DNA nanostructure decoration: a how-to tutorial

As this tutorial's scope encompasses the breadth of conceptual tools and experimental techniques required to plan a DNA nanostructure decoration workflow it is infeasible to provide protocols for all, or even a portion of the techniques we discuss.

However, it is worth briefly describing how a decoration workflow might proceed in lab to provide a sense of the time investment required and to explain why we advocate for a holistic approach in planning.

Figure 1 illustrates the steps required for the following counter-factual example (example inspired by [11]). Assume the existence of some redox active enzyme that can be labeled with DNA without impairing function. Semiconducting particles with appropriate band gaps can, when in proximity to the enzymes, optically pump them to provide energy. To create the enzyme's product from its substrate and light, one might desire a surface with densely packed, but regularly spaced enzyme-nanoparticle clusters, over which one could flow the enzyme's substrate during exposure to light.

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Designing of an origami that can cluster the enzyme and nanoparticles, choosing the labeling chemistries, and making plans for purification and verification will typically take from a month to a few months. Procuring the DNA, enzymes and nanoparticles often take slightly less than a month.

The DNA strands are pooled together into aliquots to accommodate variations of a structure with different decoration spacings or locations by grouping the strands based on which shared structure variants they will create. This usually takes a few days.

After this step a decoration project is a hierarchy of assembly steps, purification steps, and verification steps, each taking between a few hours and a few days. For example, to assemble origami one would mix buffer, salt, viral scaffold strand, structural staple pools, and the modified strands which address the decoration, and perform an overnight thermal anneal. The product origami would be purified from the reagents, e.g. by filter centrifugation, and the assembly would be verified, e.g. by atomic force microscopy. Analogous steps would be performed to label the enzymes and nanoparticles.

The labeled nanoparticles, enzymes, and origami would then be combined, annealed, purified, and deposited on a surface for verification and performance testing.

If every step works as intended, this could take as little as two to three months in total. Unfortunately, troubleshooting is unavoidable, and one only rarely knows why steps fail.

To isolate a failure mode, one works iteratively backwards from the failure point. For example, if a decorated structure fails to assemble one might confirm that the particles or enzymes really are labeled with the correct strand. It is not unusual to work as far back as re-pooling DNA strands or re-evaluating an entire nanostructure design.

Troubleshooting time can have a factorial dependence on project complexity and represents the bulk of the costs for any decoration project. Optimizing troubleshooting through careful holistic planning is crucial.

Given the broad range of possibilities (type of nanofabrication, functional element type, spacing, etc), there is considerable variation in decoration workflows. We divide these workflows into phases and the phases into process steps. Process steps include designing a DNA nanostructure, fabricating it, purifying it from its constituent oligomers, etc. The number of steps increases with each additional functional element.

We define phases of related steps as: design, assembly, purification, and verification. In design, the nanostructure is drafted and the functional elements, linker chemistries, and sticky end DNA sequences are chosen. In assembly the reagents are combined and annealed. In purification, the desired structure or decorated structure is separated from reagents and defective products. In verification, the product is characterized and evaluated to determine whether it is within tolerance of the initial design. Notably, in many projects assembly and purification are performed iteratively, while in others verification occurs in-line with purification.

A workflow is a full collection of steps, through all phases, which can result in viable product. We will discuss workflows in more detail in section 1.2 : Systems Engineering.

Note: The steps of decoration and the phases we divide them into must often be duplicated for each unique species of functional element attached to a nanostructure. In practice, some of these steps for separate functional elements may be combined or repeated, as choices made for a new decoration workflow are rarely independent.

The fabrication of a DNA nanostructure is relatively straightforward thanks to design tool advances in recent years [12–17]. However, the techniques for decorating DNA nanostructures are not yet mature. There are several major challenges which can hinder implementation. For example, there are limited purification options for decorated structures given their size [18]. The typical origami nanostructure is 4.5 × 10⁶ g·mol⁻¹ (4.5 MDa), which is too large for most traditional analytical chemistry-based purification but too small for micro- or macro-scale solutions. Yield for DNA nanostructure is difficult to define or measure, making feasibility calculations for new applications difficult. Finally, our understanding of the lifetime of the final product is limited, especially in the context of functionality. These challenges are made more difficult by limitations in the accuracy and throughput of structure metrology and have, to-date, restricted the degree of complexity of DNA nanofabrication and decoration, which in turn limits its accessible application space.

It is therefore best to begin a decoration project with a careful evaluation of the step-by-step strategy one intends to adopt. In this section we describe the key challenges and possible solutions in detail.

1.2.1. Key challenges: purification

1.2.2. Key challenges: yield

1.2.3. Key challenges: lifetime

The DNA nanostructure decoration workflow is driven by application and by the functional elements needed for those applications. To date, the DNA nanotechnology community has dedicated more effort to developing new tools rather than cataloging those tools into a well-organized toolbox. As comprehensive reviews of specific strategies exist [3, 28, 29], the following examples are meant to be representative and instructive rather than exhaustive.

1.3.1. Nano-photonic systems

1.3.2. Stand-alone biomimetic systems and theranostics

1.3.3. Interfacial systems

The defining systems engineering feature of a decoration project workflow is its interconnectedness. Any choice within a decoration phase will constrain other choices both in that phase and in others. As there are a wide array of such choices for each phase, the optimization space can become dizzyingly large. We advise the reader to consider the system holistically, and to take an iterative approach, considering first the constraints from the application, then the branching choices starting with those which most constrain the others.

Evaluating the whole system and the constraints that propagate between choices in advance allows the practitioner to cluster sets of compatible choices into feasible workflows. This facilitates comparison between them, resulting in more informed choices. To cluster choices in decoration steps, it is helpful to visually represent the phases of decoration and their relationship to an application, shown in figure 2. Figure 3 gives more specific examples of how choices in each phase can constrain choices in neighboring phases.

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To cluster steps into potentially feasible workflows, we begin with the chosen application to identify the primary constraints on each phase of decoration. Starting with the most restricted phase, we then identify feasible process step choices. For each choice, we then identify the constraints it might impose on the choices in other phases. These are then separately propagated into the next most constrained phase. This can be imagined as following potential paths in a Galton box [47] or timeline splitting in a science fiction novel. A branch of choices is discarded if it cannot create a feasible workflow—i.e. it cannot be propagated by feasible steps all the way from the most constrained phase to the least constrained phase.

This process is less daunting than it sounds, as many choices are linked by physical properties that play an obvious role in multiple phases. For example, functional elements with a high density provide mass contrast that affects both purification and verification techniques. Similarly, many choices which complicate design also complicate assembly conditions, though they may simplify verification or purification.

For example, a choice that increases mass contrast between the desired structure and the raw material will make both purification (via density gradient centrifugation) and verification, (via electron microscopy) easier. Purification (via density gradient centrifugation) would also be easier for multiple small structures, each with <5 functional elements, than it would for a single large structure with >5 elements, however, a structure built from 5 smaller structures would complicate both the design and assembly phases. As one propagates choices and constraints on each step, these couplings will result in sets of compatible interdependent choices.

Note: without a holistic approach, it is surprisingly easy to 'paint oneself into a corner.'

If one makes choices as they occur in-lab, incompatibilities at the final purification or verification could waste months of effort. While a holistic approach cannot guarantee single iteration cycles, it can minimize lost effort.

Figure 4 is recreated from the work of Douglas et al and is an archetypal example of DNA origami decoration. At first glance, it may appear to be straightforward as the system comprises an open barrel origami, two aptamer lock motifs, and a choice of two types of payload. However, these features posed interesting system design choices that required modification to existing protocols or development of new ones.

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In particular, including the sensitive aptamer-based lock required accommodations in the design, assembly, and verification phases.

