Kinetics and Thermodynamics of Dna Origami 2d Arrays

Abstract

Structural DNA nanotechnology, as exemplified by DNA origami, has enabled the design and construction of molecularly-precise objects for a myriad of applications. However, limitations in imaging, and other characterization approaches, make a quantitative understanding of the folding process challenging. Such an understanding is necessary to determine the origins of structural defects, which constrain the practical use of these nanostructures. Here, we combine careful fluorescent reporter design with a novel affine transformation technique that, together, permit the rigorous measurement of folding thermodynamics. This method removes sources of systematic uncertainty and resolves problems with typical background-correction schemes. This in turn allows us to examine entropic corrections associated with folding and potential secondary and tertiary structure of the scaffold. Our approach also highlights the importance of heat-capacity changes during DNA melting. In addition to yielding insight into DNA origami folding, it is well-suited to probing fundamental processes in related self-assembling systems.

INTRODUCTION

The sequence specificity inherent to DNA self-assembly provides nanofabrication options orthogonal to those of existing top-down methods, enabling the construction of multifunctional, addressable 3D nanostructures. Nanoparticles (1), quantum dots (2,3), fluorophores (4), biomolecules (5,6), and combinations thereof can be positioned with single-nanometer precision and accuracy (7,8) on DNA platforms. Recent work has demonstrated production at scale (9,10), facilitating the manufacture of drug delivery vehicles (11), calibration artefacts (12), and large area, functional surfaces (4,13) at low cost. However, while raw material scale-up is necessary for the industrial implementation of DNA nanofabrication technology, it is not sufficient. As observed in Moore's seminal 1965 paper, the semiconductor industry has seen success in part because 'No barrier exists comparable to the thermodynamic equilibrium considerations that often limit yields in chemical reactions' (14). If artificial macromolecular self-assembly is to replicate the success of the semiconductor manufacturing paradigm, at a minimum we must fully understand those limiting thermodynamic equilibria and be able to predict the nature of the resulting defects and their populations. This will enable the development of design, process, and assembly strategies that ensure functionality.

Unfortunately, DNA nanostructure thermodynamics and kinetics are difficult to characterize via the techniques typically employed by biophysicists, as are similar complex cooperative effects relevant in biological DNA. DNA origami (15)—in which a long, single-stranded 'scaffold' folds by binding many 'staple' oligomers—has been the focus of much work on yield and folding. Most efforts, to date, have been theoretical (16,17), indirect (18,19), or unable to resolve individual folding events (20–23). In addition, with few exceptions (24–26), these studies have examined structural yield, i.e., fidelity with respect to a designed shape, as opposed to functional yield, i.e., inclusion of all necessary active components. The large number of potential design configurations means that measurement techniques must be adapted to nanofabrication contexts, and they must also have sufficient throughput to adequately explore an extensive parameter space.

In this work, we investigate the effect of fold distance and persistence length on the thermodynamics of an initial folding event using high-throughput, quantitative Polymerase Chain Reaction (qPCR) equipment. These measurements are enabled by our modular fluorescent melt-curve reporter system, which minimizes extraneous signals, in combination with an affine transformation technique that significantly improves melt-curve baseline and background correction by iteratively collapsing numerous replicate measurements of a sample onto a single curve through linear parameters representing known sources of variation (27). While this study is motivated by a desire to understand the details of the origami assembly process, the methods and results are applicable to numerous types of DNA-based self-assembling systems.

Characterization of folding events in DNA origami is problematic due to the sheer number of hybridization events One example origami structure, the Rothemund tall rectangle (15), consists of a 7.2 kb M13 bacteriophage viral scaffold bound together with ≈ 200 synthetic staples, each of which binds two or three different and disjoint sub-sequences of the scaffold (15). It must be emphasized that this results in ≈ 600 reversible hybridization reactions, of typically 6–24 bases in length, with varying degrees of independence, collectively responsible for ≈ 200 forced links in the topology of the scaffold. Design choices include scaffold sequence permutation, staple motifs, and scaffold routing—all of which influence the folding process. Attaining the imaging resolution required to observe individual binding events is a significant challenge and has, so far, only been performed post mortem, on assembled structures (25). To develop an understanding of design-assembly relationships, functional staple yields must be characterized for numerous 'equivalent' structures of varying design under various processing conditions.

These design-assembly relationships for DNA origami are a function of the interplay between several cooperative energetic contributions (17,25). The primary contributor to hybridization comes from base stacking and base pairing as described by the nearest-neighbor model (28). Additional contributions come from coaxial end-to-end base stacking with adjacent staples, and entropic effects, as sub-sequence binding events change the topology of the scaffold (16,17,28). As each staple binds, it reduces the entropic penalties for further folds and provides base stacking for its neighbors. It also changes the equilibrium constant for the other sub-sequences on that staple from a bimolecular to a unimolecular form. While this is not the focus of this paper, we note that the complex problem of cooperative folding can be addressed using our programmable test system. Here we only explore zeroth order cooperative effects, i.e., changes in conformational entropy.

While the thermodynamics and kinetics of biological DNA hybridization (28–30) and the basic theory for loop entropy in short (tens-of-bases) ssDNA (28) and in long (kilobase) dsDNA (31,32) are all established, they are not directly applicable to DNA origami. The latter begins as long ssDNA loops, likely with intrinsic secondary structure, which are folded into smaller and smaller mixed ssDNA/dsDNA loops until the entire structure comprises dsDNA helices bound together by Holiday junctions. Neither the loop entropy model for short ssDNA nor that for long dsDNA is sufficient to predict conformational entropy in these complex, dynamic systems of mixed persistence length.

Additionally, the large thermal processing range for DNA nanofabrication (≈ 25°C to 80°C), as compared to normal physiological temperatures (36.5 °C to 37.5°C), has an important consequence: the temperature dependence of the enthalpy and entropy, expressed as the change in heat capacity on melting, ΔC _p, cannot be neglected. While the significance of ΔC _p for DNA melting is established (33,34), a general consensus on typical values and sequence dependence is lacking, and it is commonly neglected entirely in secondary structure prediction (28,35). It is worth noting that ΔC _p shifts the hybridization energetics in proportion to the difference between the evaluation temperature and the melt temperature and therefore becomes critical over the broad temperature ranges used in nanofabrication.

So far, we have discussed the importance of and need for a better understanding of the thermodynamics of DNA origami assembly. Below, we examine the limitations of current techniques when applied to this problem.

