Abstract
Compact but non-native intermediates have been implicated in the hierarchical folding of several large RNAs, but there is little information on their structure. In this article, ribonuclease and hydroxyl radical cleavage protection assays showed that base pairing of core helices stabilize a compact state of a small group I ribozyme from Azoarcus pre-tRNAile. Base pairing of the ribozyme core requires 10-fold less Mg2+ than stable tertiary interactions, indicating that assembly of helices in the catalytic core represents a distinct phase that precedes the formation of native tertiary structure. Tertiary folding occurs in <100 ms at 37°C. Such rapid folding is unprecedented among group I ribozymes and illustrates the association between structural complexity and folding time. A 3D model of the Azoarcus ribozyme was constructed by identifying homologous sequence motifs in rRNA. The model reveals distinct structural features, such as a large interface between the P4–P6 and P3–P9 domains, that may explain the unusual stability of the Azoarcus ribozyme and the cooperativity of folding.
Keywords: RNA modeling‖RNA structure‖metal ions‖hydroxyl radical footprinting
The assembly of RNA into functional structures underlies many steps in gene expression and regulation. Recent work has outlined the Mg2+-dependent folding pathways of large ribozymes (1, 2). Experimental and theoretical results suggest that the initial association of divalent cations induces collapse of the extended RNA chain into more compact structures that favor formation of tertiary interactions (3–8). The structure of the compact intermediates and the extent to which these interactions lead to the native conformation are not yet characterized.
On the one hand, individual domains of the Tetrahymena group I ribozyme and the catalytic domain of RNase P fold on a time scale (10–100 ms) similar to the initial collapse transitions of the ribozyme (6, 9, 10). On the other hand, nonspecific collapse results in an ensemble of native and non-native conformations. Many larger RNAs, such as the Tetrahymena group I and Bacillus subtilis RNase P ribozymes, fold slowly in vitro because a large fraction of the RNA population becomes trapped in misfolded intermediates (11, 12). An important question is whether RNAs with a simpler 3D architecture are more likely to fold directly to the native structure, as expected from theoretical models (4). Furthermore, we want to know whether the likelihood of misfolding can be predicted from the specificity of counterion-induced collapse.
We investigated the Mg2+-dependent equilibrium folding pathway and constructed a 3D model of the Azoarcus group I intron. The 205-nt group IC3 intron in the pre-tRNAile of the Azoarcus bacterium is the smallest known self-splicing group I intron (13). It retains the conserved catalytic core common to all group I introns, but lacks the peripheral domains that stabilize folding intermediates of the larger Tetrahymena intron (14).
We observed two macroscopic folding transitions in the Azoarcus ribozyme that correspond to hierarchical levels of the native structure. Interactions in the catalytic core require higher concentrations of Mg2+ than interactions in peripheral stem loops, consistent with the higher density of negatively charged phosphates. In the larger Tetrahymena ribozyme, the P4–P6 domain folds independently of the P3–P9 domain. In contrast, tertiary interactions in both domains of the Azoarcus intron have a similar Mg2+ dependence, as in the td group I intron (15). Time-resolved hydroxyl radical footprinting shows that the Azoarcus ribozyme folds rapidly, reaching its native structure in <100 ms.
Materials and Methods
Plasmids and RNA Preparation.
Plasmids pAz-PREt and pAz-IVS were prepared by PCR amplification of pAZO4.2 (13) and subcloned into pUC18. The T7 promoter was incorporated into the upstream PCR primer. An EarI site was included in the downstream primer. Transcription of pAz-PREt begins with G1 and ends with A79 of the mature tRNAile. In pAz-IVS, transcription starts at G11; U12 was mutated to A. Uniformly 32P-labeled pre-tRNA (284 nt) and ribozyme (195 nt) were prepared by T7 transcription of pAz-PREt or pAz-IVS digested with EarI (New England Biolabs) as described (16, 17). The 5′ end-labeled RNA was purified from a denaturing 4% polyacrylamide gel (16). The RNA was redissolved in TE (10 mM Tris⋅HCl, pH 7.5, 0.1 mM EDTA) before use.
Self-Splicing Assays.
