J Am Chem Soc 130(1): 93-102

Specific RNA self-assembly with minimal paranemic motifs

Introduction

In biomimetic nanotechnology one aims to construct complex, nano-scale supramolecular structures from modular units using a “bottom-up” approach inspired by biological systems. The pre-formed modular units are designed to undergo controlled and reversible self-assembly without external manipulation of individual molecules.¹,2 This approach imitates the self-assembly of complex objects in biological systems, which produce large complex structures such as ribosomes and splicesomes from smaller modular structures by hierarchical folding and assembly.³ Moreover, such biological structures are dynamic, comprise moving parts and successfully bind and release dissociable factors during functional cycles.

The use of RNA as a medium for nanotechnology, has been called “RNA tectonics” and involves three steps:⁴,5 1) Conceptual, modular design at the level of 3D structure using computer modeling techniques, 2) realization of the 3D design as the requisite supporting secondary structure and 3) detailed design of uniquely folding sequence.²,6-8 Recent work in RNA nanotechnology has resulted in the design of artificial RNA units that assemble to form oriented filaments, closed complexes, and 2D arrays.⁴,9-11 The programmed assembly of RNA monomers (“tecto-RNAs”) requires specific tertiary interactions. These can be identified in atomic-resolution 3D structures or selected in vitro using SELEX methods.¹² “Loop-receptor” interactions, which form between specific hairpin or internal loops and cognate receptor motifs, comprise an important type of tertiary motif that occurs recurrently in large biological RNA molecules. These interactions are found in all large biological RNA's. They are sufficiently weak to be readily reversible and occur in all large biological RNA structures. ⁴,5,13 Loop-receptor interactions avoid plectonemic braiding of individual RNA stem-loops, which would entangle the interacting units and therefore require unfolding of secondary structure to form. Therefore they can be considered a simple form of paranemic binding motif. The diversity of artificial RNA self-assembling modules (“RNA tectons”) is limited by the availability and specificity of receptor-loop motifs. Alternate binding motifs that allow for more programmability, while maintaining similar geometries, are desirable. This led to our investigating the suitability of the paranemic crossover motif for RNA self-assembly.

DNA nanotechnology generally utilizes stably branched DNA molecules that are assembled with structurally well-defined cohesion methods, most usually sticky-end Watson-Crick baseparing.¹⁴ This approach has been applied to construct regular 2D and 3D geometric molecular objects such as planar squares and triangles,¹⁵ and polyhedra such as cubes¹⁶ and truncated octahedral.¹⁷ Linear 2D and 3D arrays have also been developed using double -and triple-crossover junctions, both based on stable Holliday junctions.¹⁴,18,19 Recently, nano-mechanical devices have been developed such as stress gauges,²⁰ molecular switches,²¹,22 and DNA walking devices.²³ Both single and double paranemic cohesions have been utilized to assemble large objects into 2D arrays.²⁴ The development of new cohesion motifs including paranemic cohesion has played an important role in the development of DNA nanotechnology. It has been suggested that paranemic DNA structures occur also in living systems, participating in genes committed to or undergoing copying processes during replication.²⁵

The assembly of two RNA molecules to form the simplest possible paranemic motif, comprising two cross-overs and three double-helical half turns (3HT), is shown in Figure 1A. Figure 1B shows a paranemic motif with four crossovers and five half turns (5HT) and 1C shows another paranemic motif comprising six crossovers and seven half turns (7HT). As shown in Figure 1, when paranemic motifs form, the component strands cross over at every possible point and form inter-molecular Watson-Crick basepairs using all the bases not involved in intra-molecular basepairs. Moreover, intra-molecular Watson-Crick basepairs are not disturbed.²⁶,27 All Watson-Crick basepairs in Figure 1 are shown with vertical lines of varying lengths to depict the twist of the double helix. Dots indicate the non-Watson-Crick basepair that forms between the first U and the G of stable UUCG hairpin loops. For the interacting molecules forming the paranemic motif to be reversibly separable without denaturation, only an even number of crossovers and an odd number of half turns is permissible.²⁷ Because it is not possible to assemble two separate strands to create a paranemic motif comprising an even number of half turns, the smallest paranemic cohesion motif comprises three helical half turns. Figure 1 illustrates the alternating arrangement of major (M) and minor (m) grooves between cross-over points in paranemic motifs. Figure 1D shows the correspondence between designations used for DNA and RNA paranemic assembly. Previous workers chose to use the letters “W” (for wide) and “N” (for narrow) to designate the major groove and minor grooves in DNA paranemic assembly. These designations are not appropriate for RNA, because the double helix has a narrow but deep major groove and a wide but shallow minor groove. Therefore we chose “M” to designate the major groove and “m” for the minor groove, following another convention. As 3HT molecules have only two cross-over points, they can be designed so the cross-overs span either the major or minor groove. For this work we chose to span the major groove as this allows for a larger number of base pairs between non-self strands. Molecular Dynamic simulations of paranemic crossovers in DNA have indicated that the most structurally stable arrangement for the paranemic motif entails 6 basepairs in the major groove and 5 in the minor groove.²⁸ We shall refer to such complexes as “6W_5N” for DNA (consistent with previous work) and “6M_5m” for RNA.