Experimental characterization of DNA origami systems with existing biological techniques is often as fraught as application of existing theory. For smaller ssDNA loops, it is common to use UltraViolet–Visible (UV–Vis) spectroscopy to measure melt curves or differential scanning calorimetry (DSC) to directly measure the melting energetics (36). In both cases, a significant mass of DNA is required, and both techniques measure signal from all DNA in the sample. Sufficient resolution to distinguish one ≈ 80-base staple or, worse, an approximately 24-base staple sub-sequence, from the other 7.2 kb of DNA in the system is not yet available. For measurement of cyclization of long dsDNA, ligation reactions are often quenched with Ethylenediaminetetraacetic acid (EDTA), then gel electrophoresis is used to quantify the relative concentration of cyclized/uncyclized material for sequential snapshots of the reaction (37). In the case of origami, there is little to no gel mobility shift associated with a single staple fold of the scaffold. Intercalating dye fluorescence may be used to determine melt temperatures,(38) but there is a lack of consensus regarding baseline correction techniques (39) to which thermodynamic parameter extraction, via van't Hoff analysis (33,40,41) plotting ln(K) versus 1/T, is exceptionally sensitive. As a result, the melt temperature, T _m, is taken to be the only reliable parameter, and is often the only one reported (42). The variant of van't Hoff analysis, in which T _m is plotted against DNA concentration, common to both fluorescence and UV–Vis, is not usable for scaffold folding itself. This is because, whether a fold occurs due to the formation of secondary structure between disparate domains of the scaffold, or as the result of a second domain of an already-bound staple hybridizing, the change in topology is a unimolecular process, requiring neither the addition (removal) of another strand to (from) the structure. Therefore, the concentration terms cancel out in the equilibrium constant.

qPCR equipment, which enables high-throughput fluorimetry, has been used with intercalating dyes to measure anneal/melt curves of whole origami (16,17,19), while Förster resonance energy transfer (FRET) pairs have been used to measure local melting of origami (43), inter-origami base stacking (44), and DNA tile assembly (45). However, absent a robust baseline correction method, these techniques cannot provide quantitative information. Baseline correction is difficult because fluorophores, whether FRET pairs or intercalating dyes, have a temperature-dependent fluorescence efficiency that is also sensitive to their local environment. This includes neighboring ssDNA/dsDNA transitions, as well as the DNA sequence immediately adjacent to the fluorophore.

However, if the issues associated with local environment effects can be mitigated, and the baseline correction made rigorous, the specificity and sensitivity of FRET reporters makes them attractive for measuring folding events. Here, we overcome these difficulties by implementing a modular reporter system that maintains a uniform fluorophore environment for every fold measured and introduce an analysis approach that alleviates baseline correction issues. In this analysis we make, and validate, the assumption that we can separate the effect of the variables subject to error from the intrinsic signal. In other words, the physics responsible for FRET, i.e., the relative proximity of donor to acceptor, is the same for all samples, while the measured signal depends on the sample volume, well location, detection/excitation efficiency, alignment of equipment optics per well, etc. This assumption enables us to apply an affine transformation (see Equation 2) to the melt curve and significantly reduce subjectivity in the baseline correction process, replacing it with a more mathematically rigorous approach. With a reproducible fluorescence signal, and a robust baseline correction method in hand, we make use of the high throughput of qPCR to explore the large parameter space covering the effects of fold distance and persistence length.

MATERIALS AND METHODS

Test system

Using the design capabilities of structural DNA nanotechnology, we created a minimal, single-fold test system to observe the effects of loop entropy without the occurrence of numerous simultaneous events which can significantly obfuscate analysis.

An illustration of the measured folds is shown in Figure 1A. This system is coincidentally similar to those being used for subattomole detection of microRNA (46). Despite important distinctions between the thermodynamics of these systems, both make a strong case for the utility of simplified DNA self-assembly systems. We examined the melting of an identical sequence of DNA in a simple bimolecular no-fold system as well as with 13 different folding distances dividing the loop into figure-eights. The system which does not fold the scaffold will be referred to as the hybridization-only system. An important feature of this system is that we may vary the effective, or apparent persistence length, L_p (47–49). This is critical since, for the same length of biopolymer, L_p controls the effective number of freely-jointed units in the polymer chain, which in turn controls the number of possible configurational microstates and the entropic folding penalty. The apparent persistence length also determines the minimal fold distance below which enthalpic bending costs become a significant factor. Since the scaffold is circular, we only probe folding distances up to half the scaffold length.

Figure 1.

(A) folding transition schematics for bimolecular hybridization-only (H.O.), i.e., staple binds to scaffold, and unimolecular, i.e. bound staple hybridizes fully, fold reactions. (B) Persistence length strands: name, and schematic of oligomers/scaffold. (C) Reporter scheme: cartoon of fold and reporter strands on the scaffold and description of sub-sequences for fold and reporter strands where X' indicates the complement to X. (D) Relative positions of melt and anchor sub-sequence complements on M13 scaffold.

Figure 1.

We adjust the apparent persistence length, L_p, by varying how much of the scaffold is either dsDNA and ssDNA. To systematically do so the scaffold was divided into 37 base segments; two sets of complimentary oligos for each segment were ordered, namely a 37-base full complement and a 32-base complement omitting the last 5 bases at the 3′ end. The scaffold L_p was then varied by repeating motifs of these complement strands as shown in Figure 1B. The short and long L_p systems contained only the 32- and 37-base complements respectively, while the medium system alternated between the 32- and 37-base complements across the scaffold. In addition, a native system with no complements, and a blocked system with only 32-base complements in areas of high predicted secondary structure, SI section 1, were examined. For each L_p system, a pool of complement strands was created for all segments except those complementing the anchor, melt, and fluorophore sequences for that fold. This pool was added in 5× excess of the scaffold.

While the L_p of ssDNA and regularly-nicked dsDNA (50) have been measured, determining the persistence length of these composite constructs is beyond the scope of this work, particularly since there is some controversy regarding the persistence length of short dsDNA segments (51–54). However, we provide a rough estimate in SI section 3, for later use in allowing us to implement configurational entropy and bending enthalpy models.

Our reporter system must meet two criteria to effectively measure and compare fold distances. First, it must measure melting of the same sequence of DNA for each fold, to simplify comparison. Second, the local environment around the FRET pairs should be as uniform as possible across samples. To satisfy these constraints, we used the same fluorophore/quencher-labeled oligomers for all folds, both to minimize sequence-dependent changes in fluorescence as well as variability in concentration associated with measuring concentration and pipetting multiple strands.

One potential drawback of this approach is that the reporter strand does not create the Holiday junction-like structure found in typical origami. However, since the structure formed is the same between the hybridization-only control and the test samples, it has no effect on the excess energies due to changes in fold distance or persistence length.