Splicing reactions were carried out as described (18). RNA was allowed to fold 10 min at 50°C in 25 mM Na-Hepes, pH 7.0, plus 0–15 mM MgCl2, then incubated 2 min at 32°C before the addition of 100 μM GTP (32°C). The reaction was stopped after various times with 30 mM EDTA and 5 M urea. Progress curves were fit to first-order rate equations (Fig. 7, which is published as supporting information on the PNAS web site, www.pnas.org). The observed rate of self-splicing as a function of magnesium concentration was fit to the Hill equation.
Native Gel Electrophoresis.
Uniformly labeled 32P-RNA was incubated in 25 mM Na-Hepes (pH 7.0), 0.1 mM EDTA, 10% glycerol, 0.1% xylene cyanol, and 0–30 mM MgCl2. Reactions were incubated 5 min at 50°C, then loaded immediately on a native 10% polyacrylamide gel (29:1 acrylamide/bis; 34 mM Tris, 66 mM Hepes, 0.1 mM EDTA, 3 mM MgCl2) at 4°C (19, 20). Samples were electrophoresed at 15 W for 3–4 h at 2–8°C. Dried gels were exposed to Molecular Dynamics PhosphorImager screens and quantified with imagequant software.
RNase T1 Cleavage.
The 5′ 32P-labeled RNA was incubated 5 min at 50°C in 10 mM Tris⋅HCl, pH 7.5 plus 0–15 mM MgCl2. RNase T1 (0.01 unit) was added to each sample and incubated 1 min at 50°C. The reaction was stopped with an equal volume of formamide. Products were separated on a 6% sequencing gel and quantified as above.
Hydroxyl Radical Footprinting.
Fe(II)-EDTA cleavage reactions were carried out as in ref. 9, except that 5′ 32P-labeled RNA (150,000 cpm) was annealed 5 min at 50°C and 5 min on ice, in 14 μl of 10 mM sodium cacodylate (pH 7.5), 0.1 mM EDTA plus MgCl2, before the addition of cleavage reagents on ice. Samples were heated to 95°C in formamide before electrophoresis. The relative extent of protection (Ȳ) was determined by comparing the intensity of bands in protected regions with cleavage products whose intensity does not change with MgCl2 concentration (21).
X-ray-dependent footprinting experiments were performed as described (21, 22) at beamline X28C at the National Synchrotron Light Source, Brookhaven National Laboratory, Upton, NY). Folding reactions were in 10 mM Na-cacodylate (pH 7.5), 1 mM EDTA plus 15 mM MgCl2 (final) at 37°C. Samples were exposed to the x-ray beam for 20 ms.
Molecular Modeling.
The 3D model of the Azoarcus group I intron was interactively built as described (23) by using the software manip (24). The generated models were subjected to restrained geometrical least-square refinement by using the program nuclin/nuclsq (23, 25) to ensure geometry and stereochemistry with correct distances between interacting atoms and to avoid steric clashes. Interactive modeling followed by refinement steps were iteratively performed until solution data reported in this work could be satisfactorily explained. The color views were generated with the program drawna (26). Radii of gyration were computed with the in-house program ragyr. The accessibilities of the C4′ carbon atoms to the hydroxyl radicals were computed by using the program access (27).
Results
Magnesium Dependence of Folding.
Native PAGE was used to resolve native and non-native species of the Azoarcus intron. Uniformly radiolabeled RNA was incubated in increasing concentrations of Mg2+ at 50°C and analyzed on a 10% polyacrylamide gel containing 3 mM MgCl2 (Fig. 1a). After refolding in splicing buffer containing 15 mM MgCl2, the native RNA migrates as a sharp band (N). If the RNA is not pre-equilibrated with Mg2+ before electrophoresis, 55% of the population is trapped in non-native intermediates (I), which appear as a diffuse band of lower mobility. Previous experiments suggest that refolding is arrested when the RNA enters the gel matrix (20). Hence, the fraction of native RNA reflects the proportion of molecules that fold correctly in the short time (15–30 s) required for the sample to enter the gel matrix (11). The residual folding transition of the Azoarcus intron was mildly cooperative with respect to Mg2+ concentration, with a Hill coefficient of 1.9 and midpoint of 0.22 mM (Fig. 1b).
Figure 1.