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Figure 1

Design of RNA molecules for paranemic assembly. The cohesion of two paranemic strands designed to interact over (A) 3 half-turns (36M1 and 36M2), (B) 5 half-turns (5751 and 5752), and (C) 7 half-turns (7751 and 7752). In panels A to C, “M” indicates the major groove and “m” the minor groove. (D) Correspondence between designations used for major and minor grooves spanned by cross-overs in DNA and RNA paranemic complexes. The major groove is designated “W” in DNA and “M” in RNA paranemics, while the minor groove is designated “N” in DNA and “m” in RNA. A half-turn corresponds to between 5 and 6 basepairs. Basepairs are indicated by vertical lines connecting bases on paired RNA strands. The sugar-phosphate backbone of each strand is indicated by the thick red or blue lines.

The paranemic crossover as a cohesion motif is an attractive avenue for tecto-RNA because of the programmability of Watson-Crick base-pairing and the reversibility of binding without strand entanglement or disruption of internal helices. Here we demonstrate the feasibility of RNA paranemic assembly and characterize its specificity, binding affinity, and reversibility. We show that the minimal 3HT paranemic motif is feasible with RNA.

Material and Methods

Sequence Design

The 3HT molecules were designed with the help of two programs, RNAsoft²⁹ and Mfold.³⁰ We used the “RNA Designer” module of RNAsoft to produce over 200 possible sequences that fold into the desired secondary structure (showing Figure 1A), which comprises a stable five basepair terminal stem, a 6×6 unpaired internal loop composed of nucleotides intended to form the PX motif with a partner molecule, and a five basepair stem flanking a stable 3’-UUCG-5’ hairpin loop. The desired secondary structure was input into RNA Designer using bracket-dot notation with sequence constraints for the UUCG hairpin loop and for the 6×6 internal loop, which was taken from a paranemic crossover used in DNA. The target GC content was set to 70%. We used Mfold to check whether each strand, when folded alone, produced the desired structure and to identify sequences with relative high folding free energies. Sequences with numerous adjacent A/U basepairs were eliminated to arrive at the sequence used. The sequence obtained is designated 36M1 (ΔG = −7.4 Kcal/mol). This procedure was repeated to obtain the partner molecule 36M2 (ΔG= −11.6kcal/mol). In summary, the design strategy aimed at favoring the paranemic binding of 36M1 and 36M2 by decreasing the stability of each strand when folded alone.

The 5HT and 7HT paranemic RNA molecules were based on previously reported DNA PX sequences, ³¹,32 replacing Thymine (T) with Uracil (U), and using stable UUCG RNA tetraloops to convert DNA four-stranded systems to RNA two-strand systems.³³ The RNA molecules resemble PX dumbbell (DBs) molecules except that they are closed only on one end.²⁷ The sequences of all molecules reported in this study are provided in the figures.

RNA Preparation

RNA molecules were prepared by run-off transcription of PCR amplified DNA templates as previously described.³⁴ Synthetic DNA molecules coding for the anti-sense sequence of the desired RNA were purchased from IDT DNA (www.idtdna.com) and amplified by PCR using primers containing the T7 RNA polymerase promoter. PCR products were purified using the QiaQuick PCR purification kit (Qiagen Sciences, Maryland 20874). RNA molecules were prepared by in vitro transcription using T7 RNA polymerase (Takara Bio Inc. http://www.takara-bio.com) and purified on denaturing polyacrylamide gels (PAGE) (15% acrylamide, 8M urea). The RNA was eluted from gel slices overnight at 4°C into buffer containing 300 mM NaCl, 10 mM Tris pH 7.5, 0.5 mM EDTA, ethanol precipitated, rinsed twice with 80% ethanol, dried and dissolved in water.

Radio-labeling of RNA Molecules

T4 phosphokinase (T4PK from New England BioLabs Inc.) was used to transfer the ^{P-gamma phosphate of ATP to the 5’-end of 3’-Cytidine monophosphate (Cp) to form radio-labeled pCp. T4 RNA ligase (New England BioLabs Inc.) was used to attach radio-labeled pCP to the 3’-ends of RNA molecules (10-20 pmol). Labeled material was purified on denaturing polyacylamide gels (12% acrylamide, 19:1 bis:monomer, 8M urea).}

Assembly Experiments

Prior to the addition of the buffer and Mg(OAc)₂, RNA samples containing a fixed amount (~0.5 nM) of 3’-end labeled RNA and the unlabeled binding partner molecule (300 nM ) were heated to 90°C for one minute and immediately snap cooled on ice to avoid intermolecular base pairing. Tris-borate buffer (89 mM, pH 8.3) was added and the samples were incubated at 30°C for 5 minutes. Then Mg(OAc)₂ was added to 15 mM and incubation continued for 30 minutes. An equal volume of loading buffer (same buffer with 0.01% bromphenol blue, 0.01% xylene cyanol, 50% glycerol) was added to each sample for analysis on 7% (15:1) polyacrylamide native gels containing 15 mM Mg(OAc)₂ and run at 4°C with constant recycling of the running buffer (89 mM Tris-borate, pH 8.3/ 15 mM Mg(OAc)₂). Gels were run for 3h, at 50 mA with constant buffer recirculation, dried under vacuum, placed on a phosphor storage screen for 16 hours, and scanned using a Storm phosphoimager (Amersham, Storm 860, http://www.gehealthcare.com).