Our reporter scheme is illustrated in Figure 1C. The reporter comprises three strands and the scaffold, with four domains/sub-sequences within those strands. The melt, quench, and fluorophore sub-sequences were identical sequences for all samples, while the presence/complementary location of the anchor sub-sequence in the fold strand changed between samples to enforce fold distance. The lengths of these sub-sequences were chosen so that the melt sub-sequence T _m is >10°C below that of any other sub-sequence. The right side of Figure 1D illustrates the set of folding distances.

For all 12 replicates of each folding distance at each persistence length, the sample was pipetted, mixed, annealed and finally melted while measuring fluorescence intensity. Further details, such as the sample preparation scheme to minimize unwanted errors and fully capture pipetting variation are addressed in the methods.

Data analysis: baseline and background correction

The signal in optical melt curves, whether from FRET, UV–VIS or intercalating dye measurements, does not solely measure the completion of a hybridization reaction. The source of the signal, whether absorbance or fluorescence, is temperature dependent both in the pre- and post-melt states. Additionally, various other contributors to the measured signal, such as sample/plate autofluorescence (55) and pipetting error, will lead to variability in background intensity between replicates of the measured curves. Inherently, the methods used to remove both temperature dependent baseline and background signal will change the data in the melt transition, making rigorous correction critical.

Baseline correction of optical melt curves typically consist of a two-window function fit across user-selected windows for the high and low temperature shoulders of the sigmoid (40,56). These fits are then extrapolated across the transition of interest, and the measured signal is corrected via (Equation 1), where h(T), l(T), m(T) and σ(T) are the high-temperature plateau fit, low-temperature plateau fit, measured signal and intrinsic signal, respectively.

$$\begin{equation*}\sigma \ \left( T \right) = \frac{{m\left( T \right) - l\left( T \right)\ }}{{h\left( T \right) - l\left( T \right)\ }}\ \end{equation*}$$

(1)

The appeal of the standard two-window fit is its simplicity and nominal ability to address both temperature dependence and background signal. However, this approach is only valid if the fit function is truly representative, if the fit window does not include any points from the transition, and if the sources of measured signal variation only shift or magnify the melt curve rather than distorting it.

While these assumptions may be true for UV–Vis measurements, they are problematic for fluorescence measurements. Although examples of non-linear baseline functions have been used (39), it is not clear that any of these functions, linear or otherwise, accurately represent the complex mix of factors contributing to the baseline fluorescence. Additionally, the final analysis result can be highly dependent on user-selected fitting windows, especially if there is noise in the measurement. Given that there are not clear objective figures of merit for this window selection, the subjective nature of the two-window fitting approach creates significant uncertainty.

To address these shortcomings, we apply an approach based on affine transformations. Critically, we do not assume the functional form of the baseline or background. Rather, we assume that the physical processes contributing to the baseline are the same for every replicate of a sample, but we allow the scale of the intrinsic signal to be a variable, as a result of, e.g., pipetting error. In other words, we assume that the measured signal is related to the intrinsic signal through linear combinations of a finite number of physical processes, whose relative contributions are determined as part of the analysis. With a sufficient number of sample replicates, the figure of merit for optimization in the analysis is how well all replicate melt curves collapse onto a single intrinsic melt curve via affine transformation, as shown in Figure 2 (27).

Figure 2.

Hybridization-only (H.O.) control for the short Lp scaffold before (A), and after (B), affine transformation. The empty plate background, B(T), and fluorescence temperature dependence baseline, R(T), are subtracted from a to b, but are separately measured in control experiments.

Figure 2.

Unprocessed melt curves, acquired as described in the methods, are shown in Figure 2A. The samples share the same characteristics, i.e. melt temperature and functional form, arising from the intrinsic signal. Affine transformations were applied to collapse these curves and reveal the intrinsic signal in Figure 2B.

A detailed description of this process is included in SI. Section 2. In brief, we first use a set of empty wells to determine the plate autofluorescence and optics alignment-related background, B(T). Next, we use a set of wells containing all strands, bar the folding strand, to determine the fluorescence-temperature-dependent baseline, R(T). The functional forms of the baseline and background determined from the control experiments are then used in combination with the measured melt curves, m _i(T), to extract the intrinsic melt signal, σ(T). This is done by finding a_i , b_i and c_i affine parameters for each replicate, i, such that the measured replicate melt curves, m _i(T), collapse to the single intrinsic melt signal, σ(T) [Equation 2]. In all such cases, the relative error on the collapse is a useful metric for the uncertainty of the intrinsic melt signal.

As the transformations are applied directly to experimental data we never need to, nor do we, specify functional forms for the baseline or background. This frees us from making poor modeling choices about the actual behavior of σ, R and B, aside from needing to satisfy an equation having the general form of Equation 2.

$$\begin{equation*}{m_i}\ \left( T \right) = {a_i}\ \sigma \left( T \right)R\left( T \right) + {b_i}B\left( T \right) + {c_i}\end{equation*}$$

(2)

For the analysis presented here, we assume that FRET quenching reduces the fluorescence intensity of the folded state to a sufficiently low level that its temperature dependence is negligible. This may not be true for every system and buffer condition.

One subjective choice in the affine transformation is application of a monotonicity constraint, and the window over which it is applied. The data presented here, Figure 7 in particular, were analyzed with only a high-temperature monotonicity constraint. There are insufficient data points on the low-temperature plateau of the control and long-fold samples to apply a low-temperature monotonicity constraint without some sensitivity to window choice. This is illustrated in SI section 12.

Equation (2) may be easily modified for other systems. For example, for intercalating dyes the free-dye fluorescence temperature dependence cannot be neglected. Additionally, terms for free-dye fluorescence would be supplemented with terms for free-dye fluorescence in the presence of ssDNA. These possibilities are discussed in our best-practices paper for this analysis (27).

One limitation of this method is that the curve-collapse optimization is most effective when only one physical process dominates the measured signal.

As a counter-example, if variations in pipetted volume contribute a similar change in signal as the background, the optimization can become inefficient or even infeasible. Additionally, while this approach removes much subjectivity from the analysis, the choice of initial equation, e.g. Equation 1, and the linearity constraints at high and low temperatures are still choices for the experimentalist.

Ultimately, implementation of affine transformations in analysis of optical melt curves allows us to simultaneously perform baseline and background corrections with reduced subjective, model-choice errors.