Mg2+-dependent folding of the Azoarcus ribozyme. (a) Native gel assay for folding. Uniformly 32P-labeled RNA was equilibrated 5 min at 50°C in 0–15 mM MgCl2 as described in Materials and Methods. Band I, folding intermediates; N, native RNA. (b) Mg2+ dependence of folding. The fraction native RNA (ƒN) was determined from native gels as above, footprinting, or the observed rate of self-splicing (Fig. 7). The data were fit to the Hill equation. ○, native gels (Cm = 0.22 ± 0.01 mM, nH = 1.9 ± 0.2); ▴, RNase T1 (Cm = 0.093 ± 0.004 mM, nH = 1.8 ± 0.2); ▵, Fe-EDTA (Cm = 1.9 ± 0.08 mM, nH = 1.9 ± 0.1); ⧫, kobs self-splicing (Cm = 2.4 ± 0.6 mM, nH = 1.5 ± 0.2).
To directly assay the formation of catalytically active RNA, we measured the rate of self-splicing as a function of MgCl2 concentration. The rate of splicing increased with Mg2+ concentration to a maximum of 0.15 min−1 at 32°C (Fig. 1b). However, the midpoint of the transition was 2.4 mM, 10-fold greater than the midpoint of folding measured by native PAGE. This difference suggested that the Azoarcus intron folds in two transitions, one leading to native-like intermediates that can be trapped in a native gel, and a second leading to the active (native) conformation.
Base Pairing of Intron Core in Folding Intermediates.
To reveal the folding pathway in more detail, the secondary structure of the intron was probed by partial digestion with ribonuclease (RNase) T1, which cleaves 3′ of unpaired Gs. In the absence of Mg2+, Gs in P2, P4, P5/5a, P6a, and to some extent P9, are protected from cleavage (Fig. 2 and Fig. 8, which is published as supporting information on the PNAS web site). Thus, much of the secondary structure is stable even in 10 mM Tris⋅HCl. By contrast, Gs in P3, P6, P7, P8/8a, and P9.0 are protected from cleavage only in the presence of MgCl2. The midpoints of transitions detected by RNase T1 were 0.1–0.4 mM MgCl2 (Table 1, which is published as supporting information on the PNAS web site). Therefore, submillimolar concentrations of Mg2+ stabilize base-pairing interactions in P3 and P7 and the alignment of double helices in the core of the ribozyme. The midpoint of this transition is similar to that detected by native gel electrophoresis, but much lower than the concentration of Mg2+ needed for catalysis. As formation of P3 and P7 correlates with more folded RNA in nondenaturing gels, we conclude that preorganization of core helices increases the probability that the RNA will fold rapidly to the native state.
Figure 2.
Structure of ribozyme from chemical and nuclease protection. Shaded regions are protected from hydroxyl radical cleavage in Mg2+. Midpoints (Cm) and Hill coefficients for each protected region were obtained by fits to data as in Fig. 1b. Solid arrowheads indicate nucleotides that are protected from RNase T1 in Mg2+. Midpoints ranged from 0.1 to 0.4 mM. G70 and G110 (open arrowheads) were digested more strongly in high Mg2+ (Cm = 2.1–2.5 mM). This finding may be caused by more frequent cleavage of loop nucleotides as the proportion of correctly folded molecules increases. Nucleotides are numbered from the 5′ end of intron as in ref. 18. This numbering system differs from the one used in ref. 38 by one unit less.
Tertiary Structure of Folding Intermediates.
The tertiary folding pathway was probed by Fe(II)-EDTA-dependent hydroxyl radical cleavage, which is sensitive to the solvent accessibility of the ribose C4′ (28). Under native conditions (10 mM Na-cacodylate, 15 mM MgCl2), nucleotides throughout P3, P4, P6, P7, and J8/7 were protected from cleavage (Figs. 2 and 8). These residues are expected to become inaccessible to solvent when the catalytic core of the intron is folded (14, 28). Nucleotides in P5, P8, and P9 that form the proposed tetraloop–receptor interactions (18) were protected from cleavage (Fig. 2). Protections in P2 were too poorly resolved in sequencing gels to assign with confidence.
Each region of the ribozyme displayed a cooperative Mg2+-dependent increase in protection from hydroxyl radical cleavage, reflecting global tertiary folding of the ribozyme. The transitions measured at individual protected regions were similar, with an average midpoint of 1 mM MgCl2 and Hill coefficients of 1–2 (Fig. 2 and Table 2, which is published as supporting information on the PNAS web site). Therefore, tertiary interactions in both helical domains are formed in a single thermodynamic transition. This finding differs from the folding pathway of the larger Tetrahymena ribozyme, in which the P4–P6 domain folds independently of the rest of the ribozyme (29, 30).