As shown in figure 5(a), aptamers are short sequences of DNA that form some secondary structure which positions the charges and hydrophobic regions of the nucleotides to bind some non-DNA target molecule. By forcing some of an aptamers' ssDNA bases to engage in hybridization that competes with the binding state, one can create two metastable states whose equilibrium is controlled via analyte concentration and Le Chatelier's principle—where increasing reagent concentration will push a reaction to create more product in response.

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An aptamer can lock or move a DNA nanostructure. figure 5(b) shows the sequence of the aptamer used by Douglas et al and adapted from Green et al [48]. The arrows in figure 5(b) correspond to the five different versions of their lock, with the competing state design shown in figure 5(c). Each of the five lock designs varied the fraction of the aptamer sequence capable of nucleating the binding competent state.

This design, and most aptamer lock designs, are constrained in their energetics. The free energy of the dsDNA hybridization in the competing state must be more negative than the binding-competent state but have a higher free energy than the target bound state. Otherwise, the system would not be metastable, and would always remain locked or unlocked.

Douglas et. al manually explored the energetics to find a metastable state and avoid designs which would be fused closed and those which would spontaneously open. In this case, the aptamer locks, which could pop open, were also too weak to form the initial closed state in high yield.

This presents an informative systems engineering challenge. Douglas et al chose to address this problem with a threefold approach: first, by introducing guide strands to hold the structure closed at assembly; second, by removing the 'walls' of the barrel to allow payload loading without actuating the locks, and third, by developing a custom verification assay to measure individual opening and closing events.

These choices further altered the workflow, as Douglas et al introduced steps to remove the guide strands after the payload loading, and as they performed modeling estimates to assess whether the payload would have sufficient time to diffuse through the open barrel walls.

These workflow choices are why we chose this work as a case study. It emphasizes that the best workflow choice is the one which will work in the practitioners' own lab. Douglas et al's custom microbead assay for counting single barrel opening events, their use of live cells and flow cytometry, their choice of Fab' antibody fragment labeling chemistry, and their selection of purification for labeled AuNPs and Fab' fragments all point to the utilization of existing strengths in expertise and equipment.

One could imagine several counterfactual workflows which may, or may not, have succeeded.

• Design of a lock system reinforced with many more locks in parallel, requiring additional design work, and more intense verification to quantify the lock behavior in each design. It also would have increased the concentration of platelet-derived growth factor required to open the barrel.
• Design of a lock system using a stronger aptamer binding the same target, or a similar cell-surface protein target. This assumes one exists or assumes the resources could be dedicated to find one.
• Design of the nanostructure to act as a weaker entropic spring, or one with a neutral state closer to that of the locked barrel. This would reduce the energy required to hold the barrel closed but would likely reduce opening efficacy.
• Purification via some newly developed technique which separates the open and closed barrels. This would reduce the need for the guide strands and accommodate slightly weaker locks. However, even if possible, this choice would likely be dramatically less efficient than the guide strand approach.

Ultimately, any serious decoration project forces the practitioner to choose between a variety of such potential workflows. Navigating this space effectively is often underemphasized in the scientific literature, likely because including discarded workflow choices would be a tedious inclusion into supplementary documents.

One could imagine the same project utilizing very different workflow choices under different conditions. A collaboration with less flow cytometry expertise but more experimental and theoretical thermodynamics might have forgone a custom single barrel opening event assay for in-depth modeling and ensemble measurements. Similarly, a collaboration with significant expertise in synthesizing and testing libraries of DNA sequences for SELEX identification of aptamers might have developed a brute force approach to lock optimization. Ultimately, these counterfactual cases would have provided the scientific community with slightly different proofs-of-concept and would have had different probabilities of success.

The utility of thinking of project workflows in terms of phases, and of phases as groups of individual steps, is that it facilitates finding choices most aligned with the available resources and expertise.

Identifying and optimizing workflows, rather than individual phase-to-phase or step-to-step choices, allows prioritization for the success of the entire project. For example, both questions below could be asked of the same system.

'Should I perform (5+) multi-element decorations in a single pot anneal with a single purification, or should I divide my design into multiple single-element sub-structures with multiple purifications and combine them in an additional assembly step?'

And

'Should I pick the workflow that requires significant effort in developing purification, or the one requires significant effort in optimizing design and assembly conditions?'

Abstracting the former question into the latter enables evaluation based on available equipment and expertise. We liken this to balancing the weight of effort across the project, shown in figure 6, where the colored groups of phases represent possible effort tradeoffs. While it can take years of experience to develop an intuitive feel for how the weight of a project workflow is balanced, explicitly articulated planning is a more practical road to success.

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Each of the following sections of this tutorial will provide a primer to an individual decoration phase describing the possible steps in that phase and what the constraints on those steps imply. The assembly section also includes the thermodynamics of sticky end decoration, and the verification section primer includes a short discussion of uncertainty and potential sources thereof.

The most common tool for creating addressable locations on a nanostructure is the use of sticky ends, which are additional lengths of unpaired single-stranded DNA, ssDNA, which exit a structure. The functional element is labeled with ssDNA of complementary sequence to the sticky end on the structure. A key feature of sticky ends is that they do not benefit from the natural stoichiometric controls and cooperativity typical of origami - the target strand is not guaranteed to strand displace a partially complementary sequence incorrectly bound to the sticky end.

Best practice for sticky end driven decoration accounts for incorrect binding in two ways. First, the labeled element is only added after an initial purification to remove excess copies of the sticky end strand which could prevent binding. Second, both the sticky end strand on the nanostructure and the sticky end strand attached to the functional element are purified, typically via polyacrylamide gel electrophoresis, PAGE, to remove off-target sequences. Other approaches include using a high number of duplicate sticky ends on both structure and particle to ensure binding even if several positions do not bind appropriately. An alternative approach is direct labeling, in which the functional element is labeled with a strand that directly hybridizes to the nanostructure in the initial anneal without a facilitating sticky end. This technique is limited by both reduced flexibility and the thermostability of the functional element. However, direct label binding may result in higher yield during scale-up as it combines steps for excess staple purification and for excess functional element purification.

Note: direct labeling is incompatible with nanoparticles that require an excess of the linker modified strand, e.g. thiol/gold nanoparticle connections

Direct labeling is also incompatible with any anchor chemistry which cannot survive thermal or chemical anneal conditions.

Sticky ends are ubiquitous due to their modularity at the lab level: the same sequences are often used for multiple projects, reducing the upfront cost of expensive labeled oligomers. This also allows the location and types of functional elements to be easily exchanged within in a lab's library of raw materials. Section 3.5 will discuss sequence design for sticky ends, and the energetics of sticky ending binding will be discussed in section 4.1.

Sticky ends traditionally have spacer nucleotides between both the nanostructure and sticky end, and between the sticky end and the functional element, shown in figure 7. Generally, the longer the sticky end is, the more thermodynamically stable it will be, as discussed in section 4.1. Longer spacers will improve yield by minimizing steric and charge repulsion effects but, as shown in figure 8(b), longer and more flexible sticky ends will also have more freedom to move around the anchor point where the sticky end exits the origami.

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The length of a sticky end will also play an important role in synthesis. Phosphoramidite synthesis yield is given by equation (1). This is more critical for sticky end strands than for typical staples or tile strands because the sticky ends must be purified, to remove off-sequence products. As material is lost in the purification process, and as chemical linkers are often necessary to connect to the functional element, these strands tend to contribute disproportionately to the cost of the structure.

Note: phosphoramidite synthesis can have a per base yield, or coupling efficiency, as high as 99.5%, this can result, for strands of 20 nt, in at least 10% of sequences having at least one error.

