Equilibrium dissociation and unfolding of the Arc repressor dimer

The equilibrium unfolding reaction of Arc repressor, a dimeric DNA binding protein encoded by bacteriophage P22, can be monitored by fluorescence or circular dichroism changes. The stability of Arc is concentration dependent, and the unfolding reaction is well described as a two-state transition from folded dimer to unfolded monomer. The stability of the protein is decreased at low pH and increased by high salt concentration. The salt dependence suggests that two ions bind preferentially to the folded protein. In 10 mM potassium phosphate (pH 7.3) and 100 mM KCl, the unfolding free energy reaches a maximum near room temperature. The results suggest that at the low protein concentrations where operator DNA binding is normally measured, Arc is predominantly monomeric and unfolded.     

C‐terminal domain of SARS‐CoV main protease can form a 3D domain‐swapped dimer

SARS coronavirus main protease (M^pro) plays an essential role in the extensive proteolytic processing of the viral polyproteins (pp1a and pp1ab), and it is an important target for anti-SARS drug development. We have reported that both the M^pro C-terminal domain alone (M^pro-C) and the N-finger deletion mutant of M^pro (M^pro-Δ7) exist as a stable dimer and a stable monomer (Zhong et al., J Virol 2008; 82:4227-4234). Here, we report structures of both M^pro-C monomer and dimer. The structure of the M^pro-C monomer is almost identical to that of the C-terminal domain in the crystal structure of M^pro. Interestingly, the M^pro-C dimer structure is characterized by 3D domain-swapping, in which the first helices of the two protomers are interchanged and each is enwrapped by four other helices from the other protomer. Each folding subunit of the M^pro-C domain-swapped dimer still has the same general fold as that of the M^pro-C monomer. This special dimerization elucidates the structural basis for the observation that there is no exchange between monomeric and dimeric forms of M^pro-C and M^pro-Δ7.     

Cooperative folding units of escherichia coli tryptophan repressor.

A previously published computational procedure was used to identify cooperative folding units within tryptophan repressor. The theoretical results predict the existence of distinct stable substructures in the protein chain for the monomer and the dimer. The predictions were compared with experimental data on structure and folding of the repressor and its proteolytic fragments and show excellent agreement for the dimeric form of the protein. The results suggest that the monomer, the structure of which is currently unknown, is likely to have a structure different from the one it has within the context of the highly intertwined dimer. Application of this method to the repressor monomer represents an extension of the computations into the realm of evaluating hypothetical structures such as those produced by threading.     

The folding energy landscape of the dimerization domain of Escherichia coli Trp repressor: a joint experimental and theoretical investigation

Enhanced structural insights into the folding energy landscape of the N-terminal dimerization domain of Escherichia coli tryptophan repressor, [2-66]2 TR, were obtained from a combined experimental and theoretical analysis of its equilibrium folding reaction. Previous studies have shown that the three intertwined helices in [2-66]2 TR are sufficient to drive the formation of a stable dimer for the full-length protein, [2-107]2 TR. The monomeric and dimeric folding intermediates that appear during the folding reactions of [2-66]2 TR have counterparts in the folding mechanism of the full-length protein. The equilibrium unfolding energy surface on which the folding and dimerization reactions occur for [2-66]2 TR was examined with a combination of native-state hydrogen exchange analysis, pepsin digestion and matrix-assisted laser/desorption mass spectrometry performed at several concentrations of protein and denaturant. Peptides corresponding to all three helices in [2-66]2 TR show multi-layered protection patterns consistent with the relative stabilities of the dimeric and monomeric folding intermediates. The observation of protection exceeding that offered by the dimeric intermediate in segments from all three helices implies that a segment-swapping mechanism may be operative in the monomeric intermediate. Protection greater than that expected from the global stability for a single amide hydrogen in a peptide from the C-helix possibly and another from the A-helix may reflect non-random structure, possibly a precursor for segment swapping, in the urea-denatured state. Native topology-based model simulations that correspond to a funnel energy landscape capture both the monomeric and dimeric intermediates suggested by the HX MS data and provide a rationale for the progressive acquisition of secondary structure in their conformational ensembles.     