Azoarcus Ribozyme Folds Rapidly.
The uniform equilibrium folding transition suggested that a large fraction of the Azoarcus ribozyme population may fold rapidly, without becoming kinetically trapped in tertiary intermediates. The folding kinetics were assayed by time-resolved footprinting experiments, using a synchrotron x-ray beam to generate hydroxyl radical in solution. This method detects changes in tertiary structure on the millisecond time scale and was used to resolve folding intermediates of the Tetrahymena ribozyme (31). Surprisingly, all of the regions of the Azoarcus ribozyme that are expected to be inaccessible to hydroxyl radical in the native conformation were fully protected from cleavage in 50–100 ms, which is only slightly longer than the 20 ms dead time of our experiments (Fig. 3 and Fig. 9, which is published as supporting information on the PNAS web site). Similar results were obtained over a range of Mg2+ concentrations and temperatures (data not shown).
Figure 3.
Tertiary folding kinetics. Change in tertiary structure after addition of 15 mM MgCl2 at 37°C was probed by x-ray-dependent hydroxyl radical footprinting as described in Materials and Methods. Fractional saturation of each protected region Ȳ was determined relative to minimum protection in no Mg2+ and maximum protection 2–5 min after addition of Mg2+. ●, P3; ○, P6a. Additional data are available in Fig. 9.
We estimate that the tertiary structure of the ribozyme forms with a time constant ≤50 ms at 37°C. This finding is comparable to the shortest time required to fold the P4–P6 domain of the Tetrahymena ribozyme (9) and the catalytic domain of B. subtilis RNase P (10), and is 1,000 times shorter than the time needed to fold the core of the Tetrahymena ribozyme (31, 32). As all of the regions that are protected from hydroxyl radical under conditions that give maximal self-splicing activity are saturated within 100 ms, this transition is likely to reflect formation of native RNA.
3D Model of the Azoarcus Ribozyme.
A 3D model of the Azoarcus ribozyme was developed to better interpret the results of folding experiments (Fig. 4a). Secondary structure elements were assembled in a compact architecture, taking advantage of the 3D model of the Tetrahymena thermophila ribozyme (33) and the crystal structure of the P1–P2-depleted Tetrahymena ribozyme (34). The GAAA tetraloops in L2 and L9 were docked against their receptors in P8 and P5, respectively, as in the crystal structure of the Tetrahymena P4–P6 RNA (35).
Figure 4.
3D model of Azoarcus group I intron. (a) Ribbon diagram with solvent-inaccessible regions in blue. Nucleotides that make key tertiary interactions (see text) are represented as stick models. (b) Homology modeling of the junction between P9 and P9.0, based on similar sequences in the H. marismortui 23 S rRNA (36). (c) Model of tertiary interactions between P3 and P6/6a. Base pairs are annotated as in ref. 55 where □ and ▵ represent Hoogsteen and sugar edges, respectively; open symbol, cis; filled symbol, trans.
Crystal structures of rRNAs were scanned for homology with sequences of unknown structure in the Azoarcus ribozyme. The positive hits were inserted into the model with the sequence of the Azoarcus ribozyme. This strategy was successfully used to identify structural motifs similar to the helix junctions J6/6a and J9.0/9. For the J6/6a internal loop, a homologous structural motif from the 590 region of the Haloarcula marismortui 23S rRNA (36) was used to model this region of the td group I intron (37). In both introns, sheared A⋅A (trans Hoogsteen-Sugar edge) base pairs in J6/6a allow the formation of additional hydrogen bonds between the sugar edge of adenines in J6/6a and the shallow groove of P3.
The highly asymmetric internal loop separating P9.0 from P9 is similar to the junction formed by nucleotides 1727–1734 and 2045–2048 of H. marismortui 23S rRNA (36). In our model, P9.0 ends with a sheared A⋅A pair. The first two residues of the 3′ strand of the internal loop (A197, C198) stack on the first base pair of P9, the third residue (C199) flips out of the helix, and the last one (A200) stacks on the sheared pair of P9.0. This motif generates a 90° kink between P9.0 and P9. This sharp kink enables L9 to interact with the tetraloop–receptor J5/5a, while maintaining a smooth connection between P9.0 and P7.