• Off sequence sticky ends or complementary labels can prevent binding, or otherwise hinder assembly. To ensure binding to the correct location, BOTH structure sticky end AND functional element label complement must be purified either by the manufacturer or the practitioner.
• Most manufacturers offer purification of synthetic DNA oligomers. The cost, yield, and purity of product will vary by manufacturer and purification technique.

$$\begin{eqnarray}&&\mathrm{yield}={\mathrm{nucleotide}\,\mathrm{coupling}\,\mathrm{efficiency}}^{\mathrm{number}\,\mathrm{of}\,\mathrm{nucleotides}}\end{eqnarray} \tag{ 1 }$$

Another relevant design factor in creating sticky ends is the anti-parallel hybridization of DNA. As shown in figure 8(a), whether the sticky end is attached in the 5' or 3' direction on the functional element and nanostructure can significantly change their binding geometry. As with the addition of spacers, there is some tradeoff between the site occupancy of functional elements and the closeness of binding, likely due to steric hindrance [52].

The number of sticky ends used to connect a nanostructure and functional element can change the position of an element relative to the structure, how much mobility it has around its average position, variation in that position over many copies of a structure, and the thermodynamics of the assembly. This is shown in figure 8(b), while a schematic of a typical sticky end labeling is shown in figure 8(c).

When using multiple binding sites, polymerization is possible, especially for NPs labeled with an excess of sticky end complements. In these cases, it is possible for two or more structures to bind the same particle or vice versa, as shown in figures 8(d) and (e). This is controlled by introducing the structure and element when one or the other is in a large excess. Unfortunately, this necessitates either lower structural yield relative to input reagent or purification and recovery of the excess reagent. As clear rules have yet to be determined for predicting polymerization in these systems, some level of optimization is anticipated for most decoration projects.

While we will describe measuring yield of a desired structure in section 6, it is worth discussing design features that can contribute to improved yield. Relatively few studies have been published systematically examining the site occupancy of functional elements, likely due in part to the expansive design space [51, 52]. Relevant factors include inter-element distance, number of sticky ends on the element, size of the element, number of sticky ends on each anchor patch, and the shape of the nanostructure surface.

Work from Ko et al indicates that for biotin anchor positions binding streptavidin-coated functional elements, that three anchor positions per particle was sufficient for greater than 90% site-occupancy yield. This site occupancy dropped to below 75% for very densely spaced particles. Takabayashi et al [52] used 15 nucleotide sticky ends and tested the role of inter-element distance and number of binding sites. They examined 1, 2, and 4 binding sites, and found a yield of > 97% average site occupancy. They were able to mitigate yield loss due to reduced inter-element distance by interspersing two different sets of sticky end sequences, indicating that single particles bound to multiple binding sites was the primary mode of failure. Their theoretical analysis indicated an asymptote in site occupancy as a function of number of anchors per binding site and suggested 5 anchor positions as a reasonable maximum.

While the ideal arrangement of sticky ends for any given application must still be optimized, 3–5 anchor positions is a common place to start.

3.1.1. Sticky end positioning

As shown in figure 9, the first step in accounting for the exact X, Y, and Z position of an element follows the simple geometric rules, and depends on the number and types of linkers. Though this is complicated by variability in the internal crossover angle, see figure 12

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In theory, a practitioner can place a sticky end at any base position of a DNA nanostructure, within the resolution determined by the 0.34 nm base pair spacing along the double helix. However, the location of a sticky end is further constrained by choices made in the design of the nanostructure. The first constraint involves the stability of the sticky end's connection to the rest of the structure. While, to our knowledge, there have been no studies on stability as a function of the length of the anchor to the structure, or associated temperature dependence, it is a generally accepted rule that the sticky end should have at least 5–7 nucleotides, nt, of base pairing uninterrupted by a crossover. This is illustrated in figure 10.

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The second constraint arises from the rotation of the helix. The sticky end will exit the structure at the physical location tangential to the minor groove position for the last nucleotide in the structure, which will rotate around the helix in 3D [54]. Care should be taken to confirm that a sticky end will exit the structure in the desired direction and not point into the structure or exit in the wrong direction. Many computer-aided design (CAD) tools have visual indicators for the rotational position of the minor groove of the helix. These functionalities vary between CAD tools but are a useful feature with which to familiarize oneself.

The process or determining the orientation at a particular base is illustrated in figure 11. One may calculate the exit direction for the sticky end via the right-hand rule combined with the direction of the staple, the direction of the nearest crossover, and the helicity of dsDNA. This can be done by pointing the right-hand-thumb in the 5'→ 3' direction and the index finger initially in the direction of the crossover. As the hand moves along the dsDNA, the fingers should curl at ≈ 0.598 rad per nucleotide (34.3 ° per nucleotide) in the 3' direction. This is approximately 3π/2 rad (270°) for every 8 nucleotides.

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Other constraints include the skew of the crossover junctions, and deformation from internal or external stresses. The presence of neighboring sticky ends may also present topological limits to the length of neighboring staples. Additionally, the shape of a 2D structure can be different in solution as compared to on a surface [55].

While these constraints limit the exact positioning of a sticky end on the structure, they do not necessarily constrain the relative distance between sticky ends, or sets of sticky ends, in the same structure. This, and the lack of explicit studies on the limits of decoration precision make engineering for a predetermined positioning on the first try non-trivial. Often an iterative 'assemble-measure-and-modify' approach is taken, in which it is assumed that the initial predictions of functional element locations will be inaccurate.

Few studies have reported designed versus measured intended inter-element distances, so there is not, to our knowledge, best practice for achieving a desired spacing in a completed structure. We can, therefore, only describe useful design concepts and give general recommendations. For systems where a highly accurate initial guess is required, we recommend iterative design, and rough structure simulation (finite element [17] or coarse grained [14, 15, 56]) followed by molecular dynamics simulations [57]. For particularly demanding applications, planning alternative versions of the binding locations and strand sequences in advance may be prudent.

The primary source of decoration inaccuracy is in predicting the exact dimensions of a DNA nanostructure prior to fabrication. As shown in figure 12 the idealized shape of a structure as seen in CAD tools fails to account for the structure and angle of crossover junctions. Beyond what is shown in figure 12, Holliday junctions, the biological analogue of the crossover junction, have a small skew, which would be out-of-page in figure 9, and may flex in that direction to minimize charge density [58]. An in-plane angle of π/3 rad (60°) is a commonly accepted value in biological contexts [58, 59]. This angle is likely to be lower in DNA nanostructures, and may vary between designs, particularly for 2D and 3D structures, and quantification of these angles in origami or other DNA nanostructures has been a subject of few publications, typically in the context of mechanical properties [60], ion dependent reconfiguration [61, 62], novel characterization [63–65], and bistable physical isomorphs [66, 67].

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It is worth noting that both the schematics in figure 12, and in most CAD tools, can visually imply larger spacings than occur practically. This is because the aesthetics of traditional line representations of dsDNA under-represent the width of the helix. A more accurate, but more cluttered, representation in figure 12 would have helix widths consuming approximately half of the empty space in the lattice.

Other sources of systematic inaccuracies in a designed inter-element distance may include an inaccurate mean functional element size, and charge repulsion for large or highly-charged functional elements.

Given the lack of in-depth studies on this topic, practitioners often take an iterative 'assemble-measure-and-modify' approach, in which it is assumed that the initial predictions of function element locations will be inaccurate.

3.3.1. Inter-structure variability

For particles, the largest source of inter-particle spacing variation comes from variation in particle size. As shown in figure 13, the distribution of particle sizes, referred to as polydispersity, maps intuitively onto the inter-particle distances. It is for this reason that we highly recommend either characterizing all NP size distributions prior to decoration or purchasing NPs that include size distribution quantification in their quality control documentation.

