for the side-to-side connections (1-5, 3-7, 1-9, 9-10, 7-11) and combined with icosahedron step 5. This was then incubated over night at 37°C and 400rpm. Icosahedron step 6 formed the icosahedron with a seam where the top and bottom had not yet been combined.
Step 7 – linkage of top-to-bottom connections: A dilution of the external staples for top-to-bottom connections (4-5, 2-8, 10-11) was formed and combined with icosahedron step 6. This combination was incubated over night at 37°C and 400rpm. This final step completes the linkages necessary to form the shape of the icosahedron. Because of the small concentration of icosahedrons in this step, gel purification was not performed prior to preparing the carbon coated transmission electron microscope grid for imaging.
Version one was simply a concerted process (working stocks 11 and 12) in which form 2 internal bridge or external bridge was combined with all the external staples. This version was found to not be successful in forming the final shape of the wheel.
Version two and three were accomplished through the following steps. The difference between the two versions was the incubation period between step 2 and step 3 – 30 minutes for version 2 and overnight for version 3.
Step one: Parallelogram form 2 with internal bridge (working stock 1) was folded in a thermal ramp and gel purified.
Step two: A dilution of 7-9 external staples was formed and combined with wheel step one. This combination was then incubated at 37°C and 400rpm for either 30 minutes or overnight depending on the version.
Step three: A dilution of 6-12 and 1-3 external staples was formed and combined with wheel step two and incubated overnight. After incubation, the final wheel sample was again gel purified.
Thermal RampClick Here to Close
Gel Purification via Agarose Gel ElectrophoresisClick Here to Close
Once the gel is prepared and the sample is loaded, the gel box is inserted into an ice water bath and a 70V current is applied. Strands of shorter length or structures that are more compact will migrate with greater ease through the agarose gel. This will allow for the 10-fold excess of staples that was added in the design to be separated from the properly folded structures, as well as allow separation between well folded structures and possible dimers and trimers.
Grid PreparationClick Here to Close
Thermal RampClick Here to Close
Design ComplicationsClick Here to Close
The previously mentioned external staples were composed of the same sequences in every parallelogram. Although this design allows for self-assembly with the addition of polymerization staples into solution, it also presents difficulty in creating more complex shapes. Suppose we wish to join two form 2 parallelograms. We could make a set of 8 external staples to form a connection between the 6-side and the 12-side of different parallelograms. However, we now have an issue. The parallelogram that bound with its 6-side presents a 12-side to the solution while the parallelogram that bound with its 12-side likewise presents its 6-side to solution. The external staples in solution will thus continue the reaction and cause additional parallelograms to bind to the open sites. These parallelograms also have open binding sites allowing for even more polymerization. This polymerization is uncontrollable and will yield a distribution of unwanted products containing more than the desired two parallelograms.
To avoid this polymerization issue, we instead bind a side to its own equivalent on another connection. In other words if we take the form 2 parallelograms from the previous connection and make a 6-6 connection instead of a 6-12 connection then the parallelograms can only bind once. Once the 6-6 connection has been made between the two parallelograms these bound parallelograms do not present 6-sides to solution, their 6-sides are already bound. This strategy allows control of the folding reaction and will only create two-parallelogram structures.
An additional design problem was encountered due to DNA strand displacement. DNA strand displacement is a technique whereby a strand of DNA (designated A) that is bound to another strand (designated B) can be displaced by a strand of DNA with greater affinity for strand B (designated A’). When strands A and B are in solution they will bind together; however, when strand A’ is introduced, it will displace strand A overtime due to random thermal fluctuations and its greater binding affinity for strand B. Although cytosine (C) and guanine (G) have a greater binding energy than adenine (A) and thymine (T), the binding affinity of strand A and A’ to B in DNA origami depends primarily on their lengths because their sequences are identical excluding the extended length that A’ has over A.
Our design incorporates many single-stranded components to give it the flexibility necessary to form more complex structures. Although our design process ensured that the polymerization staples and single stranded scaffold between the trapezoids were not complementary for more than 5 consecutive base pairs, some binding between the scaffold and polymerization or external staples would occur during the folding process. This binding, however, was transient because the unwanted bindings were eliminated by DNA strand displacement from staples that had higher affinity.
