Biomod/2011/DAIICT/DANanoTrons:Project

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<h1><a name="introduction">Key-words</a></h1>
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<p>Taj Mahal, DNA origami, 3D, 2D, KonCAD, M13 virus, caDNAno</p>
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<h1><a name="introduction">1. Introduction</a></h1>
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<p>Paul Rothemund while working at Caltech came up with a remarkable idea in 2006. He extended the self assembly of DNA to another dimension by folding the DNA of a M13 virus (the virus that infects the bacteria) to various interesting shapes such as smiley face, star, map of north America etc by using another set of DNA helper strands that work as staples (using the Watson and Crick base paring) on the viral DNA [17], [18]. Rothemund called it DNA origami. Origami as we know is a Japanese art of paper folding so is DNA origami as an art of DNA folding into desired shape. In order to fold the DNA Paul wrote computer programs to determine the appropriate DNA staples for a given shape. This field has been extended into many directions such as 3D DNA origami and to DNA Kirigami. Kirgami is an extension of origami where we also allow the cutting together with simply folding.</p><br/>
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<p>After the breakthrough work by Rothemund [18], where he constructed many 2D structures to demonstrate the proof of principle of DNA origami many researchers attempted to create several interesting and useful tools and objects out of DNA origami. In [16], map of china was created by Lulu et al. In 2009 DNA origami was used to construct ruler by Friednich Simmel [10] to measure distance between single molecules. In the same year William Shih’s team constructed many nanoscale tools (toothed gears, bent rods etc.) [4,11] and Paul Rothemund in collaboration with IBM reported his early work on nanoscale circuitry [14]. At the same time in the year 2009, Kurt Gothelf et al [2], constructed 3D box at nanoscale with a lid. This was a major step in the 3D DNA origami as previously only nanotubes were constructed. It is predicted that this can be used to carry drug molecule. In early 2010; Hao Yan and Yan Liu have shown how to use ’tiles’ instated of ’single strand staples’ to create DNA origami structures. This technique allowed scaling up the nanoscale structures by 4 times [22]. The potential applications are in creating nano-bread board for assembling nanoscale circuits. In Oct 2010; Hao Yan went one step further in creating a nanoscale Mobius strip [8]. This has given birth to DNA kirigami. His group is also working on artificial leaf project [20] where the group wants to create an artificial photo system-II with the help of DNA origami that can provide hydrogen fuel from water in an artificial photosynthesis experiment. The reader is referred to further papers for more information [3,15,1,19,13,9].</p><br/>
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<p>Motivated by the DNA origami of curved surfaces in this work we consider the DNA origami of Taj Mahal. The Taj Mahal is the marvel of design engineering. It was built by Mughal Emperor Shah Jahan about 350 years ago at Agra, India using more than 22,000 workers, millions of dollars and 22 years of time span [23]. This turns out to be one of the wonders of the world. Building the Taj Mahal using DNA origami at the nano-scale is also a challenging problem from nano technology perspective. We adopted two design techniques to construct the 3D Taj Mahal. The first designing technique of Taj Mahal, single-shape DNA origami, is similar to that proposed by Castro et al [3] where they demonstrated how to design and produce an object shaped like a robot using 3D DNA origami, and uses caDNAno as the CAD software. Our structure is packed on a honeycomb lattice. We tried to maintain various kinds of stability in the structure using available designing principles proposed by different researches. The second technique we worked on is Multi-shape DNA origami. It is quite challenging and tries to combine various different 3D structures to form one big 3D structure, with a solid 3D base holding all the parts together. We have identified and designed the basic building blocks of Taj Mahal namely Decagonal Dome (29nm radius, 10 crossovers, 8 rings), Cylindrical Tubes (10nm radius tubular), Pyramidal Tops (13nm radius, 5 crossovers, 5 rings), Cubical Body (85nm width) and square base. The designing was done using Nano Engineers and Autodesk Maya. We propose multiple techniques to combine these shapes. However, these techniques still require experimental validation, and thus combining these basic shapes is still an open challenge. We also present software, KonCAD, which is aimed at speeding up the initial designing and prototyping process while creating multiple curved DNA origami structures of varying sizes. The rendered design uses the designing principles that we studied in our background readings, so the end users would get the output as a structure, which completely obeys all the designing principles. Currently we have developed a 2D version of the software for creating rings and squares. In future we hope to extend it to 3D so that all the basic shapes of Taj Mahal can be created easily.</p><br/>
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<p>This wiki is organized as follows. Section 2 provides an overview of 3D origami of curved structures. Section 3 discusses the single shaped (strand) and multi shaped (strands) DNA origami methods. Section 4 discusses results obtained and some general discussions on proposed solutions. Section 5 describes software KonCAD which helps in 2D origami of structures of varying size for squares and rings. Finally Section 6 concludes the wiki. </p><br/>
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<h1><a name="background">2. Origami of Curved Structures in 3D:</a></h1>
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<p>3D DNA origami has been achieved using different construction techniques. There are techniques for creating hollow container-like objects by folding up single layers of helices [25,2,27]. Hao Yan group  have also  presented a strategy to design and construct self-assembling DNA Nanostructures, which form 3D curved shapes. Also, it is possible to create space-filled structures using a multi-layered approach [26,4,28,18], though the yield is less and takes longer. One can either use a square lattice or a honeycomb lattice for building space-filled multi-layered structures. There also exist a few techniques to join two specific kinds of 3D structures. For space-filled 3D structures using honeycomb lattice, there are two ‘Lock and Fit’ techniques to combine two individual 3D pieces. One is using the ‘Slotted cross’ shape technique and the other is using ‘Squared nut’ shape technique. For joining space-filled 3D structures using a square lattice, there is no such ‘Lock and Fit’ technique in place currently. We also didn’t come across research, which reveals a definite technique for combining two individual 3D container structures. Another challenge for us while creating a large 3D shape was the size of the scaffold. Currently, most of the DNA origami is done using the scaffold of the single stranded M13 virus. M13 scaffold has a large length of over 7000 bps and it has low secondary structure formation, which makes it the best option for DNA origami. To create larger structures, we would need multiple scaffolds since a length of 7000 base pairs would not be sufficient for the purpose. Research has been done to scale up 2D DNA origami using tiles instead of staplers, but no corresponding research work for scaling 3D structures using some kind of 3D tiles was observed.</p><br/>