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Generally, equation (2)–(4) provide the shortest distance between two particles bound to an origami with the assumption of a Gaussian particle radius distribution, neglecting binding height variability, and other factors, shown in figure 14. Note that d_hyp is the distance between particle centers and is equal to the d_actual+r_a +r_b . To address the more common log-normal NP radius distribution we would recommend Monte Carlo simulation. We discuss uncertainty propagation more generally in section 6, though this is a useful and specific example. We will use the notation where ${\sigma }_{x}$ refers to uncertainty on some value ${d}_{x},$ represented by the standard deviation of the distribution of multiple measurements of ${d}_{x}.$ In this case ${d}_{{d}{e}{s}{i}{g}{n}{e}{d}}$ would likely come from the shape of the structure and the crossover junction angle, while ${\sigma }_{a}\,{\rm{and}}\,{\sigma }_{b}$ would be from the polydispersity of the particle a and b ensembles.

$$\begin{eqnarray}&&{d}_{\mathrm{actual}}={d}_{\mathrm{hyp}}-{r}_{a}-{r}_{b}{\rm{;}}{\sigma }_{\mathrm{actual}}=\sqrt{{{\sigma }_{\mathrm{hyp}}^{2}+\sigma }_{a}^{2}+{\sigma }_{b}^{2}}\end{eqnarray} \tag{ 2 }$$

$$\begin{eqnarray}&&{d}_{z}={r}_{a}-{r}_{b};{\sigma }_{z}=\sqrt{{\sigma }_{a}^{2}+{\sigma }_{b}^{2}}\end{eqnarray} \tag{ 3 }$$

$$\begin{eqnarray}&&{d}_{\mathrm{hyp}}=\sqrt{{d}_{\mathrm{designed}}^{2}+{d}_{z}^{2}};\end{eqnarray} \tag{ 4 }$$

$$\begin{eqnarray*}&&{\sigma }_{\mathrm{hyp}}={d}_{\mathrm{hyp}}\sqrt{{\left({2d}_{\mathrm{designed}}^{2}\displaystyle \frac{{\sigma }_{\mathrm{designed}}}{{d}_{\mathrm{designed}}}\right)}^{2}+{\left(2{d}_{z}^{2}\displaystyle \frac{{\sigma }_{z}}{{d}_{z}}\right)}^{2}}\end{eqnarray*}$$

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In this description d_designed is the designed distance between particle attachment points, d_hyp is the distance between particle centers, and d_actual is the distance between particle surfaces. If this model is accurate, we can recast the uncertainty in the true interparticle distance as a function of the particle radii and uncertainty in their radii.

${\sigma }_{\mathrm{actual}}=\sqrt{{{d}_{\mathrm{hyp}}}^{2}\left[{\left({2d}_{\mathrm{designed}}^{2}\tfrac{{\sigma }_{\mathrm{designed}}}{{d}_{\mathrm{designed}}}\right)}^{2}+{\left(2{d}_{z}^{2}\tfrac{{\sigma }_{z}}{{d}_{z}}\right)}^{2}\right]{+\sigma }_{a}^{2}+{\sigma }_{b}^{2}}$

For sensitive applications, such as FRET lifetime engineering [7], or for more complex distributions of particle radius, we suggest Monte Carlo simulation of distances.

The National Institute of Standards and Technology provides an online Monte Carlo simulation tool, the NIST uncertainty machine [68]. Documents for best practice in expression of uncertainty include the international Guide to the expression of Uncertainty in Measurement, or GUM [69].

A less easily quantifiable source of variability is degenerate binding positions for particles with a random distribution of sticky-ends, or other anchor modifications, across their surface. The three bound particles in figure 15 all would be expected to have roughly the same free energy of binding if one neglects electrostatic repulsion and the loss of nanoparticle translational entropy from left to right. One would therefore expect a distribution of those possible binding positions in any fabricated sample.

Variability between nanostructures in a single sample can also be ascribed to assembly errors, either in the binding of the functional elements, or in the structural DNA maintaining distance between those elements.

3.3.2. Structural fluctuations

Motions within individual structures over time are a final source in inter-element distance variation. There are three major sources: slack in functional element binding, fluctuation in crossover shape, and overall structural flexibility.

As we discussed in section 3.1, small spacers are often left between a structure or functional element and its linking modifications or sticky ends. These spacers can improve site occupancy [50, 59], however, they also allow functional elements to float around the center of the binding site, shown in figure 8(b).

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The angles made between strands participating in a crossover junction are not completely static, figure 16. It has been shown in the literature that they can be bistable and jump between equivalent parallelograms [67]. While these transitions are rare unless they are explicitly designed in, it is reasonable to expect that the angle of the crossover junctions to fluctuate slightly in solution, and that these fluctuations cause slight variations in the distance between functional elements. Like the exact value of the crossover junction angle, this is likely to vary between structures, particularly between 2D and 3D designs.

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Finally, structural bending will play a role in distances between functional elements, particularly for 2D structures. In the direction of the helices, 2D structures are highly rigid. However, the crossover junctions may act as hinges in the direction perpendicular to the helices. 2D structures therefore have high and low persistence lengths in the direction of, and perpendicular to, their helices [60, 70]. Most studies measuring interparticle distance have either used the highly rigid 3D six helix bundle or placed particles on the same helix of a 2D origami. As such, there is limited quantification of this phenomena, although bending has been used in conformational sensors [71].

A comprehensive list of functional elements that have been, or could be, attached to DNA nanostructures is beyond the scope of this tutorial, though we suggest the following review [28]. Similarly, there are reviews which cover specific families of functional elements in more detail, e.g. proteins [72] and aptamers [73]. Here we list common functional elements, linker moieties, and chemical modifications to DNA. Table 2 details common functional elements that have been published frequently.

Table 3 lists common linker moieties. It should be reiterated that it is far from exhaustive. The protein bioconjugation literature is deep, with a wide variety of strategies for covalent linkages [74]. We refrain from discussing them in detail as many require development of more specific skills than those new to DNA nanotechnology might be expected to have. The aptamers discussed in table 2 are sequences of nucleic acid that form a 3D structure which binds some target and can be used as a linker without requiring a chemical modification.

Table 4 shows common modified backbones that might be used in a structural context. Numerous other commercially available modified bases exist to support biochemical assays for applications ranging from fluorescent reporting to nuclease resistance and photo crosslinking. See the cited review for a more thorough description of modified bases relevant to biological applications [39].

Table 4. Common modified DNA backbones for structural applications.

Name	Chemical structure	Description
Deoxyribonucleic acid (DNA)		Standard DNA, bases attached to a sugar-phosphate backbone
Peptide nucleic acid (PNA)		Nucleic Acid in which the sugar-phosphate backbone is replaced with a peptide backbone. They are more nuclease resistant, and have less charge
Bridged nucleic acid (BNA)		A DNA backbone where the 2 and 4 carbons are connected by a bridge where X can be a variety of atoms
		This prevents the base from rotating, which in turn reduces the loss in entropy on hybridization, stabilizing the dsDNA state
Locked nucleic acid (LNA)		A class of BNA in which the bridging moiety comprises a carbon and an oxygen
Abasic DNA		A nucleotide without the nucleobase, preventing base pairing
		Often used as a spacing motif

The thermodynamics of DNA hybridization will be discussed in section 4.1, however the choice of DNA sequences in the context of design merits discussion. For DNA origami, the staple strand sequences are determined by where they bind to the scaffold. Little to no manual sequence design is necessary for origami staple strands. Sticky ends are often the only sequences that a practitioner will design.

As the number of sticky ends, or strands generally, in a system increases, so to does the probability of unintended complimentary interactions. For small numbers of sticky ends less than 30 nt in length, random sequences are often sufficient. However, as decorated DNA nanostructures increase in complexity, more rigorous design will be required.