Unfortunately, DNA strand displacement did not work for our external staples. The external staples were designed to bind to 9 single-stranded base pairs on polymerization staples on two faces of the base shape. Thus the fully bound external staple would be bound to 18 base pairs from 2 different polymerization staples. External staples are added in tenfold excess to ensure that all the sites on the structure requiring external staples are used. In this particular case, the excess of staples means that every polymerization staple was bound to an external staple; however, it is far more likely that every polymerization staple would be bound to a separate external staple rather than binding an external staple attached to another parallelogram. Thus every binding site would be full and unable to accept a bond to another parallelogram.
Moving ForwardClick Here to Close
Our design represents a method for bottom-up assembly of complex structures from DNA origami. It has the potential to save money and time during the design and manufacturing process of DNA origami structure. Moreover, the base shape could be modified to fit other applications by inducing curves in the equilateral triangles or by changing the base shape from a design based on triangles to a design based on squares. This design, and the methodology behind it’s construction, has the potential to revolutionize the formation of complex 3-D structures in DNA origami.
Detailed Design Description
Prestocks and Working Stocks
Polymerization and External Staples
The project design called for the creation of a base shape parallelogram, tetrahedron, octahedron, icosahedron, and a 3-dimensional wheel. Initially, the base shape parallelograms were imaged. There was a very high yield of the equilateral triangles proving the first step of our design was a success.
The formation of the base shape parallelogram was critical; it was the base unit used to create all other shapes. Since the design called for the parallelogram to contain pivot points, it was hard to view a perfect image of the parallelogram completely flattened out. However, there were several images that appeared to have only three equilateral triangles, with the fourth possibly folded behind its neighboring triangle due to the single stranded slack between them. Even though it was difficult to obtain images of 4 equilateral triangles coming together properly to form the base shape parallelogram, we have been able to show its success because of the high yield of the 3D tetrahedron shape. The tetrahedron was designed to contain exactly one parallelogram folded at the pivot points and imaging of the shape showed a very high yield.
A transmission electron microscope was used to show that the folding reaction was successful in creating the parallelogram base shape. The triangles during polymerization were successfully able to bind to neighboring triangles in the correct order to create parallelograms.
Figure 1: Triangles folded into parallelograms using a MgCl solution during the polymerization process. The TEM picture was taken at 100 nm at 80kV with a magnification of 98000x.
Figure 2: Triangles folded into parallelograms using a MgCl solution during the polymerization process. The TEM picture was taken at 100 nm at 80kV with a magnification of 120000x.
Figure 3: Triangles folded into parallelograms using a MgCl solution during the polymerization process. The TEM picture was taken at 100 nm at 80kV with a magnification of 120000x.
It was noticed, however, that the yield of fully bound parallelograms was very low. Triangles binding in an ordered manner of three or less were a common occurrence. Another common observation was two triangles folding on top of another two triangles. Although four triangles were successfully bound together they did not fall to the surface of the TEM grid in the proper orientation. It was hypothesized that the slack between equilateral triangles allowed them to fold on top of one another, resulting in images that appeared to have only one, two, or three triangles.
It was observed that the parallelogram working stocks were properly synthesized and successfully folded into tetrahedrons. While observing the tetrahedrons it was apparent they had a well-defined three-dimensional shape. Pivot points that were created in the design process were successful due to the nature of the folding. Corners of the tetrahedrons were properly held together with staples and scaffold. From a visual representation it appears that tetrahedrons gave the highest yield of fully polymerized geometric shapes.
Figure 4: Parallelograms folded into tetrahedrons using a MgCl solution during the polymerization process. The TEM picture was taken at 100 nm at 80kV with a magnification of 120000x.
Figure 5: Parallelograms folded into tetrahedrons using a MgCl solution during the polymerization process. The TEM picture was taken at 100 nm at 80kV with a magnification of 68000x.
Figure 6: Parallelograms folded into tetrahedrons using a MgCl solution during the polymerization process. The TEM picture was taken at 100 nm at 80kV with a magnification of 120000x.
After observing the tetrahedrons successfully folding, an experiment was developed to see if the folded devices could be successfully dismantled, and then refolded back to their proper shape. The working stock that contained the folded tetrahedrons was heated overnight at two different temperatures, 35° and 40° C. After being heat-treated the DNA solutions were immediately pipetted onto a TEM grid to prevent the tetrahedrons from refolding before observations of the unfolding could be made.