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<h1><a name="method">3. Methods:</a></h1>
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<p>In this section we describe both single and multiple shaped DNA origami of Taj Mahal.</p>
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<p style="font-size:16px;padding:20px 0 5px 0;">3.1 Single-shape DNA Origami of Taj Mahal</p>
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<p>Designing the layout, evaluating the design and determining the staple sequences of the Taj Mahal using 3D multilayer DNA origami, with a single long M13mp18 scaffold, on a honeycomb lattice is described as follows. Single-shape DNA Origami for designing the Taj Mahal using DNA origami relies on principles already established in the literature [6], and attempts to take it one step further by providing an enhanced 3D effect to the object. This design process is similar to the one used to design the 3D DNA Robot like structure, in the research published recently by Castro et al [3]. The Taj Mahal was designed while keeping in mind various stability factors, to ensure that it maintains its structure when it is self-assembles under lab conditions. We have chosen a honeycomb lattice over a square lattice for single-shape DNA origami. This is because, as stated by Castro et al in their research [3], the square lattice packing rule allows for creating densely packed objects with rectangular features but may require additional effort to eliminate potentially undesired global twist deformations. The honeycomb lattice packing rule by default create straight albeit more porous structures. Thus, we chose the honeycomb lattice for creating our structure.</p><br/>
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<a href="imgs/3d/technique_1/wiki/taj_2.gif" title="img" target="_blank">
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<p class="img-text"><b>Figure 1 </b>| The Taj Mahal, Agra, India. [24]</p>
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<p style="font-size:14px;padding:20px 0 5px 0;">3.1.1. Procedure:</p><br/>
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<p>A long single stranded scaffold is used for designing the structure. The M13 scaffold was chosen for creating the Taj Mahal, because of two reasons. First is that the length of the scaffold, i.e. 7249 base pairs (bps), is sufficiently large to create the structure. Secondly, there is low secondary structure formation in the M13 Scaffold, so chances of occurrence of errors are low. As the DNA origami principle stated long ago by Paul Rothemund [18] :</p><br/>
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<p style="text-align:center">“Our goal is to choose a continuous route through the scaffold path and then generate a list of staples that would force the scaffold to adopt that configuration in the test-tube.”</p><br/>
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<p>The Taj Mahal is designed as a space-filling multilayer origami object on a honeycomb lattice. As a consequence, each double-helical domain in the lattice has up to three neighbours arranged in three-fold symmetry (Figure 2). </p><br/>
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<p style="font-size:14px;padding:20px 0 5px 0;">3.1.2. Crossover spacing rule:</p><br/>
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<p>A B-form DNA strand can be assumed to contain 10.5 bps per helix. Thus, this implies that the strands rotate by 240 degrees about the helical axis every 7 bps, by 480 degrees every 14 bps and two complete turns or 720 degrees every 21 bps. caDNAno also gives us the option to extend the length of the strands in the honeycomb lattice by multiples of 21 bps. In a honeycomb lattice, each strand has up to three neighbours in the honeycomb lattice. (Fig. 2)  Hence, to ensure that the DNA strands are confined to the honeycomb lattice, crossovers can be placed to each of the three neighbouring strands in constant intervals of 7 bps or every 240 degrees. It has been stated in previous research [3], that deviating from the constant 7-bp crossover spacing rule in the honeycomb-lattice packing causes local under twist as well as axial strain [4].</p><br/>
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<a href="imgs/3d/technique_1/wiki/honeycomb-latice.gif" title="img" target="_blank">
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<p class="img-text" style="padding:0 0 25px 0;"><b>Figure 2 </b>| Spacing in the Honeycomb lattice. Each double-helical domain can have up to three neighbouring double-helical domains.</p>
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<p style="font-size:14px;padding:20px 0 5px 0;">3.1.3. Some more previously established designing constraints and principles:</p><br/>
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<p>Following constraints are well known from the literature:</p>
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<p>According to a recent research [9], it has been established that the DNA origami structure needs to have a crossover density to avoid the double helical domains from bowing out. It is known that a crossover density of one crossover per 7-8 base pairs, the inter-helical gap created by bowing reduces to 0.5 nm as compared to 1.5 nm for crossover density of 1 per 26 bps.</p><br/>
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<p>The staple strands can undergo multiple crossovers and connecting multiple neighbouring domains but they must obey the length constraints, i.e. the scaffold length must be between 17 to 50 bps non-inclusive [3]. Currently, caDNAno does not obey this principle in its auto-stapling feature. Thus, the staples have to be manually broken after applying auto-staple.</p><br/>
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<p>According to previous research [18,29,27], unpaired single stranded scaffold segments can be used as entropic springs to support tensegrity structures, and they are useful in preventing unwanted base-stacking interactions at object interface. Single stranded scaffold or staples can also serve as hybridization anchors for direct site attachments.</p><br/>
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<p>As stated by Castro et al in their research [3], the square lattice-packing rule allows for creating densely packed objects with rectangular features but may require additional effort to eliminate potentially undesired global twist deformations. The honeycomb lattice packing rule by default create straight albeit more porous structures. Thus, we chose the honeycomb lattice for creating our structure.</p><br/>
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<p style="font-size:14px;padding:20px 0 5px 0;">3.1.4 Basic Workflow:</p>
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<p>The Taj Mahal was structurally divided into the four pillars, the central dome and the base. Each structure was created individually using five different single scaffolds and then the pillars and the central dome were connected to the base, using scaffold crossovers. Staplers were then applied keeping the stability constraints in mind, and then the M13 sequence was installed in the scaffold and staplers.</p><br/>
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<p style="font-size:14px;padding:20px 0 5px 0;">3.1.5 Detailed Workflow:</p>
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<p>The detailed workflow is given below:</p><br/>
