Nucleobase participation in ribozyme catalysis

We constructed a modified form of the VS ribozyme containing an imidazole ring in place of adenine at position 756. The novel ribozyme is active in both cleavage and ligation reactions. The reaction is efficient, although relatively slow. The results are consistent with a role for nucleobase catalysis in the catalytic mechanism of this ribozyme.     

Active site labeling of G8 in the hairpin ribozyme: implications for structure and mechanism

There is mounting evidence that suggests that general acid/base catalysis is operative in the hairpin ribozyme, with analogy to the protein enzyme RNaseA. Nevertheless, the extent of general base catalysis as well as the identity of the specific chemical groups responsible remains the subject of some controversy. An affinity label has previously been used to alkylate histidine 12 (His12), the active general base in RNaseA. To date, no such experiment has been applied to a ribozyme. We have synthesized the analogous affinity label for the hairpin ribozyme with an electrophilic 2'-bromoacetamide group in lieu of the 2'-hydroxyl (2'OH) at the substrate cleavage site and show that guanosine 8 (G8) of the hairpin ribozyme is specifically alkylated, most likely at the N1 position. This evidence strongly implicates N1 of G8 in active site chemistry. By direct analogy to RNase A, these findings could be consistent with the hypothesis that deprotonated G8 residue functions as a general base in the hairpin ribozyme. Other mechanistic possibilities for N1 of G8 such as indirect general base catalysis mediated by a water molecule or transition state stabilization could also be consistent with our findings.     

Essential role of an active-site guanine in glmS ribozyme catalysis

The glmS ribozyme is a catalytic riboswitch that is activated for endonucleolytic cleavage by the coenzyme glucosamine-6-phosphate. Using kinetic assays and X-ray crystallography, we identify an active-site mutation of a conserved guanine that abolishes catalysis without perturbing coenzyme binding. Our results provide evidence that coenzyme function requires a specific nucleobase to interact with the nucleophile of the cleavage reaction.     

Solvent structure and hammerhead ribozyme catalysis

Although the hammerhead ribozyme is regarded as a prototype for understanding RNA catalysis, the mechanistic roles of associated metal ions and water molecules in the cleavage reaction remain controversial. We have investigated the catalytic potential of observed divalent metal ions and water molecules bound to a 2 A structure of the full-length hammerhead ribozyme by using X-ray crystallography in combination with molecular dynamics simulations. A single Mn(2+) is observed to bind directly to the A9 phosphate in the active site, accompanying a hydrogen-bond network involving a well-ordered water molecule spanning N1 of G12 (the general base) and 2'-O of G8 (previously implicated in general acid catalysis) that we propose, based on molecular dynamics calculations, facilitates proton transfer in the cleavage reaction. Phosphate-bridging metal interactions and other mechanistic hypotheses are also tested with this approach.     

Fast cleavage kinetics of a natural hammerhead ribozyme

The hammerhead ribozyme is a small RNA motif that catalyzes the cleavage and ligation of RNA. The well-studied minimal hammerhead motif is inactive under physiological conditions and requires high Mg(2+) concentrations for efficient cleavage. In contrast, natural hammerheads are active under physiological conditions and contain motifs outside the catalytic core that lower the requirement for Mg(2+). Single-turnover kinetics were used here to characterize the Mg(2+) and pH dependence for cleavage of a trans-cleaving construct of the Schistosoma mansoni natural hammerhead ribozyme. Compared to the minimal hammerhead motif, the natural Schistosoma ribozyme requires 100-fold less Mg(2+) to achieve a cleavage rate of 1 min(-1). The improved catalysis results from tertiary interactions between loops in stems I and II and likely arises from increasing the population of the active conformation. Under optimum pH and Mg(2+) conditions this ribozyme cleaves at over 870 min(-1) at 25 degrees C, further demonstrating the impressive catalytic power of this ribozyme.     