The final model successfully predicts the solvent accessibility of C4′ atoms measured by hydroxyl radical cleavage (Fig. 5), except for nucleotides 92 and 104–106 at the 3′ ends of P4 and P6, respectively. These bands were compressed and the real extent of protection was difficult to quantify. The model is also consistent with nucleotide analog interference data (38).
Figure 5.
Comparison of predicted and experimental solvent accessibility. Predicted solvent accessibility (in Å2) of C4′ atoms was computed from the 3D coordinates of the model by using a rolling sphere of radius 2.8 Å. The straight line at 12 Å2 indicates the average accessibility of a C4′ atom within an isolated and regular A-form RNA helix. Nucleotides protected from hydroxyl radical cleavage are indicated by ■.
Discussion
3D Model of the Azoarcus Intron.
Group I introns share a common core structure that contains the active site (14), but differ in the architecture of peripheral tertiary interactions among subfamilies (33). Nucleotide analog interference showed that the active site of the Azoarcus IC3 intron shares many features with the IC1 intron from T. thermophila (38). Interactions that organize the interface between the P3–P7 and P4–P6 domains include a central triple helix (14), a base triple that joins J8/7 and P4 (39), and contacts between L9 and P5 (40).
A primary difference between IC1 and IC3 introns is the length of the single-stranded J8/7 region, which is 6 nt in IC3 introns and 7 nt in IC1 introns. It has been proposed that a shorter J8/7 is compensated by the extension of J2/3 in the Azoarcus intron (38). In the Tetrahymena intron, P1 is 6 bp and is proposed to dock orthogonally to P2 and P2.1 helices (33, 41). In our model of the Azoarcus intron, the 3-bp P1 helix stacks on top of P2. As a consequence, the sugar edge of A166 of J8/7 interacts with the first base pairs of P2 (type II A-minor motif or cis sugar–sugar pair), whereas A167 of J8/7 binds to C(−3) of P1 (type I A-minor motif or trans sugar–sugar pair) as seen in the Tetrahymena intron (38, 42). After our model was constructed, we learned that interference from a carbon at position 3 of A166 is suppressed by a 2′ deoxy substitution at C12 in P2, consistent with the pair modeled between these residues (43).
Stable Tertiary Architecture.
Despite its small size, the native form of the Azoarcus intron is stable up to 70°C and in 7.5 M urea (18). An interesting problem is how the unusual stability of the intron's tertiary structure is achieved. First, interactions between the GAAA tetraloops L2 and L9 with 11-nt receptors in P8 and P5, respectively, provide long-range constraints on the tertiary structure of the intron (44). The contact between L9 and P5 is likely to be important for the stability of the intron core, as mutations that disrupt this interaction destabilize the tertiary structure of the sun Y group I intron (40). Mutations in L9 also severely inhibit folding of the Azoarcus intron (P.R. and S.A.W., unpublished work). Interactions between L2 and P8 contribute to the activity of the pre-tRNA at high temperature (18). The L2 interaction is not essential for folding of the core (P.R. and S.A.W., unpublished work), but may help position the P1 splice site helix.
Second, the large number of nucleotides protected from hydroxyl radical cleavage suggests an extensive interface between the P4–P6 and P3–P9 domains, which may also contribute to the stability and cooperativity of the tertiary structure. In our model, the domain interface is stabilized by contacts around the central triple helix, the L9 tetraloop–J5/5a interaction, and minor groove interactions between J6/6a and P3. In both the td and Azoarcus introns, the latter enclose the P3 and P7 pseudoknots, which are central to structure and catalysis in group I introns. Deviations from A-form geometry around internal loops in P6 and P8 and a sharp bend between stems P7 and P9.0 cause the two helical domains to twist around each other, maximizing the buried surface area. The extensive helical packing predicted by our model is largely consistent with the positions of 2′ OH modifications that interfere with catalytic activity (38).
Mg2+-Dependent Folding Pathway.