For single digit numbers of sticky ends, this often involves manual checks for stable hairpins and for stable, but undesirable, complementarity between supposedly orthogonal sticky ends. Hairpins on a sticky end can dramatically reduce hybridization kinetics. Unintended stable complementarity between strands can reduce their effective concentration or result in polymerization. In both cases, the kinetics of assembly are slowed [75].

Numerous webtools exist to evaluate hairpins and partial strand complements [76–80]. While most strands will have some hairpin interaction with themselves, or partial complementarity with other strands, many of these interactions will be unstable at or above room temperature.

One trick for manual sequence design and optimization is to use only three of the four nucleobases on each strand, e.g. one sticky end would only be comprised of the letters A, G, and C while its complement would only be comprised of T, C, and G. In a strand with only A, G, and C, the A bases cannot contribute to hairpin stability as they have no T bases to pair with. Similarly, two orthogonal strands which are only comprised of T, C, and G can only have partial complements between their C and G bases. However, this does have the disadvantage of reducing the number of possible sequences.

To our knowledge, there have been no studies on the optimization of large numbers of sequences in the decoration context. However, there is significant literature on sequence design for tiles and junctions [81], algorithmic assembly [82], strand displacement [75, 83, 84], and data storage. This includes tools to minimize unintended complementarity in silico, which could presumably be easily adapted to sticky end design [81, 85, 86].

Control over the melting temperature and sharpness of the melting transition are two useful but relatively underutilized design degrees of freedom. These parameters are determined by the energetics of hybridization, which can be modeled to provide a melting temperature, T_m, defined as the point at which half of the strands are released. It is also possible to determine, more or less accurately, the width of the melt curve. The degree of accuracy depends on how similar the system is to ssDNA ↔ dsDNA hybridization.

In some cases, one need only know the approximate stability of some sequence at room temperature that singly connects an element to a nanostructure. In others, a practitioner might model the energetic contributions to optimize the sticky end sequences: modifying sequence length may allow creation of structures with minute shifts in element location or may remove undesirable cross-hybridization with other strands or may simply shorten strands and reduce costs. In other projects, such modeling is critical, e.g. when engineering multiple meta-stable binding states, the population of which is controlled by temperature, pH, or analyte concentration.

For many applications, existing predictive webtools [76–78], or even empirical equations relating T_m and GC content may be sufficient. For those, it is enough to remember trends in length, GC content, concentration, and salt content, depicted in figure 17, and that unimolecular reactions like hairpins are more stable. For those practitioners who will need to model the hybridization in their own system we introduce the relevant nuances below.

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In B-form DNA the major factors controlling hybridization stability and melting temperature, T_m, are sequence, length, salt concentration, and strand concentration. The main driver of hybridization is the hydrophobic π–π stacking between bases up and down the helix, with minor contributions from hydrogen bonding between base pairs and electrostatic repulsion. The shorter a strand is, the more the unfavorable interaction between the terminal bases and water contributes relative to favorable interactions between bases within the helix. Similarly, as guanine and cytosine bases have more favorable base stacking, a higher GC content will result in a more stable helix. Salts release the water molecules bound to the phosphate backbone and shield its negative charge, entropically increasing stability. Finally, increasing strand concentration shifts equilibrium to hybridization at higher temperatures, as one would expect via Le Chatelier's principle—where increasing reactant concentration will push a reaction to create more product in response.

Typical thermodynamic prediction uses the van't Hoff relation by identifying the form of the equilibrium constant and the predicted ΔH and ΔS for a sequence under specific conditions, then solve for the fraction, or concentration, of ssDNA. Prediction of ΔH and ΔS can be done through the nearest neighbor, NN, model. Here we use the NN parameterization presented by Santa Lucia et al [87]. The conditions under which these models have been parameterized do not perfectly translate to the those present for DNA nanostructures, but they do provide a useful foundation from which to build.

To find a predicted ΔH and ΔS, proceed through the sequence in neighboring sets of bases and add up the energetic contributions for the terminal bases and each set of neighbors. For ATGCAT, one would add ΔH and ΔS pairs for A+T, T+G, G+C, C+T, and A+T, then add the appropriate energetic penalties for termination in A and T. The summed ΔH and ΔS would then be adjusted for salt concentration [88] or other DNA motifs. This model assumes ΔH and ΔS are temperature independent, i.e. they neglect change in heat capacity ΔC_p. While this is an oversimplification [89], it is sufficient for our purposes as the ΔC_p primarily increases the asymmetry of the melt curve and does not significantly shift the T_m.

The van't Hoff relation is given in equation (5), where [ ] brackets indicate concentration relative to the standard concentration (1 mol·l⁻¹), T is the temperature, and R is the gas constant.

$$\begin{eqnarray}&&\left[K\right]=\displaystyle \frac{[\mathrm{product}]}{[\mathrm{reactant}]}={e}^{-({\rm{\Delta }}H-T{\rm{\Delta }}S)/{RT}}\end{eqnarray} \tag{ 5 }$$

For unimolecular reactions the equilibrium constant is given in equation (6) where [ssDNA] is the concentration of denatured ssDNA molecules and [dsDNA] is the concentration of hybridized dsDNA. As most melt curve measurements do not give absolute concentrations, this is often rewritten in terms of the fraction of DNA that has melted, f_ss . In such cases $\left[{ssDNA}\right]={f}_{{ss}}* \,\mathrm{conc}$ where the term conc describes the total DNA concentration. It should be noted that this term is still relative to 1 mol·l⁻¹, and is thus unitless, which ensures that $\left[K\right]$ is unitless regardless of reaction form.

$$\begin{eqnarray}&&\left[{K}_{\mathrm{unimolecular}}\right]=\displaystyle \frac{[{ssDNA}]}{[{dsDNA}]}=\displaystyle \frac{{f}_{{ss}}}{1-{f}_{{ss}}}\end{eqnarray} \tag{ 6 }$$

$$\begin{eqnarray*}&&\left[{K}_{\mathrm{bimolecular}}\right]=\displaystyle \frac{\left[{ssDNA}\right]\left[{ssDNA}\right]}{\left[{dsDNA}\right]}\end{eqnarray*}$$

$$\begin{eqnarray}&&=\,\displaystyle \frac{{f}_{{ss}}{(f}_{{ss}}+\mathrm{excess}-1)* \mathrm{conc}}{1-{f}_{{ss}}}\end{eqnarray} \tag{ 7 }$$

For unimolecular reactions, the absolute concentration terms cancel to give equation (6)

The T_m is defined by the point at which f_ss = 0.5. Note a common, but poor, assumption is that this temperature can be found at the peak of the derivative of the melt curve as function of temperature [90].

If neither strand is in excess, the T_m is given by equation (8), although this is often not the case for DNA nanofabrication systems.

$$\begin{eqnarray*}&&{T}_{{\rm{m}}}=\displaystyle \frac{{\rm{\Delta }}H}{{\rm{\Delta }}S+R\,\mathrm{ln}\left(0.5{\rm{\cdot }}\mathrm{conc}\right)}\,{for}\,\mathrm{bimolecular},\end{eqnarray*}$$

$$\begin{eqnarray}&&\mathrm{and}\,{T}_{{\rm{m}}}=\displaystyle \frac{{\rm{\Delta }}H}{{\rm{\Delta }}S}\,\mathrm{for}\,\mathrm{unimolecular}\,\mathrm{reactions}\end{eqnarray} \tag{ 8 }$$

If an excess is present, it is useful to define conc as the concentration of the limiting reagent, as this is also the maximum possible dsDNA concentration. The fractional excess relative to the limiting reagent can then be used to give equation (9). For example, if two complementary strands are at concentrations of 5 nmol·l⁻¹ and 50 nmol·l⁻¹, there would be a 10× fractional excess and conc would be 5 nmol·l^-1.

$$\begin{eqnarray}&&{T}_{{\rm{m}}}=\displaystyle \frac{{\rm{\Delta }}H}{{\rm{\Delta }}S+R\,\mathrm{ln}\left((0.5+\mathrm{excess}-1){\rm{\cdot }}\mathrm{conc}\right)}\end{eqnarray} \tag{ 9 }$$

When building one's own predictions, it is advisable to note the sign conventions used for additional motifs and to compare several 'control' predictions to existing prediction webtools [76–78]. The scientific literature is not uniform in reporting in terms of energies of melting or of hybridization, making it easy to make a sign error that results in non-physical predictions.