Determination of dissociation Constants (K_d)

A fixed, small amount (~0.5 nM) of 3’-end labeled RNA was mixed with increasing concentrations of the partner RNA molecule to assemble as described above and analyzed on native gels. Autoradiography was carried out using a Molecular Dynamics phosphoimaging system. Monomers and dimers were quantified using the ImageQuant software and the percentage of dimer was calculated and plotted as a function of the RNA concentration. The data were subjected to non-linear curve fitting using the MATLAB nlinfit routine to determine K_d and the nlpredci routine to determine the 95% confidence intervals for K_d. The dissociation constant for the reaction AB → A + B can be represented as:

K_d = ([A][B]) ∕ [AB] = ([A₀] − ([AB]) × ([B₀] − [AB])) ∕ [AB]

(Eq. 1)

where [A₀] and [B₀] are the initial (or total) concentrations of A and B. The way we conduct the experiments to determine K_d, the total concentration of the radiolabeled molecule, [A₀], is kept fixed and much lower than the expected K_d and all values of [B₀]. Therefore [B] ~ [B₀]. Setting r = [AB]/[A₀], which is the percentage of complex AB measured from the gel as a function B₀, Eq. 1 simplifies to Eq. 2:

K_d = (1-r)^[B₀] ∕ r

(Eq. 2)

This equation was solved for r and fit non-linearly to obtain K_d.

Lead (Pb^{)-Induced Cleavage}

RNA samples at 300 nM concentration, including a fixed amount (1 nM) of cognate 3’-end labeled RNA, were prepared as described above. After addition of 500 mM NaOAc, lead cleavage was induced by adding 60 mM Pb(OAc)₂ and stopped after 60 min by adding 100 mM EDTA followed by ethanol precipitation. RNA fragments were electrophoresed on denaturing gels for 5 hours at room temperature. The gels were washed with 5% CH₃COOH, 30% C₂H₅OH for 5 min and dried as described above. Untreated labeled RNA was run as a control, and labeled RNA samples were treated with alkali (pH 9, 90° C, 3 min) or RNase T1 to produce sequence ladders.

Sequence Design

RNA Preparation

Radio-labeling of RNA Molecules

Assembly Experiments

Determination of dissociation Constants (K_d)

K_d = ([A][B]) ∕ [AB] = ([A₀] − ([AB]) × ([B₀] − [AB])) ∕ [AB]

(Eq. 1)

K_d = (1-r)^[B₀] ∕ r

(Eq. 2)

This equation was solved for r and fit non-linearly to obtain K_d.

Lead (Pb^{)-Induced Cleavage}

Results

Designs of RNA Molecules for Paranemic Assembly

First we explain the abbreviations used to specify the designed molecules. The abbreviations reflect the characteristics of the PX complexes they are intended to form. These characteristics include the length of the paranemic motif in half-turns, the number of basepairs between cross-over points in the major (M) groove or minor (m) groove (when relevant), and the strand number (either S1 or S2). For example, the molecule designated 5HT_7M_5m_S1 (or 5751), is the first strand of a pair of complementary molecules designed to form a motif of five half-turns, with seven basepairs between cross-overs in the major groove and five basepairs in the minor groove. It is designed to bind paranemically to 5752. An additional lower case letter after some sequence numbers was used to indicate sequences with point mutations. The number of half-turns in each helical domain flanking the central dyad axis is achieved by successful formation of the paranemic complex.²⁷ The central dyad axis lies horizontally between the assembled strands, passing through each crossover point (see Figure 1). For 3HT molecules, only one number is needed to indicate the number of basepairs between cross-over points, as there are only two. In the present work, the 3HT RNA molecules were designed to cross-over the major groove and so no minor groove designation is needed. For example molecule 3HT_6M_S1 (or 361) indicates strand one of the molecule with 6 basepairs between cross-over points spanning the major groove.

Paranemic RNA Self-assembly

Paranemic assembly was assayed using native polyacrylamide gel electrophoresis as described in the Methods. For each pair of paranemic molecules, a small amount of the radio-labeled strand was mixed with increasing amounts of the complementary unlabeled strand. A representative gel is shown in Figure 2. For each set of paranemic molecules, the first lane on the gel contains only the radio-labeled strand at a concentration of ~0.5 nM while in the adjacent lanes, the radio-labeled strand (~0.5nM) is titrated with increasing amounts of the second, unlabelled strand assay formation paranemic complexes. Formation of complexes was indicated by the appearance of a new band on the gel with the mobility expected for a dimer as determined by comparison to mobility controls, 3HT and 4HT (lanes 1 and 2 of Figure 2). Molecules 3HT (65 nucleotides) and 4HT (90 nucleotides) are H-shaped RNA molecules composed of a single 4-way junction connecting two adjacent helices. Thus, molecule 3HT is equivalent in size and shape to the 3HT paranemic complexes while 4HT is intermediate in size between paranemic 3HT and 5HT complexes.¹⁰ Additional bands with mobilities slower than dimer complexes were only observed in significant amounts for 7HT complexes and are attributed to multimer complexes.