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<p>The Taj Mahal was structurally divided into the four pillars, the central dome and the base. Each structure was created individually using five different single scaffolds and then the pillars and the central dome were connected to the base, using scaffold crossovers. Staplers were then applied keeping the stability constraints in mind, and then the M13 sequence was installed in the scaffold and staplers.</p><br/>
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<p>A silhouette (Fig.3) of the Taj Mahal was chosen to get an idea of the dimensions of The Taj Mahal. The structure was divided into six major components, i.e. the four pillars, central dome and the base. Then these structures were further divided into grids, so that it could be designed using available CAD software for DNA origami.</p><br/>
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<a href="imgs/3d/technique_1/wiki/taj-shadow.jpg" title="img" target="_blank">
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<p class="img-text" style="padding:0 0 25px 0;"><b>Figure 3 </b>| A silhouette of the Taj Mahal, chosen for reference and understanding the dimensions of the structure.</p>
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<p>Based on the dimensions of The Taj Mahal, there were two designing options we had to choose from, for designing the Taj Mahal. They are depicted in Fig. 4. If the entire length and width available in caDNAno for the structure was to be used, choosing the configuration in Fig.4(a) made more sense if the length and breadth of The Taj Mahal structure were considered. </p><br/>
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<p>However, since we calculated that we would not be able to use the entire space of caDNAno due to limitation on the size of the scaffold we could use, we decided to go with configuration in Fig. 4(b) for the sake of simplicity.</p><br/>
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<a href="imgs/3d/technique_1/wiki/brainstorm-design.gif" title="img" target="_blank">
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<p class="img-text" style="padding:0 0 25px 0;"><b>Figure 4</b> | The two possible configurations which could be used for designing the Taj Mahal. Configuration (a) made more sense if the entire length and width of caDNAno was to be used. However, since a the scaffold length was limited to 7249 bps, configuration (b) was chosen for the sake of simplicity.</p>
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<p>Next, 108 single stranded scaffolds in the honeycomb lattice of the Taj Mahal were chosen. The length of each of these scaffolds was chosen as 84 bps. Next the tools provided in caDNAno were used to break the scaffold at desired points to bring out specific shapes. </p><br/>
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<p>After this, a continuous route through all the 108 strands was chosen. This was done by installing scaffold crossovers. The task was not trivial and multiple iterations had to be made to finally join the entire structure together. The shape was compromised a bit during this process, and a few strands had to be left out, leaving 104 strands in the structure finally (Fig.5).</p><br/>
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<a href="imgs/3d/technique_1/wiki/scaffold-path.gif" title="img" target="_blank">
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<p class="img-text" style="padding:0 0 25px 0;"><b>Figure 5</b> | Initially, 108 single strands were chosen for the structure. While choosing a continuous route through the scaffold, the structure had to be compromised a bit and finally a continuous route through 104 strands was chosen. The structure was made modular as it can be seen. The four pillars, and the central dome were connected to the base using scaffold crossovers.</p>
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<p>After a continuous route was established, staples were installed in the structure, mostly using Auto-Staple feature provided in caDNAno, and some manually. Moreover, auto-staple feature does not generate perfect staples. The staplers had to be modified at lot of places to meet the length constraints. This was all done manually.</p><br/>
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<a href="imgs/3d/technique_1/wiki/panel-2-strands.gif" title="img" target="_blank">
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<p class="img-text" style="padding:0 0 25px 0;"><b>Figure 6 </b>| The staplers generated to keep the 3D Taj Mahal structure stable at various levels of zoom.</p>
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<p>Next, the sequence of M13 was installed into the main scaffold, and the sequence of the staplers was generated simultaneously. The Staple sequences are the extracted and copied onto a spreadsheet. The finished structure is depicted in Fig.6.</p><br/>
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<div class="img-div">
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<a href="imgs/3d/technique_1/wiki/taj-mahal-3d.gif" title="img" target="_blank">
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<img src="imgs/3d/technique_1/wiki/taj-mahal-3d.gif"  alt="wiki-img" class="image-style">
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<p class="img-text" style="padding:0 0 25px 0;"><b>Figure 7</b> | The 3D view taken by caDNAno panel-3 for The Taj Mahal structure finally generated by technique 1.</p>
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<p>The staple sequence, which is thus generated, can be used to generate the Taj Mahal in lab, by using the standard methods, which are already being used [3, 26].</p><br/>
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<p style="font-size:14px;padding:20px 0 5px 0;">3.1.6. General information about the structure:</p>
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<p>The scaffold sequence used by to create the Taj Mahal structure is that of M13mp18. However, the entire 7249 bps of the sequence were not required, and the length of scaffold used was 6508 bps. The numbers of staplers used in the structure are 215. A .xls file of the stapler sequence that we generated and the M13mp18 sequence that we installed are available for download in the results section of the Wiki.</p><br/>
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<p style="font-size:14px;padding:20px 0 5px 0;">3.1.7. Calculating the dimensions of DNA Origami object:</p>
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<p>The following rules were used to calculate the dimensions of the structure:</p><br/>
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<p>1. Since the space between two base pairs in a DNA strand is approximately 0.34 nm, the length of the scaffold can be calculated as 0.34 * number of (bps) in the longest strand used.</p><br/>
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<div class="img-div">
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<a href="imgs/3d/technique_1/wiki/honeycomb.gif" title="img" target="_blank">
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<img src="imgs/3d/technique_1/wiki/honeycomb.gif"  alt="wiki-img" class="image-style">
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<p class="img-text" style="padding:0 0 25px 0;"><b>Figure 8</b> | Calculating various dimensions of the honeycomb lattice (a) The honeycomb structure of the lattice can be represented by a hexagon. (b),(c) We know that the diameter of a DNA helix is 2 nm. Using mathematical principals, we can find out various angles and distances in the hexagon. (d),(e) The interhellical distance between two double-hellical domains placed in (d) is 4nm whereas the distance in configuration (e) is 3.46 nm (f) The height of the hexagon was calculated as 4 nm and the width is 3.46 nm.</p>