Three-state kinetic folding mechanism of the H2A/H2B histone heterodimer: the N-terminal tails affect the transition state between a dimeric intermediate and the native dimer

The H2A/H2B heterodimer is a component of the nucleosome core particle, the fundamental repeating unit of chromatin in all eukaryotic cells. The kinetic folding mechanism for the H2A/H2B dimer has been determined from unfolding and refolding kinetics as a function of urea using stopped-flow, circular dichroism and fluorescence methods. The kinetic data are consistent with a three-state mechanism: two unfolded monomers associate to form a dimeric intermediate in the dead-time of the SF instrument (approximately 5 ms); this intermediate is then converted to the native dimer by a slower, first-order reaction. Analysis of the burst-phase amplitudes as a function of denaturant indicates that the dimeric kinetic intermediate possesses approximately 50% of the secondary structure and approximately 60% of the surface area burial of the native dimer. The stability of the dimeric intermediate is approximately 30% of that of the native dimer at the monomer concentrations employed in the SF experiments. Folding-to-unfolding double-jump experiments were performed to monitor the formation of the native dimer as a function of folding delay times. The double-jump data demonstrate that the dimeric intermediate is on-pathway and obligatory. Formation of a transient dimeric burst-phase intermediate has been observed in the kinetic mechanism of other intertwined, segment-swapped, alpha-helical, DNA-binding dimers, such as the H3-H4 histone dimer, Escherichia coli factor for inversion stimulation and E.coli Trp repressor. The common feature of a dimeric intermediate in these folding mechanisms suggests that this intermediate may accelerate protein folding, when compared to the folding of archael histones, which do not populate a transient dimeric species and fold more slowly.     

A polymetamorphic protein

Arc repressor is a homodimeric protein with a ribbon‐helix–helix fold. A single polar‐to‐hydrophobic substitution (N11L) at a solvent‐exposed position leads to population of an alternate dimeric fold in which 3₁₀ helices replace a β‐sheet. Here we find that the variant Q9V/N11L/R13V (S‐VLV), with two additional polar‐to‐hydrophobic surface mutations in the same β‐sheet, forms a highly stable, reversibly folded octamer with approximately half the?α‐helical content of wild‐type Arc. At low protein concentration and low ionic strength, S‐VLV also populates both dimeric topologies previously observed for N11L, as judged by NMR chemical shift comparisons. Thus, accumulation of simple hydrophobic mutations in Arc progressively reduces fold specificity, leading first to a sequence with two folds and then to a manifold bridge sequence with at least three different topologies. Residues 9–14 of S‐VLV form a highly hydrophobic stretch that is predicted to be amyloidogenic, but we do not observe aggregates of higher order than octamer. Increases in sequence hydrophobicity can promote amyloid aggregation but also exert broader and more complex effects on fold specificity. Altered native folds, changes in fold coupled to oligomerization, toxic pre‐amyloid oligomers, and amyloid fibrils may represent a near continuum of accessible alternatives in protein structure space.     

Intramolecular dynamics of low molecular weight protein tyrosine phosphatase in monomer-dimer equilibrium studied by NMR: a model for changes in dynamics upon target binding