Data analysis: thermodynamics extraction

Calculation of ΔH and ΔS is performed via van't Hoff analysis; in which the equilibrium constant, K, is calculated and fitted to Equation 3 as a function of temperature.

$$\begin{equation*}\ln \left( K \right) = \frac{{ - \Delta H}}{{RT}}\ + \frac{{\Delta S}}{R}\end{equation*}$$

(3)

Equilibrium constants are calculated using Equations 4 and5 for the hybridization-only control (bimolecular) and folded samples (unimolecular) reactions, respectively. Where [ssDNA] and [dsDNA] refer to the concentration of the scaffold in the melted, or dehybridized, and the annealed, or hybridized, state respectively, while [excess] refers to the relative excess of the fold strand to the scaffold. Each of these is treated as a fraction multiplied by the total scaffold concentration, which in Equation 5 cancels out, as one would expect a unimolecular reaction to be concentration independent. As previously described, this is because the reporter signals when the melt sub-sequence of the fold strand hybridizes, Figure 1C, at which point the more stable anchor sub-sequence of that strand is already bound to the scaffold. As such, the folding (unfolding) of the scaffold neither consumes (generates) a free staple strand, and is effectively unimolecular in nature. The exception to this is the hybridization-only control, which does not fold the scaffold and is bimolecular

$$\begin{eqnarray*}K\ &=& \frac{{\left[ {{\rm ssDNA}} \right]\left[ {{\rm foldStrand}} \right]}}{{\left[ {{\rm dsDNA}} \right]}} \nonumber\\ &=& \frac{{\left[ {{\rm ssDNA}} \right]\left[ {{\rm excess}-{\rm dsDNA}} \right]}}{{\left[ {{\rm dsDNA}} \right]}}\ \nonumber\\ &=& \frac{{\left[ {{\rm ssDNA}} \right]\left[ {{\rm excess} - 1 + {\rm ssDNA}} \right]}}{{\left[ {1 - {\rm ssDNA}} \right]}}{\rm{\ }}\end{eqnarray*}$$

(4)

$$\begin{equation*}K\ = \frac{{\left[ {{\rm ssDNA}} \right]}}{{\left[ {{\rm dsDNA}} \right]}}\ = \frac{{\left[ {{\rm ssDNA}} \right]}}{{\left[ {1 - {\rm ssDNA}} \right]}}\ \end{equation*}$$

(5)

Estimating ΔS requires extrapolation to 1/T = 0, which is to say, infinite temperature. Small uncertainties in the extrapolation of ln(K) as a function of 1/T, give rise to large uncertainties in the value of the intercept at 1/T = 0, i.e., ΔS. While a linear relationship between ln(K) and 1/T is often assumed in the van't Hoff analysis, the change in heat capacity, ΔC _p, results in a nonlinearity. The relationship between ΔC _p, ΔH(T) and ΔS(T) is described in Equation 6.

$$\begin{equation*}{\rm{\Delta }}{{{C}}_{\rm{p}}} = {{\Delta H/\Delta T}} = {{T\cdot\Delta S/\Delta T}}\end{equation*}$$

(6)

$$\begin{equation*}{{\Delta T}} = {{{T}}_{{\rm{ref}}}} - {{{T}}_{\rm{m}}}\end{equation*}$$

(7)

T _ref an arbitrarily chosen temperature at which ΔH and ΔS are evaluated. It is also worth noting that fitting ΔC _p from curvature in van't Hoff analysis of optical melt curves is not always successful (35). Limited data sampling, in units of 1/T, makes the typical fitting of the curvature in that space highly dependent on the quality of the data. For a thorough discussion of this, we direct the reader to the relevant section in the review by Mikulecky and Feig (33).

Loop entropy and worm-like chain bending model

The change in entropy resulting from converting a linear polymer to a loop can be modeled using the Jacobson–Stockmayer entropy extrapolation (28). This may be readily rearranged, SI section 3, to give an estimate of the loop-to-figure-eight transition entropy shown in Equation 8. Where, in number of bases of ssDNA, N ₀ is the length of the original loop, and N ₁ and N ₂ are the lengths of the two-resulting figure-eight portions illustrated in Figure 1. ΔS _ref is the entropy lost in forming an ssDNA loop comprising C nucleotides. This value was experimentally determined for small hairpins, and is extrapolated to larger loops. In our predictions we use the values for a 30 nucleotide hairpin (28). The relationship between ΔS and the j-factor terminology used for long dsDNA cyclization is shown in Equation 9.

It is worth noting that the units for C are effectively 'nucleotides of ssDNA.' The value of C, together with the prefactor, empirically represent the effective number of bases per segment length. Applying Equation 8 to DNA nanofabrication systems requires a unit conversion from bases of the scaffold systems shown in Figure 1 to bases of ssDNA. The tentative conversion factors we used are discussed in SI section 3.

$$\begin{equation*}\Delta \ {S_{{\rm fold}}} = \ \Delta {S_{{\rm ref}}} + 2.44R\, \ln \left( {\frac{{{N_1}{N_2}}}{{30{N_0}C}}} \right)\end{equation*}$$

(8)

$$\begin{equation*}\Delta \ {S_{{\rm fold}}} = \ - R\, \ln (j)\end{equation*}$$

(9)

Implementation of the worm-like chain (WLC) model for the energy of bending, E _b, per unit length of the arc length of the polymer is given in Equation 10, where R is the radius of curvature of the bend (57). As such the ΔH associated with bending is given by Equation 11, where L ₀ is the contour length of the DNA.

$$\begin{equation*}{E_{\rm b}} = \frac{{{L_{\rm p}}{k_{\rm b}}T}}{{2{R^2}}}\ \end{equation*}$$

(10)

$$\begin{equation*}\Delta \ {H_{{\rm bend}}} = \frac{{{L_{\rm p}}{k_{\rm b}}T}}{{2{R^2}}}\ *\ {L_0} = \frac{{{L_{\rm p}}{k_{\rm b}}T}}{{2{{\left( {{\raise0.7ex\hbox{${{L_0}}$} \!\mathord{\left/ {\vphantom {{{L_0}} {2\pi }}}\right.} \!\lower0.7ex\hbox{${2\pi }$}}} \right)}^2}}}\ *{L_0}\end{equation*}$$

(11)

As noted above, our mixed dsDNA/ssDNA system is complex, and a detailed microscopic treatment, beyond the scope of this paper, would be needed to accurately describe its mechanical properties. We therefore emphasize that Equations 8–11 serve only as a rough guide to the relevant energetics.

FRET Reporter and folding strands

As noted above, it is vital to maintain a uniform environment for the fluorophores for all measured systems, including DNA sequence. We achieve this by implementing the fluorophore-quencher system illustrated in Figure 1C, in which the sequences adjacent to the fluorophore (JOE), and the quencher (Iowa BlackF), do not change. The folding distance (Figure 1A) is controlled by a 42-base anchor sequence that is adjusted to bind at different locations around the loop of the scaffold strand. To minimize non-fold-related fluorescence background, we control the stoichiometry of our system (Table 1) to ensure that, at low temperature, all fluorophores are bound to a scaffold resulting in a consistent local environment.

Table 1.