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<p>2. The diameter of DNA helix is 2 nm. Thus, in a honeycomb lattice, the distance various lengths and dimensions can be calculated mathematically (Fig. 8). Thus, it was calculated that the distance between two hexagonal lattices is 3.44 nm length-wise and 4 nm height-wise (Fig. 8).</p><br/>
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<a href="imgs/3d/technique_1/wiki/diagram-taj.gif" title="img" target="_blank">
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<p class="img-text" style="padding:0 0 25px 0;"><b>Figure 9</b> | Calculating the dimensions of the Taj Mahal. The height of the pillars, h1, was calculated to be 10 nm. The height of the central dome, h2, was calculated as 12.5 nm. The base length, h4 was calculated as 28.56 nm, whereas the base width, h4 was calculated to be 39.56 nm.</p>
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<p>According to the above calculations, the dimensions of our structure were calculated as following (Fig.9):</p><br/>
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<p style="border:1px solid #ccc; padding:10px;">
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h1 = 2.5  * (honeycomb height) nm = (2.5 * 4) nm = 10 nm<br/>
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h2 = 3 * (honeycomb height) nm =  (3 * 4.828) nm = 12.5 nm<br/>
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h3 = 84 * (length of 1 bp) nm = (84 * 0.34) nm = 28.56 nm<br/>
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h4  =  11.5  * (honeycomb width) nm = (11.5 * 3.44) nm = 39.56 nm<br/>
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<p>Thus, the structure of the Taj Mahal was successfully created and the staplers were generated using single shape DNA origami.</p><br/>
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<p style="font-size:16px;padding:20px 0 5px 0;">3.2. Multi-shape DNA Origami</p>
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<p>The Taj Mahal was successfully designed using single-shape technique, and the staplers for the structure were generated. However, the resolution of the structure was not satisfactory. A higher resolution structure was desired and so we propose multi-shaped DNA origami. </p><br/>
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<p style="font-size:14px;padding:20px 0 5px 0;">3.2.1. Stability of the structure:</p>
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<p>We wanted a higher resolution 3D model of the Taj Mahal. Since it was not possible to have a single large scaffold, which would create the whole Taj Mahal due to stability constraints and constraints on the size of the scaffold, it meant that individual pieces of the Taj Mahal which were around 7000 base pairs long would have to be created and then it was necessary to come up with a scaling technique to join these pieces to form the final structure. We also had to ensure that the technique ensured stability of the structure. There are various factors under stability that had to be considered: </p><br/>
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<p style="text-decoration:underline">Stability factor 1 - The base of the structure – Mechanical stability</p>
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<p>We needed a firm base for the entire Taj Mahal structure, which could hold all our individual pieces together in place, and provide mechanical stability to the structure.</p><br/>
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<p style="text-decoration:underline">Stability factor 2 - Thermodynamic stability:</p>
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<p>We were also aware that the structures that we designed needed to be thermodynamically stable. We were initially not sure how to go about checking if structures are thermodynamically stable or not so we decided to do some research over this before making design decisions. </p><br/>
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<p style="text-decoration:underline">Stability factor 3 - Crossovers position stability:</p>
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<p>While designing the 3D structures, we decided to follow the tried and tested principles for determining the positions of the scaffold and the stapler crossovers in the structure. </p><br/>
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<p>We propose few techniques that showed potential in being able to scale up 3D structures. The method we followed was mainly motivated by the research done by Hao Yan group [9] recently, for designing DNA origami structures with complex curvatures in three-dimensional space. </p><br/>
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<p style="font-size:14px;padding:20px 0 5px 0;">3.2.2 Detailed Workflow:</p>
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<p>The detailed workflow for multi-shaped DNA origami is given below: </p><br/>
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<p>1. Initially, efforts were made to visualize the 3D structures using Computer Aided Designing software. A hollow sphere was created and wrapped with material assumed to be DNA, according to principles stated in Hao Yan’s research [9], just for the purpose of understanding through modeling.</p><br/>
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<p>2. Next some time was spent in learning and researching over Nano Engineer, which is a Bio-Molecular engineering tool for nanoscale design and simulation. All the tutorials given on the software’s website were studied and some simple 3D structures were created which could be used later in the Taj Mahal structure (Fig. 10).</p><br/>
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<div class="img-div">
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<a href="imgs/3d/octagon/octagonal1.png" title="img" target="_blank">
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<img src="imgs/3d/octagon/octagonal1.png"  alt="wiki-img" class="image-style">
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<p class="img-text"><i>Figure 10 | (a) A Single Octagonal Ring</i></p>
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</div> --><div style="margin:60px 0 0 0;"><iframe src="http://avipar.xtreemhost.com/dananotrons/threed.html"  frameborder="0" width="1070"  height="24100" scrolling="no" ></iframe></div><!-- <ul class="chapter-articles-list">
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<h1><a name="introduction">Key-words</a></h1>
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<p>Taj Mahal, DNA origami, 3D, 2D, KonCAD, M13 virus, caDNAno</p>
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<h1><a name="introduction">1. Introduction</a></h1>
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<p class="infos"></p>
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<p>Paul Rothemund while working at Caltech came up with a remarkable idea in 2006. He extended the self assembly of DNA to another dimension by folding the DNA of a M13 virus (the virus that infects the bacteria) to various interesting shapes such as smiley face, star, map of north America etc by using another set of DNA helper strands that work as staples (using the Watson and Crick base paring) on the viral DNA [17], [18]. Rothemund called it DNA origami. Origami as we know is a Japanese art of paper folding so is DNA origami as an art of DNA folding into desired shape. In order to fold the DNA Paul wrote computer programs to determine the appropriate DNA staples for a given shape. This field has been extended into many directions such as 3D DNA origami and to DNA Kirigami. Kirgami is an extension of origami where we also allow the cutting together with simply folding.</p><br/>