Low molecular weight protein tyrosine phosphatase (LMW-PTP) dimerizes in the phosphate-bound state in solution with a dissociation constant of K(d)=1.5(+/-0.1)mM and an off-rate on the order of 10(4)s(-1). 1H and 15N NMR chemical shifts identify the dimer interface, which is in excellent agreement with that observed in the crystal structure of the dimeric S19A mutant. Two tyrosine residues of each molecule interact with the active site of the other molecule, implying that the dimer may be taken as a model for a complex between LMW-PTP and a target protein. 15N relaxation rates for the monomeric and dimeric states were extrapolated from relaxation data acquired at four different protein concentrations. Relaxation data of satisfactory precision were extracted for the monomer, enabling model-free analyses of backbone fluctuations on pico- to nanosecond time scales. The dimer relaxation data are of lower quality due to extrapolation errors and the possible presence of higher-order oligomers at higher concentrations. A qualitative comparison of order parameters in the monomeric and apparent dimeric states shows that loops forming the dimer interface become rigidified upon dimerization. Qualitative information on monomer-dimer exchange and intramolecular conformational exchange was obtained from the concentration dependence of auto- and cross-correlated relaxation rates. The loop containing the catalytically important Asp129 fluctuates between different conformations in both the monomeric and dimeric (target bound) states. The exchange rate compares rather well with that of the catalyzed reaction step, supporting existing hypotheses that catalysis and enzyme dynamics may be coupled. The side-chain of Trp49, which is important for substrate specificity, exhibits conformational dynamics in the monomer that are largely quenched upon formation of the dimer, suggesting that binding is associated with the selection of a single side-chain conformer.     

Equilibrium unfolding of dimeric and engineered monomeric forms of lambda Cro (F58W) repressor and the effect of added salts: evidence for the formation of folded monomer induced by sodium perchlorate

The equilibrium unfolding transitions of Cro repressor variants, dimeric variant Cro F58W and monomer Cro K56[DGEVK]F58W, have been studied by urea and guanidine hydrochloride to probe the folding mechanism. The unfolding transitions of a dimeric variant are well described by a two state process involving native dimer and unfolded monomer with a free energy of unfolding, DeltaG(0,un)(0), of approximately 10-11 kcal/mol. The midpoint of transition curves is dependent on total protein concentration and DeltaG(0,un)(0) is independent of protein concentration, as expected for this model. Unfolding of Cro monomer is well described by the standard two state model. The stability of both forms of protein increases in the presence of salt but decreases with the decrease in pH. Because of the suggested importance of a N2<-->2F dimerization process in DNA binding, we have also studied the effect of sodium perchlorate, containing the chaotropic perchlorate anion, on the conformational transition of Cro dimer by CD, fluorescence and NMR (in addition to urea and guanidine hydrochloride) in an attempt both to characterize the thermodynamics of the process and to identify conditions that lead to an increase in the population of the folded monomers. Data suggest that sodium perchlorate stabilizes the protein at low concentration (<1.5 M) and destabilizes the protein at higher perchlorate concentration with the formation of a "significantly folded" monomer. The tryptophan residue in the "significantly folded" monomer induced by perchlorate is more exposed to the solvent than in native dimer.     

The structure of the transition state for folding of domain-swapped dimeric p13suc1

suc1 has two native states, a monomer and a domain-swapped dimer, in which one molecule exchanges a beta strand with an identical partner. Thus, monomer and dimer have the same structures but are topologically distinct. Importantly, residues that exchange are part of the folding nucleus of the monomer and therefore forming these interactions in the dimer would be expected to incur a large entropic cost. Here we present the transition state for folding/unfolding of domain-swapped dimeric suc1 and compare it with its monomeric counterpart. The same overall structure is observed in the two transition states but the phi values are consistently higher for the domain-swapped dimer. Thus, a greater entropic penalty for bringing together the key interactions in the dimer is overcome by mobilizing more contacts in the transition state, thereby achieving a greater enthalpic gain.     