An unusual pH-independent and metal-ion-independent mechanism for hairpin ribozyme catalysis

Background: Hairpin ribozymes (RNA enzymes) catalyze the same chemical reaction as ribonuclease A and yet RNAs do not usually have functional groups analogous to the catalytically essential histidine and lysine sidechains of protein ribonucleases. Some RNA enzymes appear to recruit metal ions to act as Lewis acids in charge stabilization and metal-bound hydroxide for general base catalysis, but it has been reported that the hairpin ribozyme functions in the presence of metal ion chelators. This led us to investigate whether the hairpin ribozyme exploits a metal-ion-independent catalytic strategy.Results: Substitution of sulfur for nonbridging oxygens of the reactive phosphate of the hairpin ribozyme has small, stereospecific and metal-ionindependent effects on cleavage and ligation mediated by this ribozyme. Cobalt hexammine, an exchange-inert metal complex, supports full hairpin ribozyme activity, and the ribozyme's catalytic rate constants display only a shallow dependence on pH.Conclusions: Direct metal ion coordination to phosphate oxygens is not essential for hairpin ribozyme catalysis and metal-bound hydroxide does not serve as the general base in this catalysis. Several models might account for the unusual pH and metal ion independence: hairpin cleavage and ligation might be limited by a slow conformational change; a pH-independent or metalcation-independent chemical step, such as breaking the 5′ oxygen-phosphorus bond, might be rate determining; or finally, functional groups within the ribozyme might participate directly in catalytic chemistry. Whichever the case, the hairpin ribozyme appears to employ a unique strategy for RNA catalysis.     

Catalysis of diribonucleoside monophosphate cleavage by water soluble copper(II) complexes of calix[4]arene based nitrogen ligands

Calix[4]arenes functionalized at the 1,2-, 1,3-, and 1,2,3-positions of the upper rim with [12]ane-N(3) ligating units were synthesized, and their bi- and trimetallic zinc(II) and copper(II) complexes were investigated as catalysts in the cleavage of phosphodiesters as RNA models. The results of comparative kinetic studies using monometallic controls indicate that the subunits of all of the zinc(II) complexes and of the 1,3-distal bimetallic copper(II) complex 7-Cu(2) act as essentially independent monometallic catalysts. The lack of cooperation between metal ions in the above complexes is in marked contrast with the behavior of the 1,2-vicinal bimetallic copper(II) complex 6-Cu(2), which exhibits high catalytic efficiency and high levels of cooperation between metal ions in the cleavage of HPNP and of diribonucleoside monophosphates NpN'. A third ligated metal ion at the upper rim does not enhance the catalytic efficiency, which excludes the simultaneous cooperation in the catalysis of the three metal ions in 8-Cu(3). Rate accelerations relative to the background brought about by 6-Cu(2) and 8-Cu(3) (1.0 mM catalyst, water solution, pH 7.0, 50 degrees C) are on the order of 10(4)-fold, largely independent of the nucleobase structure, with the exception of the cleavage of diribonucleoside monophosphates in which the nucleobase N is uracil, namely UpU and UpG, for which rate enhancements rise to 10(5)-fold. The rationale for the observed selectivity is discussed in terms of deprotonation of the uracil moiety under the reaction conditions and complexation of the resulting anion with one of the copper(II) centers.     

Quantum mechanical/molecular mechanical simulation study of the mechanism of hairpin ribozyme catalysis

The molecular mechanism of hairpin ribozyme catalysis is studied with molecular dynamics simulations using a combined quantum mechanical and molecular mechanical (QM/MM) potential with a recently developed semiempirical AM1/d-PhoT model for phosphoryl transfer reactions. Simulations are used to derive one- and two-dimensional potentials of mean force to examine specific reaction paths and assess the feasibility of proposed general acid and base mechanisms. Density-functional calculations of truncated active site models provide complementary insight to the simulation results. Key factors utilized by the hairpin ribozyme to enhance the rate of transphosphorylation are presented, and the roles of A38 and G8 as general acid and base catalysts are discussed. The computational results are consistent with available experimental data, provide support for a general acid/base mechanism played by functional groups on the nucleobases, and offer important insight into the ability of RNA to act as a catalyst without explicit participation by divalent metal ions.     