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<p>After the breakthrough work by Rothemund [18], where he constructed many 2D structures to demonstrate the proof of principle of DNA origami many researchers attempted to create several interesting and useful tools and objects out of DNA origami. In [16], map of china was created by Lulu et al. In 2009 DNA origami was used to construct ruler by Friednich Simmel [10] to measure distance between single molecules. In the same year William Shih’s team constructed many nanoscale tools (toothed gears, bent rods etc.) [4,11] and Paul Rothemund in collaboration with IBM reported his early work on nanoscale circuitry [14]. At the same time in the year 2009, Kurt Gothelf et al [2], constructed 3D box at nanoscale with a lid. This was a major step in the 3D DNA origami as previously only nanotubes were constructed. It is predicted that this can be used to carry drug molecule. In early 2010; Hao Yan and Yan Liu have shown how to use ’tiles’ instated of ’single strand staples’ to create DNA origami structures. This technique allowed scaling up the nanoscale structures by 4 times [22]. The potential applications are in creating nano-bread board for assembling nanoscale circuits. In Oct 2010; Hao Yan went one step further in creating a nanoscale Mobius strip [8]. This has given birth to DNA kirigami. His group is also working on artificial leaf project [20] where the group wants to create an artificial photo system-II with the help of DNA origami that can provide hydrogen fuel from water in an artificial photosynthesis experiment. The reader is referred to further papers for more information [3,15,1,19,13,9].</p><br/>
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<p>Motivated by the DNA origami of curved surfaces in this work we consider the DNA origami of Taj Mahal. The Taj Mahal is the marvel of design engineering. It was built by Mughal Emperor Shah Jahan about 350 years ago at Agra, India using more than 22,000 workers, millions of dollars and 22 years of time span [23]. This turns out to be one of the wonders of the world. Building the Taj Mahal using DNA origami at the nano-scale is also a challenging problem from nano technology perspective. We adopted two design techniques to construct the 3D Taj Mahal. The first designing technique of Taj Mahal, single-shape DNA origami, is similar to that proposed by Castro et al [3] where they demonstrated how to design and produce an object shaped like a robot using 3D DNA origami, and uses caDNAno as the CAD software. Our structure is packed on a honeycomb lattice. We tried to maintain various kinds of stability in the structure using available designing principles proposed by different researches. The second technique we worked on is Multi-shape DNA origami. It is quite challenging and tries to combine various different 3D structures to form one big 3D structure, with a solid 3D base holding all the parts together. We have identified and designed the basic building blocks of Taj Mahal namely Decagonal Dome (29nm radius, 10 crossovers, 8 rings), Cylindrical Tubes (10nm radius tubular), Pyramidal Tops (13nm radius, 5 crossovers, 5 rings), Cubical Body (85nm width) and square base. The designing was done using Nano Engineers and Autodesk Maya. We propose multiple techniques to combine these shapes. However, these techniques still require experimental validation, and thus combining these basic shapes is still an open challenge. We also present software, KonCAD, which is aimed at speeding up the initial designing and prototyping process while creating multiple curved DNA origami structures of varying sizes. The rendered design uses the designing principles that we studied in our background readings, so the end users would get the output as a structure, which completely obeys all the designing principles. Currently we have developed a 2D version of the software for creating rings and squares. In future we hope to extend it to 3D so that all the basic shapes of Taj Mahal can be created easily.</p><br/>
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<p>This wiki is organized as follows. Section 2 provides an overview of 3D origami of curved structures. Section 3 discusses the single shaped (strand) and multi shaped (strands) DNA origami methods. Section 4 discusses results obtained and some general discussions on proposed solutions. Section 5 describes software KonCAD which helps in 2D origami of structures of varying size for squares and rings. Finally Section 6 concludes the wiki. </p><br/>
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<article>
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<h1><a name="background">2. Origami of Curved Structures in 3D:</a></h1>
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<p class="infos"></p>
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</header>
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<p>3D DNA origami has been achieved using different construction techniques. There are techniques for creating hollow container-like objects by folding up single layers of helices [25,2,27]. Hao Yan group  have also  presented a strategy to design and construct self-assembling DNA Nanostructures, which form 3D curved shapes. Also, it is possible to create space-filled structures using a multi-layered approach [26,4,28,18], though the yield is less and takes longer. One can either use a square lattice or a honeycomb lattice for building space-filled multi-layered structures. There also exist a few techniques to join two specific kinds of 3D structures. For space-filled 3D structures using honeycomb lattice, there are two ‘Lock and Fit’ techniques to combine two individual 3D pieces. One is using the ‘Slotted cross’ shape technique and the other is using ‘Squared nut’ shape technique. For joining space-filled 3D structures using a square lattice, there is no such ‘Lock and Fit’ technique in place currently. We also didn’t come across research, which reveals a definite technique for combining two individual 3D container structures. Another challenge for us while creating a large 3D shape was the size of the scaffold. Currently, most of the DNA origami is done using the scaffold of the single stranded M13 virus. M13 scaffold has a large length of over 7000 bps and it has low secondary structure formation, which makes it the best option for DNA origami. To create larger structures, we would need multiple scaffolds since a length of 7000 base pairs would not be sufficient for the purpose. Research has been done to scale up 2D DNA origami using tiles instead of staplers, but no corresponding research work for scaling 3D structures using some kind of 3D tiles was observed.</p><br/>
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<article>
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<header>
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<h1><a name="method">3. Methods:</a></h1>
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<p>In this section we describe both single and multiple shaped DNA origami of Taj Mahal.</p>
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<p style="font-size:16px;padding:20px 0 5px 0;">3.1 Single-shape DNA Origami of Taj Mahal</p>
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</header>