Strand concentration, absolute and relative to scaffold

	Absolute concentration	Relative excess (to scaffold)
Scaffold	45 nmol.L^-1	–
Fold strand	225 nmol.L^-1	5×
L _p strands	225 nmol.L^-1	5×
Quencher	450 nmol.L^-1	10×
Fluorophore	30 nmol.L^-1	0.67×

	Absolute concentration	Relative excess (to scaffold)
Scaffold	45 nmol.L^-1	–
Fold strand	225 nmol.L^-1	5×
L _p strands	225 nmol.L^-1	5×
Quencher	450 nmol.L^-1	10×
Fluorophore	30 nmol.L^-1	0.67×

Table 1.

Strand concentration, absolute and relative to scaffold

	Absolute concentration	Relative excess (to scaffold)
Scaffold	45 nmol.L^-1	–
Fold strand	225 nmol.L^-1	5×
L _p strands	225 nmol.L^-1	5×
Quencher	450 nmol.L^-1	10×
Fluorophore	30 nmol.L^-1	0.67×

	Absolute concentration	Relative excess (to scaffold)
Scaffold	45 nmol.L^-1	–
Fold strand	225 nmol.L^-1	5×
L _p strands	225 nmol.L^-1	5×
Quencher	450 nmol.L^-1	10×
Fluorophore	30 nmol.L^-1	0.67×

To explore the effect of zeroth-order topology changes on melting behavior, we use 13 different folding distances, controlled by the binding location of the anchor sequence (Figure 1D). The fluorophore, quencher, and anchor sub-sequences all have a predicted T _m of ≈ 70°C under our buffer conditions as evaluated by typical nearest neighbor models (30,58). These temperatures are well above the predicted 35°C T _m of the melt sub-sequence, ensuring that the fluorophore is unquenched only when the melt sub-sequence dehybridizes.

Buffer conditions were chosen to match standard DNA nanofabrication protocols: 50 mmol.L^-1 cacodylate buffer, 12.5 mmol.L^-1 Mg acetate, 1 mmol.L^-1 EDTA, pH 7.2. Cacodylate was chosen as it buffers pH well across a wide temperature range. DNA sequences are given in section 11 of the SI.

Persistence length

The systems with different apparent persistence lengths illustrated in Figure 1B are the native scaffold, short (repeating 32 base dsDNA interspersed by 5 bases ssDNA or free scaffold), medium (repeating 32 bases dsDNA, 5 bases ssDNA, 37 bases dsDNA, followed by 32 bases dsDNA), and long (repeating 37 bases dsDNA separated by nicks) This varies L _p between that of ssDNA (L _p ≈ 1 nm to 3 nm (59)) and regularly nicked dsDNA (L _p ≈ 14 nm to 43 nm depending on counterion charge and concentration (50)).

The lowest persistence length, ssDNA native M13 scaffold, will in practice contain a great deal of secondary structure. We identified some scaffold locations which could form >10-base secondary structure across long scaffold distances (SI. section 1), with T _m on the same order as that of the melt sub-sequence. As such, we included an additional scaffold system to investigate the effect of this secondary structure. In this system, we introduce a number of 'blocking' strands, designed to hybridize with and out compete this long-distance secondary structure.

We denote the variants of our scaffold, in order of persistence length, as 'native', 'blocked', short, medium, and long. A description of the blocked system and potential secondary structure is given in SI section1, while the sequences for strands creating different apparent persistence lengths, L _p, are given in SI section 14.

Melt experiments

Our experimental matrix consists of 13-fold distances across scaffolds with 5 different persistence lengths. In addition, it is desirable to replicate each configuration a sufficient number of times to assess the variation due to pipetting while also identifying and removing spurious data sets such as those compromised by bubbles in the wells. We therefore choose to perform 12 replicates of each experiment to ensure high-quality data.

The melt protocol consisted of an initial denaturing step (80°C for 1 min) an annealing sequence (75°C to 15°C, 0.61°C steps, 3.5 min hold) and finally melting (15°C to 75°C, 0.61°C steps, 3.5 min hold) in which the fluorescence was measured. The raw fluorescence intensity in the green channel, rather than the calculated multicomponent intensity, was used, as uncertainties in the instrument's multicomponent intensity calculation were unknown.

Samples were distributed over two plates for each persistence length set. These plates consisted of 12 replicates of each fold distance, 12 replicates of a fluorescence baseline control containing no fold strand and 24 empty background wells.

To ensure a consistent sampling of pipetting error simultaneously with manageable sample preparation, 12 replicates of all buffer and strands except the fold strand were independently prepared. These master replicates were used as a base stock for the 12 replicates of each fold distance by multichannel pipettor through the two plates for each scaffold persistence length. As such, pipetting variability within any fold distance is uncorrelated, but pipetting variation is correlated between the Nth replicate of all folding distances.

The qPCR equipment had a certified temperature precision of 0.31°C, and an optical shot noise of ≈ 50 to 100 intensity counts with experiments measuring an intensity change of ≈ 0 to ≈ 20 000 intensity counts.

Differential scanning calorimetry

DSC scans were performed on equipment with a 300 μL active volume, baseline repeatability of 0.028 μW, and short-term noise of 0.015 μW, courtesy of the University of Maryland/NIST Institute for Bioscience & Biotechnology Research (IBBR).

While the buffer conditions were identical to the melt experiments performed in qPCR equipment, the strand concentrations and excesses were modified to obtain sufficient signal. Specifically, strand concentrations were much higher and were kept at a 1:1 ratio to avoid measuring the formation of secondary structure in excess strands.

To identify the annealing peaks, scans were performed on subsets of the reporter with increasing numbers of strands. Initial scans were run with equimolar melt and truncated scaffold strands at ≈ 90 μmol.L^-1. This sample was removed from the DSC, measured, and equimolar fluorophore strand was added for a final concentration of ≈ 75 μmol.L^-1. The sample removal was repeated, and the quencher strand was added for a final concentration of ≈ 62 μmol.L^-1. Reuse of the same sample allowed confirmation of individual peak identities.

This final sample containing equimolar concentrations of all strands was then pipetted to a 96-well plate and run in the qPCR for comparison. Unfortunately, running a full 10 μL, the minimal sample volume, at the same concentration as the DSC sample would create signal well outside the dynamic range of the detector in the qPCR unit, which would result in significant measurement error. As dilution could significantly change the melt temperature, we chose to take 0.76 μL of DSC sample and pipetted it into 9.25 μL of mineral oil (a mixture of alkanes and cycloalkanes) in the PCR plate. As the mineral oil is not miscible with the water, and floats to form a capping layer, this allowed us to measure the DSC sample without losing water to evaporation. All scans were performed from 5°C to 100°C at a rate of 1°C/min.