Rough energy landscapes in protein folding: dimeric E. coli Trp repressor folds through three parallel channels

The folding mechanism of the dimeric Escherichia coli Trp repressor (TR) is a kinetically complex process that involves three distinguishable stages of development. Following the formation of a partially folded, monomeric ensemble of species, within 5 ms, folding to the native dimer is controlled by three kinetic phases. The rate-limiting step in each phase is either a non-proline isomerization reaction or a dimerization reaction, depending on the final denaturant concentration. Two approaches have been employed to test the previously proposed folding mechanism of TR through three parallel channels: (1) unfolding double-jump experiments demonstrate that all three folding channels lead directly to native dimer; and (2) the differential stabilization of the transition state for the final step in folding and the native dimer, by the addition of salt, shows that all three channels involve isomerization of a dimeric species. A refined model for the folding of Trp repressor is presented, in which all three channels involve a rapid dimerization reaction between partially folded monomers followed by the isomerization of the dimeric intermediates to yield native dimer. The ensemble of partially folded monomers can be captured at equilibrium by low pH; one-dimensional proton NMR spectra at pH 2.5 demonstrate that monomers exist in two distinct, slowly interconverting conformations. These data provide a potential structural explanation for the three-channel folding mechanism of TR: random association of two different monomeric forms, which are distinguished by alternative packing modes of the core dimerization domain and the DNA-binding, helix-turn-helix, domain. One, perhaps both, of these packing modes contains non-native contacts.     

Solution structure of switch Arc,a mutant with 3(10) helices replacing a wild-type beta-ribbon

Adjacent N11L and L12N mutations in the antiparallel beta-ribbon of Arc repressor result in dramatic changes in local structure in which each beta-strand is replaced by a right-handed helix. The full solution structure of this "switch" Arc mutant shows that irregular 3(10) helices compose the new secondary structure. This structural metamorphosis conserves the number of main-chain and side-chain to main-chain hydrogen bonds and the number of fully buried core residues. Apart from a slight widening of the interhelical angle between alpha-helices A and B and changes in side-chain conformation of a few core residues in Arc, no large-scale structural adjustments in the remainder of the protein are necessary to accommodate the ribbon-to-helix change. Nevertheless, some changes in hydrogen-exchange rates are observed, even in regions that have very similar structures in the two proteins. The surface of switch Arc is packed poorly compared to wild-type, leading to approximately 1000A(2) of additional solvent-accessible surface area, and the N termini of the 3(10) helices make unfavorable head-to-head electrostatic interactions. These structural features account for the positive m value and salt dependence of the ribbon-to-helix transition in Arc-N11L, a variant that can adopt either the mutant or wild-type structures. The tertiary fold is capped in different ways in switch and wild-type Arc, showing how stepwise evolutionary transformations can arise through small changes in amino acid sequence.     

NMR structural analysis of cadmium sensing by winged helix repressor CmtR

CmtR from Mycobacterium tuberculosis is a winged helical DNA-binding repressor of the ArsR-SmtB metal-sensing family that senses cadmium and lead. Cadmium-CmtR is a dimer with the metal bound to Cys-102 from the C-terminal region of one subunit and two Cys associated with helix alphaR from the other subunit, forming a symmetrical pair of cadmium-binding sites. This is a significant novelty in the ArsR-SmtB family. The structure of the dimer could be solved at 312 K. The apoprotein at the same temperature is still a dimer, but it experiences a large conformational exchange at the dimer interface and within each monomer. This is monitored by an overall decrease of the number of nuclear Overhauser effects and by an increase of H(2)O-D(2)O exchange rates, especially at the dimeric interface, in the apo form with respect to the cadmium-bound state. The C-terminal tail region is completely unstructured in both apo and cadmium forms but becomes less mobile in the cadmium-bound protein due to the recruitment of Cys-102 as a metal-ligand. DNA binds to the apo dimer with a ratio 1:3 at millimolar concentration. Addition of cadmium to the apo-CmtR-DNA complex causes DNA detachment, restoring the NMR spectrum of free cadmium-CmtR. Cadmium binding across the dimer interface impairs DNA association by excluding the apo-conformers suited to bind DNA.     