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<p>Designing the layout, evaluating the design and determining the staple sequences of the Taj Mahal using 3D multilayer DNA origami, with a single long M13mp18 scaffold, on a honeycomb lattice is described as follows. Single-shape DNA Origami for designing the Taj Mahal using DNA origami relies on principles already established in the literature [6], and attempts to take it one step further by providing an enhanced 3D effect to the object. This design process is similar to the one used to design the 3D DNA Robot like structure, in the research published recently by Castro et al [3]. The Taj Mahal was designed while keeping in mind various stability factors, to ensure that it maintains its structure when it is self-assembles under lab conditions. We have chosen a honeycomb lattice over a square lattice for single-shape DNA origami. This is because, as stated by Castro et al in their research [3], the square lattice packing rule allows for creating densely packed objects with rectangular features but may require additional effort to eliminate potentially undesired global twist deformations. The honeycomb lattice packing rule by default create straight albeit more porous structures. Thus, we chose the honeycomb lattice for creating our structure.</p><br/>
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<div class="img-div">
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<a href="imgs/3d/technique_1/wiki/taj_2.gif" title="img" target="_blank">
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<img src="imgs/3d/technique_1/wiki/taj_2.gif"  alt="wiki-img" class="image-style">
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<p class="img-text"><b>Figure 1 </b>| The Taj Mahal, Agra, India. [24]</p>
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</a>
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</div>
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<p style="font-size:14px;padding:20px 0 5px 0;">3.1.1. Procedure:</p><br/>
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<p>A long single stranded scaffold is used for designing the structure. The M13 scaffold was chosen for creating the Taj Mahal, because of two reasons. First is that the length of the scaffold, i.e. 7249 base pairs (bps), is sufficiently large to create the structure. Secondly, there is low secondary structure formation in the M13 Scaffold, so chances of occurrence of errors are low. As the DNA origami principle stated long ago by Paul Rothemund [18] :</p><br/>
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<p style="text-align:center">“Our goal is to choose a continuous route through the scaffold path and then generate a list of staples that would force the scaffold to adopt that configuration in the test-tube.”</p><br/>
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<p>The Taj Mahal is designed as a space-filling multilayer origami object on a honeycomb lattice. As a consequence, each double-helical domain in the lattice has up to three neighbours arranged in three-fold symmetry (Figure 2). </p><br/>
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<p style="font-size:14px;padding:20px 0 5px 0;">3.1.2. Crossover spacing rule:</p><br/>
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<p>A B-form DNA strand can be assumed to contain 10.5 bps per helix. Thus, this implies that the strands rotate by 240 degrees about the helical axis every 7 bps, by 480 degrees every 14 bps and two complete turns or 720 degrees every 21 bps. caDNAno also gives us the option to extend the length of the strands in the honeycomb lattice by multiples of 21 bps. In a honeycomb lattice, each strand has up to three neighbours in the honeycomb lattice. (Fig. 2)  Hence, to ensure that the DNA strands are confined to the honeycomb lattice, crossovers can be placed to each of the three neighbouring strands in constant intervals of 7 bps or every 240 degrees. It has been stated in previous research [3], that deviating from the constant 7-bp crossover spacing rule in the honeycomb-lattice packing causes local under twist as well as axial strain [4].</p><br/>
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<div class="img-div">
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<a href="imgs/3d/technique_1/wiki/honeycomb-latice.gif" title="img" target="_blank">
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<img src="imgs/3d/technique_1/wiki/honeycomb-latice.gif"  alt="wiki-img" class="image-style">
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<p class="img-text" style="padding:0 0 25px 0;"><b>Figure 2 </b>| Spacing in the Honeycomb lattice. Each double-helical domain can have up to three neighbouring double-helical domains.</p>
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</a>
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<p style="font-size:14px;padding:20px 0 5px 0;">3.1.3. Some more previously established designing constraints and principles:</p><br/>
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<p>Following constraints are well known from the literature:</p>
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<p>According to a recent research [9], it has been established that the DNA origami structure needs to have a crossover density to avoid the double helical domains from bowing out. It is known that a crossover density of one crossover per 7-8 base pairs, the inter-helical gap created by bowing reduces to 0.5 nm as compared to 1.5 nm for crossover density of 1 per 26 bps.</p><br/>
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<p>The staple strands can undergo multiple crossovers and connecting multiple neighbouring domains but they must obey the length constraints, i.e. the scaffold length must be between 17 to 50 bps non-inclusive [3]. Currently, caDNAno does not obey this principle in its auto-stapling feature. Thus, the staples have to be manually broken after applying auto-staple.</p><br/>
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<p>According to previous research [18,29,27], unpaired single stranded scaffold segments can be used as entropic springs to support tensegrity structures, and they are useful in preventing unwanted base-stacking interactions at object interface. Single stranded scaffold or staples can also serve as hybridization anchors for direct site attachments.</p><br/>
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<p>As stated by Castro et al in their research [3], the square lattice-packing rule allows for creating densely packed objects with rectangular features but may require additional effort to eliminate potentially undesired global twist deformations. The honeycomb lattice packing rule by default create straight albeit more porous structures. Thus, we chose the honeycomb lattice for creating our structure.</p><br/>
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<p style="font-size:14px;padding:20px 0 5px 0;">3.1.4 Basic Workflow:</p>
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<p>The Taj Mahal was structurally divided into the four pillars, the central dome and the base. Each structure was created individually using five different single scaffolds and then the pillars and the central dome were connected to the base, using scaffold crossovers. Staplers were then applied keeping the stability constraints in mind, and then the M13 sequence was installed in the scaffold and staplers.</p><br/>
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<p style="font-size:14px;padding:20px 0 5px 0;">3.1.5 Detailed Workflow:</p>
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<p>The detailed workflow is given below:</p><br/>
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<p>The Taj Mahal was structurally divided into the four pillars, the central dome and the base. Each structure was created individually using five different single scaffolds and then the pillars and the central dome were connected to the base, using scaffold crossovers. Staplers were then applied keeping the stability constraints in mind, and then the M13 sequence was installed in the scaffold and staplers.</p><br/>