RESULTS

DSC confirmation of fluorescent reporter

We use DSC as an orthogonal measurement technique to confirm that the fluorescence reporter system is measuring the anticipated reaction. We do this using a reduced system that allows direct comparison between DSC and fluorescence measurements.

Given that the scaffold is approximately seven hundred times more massive than the 10-base melt sub-sequence, a DSC sample with sufficient melt sub-sequences to provide measurable signal would strain solubility, in addition to being exorbitant in cost. It would also be difficult to analyze due to the additional noise associated with 7.2 kb of DNA. DSC was therefore run against a synthetic model system identical in sequence to the reporter, but with a truncated scaffold 100 bases in length. Additionally, the fold strand contained no anchor sub-sequence. All sequences and fluorophores were otherwise identical. In other words, the model system differs from the bimolecular hybridization-only system by omission of 7.15 kb of scaffold. Details of the DSC scans are addressed in the methods.

The results of DSC scans are shown in Figure 3. From (A) through (C), the sample was removed from the DSC and an additional strand was added, as indicated by the inset schematics in Figure 3. As the strands were added sequentially, we can readily identify the peaks associated with the dissociation of the sub-sequences illustrated in Figure 1C: α (melt), β (fluorophore), γ (quencher). Table 2 shows the calculated T _m for each sub-sequence. As strands are added the shift in the α peak and loss of the secondary shoulder apparent in Figure 3A versus Figures3B andC suggests that there is some unintended interaction between the nominally non-binding regions of the fold and scaffold strands, enhancing the stability of the intended fold-scaffold duplex. The shifts in both α and δ peaks between Figures3B andC are likely due to minor base stacking between the melt and fluorophore strands.

Figure 3.

DSC scans of reporter analog: (A) only fold and scaffold strands; (B) fold, scaffold, and fluorophore strands; (C) all reporter strands. Red curve, derivative of fluorescence for the same sample. Peaks and sub-sequences labeled to match

Figure 3.

Table 2.

T _m for reporter from nearest-neighbor, DSC and fluorescence. Uncertainties are one standard deviation derived from three repeat runs on each sample

	Peak
	α	β	δ
Nearest-neighbor model	54.9°C	79.8°C	80.9°C
DSC	51.0 ± 2.3°C	81.2 ± 0.5°C	84.7 ± 0.3°C
Fluorescence (maximum ofδF/δT)	54.4 ± 0.25°C	N/A	N/A

	Peak
	α	β	δ
Nearest-neighbor model	54.9°C	79.8°C	80.9°C
DSC	51.0 ± 2.3°C	81.2 ± 0.5°C	84.7 ± 0.3°C
Fluorescence (maximum ofδF/δT)	54.4 ± 0.25°C	N/A	N/A

Table 2.

T _m for reporter from nearest-neighbor, DSC and fluorescence. Uncertainties are one standard deviation derived from three repeat runs on each sample

	Peak
	α	β	δ
Nearest-neighbor model	54.9°C	79.8°C	80.9°C
DSC	51.0 ± 2.3°C	81.2 ± 0.5°C	84.7 ± 0.3°C
Fluorescence (maximum ofδF/δT)	54.4 ± 0.25°C	N/A	N/A

	Peak
	α	β	δ
Nearest-neighbor model	54.9°C	79.8°C	80.9°C
DSC	51.0 ± 2.3°C	81.2 ± 0.5°C	84.7 ± 0.3°C
Fluorescence (maximum ofδF/δT)	54.4 ± 0.25°C	N/A	N/A

The T _m shown in Table 2 display a reasonable match with nearest-neighbor model predictions. The progression of, and the peaks in Figures 3A–C, compared to the fluorescence measurements shown in Figure 3C (red), confirm that the FRET reporter is probing the intended melt sequence illustrated in Figure 1C. It is reasonable to infer that the fluorescence melt curves measured here are coming from the melt sub-sequence, α, rather than from some spurious side reaction.

ΔH extracted from the DSC data shown in Figure 3 is addressed in SI section 4. These values are not discussed here due to the significant uncertainty introduced by the ambiguity of the DSC baseline correction arising from the close spacing of the peaks.

Melt experiments

The melt curves shown in Figure 4A, demonstrate the low noise resulting from affine transformation across 12 replicates. By design, the melt sub-sequence responsible for these melt curves does not change. As such, all differences between these samples should result from the shift between unimolecular and bimolecular reaction types, entropic folding penalties, and potential enthalpic helix-bending penalties, where the latter two result from, e.g., different conformational microstates.

Figure 4.

Averaged melt data and van't Hoff plots from the short Lp scaffold. H.O. indicates the hybridization-only control. The numbers in the legend refer to the number of bases between the melt and anchor subsequences for that curve. Error bars are one standard deviation above and below the mean of the replicate values.

Figure 4.

The trends shown in Figure 4A, for the short persistence length, match with thermodynamic intuition. The hybridization-only sample is less stable than the others as it involves a bimolecular reaction, at low concentration, rather than a unimolecular reaction. For the folded samples, increasing fold distances shift the melt curve to lower temperatures indicating an increasing entropy change on melting, as expected. The error bars shown in Figure 4, and all other figures presented, represent one standard deviation above and below the mean of the replicates.

Figure 4B shows van't Hoff plots for the folded samples. The hybridization-only sample is not shown here as its equilibrium constant is calculated for a bimolecular reaction, and is therefore outside the plotted range. The van't Hoff plots exhibit a slight curvature associated with ΔC _p.

The T _m from these curves is reported on a semi-log₂ plot in Figure 5. While changes in T _m are specific to this system, they effectively illustrate the energetics associated with these changes in fold distance and L _p.

Figure 5.

Tm as a function of fold distance (log2) and system Lp. H.O. indicates the hybridization-only control. The single error bar represents the 0.3°C temperature uncertainty as supplied by the manufacturer. The scatter in loop distance was added to the plot to allow the individual Tm values to be visualized.

T _m as a function of fold distance (log₂) and system L _p. H.O. indicates the hybridization-only control. The single error bar represents the 0.3°C temperature uncertainty as supplied by the manufacturer. The scatter in loop distance was added to the plot to allow the individual T _m values to be visualized.

Figure 5.

It is apparent from Figure 5 that the melt temperature of the native scaffold systems generally occurs at a higher temperature than the other L _p systems. This is consistent with the varied and extensive secondary structure expected in the native scaffold. Due to this local secondary structure, in the form of hairpins, the native scaffold may have much smaller effective looping lengths than the other L _p systems, resulting in a lower entropy penalty on folding.