To illustrate the general trends of DNA melting, we plot modeled T_m as a function of length, GC content, salt concentration, and DNA concentration, as modeled by [86]. All data points in figure 17 represent 50 random sequences, even if there are fewer than 50 possible sequences for that combination of length and GC content.

The T_m is most sensitive to DNA length followed by GC content, and salt concentration. The T_m dependence on concentration varies significantly between more and less stable strands. Divalent salts are more effective at charge screening than monovalent salts, and in the typical concentration range, (0.1–50) mmol·l^-1, Mg²⁺ increases stability more than Na⁺. Generally, the T_m of a less stable strand will shift more for the same change in length, GC content, salt concentration, or DNA concentration than a more stable strand, as seen in the last two panels of figure 15.

While there are not NN model corrections for polyamine multivalent salts, e.g. spermine, putrescine, spermidine, etc, or oligolysine both the former [91–93] and the latter [94, 95] can dramatically increase the T_m, and can protect DNA from damage in biological systems.

4.1.1. Example use cases

The binding of a functional element can be much more complex than typical hybridization. The functional element can only decouple from the structure if all its sticky end connections are melted. The probability of an element being connected, f_c , is the probability that each of its N sticky end connections are melted, described in equation (10).

$$\begin{eqnarray}&&{f}_{c}\left(T\right)={{f}_{{ss}}\left(T\right)}^{N}\end{eqnarray} \tag{ 10 }$$

These equations can be rearranged to give the decoupling T_m, at which F_c = 0.5, as a function of N, as shown in equation (11) [97].

$$\begin{eqnarray}&&{T}_{{\rm{m}}}=\displaystyle \frac{{\rm{\Delta }}H}{{\rm{\Delta }}S+\tfrac{R\,\mathrm{ln}\left((0.5+\mathrm{excess}-1){\rm{\cdot }}\mathrm{conc}\right)}{N}}\end{eqnarray} \tag{ 11 }$$

In figure 18 we plot the probability of disassociation for functional element decoupling for a single random 14 nucleotide sequence as a function of number of sticky end connections. As the number of sticky ends increases, so too does the sharpness and T_m of the melt curves.

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Unfortunately predicting the T_m and melt transition breadth is much more complicated than equation (11) and figure 18 may imply. The NN model assumes that the final dsDNA will have 3 rotational and 3 translational degrees of freedom. However, when multiple sticky ends connect a single functional element, they will have fewer degrees of freedom. By equipartition theorem, one would anticipate a loss in entropy for each lost degree of rotational or translational freedom. When performed carefully this type of modeling can even predict complex binding topologies such as those considered by Dreyfus et al [97]. There are also enthalpic interpretations of the increased binding stability of ssDNA with ssDNA anchored to particles that may be relevant [98].

This additional means of control over T_m and transition width can provide options in nanostructure design. In the context of figure 18, elements bound to a nanostructure with the same T_m may be held closer or further from the structure depending on the number and length of the sticky ends. Similarly, as missing staples in an origami are not improbable, the number and length of sticky ends could be tuned to either minimize loss in decoration precision, e.g. figure 8(b), or to ensure that origami with missing staples are unable to bind the functional element at all.

This source of energetic control is particularly relevant for controlling nanostructure or functional element conformation, as in the case study in figures 4 and 6. It is possible to re-arrange equations (5), (7), and (10) to solve for fraction of aptamers held or released as a function of target molecule concentration.

The depth to which a practitioner will model the thermal behavior of sticky end connections will depend on the complexity of the system and how important its behavior is. While this type of modeling is not currently common place for experimental design, we anticipate it becoming a useful tool for designing the free energy landscape of multiple states to create dynamic motion [10].

Example cases: In engineering plasmon resonance, large particles must often be brought into proximity, taking advantage of multiple connections to use shorter strands to bring the particles in closer proximity cold be valuable. For rapid reconfiguration of a system at a specific temperature, controlling the breadth of the transition between states will also be vital. In the first case simple modeling may confirm the stability of the shorter strands as a function of number of connections, while in the latter more in-depth modeling may be necessary.

Given the complexity of these systems, any general rule would have a broad array of exceptions. However, in most cases one could rank the factors changing stability by magnitude, from largest to smallest, as follows:

• Longer sticky ends
• Higher GC content
• Increased number of binding sites (# of sticky ends)
• Higher salt concentration
• Additional degree of freedom penalties
• Higher functional element (or DNA) concentration

As a rule, the T_m of a bound functional element will be higher than its sticky end's NN model predicted T_m, except in cases where steric hinderance destabilizes the binding.

Annealing protocols ensure the molecules can explore a large free-energy landscape comprising a variety of configurations and hybridization states, steadily progressing to the lowest energy state, which is presumably the target nanostructure.

DNA hybridization is a reversible reaction: above the T_m, hybridized dsDNA is unfavorable, and below the T_m that states are increasingly favorable. However, at lower temperatures the kinetics of a DNA strand finding an optimal binding position are much slower than the kinetics of suboptimal or defect positions. There are many possible unique, undesired, binding positions in a DNA nanostructure that compete with the target structure, which leads to a relatively high probability of defective binding of the wrong strand, i.e. site poisoning.

In DNA nanostructures, particularly DNA origami, each hybridization reaction is unique and energetically reinforces its neighbors, making the assembly process a cooperative one. As a result, annealing protocols often only require mixing all the DNA sequences in a single vial, using temperature to fully de-hybridize the DNA, and then slowly cooling down the mix. This is often sufficient to get decent structural yields; 60% to 80% with minimum effort. Early anneal protocols were as simple as polystyrene boxes filled with boiling water in which the vials were left overnight. Many protocols for annealing have been developed ranging from isothermal [21, 99], to those using chemical rather than thermal energy [100], to speculative applications of mechanical denaturation [101].

However, as structures get larger there is a higher probability of unwanted sequence crosstalk, and as they become more complicated, particularly 3D DNA origami or DNA bricks [20], the kinetic traps become more problematic. In such cases, optimization of annealing protocols becomes more important and more complex.

In complex 3D origami or large DNA bricks assemblies, attention should be paid to the design itself and to ensuring nucleation occurs at the center of a structure. Failure to do so could result in kinetically trapped defective structures if the outside of the structure is fully folded and prevents diffusion of staples to its center. Another issue to consider is the thermal, or chemical, stability of the functional element.

We encourage the practitioner to treat annealing as an optimization step—a fine-tuned anneal protocol can improve yield whether through higher reactant oligo concentration or a slower anneal rate. However, if several initial anneals do not result in a measurable amount of desired structure, it is probable that no such protocol exists. In such cases the practitioner should consider either going back to the design stage, or (for tile-like systems) performing stepwise combination of reactant strands to troubleshoot which interactions are not hybridizing as expected.