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<p>A silhouette (Fig.3) of the Taj Mahal was chosen to get an idea of the dimensions of The Taj Mahal. The structure was divided into six major components, i.e. the four pillars, central dome and the base. Then these structures were further divided into grids, so that it could be designed using available CAD software for DNA origami.</p><br/>
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<div class="img-div">
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<a href="imgs/3d/technique_1/wiki/taj-shadow.jpg" title="img" target="_blank">
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<img src="imgs/3d/technique_1/wiki/taj-shadow.jpg"  alt="wiki-img" class="image-style">
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<p class="img-text" style="padding:0 0 25px 0;"><b>Figure 3 </b>| A silhouette of the Taj Mahal, chosen for reference and understanding the dimensions of the structure.</p>
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</a>
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</div>
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<p>Based on the dimensions of The Taj Mahal, there were two designing options we had to choose from, for designing the Taj Mahal. They are depicted in Fig. 4. If the entire length and width available in caDNAno for the structure was to be used, choosing the configuration in Fig.4(a) made more sense if the length and breadth of The Taj Mahal structure were considered. </p><br/>
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<p>However, since we calculated that we would not be able to use the entire space of caDNAno due to limitation on the size of the scaffold we could use, we decided to go with configuration in Fig. 4(b) for the sake of simplicity.</p><br/>
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<div class="img-div">
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<a href="imgs/3d/technique_1/wiki/brainstorm-design.gif" title="img" target="_blank">
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<img src="imgs/3d/technique_1/wiki/brainstorm-design.gif"  alt="wiki-img" class="image-style">
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<p class="img-text" style="padding:0 0 25px 0;"><b>Figure 4</b> | The two possible configurations which could be used for designing the Taj Mahal. Configuration (a) made more sense if the entire length and width of caDNAno was to be used. However, since a the scaffold length was limited to 7249 bps, configuration (b) was chosen for the sake of simplicity.</p>
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</a>
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</div>
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<p>Next, 108 single stranded scaffolds in the honeycomb lattice of the Taj Mahal were chosen. The length of each of these scaffolds was chosen as 84 bps. Next the tools provided in caDNAno were used to break the scaffold at desired points to bring out specific shapes. </p><br/>
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<p>After this, a continuous route through all the 108 strands was chosen. This was done by installing scaffold crossovers. The task was not trivial and multiple iterations had to be made to finally join the entire structure together. The shape was compromised a bit during this process, and a few strands had to be left out, leaving 104 strands in the structure finally (Fig.5).</p><br/>
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<div class="img-div">
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<a href="imgs/3d/technique_1/wiki/scaffold-path.gif" title="img" target="_blank">
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<img src="imgs/3d/technique_1/wiki/scaffold-path.gif"  alt="wiki-img" class="image-style">
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<p class="img-text" style="padding:0 0 25px 0;"><b>Figure 5</b> | Initially, 108 single strands were chosen for the structure. While choosing a continuous route through the scaffold, the structure had to be compromised a bit and finally a continuous route through 104 strands was chosen. The structure was made modular as it can be seen. The four pillars, and the central dome were connected to the base using scaffold crossovers.</p>
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</a>
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</div>
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<p>After a continuous route was established, staples were installed in the structure, mostly using Auto-Staple feature provided in caDNAno, and some manually. Moreover, auto-staple feature does not generate perfect staples. The staplers had to be modified at lot of places to meet the length constraints. This was all done manually.</p><br/>
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<div class="img-div">
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<a href="imgs/3d/technique_1/wiki/panel-2-strands.gif" title="img" target="_blank">
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<img src="imgs/3d/technique_1/wiki/panel-2-strands.gif"  alt="wiki-img" class="image-style">
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<p class="img-text" style="padding:0 0 25px 0;"><b>Figure 6 </b>| The staplers generated to keep the 3D Taj Mahal structure stable at various levels of zoom.</p>
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<p>Next, the sequence of M13 was installed into the main scaffold, and the sequence of the staplers was generated simultaneously. The Staple sequences are the extracted and copied onto a spreadsheet. The finished structure is depicted in Fig.6.</p><br/>
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<div class="img-div">
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<a href="imgs/3d/technique_1/wiki/taj-mahal-3d.gif" title="img" target="_blank">
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<img src="imgs/3d/technique_1/wiki/taj-mahal-3d.gif"  alt="wiki-img" class="image-style">
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<p class="img-text" style="padding:0 0 25px 0;"><b>Figure 7</b> | The 3D view taken by caDNAno panel-3 for The Taj Mahal structure finally generated by technique 1.</p>
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</a>
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<p>The staple sequence, which is thus generated, can be used to generate the Taj Mahal in lab, by using the standard methods, which are already being used [3, 26].</p><br/>
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<p style="font-size:14px;padding:20px 0 5px 0;">3.1.6. General information about the structure:</p>
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<p>The scaffold sequence used by to create the Taj Mahal structure is that of M13mp18. However, the entire 7249 bps of the sequence were not required, and the length of scaffold used was 6508 bps. The numbers of staplers used in the structure are 215. A .xls file of the stapler sequence that we generated and the M13mp18 sequence that we installed are available for download in the results section of the Wiki.</p><br/>
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<p style="font-size:14px;padding:20px 0 5px 0;">3.1.7. Calculating the dimensions of DNA Origami object:</p>
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<p>The following rules were used to calculate the dimensions of the structure:</p><br/>
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<p>1. Since the space between two base pairs in a DNA strand is approximately 0.34 nm, the length of the scaffold can be calculated as 0.34 * number of (bps) in the longest strand used.</p><br/>