To examine whether the controlling secondary structure comprises many relatively short dsDNA regions or a small number of long-distance folds, an additional 'blocked' scaffold system was tested. In this, regions of potential long-distance intra-scaffold folds were blocked with ssDNA oligos, SI section 1. This system follows the same trend as the native scaffold, suggesting that the long-distance secondary structure is not responsible for the increased T _m. However, the blocked scaffold has a higher T _m for the large folds, suggesting that some competition with native secondary structure has been removed, as intended, by the introduction of the blocking staples.

Excepting the shortest fold for the most rigid scaffold, the remaining samples follow two clear trends. Increasing loop distance depresses the T _m, as does increasing persistence length, primarily at short fold distances. The 138-base fold for the fully dsDNA scaffold has only four jointed sections of dsDNA interspersed with nicks. As such, it may be that the low number of sections allows for some unusually stable conformation (60) and a T _m higher than expected, a feature also seen for the short and long persistence lengths.

As it relates to DNA origami, the melt curves in Figure 4, and the melt temperatures in Figure 5, tell an interesting story which corroborates those developed in previous work (16–18,21). The relatively low melt temperature for the hybridization-only control, combined with the temperature increase for unimolecular reactions suggests that full origami folding follows a three-step process, although confirming this process will require additional testing in systems with multiple folds. First, the long staple sub-sequences (≥16 bases) would bind through bimolecular reactions. Second, the free ends of these partially-bound staples would hybridize in a unimolecular reaction. Third, these folds should dramatically increase the rate of subsequent unimolecular folding events by effectively decreasing the remaining fold distances. We note that, as can be seen in Figure 5, the increase in melt temperature due to a short versus a long fold distance can be > 10°C. As this difference is due to an increase in ΔS, the change in T _m will depend on the magnitude of ΔH and/or ΔS for that reaction, and will be more pronounced for shorter sub-sequences.

van't Hoff analysis & heat capacity corrections

Figure 6 illustrates the van't Hoff analysis of optical melt curves, and the effect of neglecting ΔC _p terms. It is worth reiterating that extraction of ΔC _p, and ΔH and/or ΔS temperature dependence are equivalent actions as per Equation (6).

Figure 6.

van't Hoff analysis and residuals for the short Lp, 286 base fold. The top fold data points are individual measurements; the uncertainty is captured in the spread of these points.

van't Hoff analysis and residuals for the short L _p, 286 base fold. The top fold data points are individual measurements; the uncertainty is captured in the spread of these points.

Figure 6.

van't Hoff analysis and residuals for the short Lp, 286 base fold. The top fold data points are individual measurements; the uncertainty is captured in the spread of these points.

van't Hoff analysis and residuals for the short L _p, 286 base fold. The top fold data points are individual measurements; the uncertainty is captured in the spread of these points.

The curvature in the van't Hoff plot can be subtle, making extraction of reliable values for ΔC _p problematic. This is exemplified by earlier work (61) which indicated that it was not possible to extract ΔC _p from optical melt curves. Our ability to do so in this case can be attributed both to our affine transformations as well as to improvements in equipment and experimental protocols since the 1990s.

While there is a debate in the literature regarding whether it is acceptable to neglect ΔC _p in thermodynamic parameter prediction/extraction (33,45), we consider these results to be evidence of the non-negligible effect of ΔC _p in DNA melting.

Additional considerations regarding fitting choices, such as fixing individual thermodynamic parameters during fitting, or the role of pipetting errors on van't Hoff analysis uncertainties, are discussed in SI sections 5–9. Entropy–enthalpy compensation is addressed in SI section 10, where we give evidence that the apparent compensation in this system is likely due to neglect of ΔC _p (62).

The results of van't Hoff analysis for the short L _p system are shown in Figure 7. Here, we use a three-parameter fit, and ΔH and ΔS are reported referenced to 44°C, as this is approximately the mid-point of the T _m range. A discussion of this choice of convention is in SI section 13. A benefit of this choice is that it better represents the uncertainty in the system. The error in the fit is amplified as the reference temperature diverges from the range over which the data is fitted.

Figure 7.

Fitted ΔH44°C, ΔS44°C and ΔCp for the short Lp scaffold. Dotted lines indicate the minimal literature models for the energetic effects of folding a circular worm-like-chain. Error bars are one standard deviation above and below the mean of the replicate values. H.O. indicates the hybridization-only control, and is plotted at a loop distance of 0.

Fitted ΔH ^44°C, ΔS ^44°C and ΔC _p for the short L _p scaffold. Dotted lines indicate the minimal literature models for the energetic effects of folding a circular worm-like-chain. Error bars are one standard deviation above and below the mean of the replicate values. H.O. indicates the hybridization-only control, and is plotted at a loop distance of 0.

Figure 7.

The trends reported in Figure 7 all agree with thermodynamic intuition. For ΔH(T), above some critical maximum curvature one would expect to pay an enthalpic penalty for bending the helix. One would expect this to bending term to be large initially, and to diminish quickly with increasing loop size. For ΔS(T), one would expect a long-distance fold to reduce the number of configurational microstates more than a short fold. Overall, we would not anticipate ΔC _p to change with topology to a measurable extent, and this is what we observe, within error, and the values are consistent with the wide range of per-base ΔC _p values found in the literature (33).

The composite construct is much stiffer than ssDNA, and calculating its behavior is non-trivial. This affects the estimation of both ΔH(T) and ΔS(T).

For excess ΔH(T), the composite will have a higher enthalpy of bending at a given radius of curvature than ssDNA. Unfortunately, a rigorous model for this composite system is significantly beyond the scope of this work, particularly for folds with few composite repeat units, where the ssDNA and dsDNA segments would have to be treated independently.

In order to estimate the excess ΔH(T), we used the bending energy from the Worm-Like-Chain (WLC) model and the L _p of dsDNA, 50 nm (57). This choice requires a caveat for two reasons. First, the short fold distances, where excess ΔH(T) is highest, comprise only a small number of composite repeat units, limiting the applicability of the WLC model. Second, the L _p of these composite constructs at lengths long enough for this continuum model to apply is unknown.

To estimate ΔS(T), we use the Jacobson–Stockmayer extrapolation for ssDNA, but we need to account for the fact that the same length of ssDNA, as compared to our composite, will contain many more Kuhn lengths and thus be able to sample many more configurational states. We use the Kuhn lengths of ssDNA and dsDNA to derive an appropriate conversion factor, SI section 3, assuming that the number of repeat units is sufficiently large to behave statistically.

The dotted lines in Figure 7 are derived using these approximations, and therefore serve only as an indication of the energetic effects that should be borne in mind when considering the observed trends. Further details of the approximations are discussed in section 3 of the SI.