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Figure 2

Native gel electrophoresis assay of formation of paranemic RNA complexes with 3, 5, and 7 half-turns (3HT, 5HT and 7HT complexes). Lanes 1 and 2 are size markers 3HT and 4HT. Concentrations of unlabeled molecules are given in μM units. The radio-labeled strand in each lane is indicated by (*) and is present at ~0.5 nM. Each series of experiments is separated by vertical bars. The first lane in each series contains only the labeled monomer strand. The monomer bands are indicated with “m”, dimers with “d”, and multimers by “M”.

Figure 2 shows assays for the formation of RNA paranemic complexes 3HT_6M (lanes 3-5), 5HT_5M_5m (lanes 6-7), 5HT_6M_5m (lanes 8-10), 5HT_7M_5m (lanes 11-13), 5HT_8M_5m (lanes 17-18) and 7HT_7M_5m (lanes 19-21). Lanes 3 - 5 demonstrate the successful assembly of a 3HT complex by molecules 36M1* and 36M2. Lanes 6 and 7 show that even with addition of 5552 at 1 μM concentration the assembly of 5551* and 5552 is not complete. Lanes 8-10 show that 5651* and 5652 assemble at 0.5 μM concentration to form dimers with only a trace amount of monomer still present. Lanes 11-16 show that assembly of 5751 and 5752 is complete at 0.5μM and does not depend on which strand is labeled, 5751 or 5752. Lanes 17-18 show that the complex 5851/5852 forms readily at 1.0μM concentration, but a faint band occurs above the dimer, that can be attributed to a multimer complex. Lanes 19-21 show the assembly of the 7HT complex, 7751/7752, which forms a significant amount of a multimer band in addition to the dimer band.

Using Pb(II) to probe the formation of paranemic complexes

Pb(II) is widely used as a conformational probe for RNA because it preferentially cleaves the phosphodiester backbone in non-canonically paired motifs or flexible regions of RNA molecules.³⁴ Pb(II) cleavage experiments were carried out to confirm that in the binding of 36M1 and 36M2, which was shown to occur using native electrophoresis (see Figure 2), the predicted inter-molecular basepairs do in fact form and that 3HT paranemic assembly does indeed occur when 36M1 binds to 36M2. Radio-labeled 36M2 was treated with Pb(II) in the monomer form and in the presence of an excess of 36M1 as described in Materials and Methods and the results are shown in Figure 3. The products of the cleavage reaction are run on denaturing gels, which separate the strands by length with nucleotide resolution. Only fragments bearing the intact 3’-end which contains the radio-label are visible on the autoradiogram shown in Figure 3, allowing one to determine where the cleavage occurs. Figure 3 lane 2 shows that molecule 36M2, in the monomer state, was cleaved by Pb(II) at nucleotides 6-11 and 26-31, which correspond to the position of the internal loop that is intended to form the paranemic interaction, and at nucleotides 17-20, which correspond to the UUCG hairpin loop. The gel data are summarized in the schematic diagrams, which show the correspondence between bands on the gel and nucleotides in the sequence. Thus, as expected, nucleotides 6-11 and 26-31, which are not expected to base pair in the monomer, are sensitive to Pb(II)-cleavage. When bound to 36M1, however, 36M2 is preferentially cleaved by Pb(II) in the hairpin loop, nucleotides 17-20, and not at the nucleotides of the internal loop (Figure 3, lane 3). Because 36M2 is radioactively end-labeled, RNA fragments that result from more than one cut are not visualized by autoradiography. The results shown in Figure 3 thus provide evidence that assembly does in fact occur by formation of the desired paranemic motif.

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Figure 3

Pb^{probing of}36M2* in the monomer form and complexed with 36M1. (Right) Denaturing gel analysis of Pb^{probing of radiolabeled}36M2 (10 nM) in the monomer state and complexed to 36M1 (0.3 μM). “OH” indicates alkali-treated RNA. (Left) Arrows indicate Lead(II)-induced cleavages within molecule 36M2 in the monomer state (upper left) and complexed to 36M1 (lower left). The red star indicates the labeled 3’-end of 36M2.

Kinetic Exchange

One of the salient characteristics of paranemic cohesion is that interacting molecules bind to each other without unfolding internal helices and thus are not braided plectonemically. One therefore expects binding to be reversible. In other words, the paranemically bound strands should be able to dissociate without the need to raise the temperature to denature the internal structure of the monomers. To test this we carried out kinetic exchange experiments on the 36M complex at 30°C. Figure 4A provides the scheme for the exchange reaction employed in these experiments.