SecA folds via a dimeric intermediate

Though many proteins in the cell are large and multimeric, their folding has not been extensively studied. We have chosen SecA as a folding model because it is a large, homodimeric protein (monomer molecular mass of 102 kDa) with multiple folding domains. SecA is the ATPase for the Sec-dependent preprotein translocase of many bacteria. SecA is a soluble protein that can penetrate into the membrane during preprotein translocation. Because SecA may partially unfold prior to its insertion into the membrane, studies of its stability and folding pathway are important for understanding how it functions in vivo. Kinetic folding transitions in the presence of urea were monitored using circular dichroism and tryptophan fluorescence, while equilibrium folding transitions were monitored using the same techniques as well as a fluorescent ATP analogue. The reversible equilibrium folding transition exhibited a plateau, indicating the presence of an intermediate. Based on the data presented here, we propose a three-state model, N(2) if I(2) if 2U, where the native protein unfolds to a dimeric intermediate which then dissociates into two unfolded monomers. The SecA dimer was determined to have an overall stability (DeltaG) of -22.5 kcal/mol. We also investigated the stability of SecA using analytical ultracentrifugation equilibrium and velocity sedimentation, which again indicated that native or refolded SecA was a stable dimer. The rate-limiting step in the folding pathway was conversion of the dimeric intermediate to the native dimer. Unfolding of native, dimeric SecA was slow with a relaxation time in H(2)O of 3.3 x 10(4) s. Since SecA is a stable dimer, dissociation to monomeric subunits during translocation is unlikely.     

Subunit structure and activity of the mannitol-specific enzyme II of the Escherichia coli phosphoenolpyruvate-dependent phosphotransferase system solubilized in detergent

The original proposal of Saier stating that P-enolpyruvate-dependent mannitol phosphorylation is catalyzed by the monomeric form of the bacterial phosphotransferase enzyme IImtl, which would be the form predominantly existing in the phospholipid bilayer, whereas mannitol/mannitol-P exchange would depend on the transient formation of functional dimers, is refuted [Saier, M.H. (1980) J. Supramol. Struct. 14, 281-294]. The correct interpretation of the proportional relation between the rate of mannitol phosphorylation in the overall reaction and the enzyme concentration is that enzyme IImtl is dimeric under the conditions employed. Differences measured in the enzyme concentration dependency of the overall and exchange reactions were caused by different assay conditions. The dimer is favored over the monomer at high ionic strength and basic pH. Mg2+ ions bind specifically to enzyme IImtl, inducing dimerization. A complex formed by mixing inorganic phosphate, F-, and Mg2+ at sufficiently high concentrations inhibits enzyme IImtl, in part, by dissociation of the dimer. Enzyme IImtl was dimeric in 25 mM Tris, pH 7.6, and 5 mM Mg2+ over a large enzyme concentration range and under many different turnover conditions. The association/dissociation equilibrium was demonstrated in phosphate bufers, pH 6.3. The dimer was the most active form both in the overall and in the exchange reaction under the conditions assayed. The monomer was virtually inactive in mannitol/mannitol-P exchange but retained 25% of the activity in the overall reaction.     

Four-alpha-helix bundle with designed anesthetic binding pockets. Part I: structural and dynamical analyses