This experiment showed that the tetrahedrons were successfully able to unfold after being heat treated at 35℃ and 40℃. Although both temperatures were successful in unfolding tetrahedrons into parallelograms, it is apparent that reheating the DNA structures to 40℃ yields greater results of unfolding. We hypothesized that the structures heated to 35° C were able to begin the refolding process while they were being prepared on the TEM grid. By increasing the temperature to 40℃, the structures were at an elevated temperature for a longer period of time, thus reducing their ability to refold while preparing them on the TEM grid.
Figure 7: Tetrahedrons were unfolded by increasing the temperature to 35℃ during the polymerization process. The TEM picture was taken at 100 nm at 80kV with a magnification of 98000x.
Additionally, some of the unfolded tetrahedrons were left over night at 4° C. After they were given ample time to refold, new TEM grids were prepped to show that the structures successful reformed into their tetrahedron shape. The ability to have DNA structures unfold and refold demonstrates how our design can be effectively reused. However, it was observed that working stocks that were heat treated to refold contained a lower yield of geometrically viable shapes. Although perfectly folded tetrahedrons were present in TEM pictures after refolding there was an increase in deformed tetrahedrons. Images showed that the tetrahedrons in the working stock that was heat treated to 40℃ contained a higher yield of properly folded tetrahedrons compared to the heat-treated 35℃ working stock.
Figure 8: Tetrahedrons that were unfolded at a temperature of 35℃ were refolded during the polymerization process. The TEM picture was taken at 100 nm at 80kV with a magnification of 98000x.
Figure 9: Tetrahedrons that were unfolded at a temperature of 40℃ were refolded during the polymerization process. The TEM picture was taken at 100 nm at 80kV with a magnification of 120000x.
Purified versus Non. Purified
An experiment was done to determine if unpurified gels had a greater yield than purified gels. The thought behind this hypothesis is that unpurified gels will have a higher yield because they are essentially unfiltered. By having an unfiltered gel the TEM grid could potentially have a higher yield of synthesized origami shapes. The result concluded that purified gels were more applicable for observing origami shapes. Unpurified gels contained a large amount of impurities, monomers, and deformed origami shapes. The unpurified gel TEM grids were extremely cluttered and were observed to have greater dye absorption. Unpurified gels were observed to have no increase in origami figures; however there was an increase in monomers binding to origami figures yielding an increase in deformed structures. In conclusion purified gels should be the most appropriate choice when viewing DNA origami with a transmission electron microscope.
Once agarose gel electrophoresis is complete utilizing ethidium bromide in staining, the DNA in the gel is viewed on a FOTO/Convertible Dual Wavelength UV light. An example of what would be seen at this point can be viewed in figure 1. This is then imaged through an ethidium bromide filter. As an example, an image of a gel generated from the 60-hour ramp of variations in the folding of the parallelogram can be seen in figure 2. 6 µl of 1kb ladder was loaded into well 1 to be used as a reference to the speed at which our structures travelled in comparison to a control known length segment of DNA and can be seen at the bottom of figure 4. Wells 3 through 10 were loaded with variations of the parallelograms including alternating the concentration of magnesium chloride utilized prior to the folding reaction. The specifics of each well for this image are indicated in figure 3.
In agarose gel electrophoresis, molecules of smaller size migrate with less resistance through the pores of the gel. In creating each shape, staples were added in 10-fold excess, which results in an extremely bright band of surplus staples. The bright band that travelled farther within the gel (the “fast” band) is indicative of properly folded structures while the minor band closer to the well shows the presence of dimer structure. Both of these bands were extracted from the gel for analysis. In order to avoid contaminating the samples, a new sterile scalpel was used to cut out each band from the gel.
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Rothemund, Paul W. K. Folding DNA to create nanoscale shapes and patterns. Supplementary Note 12. Nature 2006; 440: 297-302. http://www.nature.com/nature/journal/v440/n7082/extref/nature04586-s2.pdf
Rothemund, Paul W. K. Folding DNA to create nanoscale shapes and patterns. Nature 2006; 440: 297-302. http://www.nature.com/nature/journal/v440/n7082/full/nature04586.html
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