Electrochemical Detection of Abasic Site‐Containing DNA

A simple and rapid approach for detecting apurinic (AP) sites in DNA, based on direct stripping chronopotentiometric measurements of the adenine and guanine nucleobases at a graphite electrode is described. Tetrahydrofuranyl residues, lacking a nucleobase moiety, were utilized for designing the AP sites and were incorporated in 19‐mer oligonucleotides. The change of adenine‐to‐guanine response ratio (A/G) in one‐, two‐ or three‐substituted adenosine residues for stable analogs of AP sites was exploited for electrochemical measurements of the adenine loss. The resulting A/G response ratio decreases linearly upon increasing the number of AP sites in the oligonucleotides; the values of A/G electrochemical signals were slightly enhanced when compared to the actual purine content. HPLC analysis of the released nucleobases confirmed that the sulfuric acid‐induced oligonucleotide cleavage provides complete apurination and dissolution of the released nucleobases in aqueous solution. Additional experiments with mixtures of free nucleobases and purine nucleosides reveal that the larger A/G ratio observed in the electrochemical analysis of AP‐site‐containing oligomers is attributed to the influence of the acid and/or thermal decomposition products (particularly the sugar fragments). This study represents the first step in developing a simple and direct electrochemical assay of AP sites in single‐stranded DNA.     

Cross-modulation of the pKa of nucleobases in a single-stranded hexameric-RNA due to tandem electrostatic nearest-neighbor interactions

The pH titration studies (pH 6.7-12.1) in a series of dimeric, trimeric, tetrameric, pentameric, and hexameric oligo-RNA molecules [GpA (2a), GpC (3a), GpApC (5), GpA(1)pA(2)pC (6), GpA(1)pA(2)pA(3)pC (7), GpA(1)pA(2)pA(3)pA(4)pC (8)] have shown that the pK(a) of N(1)-H of 9-guaninyl could be measured not only from its own deltaH8G, but also from the aromatic marker protons of other constituent nucleobases. The relative chemical shift differences [Deltadelta((N)(-)(D))] between the protons in various nucleotide residues in the oligo-RNAs at the neutral (N) and deprotonated (D) states of the guanine moiety show that the generation of the 5'-(9-guanylate ion) in oligo-RNAs 2-8 reduces the stability of the stacked helical RNA conformation owing to the destabilizing anion(G(-))-pi/dipole(Im(delta)(-)) interaction. This destabilizing effect in the deprotonated RNA is, however, opposed by the electrostatically attractive atom-pisigma (major) as well as the anion(G(-))-pi/dipole(Py(delta)(+)) (minor) interactions. Our studies have demonstrated that the electrostatically repulsive anion(G(-))-pi/dipole(Im(delta)(-)) interaction propagates from the first to the third nucleobase quite strongly in the oligo-RNAs 6-8, causing destacking of the helix, and then its effect is gradually reduced, although it is clearly NMR detectable along the RNA chain. Thus, such specific generation of a charge at a single nucleobase moiety allows us to explore the relative strength of stacking within a single-stranded helix. The pK(a) of 5'-Gp residue from its own deltaH8G in the hexameric RNA 8 is found to be 9.76 +/- 0.01; it, however, varies from 9.65 +/- 0.01 to 10.5 +/- 0.07 along the RNA chain as measured from the other marker protons (H2, H8, H5, and H6) of 9-adeninyl and 1-cytosinyl residues. This nucleobase-dependent modulation of pK(a)s (DeltapK(a) +/- 0.9) of 9-guaninyl obtained from other nucleobases in the hexameric RNA 8 represents a difference of ca. 5.1 kJ mol(-)(1), which has been attributed to the variable strength of electrostatic interactions between the electron densities of the involved atoms in the offset stacked nucleobases as well as with that of the phosphates. The chemical implication of this variable pK(a) for guanin-9-yl deprotonation as obtained from all other marker protons of each nucleotide residue within a ssRNA molecule is that it enables us to experimentally understand the variation of the electronic microenvironment around each constituent nucleobase along the RNA chain in a stepwise manner with very high accuracy without having to make any assumption. This means that the pseudoaromaticity of neighboring 9-adeninyl and next-neighbor nucleobases within a polyanionic sugar-phosphate backbone of a ssRNA can vary from one case to another due to cross-modulation of an electronically coupled pi system by a neighboring nucleobase. This modulation may depend on the sequence context, spatial proximity of the negatively charged phosphates, as well as whether the offset stacking is ON or OFF. The net outcome of this electrostatic interaction between the neighbors is creation of new sequence-dependent hybrid nucleobases in an oligo- or polynucleotide whose properties are unlike the monomeric counterpart, which may have considerable biological implications.     