The four-α-helix bundle mimics the transmembrane domain of the Cys-loop receptor family believed to be the protein target for general anesthetics. Using high resolution NMR, we solved the structure (Protein Data Bank ID: 2I7U) of a prototypical dimeric four-α-helix bundle, (Aα₂-L1M/L38M)₂, with designed specific binding pockets for volatile anesthetics. Two monomers of the helix-turn-helix motif form an antiparallel dimer as originally designed, but the high-resolution structure exhibits an asymmetric quaternary arrangement of the four helices. The two helices from the N-terminus to the linker (helices 1 and 1′) are associated with each other in the dimer by the side-chain ring stacking of F12 and W15 along the long hydrophobic core and by a nearly perfect stretch of hydrophobic interactions between the complementary pairs of L4, L11, L18, and L25, all of which are located at the heptad e position along the helix-helix dimer interface. In comparison, the axes of the two helices from the linker to the C-terminus (helices 2 and 2′) are wider apart from each other, creating a lateral access pathway around K47 from the aqueous phase to the center of the designed hydrophobic core. The site of the L38M mutation, which was previously shown to increase the halothane binding affinity by ∼3.5-fold, is not part of the hydrophobic core presumably involved in the anesthetic binding but shows an elevated transverse relaxation (R₂) rate. Qualitative analysis of the protein dynamics by reduced spectral density mapping revealed exchange contributions to the relaxation at many residues in the helices. This observation was confirmed by the quantitative analysis using the Modelfree approach and by the NMR relaxation dispersion measurements. The NMR structures and Autodock analysis suggest that the pocket with the most favorable amphipathic property for anesthetic binding is located between the W15 side chains at the center of the dimeric hydrophobic core, with the possibility of two additional minor binding sites between the F12 and F52 ring stacks of each monomer. The high-resolution structure of the designed anesthetic-binding protein offers unprecedented atomistic details about possible sites for anesthetic-protein interactions that are essential to the understanding of molecular mechanisms of general anesthesia.     

The solution structure and dynamics of an Arc repressor mutant reveal premelting conformational changes related to DNA binding.

The solution structure of the hyperstable MYL mutant (R31M/E36Y/R40L) of the Arc repressor of bacteriophage P22 was determined by NMR spectroscopy and compared to that of the wild-type Arc repressor. A backbone rmsd versus the average of 0.37 A was obtained for the well-defined core region. For both Arc-MYL and the wild-type Arc repressor, evidence for a fast equilibrium between a packed ("in") conformation and an extended ("out") conformation of the side chain of Phe 10 was found. In the MYL mutant, the "out" conformation is more highly populated than in the wild-type Arc repressor. The Phe 10 is situated in the DNA-binding beta-sheet of the Arc dimer. While its "in" conformation appears to be the most stable, the "out" conformation is known to be present in the operator-bound form of Arc, where the Phe 10 ring contacts the phosphate backbone [Raumann, B. E., et al. (1994) Nature 367, 754-757]. As well as DNA binding, denaturation by urea and high temperatures induces the functionally active "out" conformation. With a repacking of the hydrophobic core, this characterizes a premelting transition of the Arc repressor. The dynamical properties of the Arc-MYL and the wild-type Arc repressor were further characterized by 15N relaxation and hydrogen-deuterium exchange experiments. The increased main chain mobility at the DNA binding site compared to that of the core of the protein as well as the reorientation of the side chain of Phe 10 is suggested to play an important role in specific DNA binding.     

Intermediates control domain swapping during folding of p13suc1

The 13-kDa protein p13(suc1) has two folded states, a monomer and a structurally similar domain-swapped dimer formed by exchange of a beta-strand. The refolding reaction of p13(suc1) is multiphasic, and in this paper we analyze the kinetics as a function of denaturant and protein concentration and compare the behavior of wild type and a set of mutants previously designed with dimerization propensities that span 9 orders of magnitude. We show that the folding reactions of wild type and all mutants produce the monomer predominantly despite their very different equilibrium behavior. However, the addition of low concentrations of denaturant in the refolding buffer leads to thermodynamic control of the folding reaction with products that correspond to the wild type and mutant equilibrium dimerization propensities. We present evidence that the kinetic control in the absence of urea arises because of the population of the folding intermediates. Intermediates are usually considered to be detrimental to folding because they slow down the reaction; however, our work shows that intermediates buffer the monomeric folding pathway against the effect of mutations that favor the nonfunctional, dimeric state at equilibrium.     