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Figure 4

Kinetic exchange of 36M1/36M2 complexes. (A) Schematic representation of the kinetic exchange which results from dissociation of the pre-formed, unlabeled complex composed of 36M1 (in red) and 36M2 (in light blue) and formation of the labeled complex composed of 36M1 bound to labeled 36M2* (dark blue), displacing unlabeled 36M2 (light blue). (B Left) Radiolabeled 36M2* (0.5 nM) was added (at time = 0) to the pre-formed complex of unlabeled 36M2 (0.4 μM) and 36M1 (0.3 μM). Aliquots were withdrawn at the indicated times and frozen immediately on dry ice. Samples were thawed and loaded on native gels for analysis in reverse order. (B Right) The data from two separate gels were combined and fitted with a single exponentially decaying curve, giving the exchange half-time t_1/2= 100 ± 12 minutes.

First, a stoichiometric excess (0.4μM) of unlabeled 36M2 (shown in light blue) was mixed with 0.3 μM unlabeled 36M1 (shown in red) at 30°C in the presence of 15 mM Mg^{as described in Methods, to form the paranemic complex. At time = 0, a small amount (~0.5 nM) of radio-labeled}36M2* (shown in dark blue) was added to initiate the exchange reaction between the unlabeled 36M2 strands in the complex and the free, radio-labeled 36M2* monomers in solution. Aliquots (10μl) were taken at successive time intervals, mixed with loading buffer (10μl, 0°C) containing 15 mM Mg^{and immediately placed on dry ice to stop the reaction. Samples were loaded on native analysis gels in reverse order of withdrawal to minimize the time between loading and running for aliquots with short incubation times. A representative autoradiogram of an exchange experiment is shown in}Figure 4B.

As shown in the scheme in Figure 4, panel A, radio-labeled 36M2* can only bind to 36M1 molecules that have first dissociated from unlabelled 36M2. Upon complex formation, the radio-labeled monomers make the detection of the exchange reaction products possible and thus provide a tool for monitoring the exchange kinetics until equilibrium is again reached, at which point the radioactive 36M2 is distributed between monomer and dimer in a ratio of ~1:3. This ratio is set by the 0.1 μM excess in the total concentration of 36M2 (0.4 μM) compared to the total 36M1 concentration (0.3 μM). Thus the maximum concentration of dimer is limited by the concentration of 36M1 to no more than 0.3 μM in which case the monomer concentration is 0.1 μM. A complete analysis of the exchange kinetics is provided in the Supporting Information.

Lane 1 is the monomer 36M2* as a control. Lanes 2-19 are aliquots taken at the indicated times after addition of 36M2*. Within 30 seconds a noticeable amount of free 36M2* has incorporated into the complex, and by about two hours equilibrium is reached. The data were analyzed by non-linear fitting to single exponential curves. A pseudo-first order rate constant of 9.8×10^min^{(corresponding t}_1/2=100 ± 12 min) was obtained from the fitting. Dissociation and association constants k_d and k_a were calculated as described in the Supporting Information and found to be k_d = 5.11×10^sec^{and k}_a = 5.11×10^M^sec^{. From the value of k}_d an exchange half time (T_1/2) for 36M1/36M2 complex was determined to be T_1/2 = 220 min.

The kinetic exchange experiment reveals that RNA paranemic complexes do in fact disassemble and reassemble at significant rates below the expected melting temperatures. This shows that the 3HT paranemic complex is dynamic, yet also relatively stable kinetically, with a half-life of almost four hours.

Sequence Specificity

To be useful for RNA nanotechnology, paranemic assembly motifs must display sufficient sequence specificity and programmability. We examined two aspects of specificity – matching of the number of bases between cross-over points and Watson-Crick complementarity of bases programmed to pair. Therefore, we attempted to assemble pairs of strands that differed either in the number of expected base pairs between cross-over points or in Watson-Crick base complementarity for inter-molecular basepairs. An experiment involving 5HT molecules is shown in Figure 5. In these experiments, all labeled molecules are present at 0.5 nM. Lanes 1 and 2 are the mobility markers 3HT and 4HT. In lanes 3 through 5, labeled 5651* is run alone, in the presence of its complement, 5652, and with 5552. Molecule 5551 is the complement of molecule 5552 and has two fewer nucleotide pairs than 5651 in the major (M) groove. The sequence of 5552 differs from that of 5652 by the elimination one basepair for each wide groove crossover segment, and there are two wide grooves for 5HT paranemic assemblies. These sequence alterations are illustrated in the lower part of Figure 5. Lanes 3-5 show that 5651 only assembles in the presence of its complement 5652.

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Figure 5

Molecule 5651 assembles paranemically with 5652 but not 5552. Molecules 5651 and 5652 form six basepairs in the major groove, whereas 5552 can only form five. (Upper panel) Lanes 1 and 2: size markers; lanes 3 to 5: 5651* (0.5 nM) alone; with 5652 (1.0μM); with 5552 (1.0μM). (Lower panel) The sequences of 5552 and 5652 are compared. Red letters indicate insertions; dark blue letters indicate the terminal UUCG tetraloops.