An active-site guanine participates in glmS ribozyme catalysis in its protonated state

Active-site guanines that occupy similar positions have been proposed to serve as general base catalysts in hammerhead, hairpin, and glmS ribozymes, but no specific roles for these guanines have been demonstrated conclusively. Structural studies place G33(N1) of the glmS ribozyme of Bacillus anthracis within hydrogen-bonding distance of the 2'-OH nucleophile. Apparent pK(a) values determined from the pH dependence of cleavage kinetics for wild-type and mutant glmS ribozymes do not support a role for G33, or any other active-site guanine, in general base catalysis. Furthermore, discrepancies between apparent pK(a) values obtained from functional assays and microscopic pK(a) values obtained from pH-fluorescence profiles with ribozymes containing a fluorescent guanosine analogue, 8-azaguanosine, at position 33 suggest that the pH-dependent step in catalysis does not involve G33 deprotonation. These results point to an alternative model in which G33(N1) in its neutral, protonated form donates a hydrogen bond to stabilize the transition state.     

A conformationally restricted guanosine analog reveals the catalytic relevance of three structures of an RNA enzyme

Recent studies indicate that RNA function can be enhanced by the incorporation of conformationally restricted nucleotides. Herein, we use 8-bromoguanosine, a nucleotide analog with an enforced syn conformation, to elucidate the catalytic relevance of ribozyme structures. We chose to study the lead-dependent ribozyme (leadzyme) because structural models derived from NMR, crystal, and computational (MC-Sym) studies differ in which of the three active site guanosines (G7, G9, or G24) have a syn glycosidic torsion angle. Kinetic assays were carried out on 8BrG variants at these three guanosine positions. These data indicate that an 8BrG24 leadzyme is hyperactive, while 8BrG7 and 8BrG9 leadzymes have reduced activity. These findings support the computational model of the leadzyme, rather than the NMR and crystal structures, as being the most relevant to phosphodiester bond cleavage.     

Probing general base catalysis in the hammerhead ribozyme

Recent structural and computational studies have shed new light on the catalytic mechanism and active site structure of the RNA cleaving hammerhead ribozyme. Consequently, specific ribozyme functional groups have been hypothesized to be directly involved in general/acid base catalysis. In order to test this hypothesis, we have developed an affinity label to identify the functional general base in the S. mansoni hammerhead ribozyme. The ribozyme was reacted with a substrate analogue bearing a 2'-bromoacetamide group in place of the nucleophilic 2'-hydroxyl group which would normally be deprotonated by a general base. The electrophilic 2'-bromoacetamide group is poised to alkylate the general base, which is subsequently identified by footprinting analysis. Herein, we demonstrate alkylation of N1 of G12 in the hammerhead ribozyme in a pH and [Mg(2+)] dependent manner that is consistent with the native cleavage reaction. These results provide substantial evidence that deprotonated N1 of G12 functions directly as a general base in the hammerhead ribozyme; moreover, our experiments provide evidence that the pKa of G12 is perturbed downward in the context of the active site structure. We also observed other pH-independent alkylations, which do not appear to reflect the catalytic mechanism, but offer further insight into ribozyme conformation and structure.     

Mechanistic characterization of the HDV genomic ribozyme: solvent isotope effects and proton inventories in the absence of divalent metal ions support C75 as the general acid

The hepatitis delta virus (HDV) ribozyme uses the nucleobase C75 and a hydrated Mg(2+) ion as the general acid-base catalysts in phosphodiester bond cleavage at physiological salt. A mechanistic framework has been advanced that involves one Mg(2+)-independent and two Mg(2+)-dependent channels. The rate-pH profile for wild-type (WT) ribozyme in the Mg(2+)-free channel is inverted relative to the fully Mg(2+)-dependent channel, with each having a near-neutral pKa. Inversion of the rate-pH profile was used as the crux of a mechanistic argument that C75 serves as general acid both in the presence and absence of Mg(2+). However, subsequent studies on a double mutant (DM) ribozyme suggested that the pKa observed for WT in the absence of Mg(2+) arises from ionization of C41, a structural nucleobase. To investigate this further, we acquired rate-pH/pD profiles and proton inventories for WT and DM in the absence of Mg(2+). Corrections were made for effects of ionic strength on hydrogen ion activity and pH meter readings. Results are accommodated by a model wherein the Mg(2+)-free pKa observed for WT arises from ionization of C75, and DM reactivity is compromised by protonation of C41. The Br?nsted base appears to be water or hydroxide ion depending on pH. The observed pKa's are related to salt-dependent pH titrations of a model oligonucleotide, as well as electrostatic calculations, which support the local environment for C75 in the absence of Mg(2+) being similar to that in the presence of Mg(2+) and impervious to bulk ions. Accordingly, the catalytic role of C75 as the general acid does not appear to depend on divalent ions or the identity of the Br?nsted base.     