4.3.1. One pot versus multi-step assemblies

Ultrafiltration spin columns are popular for purification of DNA nanostructures, largely due to their simplicity, fast execution, and minimal equipment requirements, like a benchtop microcentrifuge. These columns contain a porous membrane filter insert which may have a large range of molecular weight cutoffs. The desired product is retained by the filter in some minimal retentate volume, and the filter cup is typically refilled for repeated centrifugation. Multiple filtration steps are necessary as each cycle only purifies some percent of the impurities. The final retentate is then recovered by inverting the filter into a fresh vial and spinning gently.

Filter spin columns can load large volumes (0.5–15 ml) of sample, often do not demand significant protocol adjustments beyond optimizing the number of wash cycles and are relatively quick. However some decoration elements with heavy mass like NPs can stick to the membrane more strongly, as can decoration elements with some chemical affinity for the membrane.

Size exclusion spin columns using resins like those in column chromatography, described below, are also common, and utilize the longer path of travel for smaller molecules in a porous medium.

Dialysis operates by a similar mechanism to filtration but is gentler and therefore preferred for structures that are very sensitive to temperature, to physical deformation, or are chemically unstable. In dialysis no force pushes impurities through the membrane, rather they simply diffuse into a large reservoir. Dialysis membranes have a wide range of molecular weight cutoffs but also have a longer protocol execution time of 1 h to >18 h.

Magnetic bead purification requires an additional pre-designed chemistry to bind to the DNA nanostructure. The beads are introduced to the sample and are separated from solution by a magnetic field, supernatant is removed, new buffer is added, the magnetic field is removed, and the product is cleaved from the particle. This purifies only those structure which have the correct binding and unbinding from the magnetic particles [102]. Usually, the binding is a reversible/competitive chemical reaction like antibody-ligand recognition, biotin-streptavidin affinity, or toehold-mediated DNA strand displacement.

Affinity tag separation is based on a similar principle to magnetic bead purification. In this case the column or surface is coated with a ligand which binds specifically to some chemical tag, and the DNA nanostructures are modified to include this tag. Again the desired product is retained and after a washing step is eluted out by a competitive reaction for the tag. Both techniques are efficient due to the chemical specificity of the purification but require substantial pre-design and modification of the structure.

Polyethylene glycol, PEG, precipitation is a centrifugation technique for separation of DNA structures from small oligomers. In the presence of PEG and positive ions, DNA of larger mass will precipitate, allowing centrifugation and separation from smaller oligomers [103]. This is typically used to separate very large origami from staples and can be difficult to tune for smaller changes in mass [3, 104]. Similarly, DNA will precipitate in the presence of ethanol or isopropanol, and positively charged ions. Ethanol and isopropanol precipitation are not gentle, and are generally thought to damage DNA origami, though they are often used to purify plain dsDNA and ssDNA.

Practical considerations of time, throughput, quantity to be purified, and equipment availability often dominate the choice of purification technique. There are several compatibility considerations, particularly regarding mass, number, and stability of functional elements. However, few studies exist in the literature quantifying the effect of these compatibilities on yield by direct comparison between purification techniques [18].

Techniques which can simultaneously purify and provide analytical information bridge the purification and verification phases of a decoration workflow. This section will provide a general introduction to these techniques and their use for purification, and section 6.1 will be constrained to a shorter discussion of compatibility and uncertainty considerations.

Gel electrophoresis is arguably the most used purification technique that provides analytical information, as its low-cost instrumentation is present in nearly every bio-lab. The gel acts like a filter net, slowing down charged molecules which are pulled by an electric field between the two sides of the gel. Their rate of motion, or electrophoretic mobility, depends on the hydrodynamic volume, flexibility, and charge of the molecule as well as the gel matrix type (usually agarose or polyacrylamide), the gel concentration, the ionic strength of the running buffer, and the strength of the electric field. Dedicated tools exist both to teach the fundamentals of, and simulate, electrophoretic mobility such as the GelBox program [105].

The bands of presumably separated products can then be excised, and the product recovered by squeezing protocols or elution [106]. Squeezing protocols typically involve pulverizing the excised band, followed by spin filtration to separate the product from the gel matrix. Elution protocols are gentler and either involve incubating the excised band in buffer or applying voltage to pull the sample out of the matrix and into a filter cup.

Different ranges of mass resolution may be accessed by tuning gel density, shown in table 6 for dsDNA. The ranges of separation in this table should only be used as a general guide, as ssDNA, plasmid dsDNA, coiled plasmid dsDNA, and various DNA nanostructures will all have different electrophoretic mobilities as a function of size. As the typical size of a DNA origami is approximately 7200 nt, a 1% agarose gel is a popular choice. A six strand DNA tile has 300–600 nt, making 5% acrylamide gels typical. A common issue is the heat generated by the electrophoretic field, as high temperature can denature the DNA nanostructure in the gel or melt the gel itself. For long runs and high currents, it is necessary to run in a refrigerated bath, in trays filled with ice, or in a cold room or deli-fridge.

Gels are, generally, more suitable for small scale purification as running the gel, excising the bands, and extracting the desired material can be labor intensive. It is difficult to load large quantities of sample into a gel as bands will begin to smear if more than approximately 200 ng of DNA are loaded in the well. The exact limit depends on the gel matrix and well size in addition to the structure size and geometry. Additionally, the squeezing and elution processes can sometimes provide low yield. To cut out a band prior to squeezing or elution, one must be able to see it. At high concentration DNA will create a shadow band in UV or blue light, as it absorbs in the 260–280 nm wavelengths. DNA can also be stained using intercalating dyes, which typically involve using a camera with a filter specific to the dye's emission wavelength to maximize contrast. Unfortunately, these dyes can remain intercalated in the purified structure. One workaround is to run duplicate gels, then stain one and use it to find the location of the band to be excised on the second.

Regardless of the visualization technique, this step can cause photo-induced damage. This can be mitigated by careful choice of the dye stain and excitation wavelength. Residues from the gel can also be present in the purified sample. This may not affect the functionality of the DNA nanostructure but if gel residue contamination might interfere with the workflow, elution is typically used rather than gel-squeezing.

Gel electrophoresis is often used as a general-purpose technique and for separation of structures with one to three NPs attached [107]. Ultracentrifugation and chromatography usually require more optimization which is justified either by their potentially higher resolution for higher numbers of conjugates, or potential to purify larger masses of structures more quickly once optimized [108].

Free-flow electrophoresis, FFE, is a similar technique in which biomolecules are separated only by their charge and electrophoretic mobility in an aqueous medium [109]. Although it requires more costly and elaborate instrumentation, it can be faster than gel-electrophoresis and is potentially useful in separating small amounts of DNA nanostructures conjugated with cell biomolecules such as proteins and enzymes.

Ultracentrifugation purifies via difference in density, in contrast to electrophoresis which purifies via difference in electrophoretic mobility. In isopycnic density gradient ultracentrifugation the sample is loaded on top of a chemical medium, usually glycerol or sucrose, with a density gradient. The sample is then subjected to a very high centrifugal acceleration, 4.9 × 10⁵–2.9 × 10⁶ nm.s⁻² (50 000-300 000 × g or Relative Centrifugal Force). Less dense molecules stay at the top of the column, at equilibrium with lower density medium, while denser DNA structures migrate to the bottom with higher density medium. These bands can be collected and the desired product can be purified from the medium by dialysis [110]. This technique is especially useful to separate DNA nanostructures conjugated to denser functional elements like metal NPs and QDs.

Column chromatography purifies by the difference in time it takes a molecule to migrate through a resin packed column. The components are loaded in a liquid phase, typically aqueous buffer, and are separated based on their retention times. As for size exclusion spin columns, size exclusion chromatography (SEC) separates components that are small enough to enter porous resin beads from those too large to do so via difference in retention time [111]. In contrast, reverse phase-high pressure liquid chromatography (RP-HPLC) modulates retention time via solvent gradients across which there is differential binding of polar and non-polar groups to the resin. Fast protein liquid chromatography (FPLC) is like HPLC, but typically operate at lower pressure and is more suitable for NP or protein conjugates than for DNA constructs [102]. As the product is collected in high volume fractions, column chromatography often requires a concentration or desalting step. Generally, these forms of chromatography require both instrumentation and expertise, and may take non-trivial time to optimize [96, 97].