To demonstrate the base-pairing specificity of a paranemic strand for its complement, molecules 5752b, 5752c, and 5752d were prepared which differ from 5752 by one or two base substitutions. These molecules are identical to 5752 except for the base changes shown in Figure 6A. These changes occur only in the major groove between cross-over points, and do not affect the free energy of folding of individual strands, in agreement with folding predictions carried out for the individual strands using Mfold, which showed that the mutations did not change the pre-folding of the monomers. The results of the gel in Figure 6B show that when molecule 5751 is mixed with 5752b* (lane 6), 5752c* (lane 7), or 5752d* (lane 8), the monomer is favored. The results also show that a single WC mismatch (5752b) compromises dimer assembly, and two WC mismatches (5752c and 5752d) largely prevent it, even at 1.0μM concentration. Given the large number of basepairs formed when 5HT complexes form, it is not surprising that some assembly occurs when there is a single mismatch, as in the 5751/5752b complex. Therefore, further studies were carried out on the 3HT system.

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Figure 6

Specificity of paranemic assembly for the 5HT system. (A) Point mutations introduced in 5752 to test binding specificity. In 5752b one substitution is present, in 5752c two substitutions are present in the same groove, and in 5752d two substitutions are present in different grooves. (B) Sequence specificity assembly experiments in which unlabeled 5751 is mixed with labeled 5752b*, 5752c* and 5752d*.

Figure 7 shows experiments in which single nucleotide substitutions and compensating changes were made in molecules 36M1 and 36M2. New molecules 36M1a and 36M2a have compensating mutations at the crossover point while 36M1b and 36M2b have compensating mutations one base-pair away from the crossover point. Assembly experiments shown in the left panel of Figure 7 demonstrated that for any combination of molecules having one basepair mismatch, paranemic assembly does not occur. This includes 36M1/36M2a, 36M1/36M2b, 36M1a/36M2, 36M1a/36M2b, and 36M1b/36M2a, however 36M1b/36M2 forms some dimer but not in a clear fashion. Dimer formation is restored in the 36M1a/36M2a and 36M1b/36M2b pairs which contain compensating substitutions that restore intermolecular Watson-Crick basepairing.

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Figure 7

Specificity of RNA paranemic assembly with 3HT molecules. (Left) Native PAGE gel shows that cognate paranemic molecules 36M1+36M2, 36M1a+36M2a, and 36M1b+36M2b, all form dimer complexes, while non-cognate pairs 36M1a+36M2, 36M1a+36M2b, 36M1b+36M2, and 36M1b+36M2a, do not. Radiolabeled molecules are indicated by * and are at 0.5nM, while unlabeled molecules are at 50 nM. (Right) the mutations (indicated by colors) introduced in 36M1 and 36M2 to test the specificity of binding. Molecules 36M1a and 36M2a contain compensating mutations, as do 36M1b and 36M2b.

We also studied the effect of major (M) groove size on the paranemic assembly of 3HT molecules (Figure 8). New pairs of molecules 3iM1 and 3iM2, with i = 4, 5, 6, 7 and 8, were designed by modification of 36M1 and 36M2 by insertion or deletion of complementary nucleotides. The sequences of all of these molecules are shown in Figure 8B. Native PAGE gel experiments show that paranemic molecules 38M1/385M2, 37M1/37M2, 35M1/35M2 and 37M1/38M2, all form dimer complexes. 37M1/38M2 is the only complex formed by two molecules that differ in the number of bases between cross-over points. Interestingly, 34M1 does not assemble with any other molecule, not even 34M2.

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Figure 8

Effect of a groove size on paranemic assembly with 3HT molecules. (A) Native PAGE gel shows that only combinations of 38M1+38M2, 37M1+37M2, 35M1+35M2 and 37M1+38M2, form paranemic dimer complexes. Radiolabeled molecules are indicated by * and are at 0.5nM, while unlabeled molecules are at 200 nM. (B) Sequences of all molecules used for this experiment. Red letters indicate insertion mutations. Red gaps indicate deletion mutations.

Determination of Dissociation Constant for 3HT complexes

We determined the binding affinity of the 3HT paranemic cognate complexes 35M1/35M2, 36M1/36M2, 37M1/37M2 (Figure 9), 38M1/38M2, and the non-cognate complex 38M1/37M2. The fraction of dimer was determined by native gel electrophoresis using a fixed amount of radiolabeled 35M2, 36M2, 37M2, and 38M2 (~0.5nM). The concentrations of added unlabelled molecules 35M1, 36M1, 37M1, and 38M1 were varied from 1 nM to 3.0 μM. The relative concentrations of monomer and dimer bands were determined by integrating the autoradiograms. The percentage of dimer was plotted as a function of total concentration of the added, unlabeled molecule and the data were subjected to non-linear fitting as described in Methods to obtain the dissociation constants (K_d) and 95% confidence ranges for the non-linear fitting. The K_d's, presented in Table 1, show that the most stable 3HT complexes are obtained with 6 basepairs in the major groove between the cross-over points.

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Figure 9

Determination of the dissociation constants (K_d's) for 35M1/35M2, 36M1/36M2, and 37M1/37M2 dimers. (A) Schematic representation of the assembly process for 36M1 and radiolabeled 36M2* paranemic molecules. (B) Radiolabeled 35M2*, 36M2*, and 37M2* (~0.5nM) were titrated with increasing amounts on 35M1, 36M1, and 37M1 (indicated in _M units). C: Quantification of gel data for K_d determinations, each represents combined fitting of 2 datasets. The Axes are marked in units of nM.