Direct analysis of backbone-backbone hydrogen bond formation in protein folding transition states

Here we investigate the role of backbone-backbone hydrogen bonding interactions in stabilizing the protein folding transition states of two model protein systems, the B1 domain of protein L (ProtL) and the P22 Arc repressor. A backbone modified analogue of ProtL containing an amide-to-ester bond substitution between residues 105 and 106 was prepared by total chemical synthesis, and the thermodynamic and kinetic parameters associated with its folding reaction were evaluated. Ultimately, these parameters were used in a Phi-value analysis to determine if the native backbone-backbone hydrogen bonding interaction perturbed in this analogue (i.e. a hydrogen bond in the first beta-turn of ProtL's beta-beta-alpha-beta-beta fold) was formed in the transition state of ProtL's folding reaction. Also determined were the kinetic parameters associated with the folding reactions of two Arc repressor analogues, each containing an amide-to-ester bond substitution in the backbone of their polypeptide chains. These parameters were used together with previously established thermodynamic parameters for the folding of these analogues in Phi-value analyses to determine if the native backbone-backbone hydrogen bonding interactions perturbed in these analogues (i.e. a hydrogen bond at the end of the intersubunit beta-sheet interface and hydrogen bonds at the beginning of the second alpha-helix in Arc repressor's beta-alpha-alpha structure) were formed in the transition state of Arc repressor's folding reaction. Our results reveal that backbone-backbone hydrogen bonding interactions are formed in the beta-turn and alpha-helical transition state structures of ProtL and Arc repressor, respectively; and they were not formed in the intersubunit beta-sheet interface of Arc repressor, a region of Arc repressor's polypeptide chain previously shown to have other non-native-like conformations in Arc's protein folding transition state.     

Symmetry and structure of RNA and DNA triple helices

Despite wide interest in nucleic acid triple helices, there has beenno stereochemically satisfactory structure of an RNA triple helixin atomic detail. An RNA triplex structure has previously been proposed based on fiber diffraction and molecular modeling [S. Arnott and P. J. Bond (1973) Nature New Biology, Vol. 244. pp. 99–101; S. Arnott. P. J. Bond. E. Seising, and P. J. C. Smith (1976) Nucleic Acids Research, Vol. 3. pp.2459–2470], but it has nonallowed close contacts at every triplet and is therefore not stereochemically acceptable. We propose here a new modelfor an RNA triple helix in which the three chains have identical backbone conformations and are symmetry related. There are no short contacts. The modeling employs a novel geometrical approach using the linked atom least squares [P. J. C. Smith and S. Arnott (1978) Acta Crystallographica, Vol. A34, pp. 3–11] program and is not based on energy minimization. In general, the method leads to a range of possible structures rather than a unique structure. In the present case, however, the constraints resulting from theintroduction of a third strand limit the possible structures to a very small range of conformation space. This method was used previously to obtain a model for DNA triple helices [G. Raghunathan, H. T. Miles, and V. Sasisekharan (1993) Biochemistry, Vol. 32, pp. 455–462], subsequently confirmed by fiber-type x-ray diffraction of oligomeric crystals [K. Liu. H. T. Miles. K. D. Parris, and V. Sasisekharan (1994) Nature Structural Biology, Vol. 1. pp. 11–12]. The above triple helices have Watson–Crick–Hoogsteen [K. Hoogsteen (1963) Acta Crystallographica, Vol. 16. pp. 907–916] pairing of the three bases. The same modeling method was used to investigate the feasibility of three-dimensional structures based on the three possible alternative hydrogen-bonding schemes: Watson–Crick–reverse Hoogsteen, Donogue [J. Donohue (1953) Proceeding of the national Academy of Science USA, Vol. 39, pp. 470–475] (reverse Watson–Crick)–Hoogsteen, and Donohue–reverse Hoogsteen. We found that none of these can occur in either RNA or DNA helices because they give rise only to structures with prohibitively short contacts between backbone and base atoms in the same chain. © 1995 John Wiley & Sons, Inc.