Arrhenius activation parameters for the loss of neutral nucleobases from deprotonated oligonucleotide anions in the gas phase

Arrhenius activation parameters (E(a) and A) for the loss of neutral nucleobase from a series of doubly deprotonated oligodexoynucleotide 10-mers of the type XT(9), T(9)X, and T(5)XT(4), where X = A, C, and G, have been determined using the blackbody infrared radiative dissociation technique. At temperatures of 120 to 190 degrees C, the anions dissociate exclusively by the loss of a neutral nucleobase (XH), followed by cleavage of the sugar 3' C-O bond leading to (a-XH) and w type ions or, in the case of the T(9)X(2-) ions, the loss of H(2)O. The dissociation kinetics and energetics are sensitive to the nature and position of X. Over the temperature range investigated, the kinetics for the loss of AH and GH were similar, but approximately 100 times faster than for the loss of CH. For the loss of AH and GH, the values of E(a) are sensitive to the position of the base. The order of the E(a)s for the loss of XH from the 5' and 3' termini is: C > G > A; while for T(5)XT(4) the order is: C > A > G. The trends in the values of E(a) do not parallel the trend in deprotonation enthalpies or proton affinities of the nucleobases in the gas phase, indicating that the energetic differences do not simply reflect differences in their gas phase acidity or basicity. The pre-exponential factors (A) vary from 10(10) to 10(15) s(-1), depending on the nature and position of X. These results suggest that the reactivity of individual nucleobases is influenced by stabilizing intramolecular interactions.     

The chemical nature of the 2'-substituent in the pentose-sugar dictates the pseudoaromatic character of the nucleobase (pKa) in DNA/RNA

We here show that the pKa (error limit: 0.01 to 0.03 pKa unit) of a nucleobase in a nucleotide can be modulated by the chemical nature of the 2'-substituent at the sugar moiety. This has been evidenced by the measurement of nucleobase pKa in 47 different model nucleoside 3',5'-bis- and 3'-mono-ethylphosphates. The fact that the electronic character of each of the 2'-substituents (Fig. 1) alters the chemical shift of the H2' sugar proton, and also alters the pKa of the nucleobase in the nucleotides has been evidenced by a correlation plot of pKa of N3 of pyrimidine (T/C/U) or pKa of N7 of 9-guaninyl with the corresponding deltaH2' chemical shifts at the neutral pH, which shows linear correlation with high Pearson's correlation coefficients (R = 0.85-0.97). That this modulation of the pKa of the nucleobase by a 2'-substituent is a through-bond as well as through-space effect has been proven by ab initio determined pKa estimation. Interestingly, experimental pKas of nucleobases from NMR titration and the calculated pKas (by ab initio calculations utilizing closed shell HF 6-31G** basis set) are linearly correlated with R = 0.98. It has also been observed that the difference of ground and protonated/de-protonated HOMO orbital energies (DeltaHOMO, a.u.) for the nucleobases (A/G/C/T/U) are well correlated with their pK(a)s in different 2'-substituted 3',5'-bis-ethylphosphate analogs suggesting that only the orbital energy of HOMO can be successfully used to predict the modulation of the chemical reactivity of the nucleobase by the 2'-substituent. It has also been demonstrated that pKa values of nucleobases in 3',5'-bis-ethylphosphates (Table 1) are well correlated with the change in dipole moment for the respective nucleobases after protonation or de-protonation. This work thus unambiguously shows that alteration of the thermodynamic stability (Tm) of the donor-acceptor complexes [ref. 20], as found with various 2'-modified duplexes in the antisense, siRNA or in triplexes by many workers in the field, is a result of alteration of the pseudoaromatic character of the nucleobases engineered by alteration of the chemical nature of the 2'-substitution.     