Table 1

Dissociation constants (K_d′s) determined for selected 3HT complexes. K_d's were obtained by non-linear data fitting of native gel data as described under Methods. Fitted K_d values are reported with 95% confidence intervals.

	K_d's in nM (95% confidence limits)
Complexes	Experiment 1	Experiment 2	Combined data
35M1/35M2	99 (40 to 159) nM	94 (40-148) nM	97 (63-131) nM
36M1/36M2	16 (4 to 27) nM	7 (5 to 10) nM	10 (6 to 14) nM
37M1/37M2	74 (47 to 102) nM	49 (25 to 73) nM	61 (43 to 78) nM
38M1/38M2	169 (81 to 257) nM
38M1/37M2	183 (92 to 274) nM

Designs of RNA Molecules for Paranemic Assembly

Table 1

	K_d's in nM (95% confidence limits)
Complexes	Experiment 1	Experiment 2	Combined data
35M1/35M2	99 (40 to 159) nM	94 (40-148) nM	97 (63-131) nM
36M1/36M2	16 (4 to 27) nM	7 (5 to 10) nM	10 (6 to 14) nM
37M1/37M2	74 (47 to 102) nM	49 (25 to 73) nM	61 (43 to 78) nM
38M1/38M2	169 (81 to 257) nM
38M1/37M2	183 (92 to 274) nM

Discussion

The results presented show that specific, reversible, yet high-affinity RNA self-assembly can be achieved with minimal 3HT paranemic motifs in which the two cross-over points span the major groove. The K_d determinations clearly show that 3HT_6M motifs, which comprise six basepairs between the cross-over points, are most stable (K_d ~ 10 nM) by almost an order of magnitude compared to the next most stable, the 3HT_5M motifs (K_d ~ 100 nM) and the 3HT_7M motifs (K_d ~ 60 nM) of similar sequence. Nonetheless the 3HT_5M and 3HT_7M paranemic motifs are worth studying further, as the binding affinities can be expected to vary considerably depending on the sequence. Moreover, these three motif families appear to be largely orthogonal to each other, showing little binding affinity for each other, even when they share almost identical sequences. The one exception is the binding of 3HT_8M to 3HT_7M. The K_d measurements show that 3HT_8M1 binds 3HT_8M2 and 3HT_7M2 with comparable affinity. The gel experiment in Figure 8 shows further that 3HT_8M2 binds 3HT_7M1. This suggests that all the inter-strand basepairs may not be forming in the 3HT_8M complexes. Further work will be needed to clarify this point.

Twelve inter-molecular Watson-Crick basepairs, six in each helix, form during 3HT_6M paranemic assembly. The average number of nucleotide pairs per helical turn is ~11 for RNA, while the number of pairs in the 5HT complexes obtained in this work is 11 basepairs for the 6:5 (M:m) complexes, 12 for 7:5 and 13 for 8:5. In DNA, Molecular Dynamics (MD) simulations have suggested that the extra nucleotide pairs are accommodated primarily by a change in the writhing of the helix axis.²⁵ This writhing, which can lead to twisting of the individual helices around the central dyad access, may be essential for paranemic binding, and is therefore accommodated by the excess of basepairs over the normal 11 basepairs per turn.

This work shows that a single base mismatch disrupts assembly in 3HTM complexes at relevant concentrations (nano- to micro-molar) and that compensating base substitutions that restore Watson-Crick basepairing restore binding affinity. These results are consistent with the Pb^{-cleavage data that show that the internal loop that participates in inter-molecular basepairing is susceptible to hydrolysis in the monomer state, but is protected in the dimer state. Likewise, the kinetic exchange data lends further support to the conclusion that the desired paranemic complexes form.}

The 3HTM paranemic crossover motif thus offers a repertoire of complementary receptors that bind through programmable Watson-Crick base pairing but are completely unlinked topologically, facilitating reversible assembly and complex and dynamic functional cycles. The incorporation of stable UNCG tetraloops to link pairs of RNA strands favors pre-folding of each monomer in the desired stem-loop structure required for paranemic assembly.

Conclusion

The interest in RNA as a medium for nano-technology resides in its ability to form complex, dynamic, protein-like structures, stabilized by extensive tertiary interactions, with the design advantages and programmability of DNA. Important molecular machines in the cell, such as ribosomes and splicesomes, are RNA-based. Biological RNA molecules rely on long-range, tertiary interactions to initiate, guide and stabilize the compactly folded 3D structures required for their functioning. RNA molecular machines rely on reversible tertiary and quaternary interactions to cycle between functional states. In the “bottom-up” approach to nanotechnology, large complex structures are produced by self-assembly of smaller, pre-folded units presenting interaction motifs in the appropriate orientations. This approach requires an extensive library of high affinity, high specificity interaction motifs. RNA-RNA interaction motifs, identified in 3D structures of biological RNAs, including kissing hairpins, pseudoknots, and loop-receptor interactions, have been used in the design of self-assembling RNA molecules. Additional motifs have been identified in sequence libraries or have been selected by in vitro combinatorial methods. However the number of tertiary RNA interacting motifs that is currently available is still limited and many are not as specific as desirable for nanotechnology applications. There is therefore a clear need for additional interaction motifs for RNA nanotechnology, ones that are programmable, specific, reversible, and that have adequate (and tunable) binding affinities. The minimal paranemic 3HT motifs explored in this work meet these criteria.