However, even with these limitations, our extracted ΔH(T) and ΔS(T) show similar trends compared to our estimates. It is thus reasonable to interpret the dip in ΔH(T) relative to the hybridization-only control at short folds as being consistent with a bending energy penalty. Similarly, it is reasonable to assign the increase in ΔS(T) as a function of fold distance to configurational entropy costs.

We note here that, while the melt curves for medium and long L _p systems, shown in SI section 8, appear by eye to be of equally high quality as that of the short L _p scaffold, their slightly higher uncertainty propagates aggressively through the van't Hoff analysis. This, combined with the relatively minimal difference in anticipated L _p, prevent us from being able to evaluate trends between the various L _p systems in the same way we could for melt temperatures (Figure 5).

The complexity of predicting both ΔH(T) and ΔS(T) as a function of topology change in a partially folded DNA origami will likely require sufficiently nuanced modelling to capture not only changes in folding, but also changes in L _p associated with single staple-subsequence binding events. The uncertainties in ΔH(T), ΔS(T) and ΔC _p are correlated, and their variations as a function of L _p and fold distance are small compared to the hybridization-only control. Higher resolution data is needed to detect these subtle effects, but would require equipment with a temperature control precision better than 0.3°C, and with a data sampling density greater than one measurement per 0.6°C.

The improvements provided by the affine transformation and the high number of replicates is dramatic, allowing us to fit ΔC _p then correct for it, a task often not possible with optical data (61). Even though the uncertainties in ΔS(T) are inherently greater than those in ΔG(T) (62), we are able to measure a <10% change in ΔS(T).

DISCUSSION

Structural DNA nanotechnology's recent success can be attributed to the unusual ease with which even novices can design, fabricate, and image new nanostructures. However, imaging resolution limits the field to purely qualitative measurements of yield. Bridging the gap to implementation demands quantitative measures of the yield for all necessary, active components. If a plasmonic structure fails to contain functional strands addressing metallic nanoparticles to their correct locations, or a drug delivery system is missing a targeting moiety, it will be of little solace that the structure is otherwise of the correct shape. It is critical to understand the folding process sufficiently to predict such functional yields. An essential first step in predicting functional yield is to understand the driving thermodynamics.

We have performed an initial exploration of conformational entropy and bending enthalpy in a model DNA origami fold system. Our results indicate that, while existing theoretical models for loop energy, when modified for the composite construct stiffness, show a similar trend and magnitude to the observed folds, much more sophisticated modeling is needed to predict multi-step folding in full origami systems. However, our results suggest that folding proceeds along the following lines. Among the sub-sequences on a staple, the longest binds first in a bimolecular reaction, consistent with the nucleation seed subsequence concept (63). After this first event, the subsequent subsequences bind unimolecularly, sequentially, as controlled by loop entropy (Figure 4), strongly favoring the short folds. These short folds further reduce the loop entropy for nearby staples and the system assembles progressively. As loop entropy and other cooperative energetics are sequence-agnostic, and capable of overwhelming the sequence-dependent energetics, this would explain why qualitative experimental work has found origami folding to proceed like a traditional nucleation and growth system with predetermined nucleation sites (19,21,22).

We obtained these results by applying our newly-developed tools, which allow high-throughput, quantitative thermodynamic measurement of the smallest unit process of DNA origami folding. These tools enable exploration of the extensive parameter space associated with origami design and the many coupled reversible reactions which define the folding process for each possible design. The approach presented here may also be applied to the measurement of relatively small energy changes arising in biological DNA systems. While this experiment, run on basic qPCR equipment, did not resolve the even smaller differences in ΔH, ΔS and ΔC _p associated with small changes in persistence length, these changes were clearly visible in melt temperature trends. Further reductions in the uncertainties of the raw data should enable the extraction of these small thermodynamic differences. In the future, we will conduct a sensitivity analysis to determine the quality and number of replicates required to extract entropic and enthalpic penalties with sufficient precision to simultaneously measure and distinguish persistence length effects and loop distance effects.

Our ability to make these measurements relies on careful design of the fluorescence reporter, sample stoichiometry and the application of affine transformations. The latter, by removing systematic errors associated with typical fluorescence baseline corrections, enables the use of replicate data sets to significantly reduce measurement uncertainty. We are thus able to measure changes in ΔS(T) well below 10% of the total value, all with cost-effective qPCR equipment and reagents.

Importantly, the potential to extract high-quality thermodynamic data that we demonstrate here is a positive indication that, by using the entire dataset obtained in standard fluorescence DNA melting experiments useful additional information can be extracted with minimal extra effort.

By improving operando characterization of origami folding, we hope to complement existing approaches to measurement of functional yield in order to develop design heuristics for DNA nanotechnology as a whole. Finally, we note that the type of variable persistence-length system we introduce here could be valuable as a model to explore the control of stiffness and topology in polymer physics. Supplementary Data are available at NAR online.

SUPPLEMENTARY DATA

Supplementary Data are available at NAR Online.

ACKNOWLEDGEMENTS

Special thanks to the University of Maryland/NIST Institute for Bioscience & Biotechnology Research (IBBR) for access to their DSC equipment.

FUNDING

Funding for open access charge: Project funds.

Conflict of interest statement. None declared.

Notes

Present address: J. Alexander Liddle, 100 Bureau Drive, Gaithersburg, MD 20899-6203, USA.

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Published by Oxford University Press on behalf of Nucleic Acids Research 2020.

This work is written by (a) US Government employee(s) and is in the public domain in the US.

Kinetics and Thermodynamics of Dna Origami 2d Arrays

Source: https://academic.oup.com/nar/article/48/10/5268/5826806

Kinetics and Thermodynamics of Dna Origami 2d Arrays

Abstract

INTRODUCTION

MATERIALS AND METHODS

Test system

Data analysis: baseline and background correction

Data analysis: thermodynamics extraction

Loop entropy and worm-like chain bending model

FRET Reporter and folding strands

Persistence length

Melt experiments

Differential scanning calorimetry

RESULTS

DSC confirmation of fluorescent reporter

Melt experiments

van't Hoff analysis & heat capacity corrections

DISCUSSION

SUPPLEMENTARY DATA

ACKNOWLEDGEMENTS

FUNDING

Notes

REFERENCES

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Kinetics and Thermodynamics of Dna Origami 2d Arrays

Abstract

INTRODUCTION

MATERIALS AND METHODS

Test system

Data analysis: baseline and background correction

Data analysis: thermodynamics extraction

Loop entropy and worm-like chain bending model

FRET Reporter and folding strands

Persistence length

Melt experiments

Differential scanning calorimetry

RESULTS

DSC confirmation of fluorescent reporter

Melt experiments

van't Hoff analysis & heat capacity corrections

DISCUSSION

SUPPLEMENTARY DATA

ACKNOWLEDGEMENTS

FUNDING

Notes

REFERENCES

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