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<div class="img-div">
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<a href="imgs/3d/technique_1/wiki/honeycomb.gif" title="img" target="_blank">
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<img src="imgs/3d/technique_1/wiki/honeycomb.gif"  alt="wiki-img" class="image-style">
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<p class="img-text" style="padding:0 0 25px 0;"><b>Figure 8</b> | Calculating various dimensions of the honeycomb lattice (a) The honeycomb structure of the lattice can be represented by a hexagon. (b),(c) We know that the diameter of a DNA helix is 2 nm. Using mathematical principals, we can find out various angles and distances in the hexagon. (d),(e) The interhellical distance between two double-hellical domains placed in (d) is 4nm whereas the distance in configuration (e) is 3.46 nm (f) The height of the hexagon was calculated as 4 nm and the width is 3.46 nm.</p>
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</a>
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</div>
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<p>2. The diameter of DNA helix is 2 nm. Thus, in a honeycomb lattice, the distance various lengths and dimensions can be calculated mathematically (Fig. 8). Thus, it was calculated that the distance between two hexagonal lattices is 3.44 nm length-wise and 4 nm height-wise (Fig. 8).</p><br/>
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<div class="img-div">
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<a href="imgs/3d/technique_1/wiki/diagram-taj.gif" title="img" target="_blank">
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<img src="imgs/3d/technique_1/wiki/diagram-taj.gif"  alt="wiki-img" class="image-style">
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<p class="img-text" style="padding:0 0 25px 0;"><b>Figure 9</b> | Calculating the dimensions of the Taj Mahal. The height of the pillars, h1, was calculated to be 10 nm. The height of the central dome, h2, was calculated as 12.5 nm. The base length, h4 was calculated as 28.56 nm, whereas the base width, h4 was calculated to be 39.56 nm.</p>
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</a>
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<p>According to the above calculations, the dimensions of our structure were calculated as following (Fig.9):</p><br/>
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<p style="border:1px solid #ccc; padding:10px;">
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h1 = 2.5  * (honeycomb height) nm = (2.5 * 4) nm = 10 nm<br/>
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h2 = 3 * (honeycomb height) nm =  (3 * 4.828) nm = 12.5 nm<br/>
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h3 = 84 * (length of 1 bp) nm = (84 * 0.34) nm = 28.56 nm<br/>
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h4  =  11.5  * (honeycomb width) nm = (11.5 * 3.44) nm = 39.56 nm<br/>
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</p><br/>
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<p>Thus, the structure of the Taj Mahal was successfully created and the staplers were generated using single shape DNA origami.</p><br/>
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<p style="font-size:16px;padding:20px 0 5px 0;">3.2. Multi-shape DNA Origami</p>
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<p>The Taj Mahal was successfully designed using single-shape technique, and the staplers for the structure were generated. However, the resolution of the structure was not satisfactory. A higher resolution structure was desired and so we propose multi-shaped DNA origami. </p><br/>
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<p style="font-size:14px;padding:20px 0 5px 0;">3.2.1. Stability of the structure:</p>
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<p>We wanted a higher resolution 3D model of the Taj Mahal. Since it was not possible to have a single large scaffold, which would create the whole Taj Mahal due to stability constraints and constraints on the size of the scaffold, it meant that individual pieces of the Taj Mahal which were around 7000 base pairs long would have to be created and then it was necessary to come up with a scaling technique to join these pieces to form the final structure. We also had to ensure that the technique ensured stability of the structure. There are various factors under stability that had to be considered: </p><br/>
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<p style="text-decoration:underline">Stability factor 1 - The base of the structure – Mechanical stability</p>
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<p>We needed a firm base for the entire Taj Mahal structure, which could hold all our individual pieces together in place, and provide mechanical stability to the structure.</p><br/>
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<p style="text-decoration:underline">Stability factor 2 - Thermodynamic stability:</p>
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<p>We were also aware that the structures that we designed needed to be thermodynamically stable. We were initially not sure how to go about checking if structures are thermodynamically stable or not so we decided to do some research over this before making design decisions. </p><br/>
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<p style="text-decoration:underline">Stability factor 3 - Crossovers position stability:</p>
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<p>While designing the 3D structures, we decided to follow the tried and tested principles for determining the positions of the scaffold and the stapler crossovers in the structure. </p><br/>
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<p>We propose few techniques that showed potential in being able to scale up 3D structures. The method we followed was mainly motivated by the research done by Hao Yan group [9] recently, for designing DNA origami structures with complex curvatures in three-dimensional space. </p><br/>
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<p style="font-size:14px;padding:20px 0 5px 0;">3.2.2 Detailed Workflow:</p>
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<p>The detailed workflow for multi-shaped DNA origami is given below: </p><br/>
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<p>1. Initially, efforts were made to visualize the 3D structures using Computer Aided Designing software. A hollow sphere was created and wrapped with material assumed to be DNA, according to principles stated in Hao Yan’s research [9], just for the purpose of understanding through modeling.</p><br/>
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<p>2. Next some time was spent in learning and researching over Nano Engineer, which is a Bio-Molecular engineering tool for nanoscale design and simulation. All the tutorials given on the software’s website were studied and some simple 3D structures were created which could be used later in the Taj Mahal structure (Fig. 10).</p><br/>
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<div class="img-div">
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<a href="imgs/3d/octagon/octagonal1.png" title="img" target="_blank">
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<img src="imgs/3d/octagon/octagonal1.png"  alt="wiki-img" class="image-style">
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<p class="img-text"><i>Figure 10 | (a) A Single Octagonal Ring</i></p>
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