The kinetic studies show that RNA PX assembly with 3HT is reversible. As for DNA, RNA PX assembly does not require plectonemic braiding and complexes can form from pre-annealed hairpin molecules without disrupting internal basepairs. This result opens avenues for RNA design that exploit the specificity and programmability of the PX motif to design molecular switches that do not require denaturation to undock, as has been partially explored with the DNA PX/JX switching machine.²⁴

The similarity between Watson-Crick RNA paranemic cohesion explored in this paper and the loop-receptor interactions that are commonly observed in large RNA molecules is noteworthy. Therefore, this system will enhance tecto-RNA design, taking advantage of the same principles that make loop-receptor interactions appealing, but with the additional benefit of programmability to provide greater variety and flexibility of molecular design.

Supplementary Material

1si20071018_04

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1si20071018_04

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Acknowledgments

The authors thank Irina V. Novikova and Jennifer L. Benson for technical assistance and professor Michael A. J. Rodgers of the Ohio Laboratory for Kinetic Spectrometry for helpful discussion. This work was supported by grants from the American Chemical Society (ACS PRF# 42357-AC 4) and the National Institutes of Health (2 R15GM055898-04).

^{Department of Chemistry and Center for Photochemical Sciences, Bowling Green State University, Bowling Green, OH 43403, USA.}

^{Department of Chemistry and Center for Biomolecular Sciences, Bowling Green State University, Bowling Green, OH 43403, USA.}

^{Corresponding author,}ude.usgb@sitnoel

Abstract

The paranemic crossover (PX) is a motif for assembling two nucleic acid molecules using Watson-Crick (WC) basepairing without unfolding pre-formed secondary structure in the individual molecules. Once formed, the paranemic assembly motif comprises adjacent parallel double helices that cross over at every possible point over the length of the motif. The interaction is reversible as it does not require denaturation of basepairs internal to each interacting molecular unit. Paranemic assembly has been demonstrated for DNA but not for RNA, and only for motifs with four or more cross-over points and lengths of five or more helical half-turns. Here we report the design of RNA molecules that paranemically assemble with the minimum number of two cross-overs spanning the major groove to form paranemic motifs with a length of three half-turns (3HT). Dissociation constants (K_ds) were measured for series of molecules in which the number of basepairs between the cross-over points was varied from five to eight basepairs. The paranemic 3HT complex with six basepairs (3HT_6M) was found to be the most stable with K_d = 1×10^{M. The half-time for kinetic exchange of the 3HT_6M complex was determined to be ~100 minutes, from which we calculated association and dissociation rate constants k}_a = 5.11×10^M^sec^andk_d = 5.11×10^sec^{. RNA paranemic assembly of 3HT and 5HT complexes is blocked by single-base substitutions that disrupt individual inter-molecular Watson-Crick basepairs and is restored by compensatory substitutions that restore those basepairs. The 3HT motif appears suitable for specific, programmable, and reversible tecto-RNA self-assembly for constructing artificial RNA molecular machines.}

Keywords: RNA Motif, RNA Nanotechnology, Self-assembly, Paranemic Crossover Motif

Abstract

Footnotes

Supporting information is available. Detailedanalysis concerning the calculation of association and dissociation constants (k_d and k_a) are from the kinetic data for 36M1 and 36M2 are provided.

Footnotes

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Specific RNA self-assembly with minimal paranemic motifs

Introduction

Material and Methods

Sequence Design

RNA Preparation

Radio-labeling of RNA Molecules

Assembly Experiments

Determination of dissociation Constants (Kd)

Lead (Pb)-Induced Cleavage

Sequence Design

RNA Preparation

Radio-labeling of RNA Molecules

Assembly Experiments

Determination of dissociation Constants (Kd)

Lead (Pb)-Induced Cleavage

Results

Designs of RNA Molecules for Paranemic Assembly

Paranemic RNA Self-assembly

Using Pb(II) to probe the formation of paranemic complexes

Kinetic Exchange

Sequence Specificity

Determination of Dissociation Constant for 3HT complexes

Table 1

Designs of RNA Molecules for Paranemic Assembly

Paranemic RNA Self-assembly

Using Pb(II) to probe the formation of paranemic complexes

Kinetic Exchange

Sequence Specificity

Determination of Dissociation Constant for 3HT complexes

Table 1

Discussion

Conclusion

Supplementary Material

1si20071018_04

1si20071018_04

Acknowledgments

Abstract

Footnotes

REFERENCES

References

Determination of dissociation Constants (K_d)

Lead (Pb^{)-Induced Cleavage}

Determination of dissociation Constants (K_d)

Lead (Pb^{)-Induced Cleavage}