Evaluating the contributions of desolvation and base-stacking during translesion DNA synthesis

DNA polymerases catalyze the insertion of a nucleoside triphosphate into the growing polymer chain using the template strand as a guide. Numerous factors such as hydrogen bonding interactions, base-stacking contributions, and desolvation play important roles in controlling the efficiency and fidelity of this process. We previously demonstrated that 5-nitro-indolyl-2'-deoxyriboside triphosphate, a non-natural nucleobase with enhanced base-stacking properties, was more efficiently inserted opposite a non-templating DNA lesion compared to natural templating nucleobases (E. Z. Reineks and A. J. Berdis, Biochemistry, 2004, 43, 393-404). The catalytic enhancement was proposed to reflect increased base-stacking interactions of the non-natural nucleobase with the polymerase and DNA. However, the effects of desolvation could not be unambiguously refuted. To further address the contributions of base stacking and desolvation during translesion DNA replication, we synthesized indolyl-2'-deoxyriboside triphosphate, a nucleobase devoid of nitro groups, and measured its efficiency of enzymatic insertion into modified and unmodified DNA. Removal of the nitro group reduces the catalytic efficiency for insertion opposite an abasic site by 3600-fold. This results from a large decrease in the rate of polymerization (similar 450-fold) coupled with a modest decrease in binding affinity (similar 8-fold). Since both non-natural nucleobases show the same degree of hydrophobicity, we attribute this reduction to the loss of base-stacking contributions rather than desolvation capabilities. Indolyl-2'-deoxyriboside triphosphate can also be inserted opposite natural nucleobases. Surprisingly, the catalytic efficiency for insertion is nearly identical to that measured for insertion opposite an abasic site. These data are discussed within the context of pi-electron interactions of the incoming nucleobase with the polymerase:DNA complex. Despite this lack of insertion selectivity, the polymerase is unable to extend beyond the non-natural nucleobase. This result indicates that indolyl-2'-deoxyriboside triphosphate acts as an indiscriminate chain terminator of DNA synthesis that may have unique therapeutic applications.     

Role of Mg2+ in hammerhead ribozyme catalysis from molecular simulation

Molecular dynamics simulations have been performed to investigate the role of Mg2+ in the full-length hammerhead ribozyme cleavage reaction. In particular, the aim of this work is to characterize the binding mode and conformational events that give rise to catalytically active conformations and stabilization of the transition state. Toward this end, a series of eight 12 ns molecular dynamics simulations have been performed with different divalent metal binding occupations for the reactant, early and late transition state using recently developed force field parameters for metal ions and reactive intermediates in RNA catalysis. In addition, hybrid QM/MM calculations of the early and late transition state were performed to study the proton-transfer step in general acid catalysis that is facilitated by the catalytic Mg2+ ion. The simulations suggest that Mg2+ is profoundly involved in the hammerhead ribozyme mechanism both at structural and catalytic levels. Binding of Mg2+ in the active site plays a key structural role in the stabilization of stem I and II and to facilitate formation of near attack conformations and interactions between the nucleophile and G12, the implicated general base catalyst. In the transition state, Mg2+ binds in a bridging position where it stabilizes the accumulated charge of the leaving group while interacting with the 2'OH of G8, the implicated general acid catalyst. The QM/MM simulations provide support that, in the late transition state, the 2'OH of G8 can transfer a proton to the leaving group while directly coordinating the bridging Mg2+ ion. The present study provides evidence for the role of Mg2+ in hammerhead ribozyme catalysis. The proposed simulation model reconciles the interpretation of available experimental structural and biochemical data, and provides a starting point for more detailed investigation of the chemical reaction path with combined QM/MM methods.     

Reversible diselenide cross-links are formed between oligonucleotides containing 2′-deoxy-6-selenoinosine

We have synthesized and characterized a phosphoramidite derivative of 2′-deoxy-6-selenoinosine (d^6SeI) and incorporated this modification into an oligonucleotide by solid-phase synthesis. During cleavage from the solid-support and deprotection, spontaneous dimerization of this oligonucleotide occurs via formation of a diselenide cross-link between the modified nucleobases. This cross-link can be readily reduced to restore the single-stranded oligonucleotide. UV thermal denaturation and circular dichroism spectroscopy of duplexes with d^6SeI paired against all four native nucleobases revealed minor differences in stability and structure relative to 2′-deoxyinosine. This selenium containing nucleobase modification may be useful for applications in DNA nanomaterials and X-ray crystallography.