The Mg2+ dependence of the nuclease and hydroxyl radical protection patterns show that the equilibrium folding pathway involves at least two macroscopic transitions (Fig. 6). The stability of the Azoarcus ribozyme enabled us to observe specific interactions formed during these transitions in unusual detail. At low ionic strength, the RNA is in largely extended conformations (U), which contain terminal stem loops but few stable tertiary interactions. Under these conditions, base pairs in the core of the intron are disordered. Submillimolar Mg2+, however, is sufficient to stabilize paired helices P3, P6, and P7, although stable tertiary interactions are not yet detectable. Because the P3 and P7 join distant parts of the sequence, the formation of this pseudoknot, along with helices P4 and P6, constrains the path of the RNA and creates an ensemble of intermediates (IC) that are expected to be more compact than the unfolded RNA. This expectation is supported by a reduction in the radius of gyration over the same Mg2+ concentration range, measured by small angle neutron scattering (U. Perez-Salas, P.R., S. Krueger, R. Briber, D. Thirumalai, and S.A.W., unpublished work). That assembly of core helices requires submillimolar concentrations of Mg2+ reflects the greater density of phosphates in the intron core (45).
Figure 6.
Structural and electrostatic hierarchy in folding of Azoarcus ribozyme. Mg2+-dependent folding involves at least two macroscopic transitions. Extended conformations in the unfolded state contain most of the secondary structure helices. Low Mg2+ concentrations ([Mg2+]1/2 ≈ 0.2 mM) stabilize the P3/P7 pseudoknot and induce the assembly of core helices. This results in an ensemble of conformations (IC) that are more ordered and more compact than U. Higher magnesium concentrations ([Mg2+]1/2 ≈ 1.7 mM) stabilize native tertiary interactions (N) and support catalytic activity.
In the second transition, higher concentrations of Mg2+ (Cm ≈ 1.7 mM) induce the formation of native tertiary structure (N), as judged by hydroxyl radical footprinting and the concomitant increase in catalytic activity. As folding and catalysis have similar Mg2+ requirements, self-splicing activity appears tightly coupled to formation of tertiary structure. This is unlike the VS ribozyme, which requires higher Mg2+ concentrations for self-cleavage than folding, presumably to saturate a low affinity “catalytic” metal ion binding site (46).
As our experimental probes detect only the average conformation of the RNA population, the microscopic folding pathways may be more complex than suggested by Fig. 6. For example, the ensemble of structures in IC may contain tertiary interactions that are too transient to be detected by hydroxyl radical footprinting. Nucleotides in P6a, P3, J8/7, and P7 can form alternative secondary structures, which may be present in the “unfolded” population.
Nonetheless, we observe a correlation between Mg2+ concentration and net charge of the RNA and the degree of native structure. The greater sensitivity of tertiary interactions to divalent metal ions compared with secondary structure has been observed in many RNAs (e.g., see refs. 47–49). What is unusual in this system is that the assembly of core helices (IC) is separated by its Mg2+ requirement from the formation of stable tertiary interactions (N). Although the presence of compact but non-native intermediates have been inferred in several RNAs, there has been little information on their structure. Importantly, we find that the transition to a more compact state precedes the formation of specific tertiary contacts. Stabilization of the native state may require higher Mg2+ concentrations because a larger number of specific metal ion binding sites must be filled simultaneously.
Correlation of Native Architecture with Folding Time.
From our time-resolved footprinting and native gel experiments, we estimate that 45% of the Azoarcus ribozyme reaches the native state in <100 ms when preincubated in 10 mM Tris⋅HCl. By contrast, only a few percent of the Tetrahymena RNA folds rapidly (≈1 s−1) under these conditions (50, 51). In the Tetrahymena ribozyme, interactions among peripheral helices stabilize misfolded intermediates (52–54). In the Azoarcus intron, these interactions are replaced by minor groove contacts between P2 and P8, as well as between P3 and P6/6a, that may be more dynamic. Moreover, the large interface between the P4–P6 and P3–P8 domains should increase the cooperativity of tertiary folding, also reducing the probability that non-native structures will persist.
Hence, the relatively simple, yet stable, architecture of the Azoarcus ribozyme enables a much larger fraction of the population to reach the native structure in a short time. Our results illustrate the association between cooperativity and the directness of the folding process. This connection, which remains to be tested in more detail, has important consequences for the evolution of RNA sequences.
Supplementary Material
Acknowledgments
We thank M. Deras, M. Brenowitz, and M. Sullivan for assistance with x-ray footprinting experiments and D. Thirumalai for helpful discussions. This work was supported by grants from the National Institutes of Health (to S.A.W.) and the Institut Universitaire de France (to E.W.).
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