As migratory methods which provide both purification and verification were discussed in depth above, we limit ourselves here to a brief discussion of uncertainty and compatibility considerations common to these techniques.

6.1.1. Examples of uncertainty considerations for migratory techniques

6.1.2. Examples of compatibility considerations

6.1.3. Practical considerations

The atomic force microscope (AFM) is one of the primary workhorse analytical techniques for DNA nanotechnology. In the context of verification, it is often used to characterize the shape of a nanostructure, the number of and distance between functional elements, and actuation on a surface. Since AFM operates with a physical tip interacting with the surface, its images are the convolution of the shape of the surface and the tip as shown in figure 19. The tip aspect ratio therefore limits the height and spacings of a sample that can be resolved.

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6.2.1. Examples of uncertainty considerations in AFM experiments

6.2.2. Examples of compatibility considerations for AFM experiments

6.2.3. Practical considerations

Transmission electron microscopy (TEM) is another widely used verification technique for DNA nanostructures. EM works similarly to optical microscopy, except that electrons are used instead of photons. Electrons have a much smaller wavelength compared to photons, allowing for a smaller diffraction limit, but typically must travel in vacuum. Any general rules for classes of techniques as broad as AFM and EM will be full of exceptions. However for the equipment available to a typical lab, EM methods will often provide images of larger areas, often at higher lateral resolution, but will require more sample preparation.

Low atomic number elements such as those in DNA interact weakly with electrons, resulting in poor contrast relative to an underlying support grid, often made of carbon. Chemical stains using salts containing a high atomic number element are used to enhance contrast and may be necessary for imaging in some cases. High contrast functional elements, e.g. metallic or semiconducting nanoparticles, often obviate contrast concerns entirely, especially when the distance between them is the figure of merit.

Another mitigation strategy for the low contrast of biomolecules is class averaging. In brief, images containing structures are taken, then images of individual structures are binned into classes, usually based on rotation and alignment of some model 2D or 3D structure. Finally, all the aligned structures in each class are averaged to create idealized examples, even allowing for 3D reconstructions. Class averaging can create beautiful and highly precise images, but by its nature abstracts variation within a class. This is a powerful tool if most of the variation comes from imaging artifacts, such as variation in stain depth, but is potentially problematic if the variation within the imaged structures comes from a relevant structural feature, e.g. damage, missing staples, or structure motion.

6.3.1. Examples of uncertainty considerations in TEM experiments

6.3.2. Examples of compatibility considerations for TEM experiments

6.3.3. Practical considerations

Cryo-electron microscopy, Cryo-EM, is a variant of TEM in which the sample is cryo-fixed in vitreous ice, rather than dried and immobilized to a surface. Because the sample is frozen in its solvated state, the spatial relationships between molecular components are kept close to those of the solution state [125]. Cryo-EM is also often used when lower low doses are needed to avoid damage to the molecules. This is true for tomography where images are taken at multiple angles for the same structure to enable a 3D reconstruction. Each image must be acquired at a low dose to keep the cumulative dose at an acceptable level. The low signal-to-noise images require sophisticated processing to reconstruct 3D images, including class averaging. This allows information from multiple molecules to be combined to improve signal-to-noise.

6.4.1. Examples of uncertainty considerations in Cryo-EM experiments

6.4.2. Examples of compatibility considerations for Cryo-EM experiments

6.4.3. Practical considerations

The super resolution microscopy (SRM) class of techniques exchanges resolution in time for additional resolution in space using statistical inference. This is to say, rather than imaging a structure with fluorescent molecules, photon counts are acquired across the imaging space and statistical models for the diffraction of photons are fit to these counts. This allows localization of the emitters at a resolution below that set by diffraction [128–130].

The model for the diffraction of photons from a single molecule emitter is called a Point Spread Function, or PSF [129, 130]. Typically, fluorophores switching between ON and OFF fluorescent states, or blinking, ensures that only one within a region the size of the PSF is emitting at a time. Under these circumstances, the location of an individual fluorophore may be determined with nanometer precision. Not all SRM techniques depend on the blinking behavior of the fluorophores themselves. Point Accumulation in Nanoscale Topography, PAINT, [131] achieves the same effect by means of the temporary binding of fluorescent probes diffusing in solution. The DNA-PAINT technique controls blinking through the transient hybridization of a fluorophore-labelled DNA oligomer (imager probe) with an immobilized complementary DNA strand, or docking strand [132]. The transient fluorescent signal is then captured by a fast acquisition camera and its position recorded over time acquiring a series of imaging frames. DNA-PAINT is often used in combination with a total internal reflection fluorescence, TIRF, microscope to excite imager probes close to the sample surface and reduce background fluorescence. Usually, the camera integration time is kept close to the binding time of the imager probe/docker pair to establish a high signal-to-noise ratio [133].

Since it directly targets short strand hybridization, DNA-PAINT can image the position of strands that are active in the decoration process like sticky ends or their complementary strands. It is also helpful to troubleshoot measuring the availability of sticky ends, especially if it is combined with other techniques like AFM [134].

6.5.1. Examples of uncertainty considerations in DNA-PAINT experiments

6.5.2. Examples of compatibility considerations for DNA-PAINT experiments

6.5.3. Practical considerations

Spectroscopy, particularly fluorescent or ultraviolet-visible spectroscopy, UV-Vis, can be used for bulk verification. In both, one typically infers a concentration, or similar quantity, through a modeled extinction coefficient or fluorescence efficiency. UV-Vis can also provide information on hybridization as the hyperchromicity of DNA means that ssDNA can absorb as much as 40% more than dsDNA. UV-Vis concentration data is typically measured at the 260 nm wavelength, and protein contamination is usually estimated via the ratio of absorption at 260 nm and 280 nm. There are sequence dependent models for UV-Vis extinction coefficients [140, 141], though the accuracy of these for large fully assembled structures has not been tested.

Circular dichroism, CD, uses the same wavelengths as UV-Vis but reports the difference in absorption between left-polarized and right-polarized light. It provides information on a sample's chirality and can more clearly differentiate between coiled ssDNA and helical dsDNA than absorbance hyperchromicity. Förster resonance energy transfer, FRET, is one of the most common spectroscopy techniques for DNA nanostructures and DNA origami [142]. It relies on the separation-dependent (typically sixth power as a function of distance) energy transfer between a donor and an acceptor dye molecule. The characteristic distances for FRET are typically 5 nm to 10 nm. For this reason it is used to detect distance changes, often between parts of DNA nanostructures, e.g. to detect actuation when DNA nanocontainer or nanocages are being analyzed [143–145]. Fluorophores can be easily linked to specific locations of the structure via labelled DNA strands and their signal acquired with a fluorescence microscope. This has also been used for real-time monitoring of assembly [146] and conformational folding [147].

FRET pairs offer a reliable verification tool with relatively non-invasive structure modifications and are particularly well suited to structures whose function is optical signaling such as FRET beacons [148], sensors [149] and rulers [150]. However, measuring absolute concentrations with FRET requires knowledge of the fluorescence efficiency in multiple states, which makes absolute quantification uncertain. Most typically it is used to extract the relative fraction of pairs in the signaling state.

6.6.1. Examples of uncertainty considerations in spectroscopy experiments

6.6.2. Examples of compatibility considerations for spectroscopy experiments

6.6.3. Practical considerations