monovalent cations mediate formation of native tertiary structure of tetrahymena thermophila...

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letters nature structural biology • advance online publication 1 Monovalent cations mediate formation of native tertiary structure of the Tetrahymena thermophila ribozyme Keiji Takamoto 1,2 , Qin He 1,2 , Stephanie Morris 3 , Mark R. Chance 1–3 and Michael Brenowitz 2,3 1 Department of Physiology and Biophysics, 2 Center for Synchrotron Biosciences and 3 Department of Biochemistry, Albert Einstein College of Medicine, 1300 Morris Park Avenue, Bronx, New York 10461, USA. Published online 18 November 2002; doi:10.1038/nsb871 The formation of individual tertiary contacts of the Tetrahymena L-21 Sca I ribozyme has been monitored by hydroxyl radical footprinting and its global conformation by analytical ultracentrifugation as a function of mono- valent ion concentration in the absence of divalent ions. Advanced methods of data analysis, which allow the hydro- xyl radical reactivity of every nucleotide to be quantified, permit monitoring of each and every structural element of the RNA. Monovalent ion-mediated global compaction of the ribozyme is accompanied by the formation of native tertiary contacts; most native tertiary contacts are evident except several that are located near where divalent ions are observed in crystallographic structures. Non-native tertiary contacts are also observed at low but not high concentra- tions of monovalent ions. In light of recent studies that have shown that the presence of monovalent ions greatly acceler- ates the Mg 2+ -dependent folding of the Tetrahymena ribozyme, the present studies suggest that Na + concentra- tion changes not only the starting position of the RNA on its folding funnel but also pushes it deep into the well by form- ing native tertiary contacts and, thus, favoring fast and cor- rect folding pathways. Although Mg 2+ has been long known to be required for the folding and catalytic activity of the Tetrahymena thermophila group I ribozyme 1 , monovalent cations can compact the ribozyme 2–5 and accelerate and dictate the predominant path- ways it uses for folding 6–12 . Here we explore the ability of a monovalent cation (Na + ), in the absence of magnesium, to mod- ulate the structure of the Tetrahymena Sca I ribozyme. Hydroxyl radical ‘footprinting’ and analytical ultracentrifugation are used to demonstrate the formation of native and non-native, and dis- ruption of non-native, tertiary contacts by Na + alone. The impli- cations of these results for the acceleration of rates of folding 9,11 and the partitioning of RNA among multiple pathways 10 are dis- cussed. Single nucleotide structural analysis Hydroxyl radical (OH ) footprinting titrations of the Sca I ribozyme were conducted as a function of [NaCl] in the absence of Mg 2+ . To obtain a comprehensive and objective OH reactivity map with single nucleotide resolution, a ‘single-band’ analysis protocol 13,14 was developed and applied to the autoradiograms obtained for the Tetrahymena ribozyme (Fig. 1ac). Hydroxyl radical footprinting reports the solvent accessibility of individ- ual nucleotides. Experiments conducted with RNA separately labeled at the 3and 5termini, together with increasing dura- tions of electrophoretic separation, allow almost all the nucleotides of the ribozyme to be quantitatively analyzed (Fig. 1d). The use of the single-band quantitative analysis and display techniques may account for the observation of Na + -dependent effects on formation of specific tertiary contacts that have previously gone undetected 15 . The results of this analysis are summarized in a false-color map (Fig. 2) whose color mapping is referenced to the lowest [Na + ] studied (CE buffer), which was the starting point for bio- chemical analysis of the Tetrahymena ribozyme 16–18 . The bar below the Na + titration (Fig. 2) summarizes the OH reactivity profile of the ribozyme folded in the presence of Mg 2+ , which is 0 100 200 300 400 0 100 200 300 400 500 600 700 800 Lane 1 Lane 2 Pixels Intensity 22 409 54-91 64-134 79-152 85-210 141-205 171-246 313-395 289-368 258-317 266-315 202-276 3' 5' L-21 Sca I Ribozyme 3' end labeled 5' end labeled Lane 1 Lane 2 Fig. 1 Summary of the data analysis procedures. a, A ‘line profile’ encompassing the middle 50% of a lane, defined in the 16-bit digital image of an autoradiogram of a gel using ImageQuant (Molecular Dynamics). Lane 2 is a region of the Tetrahymena ribozyme in CE buffer containing 10 mM Na + . Lane 1 is ribozyme in CE buffer containing 10 mM Na + and 10 mM MgCl 2 . b, The density profile calculated using ImageQuant and transferred to Origin 6.1 (OriginLab) equipped with their Peak Fitting Module. c, Deconvolution of the data in (b) carried out by fitting the peaks to a series of Lorentzian curves, taking care to ensure that the global minimum was reached in each analysis. The numerical peak as a function of nucleotide position were used to create the false color image in Fig. 2. d, Schematic representation of the overlapping regions of either 5- or 3-labeled ribozyme sequence that were individu- ally analyzed using a sequential series of electrophoresis durations. a b c d © 2002 Nature Publishing Group http://www.nature.com/naturestructuralbiology

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Page 1: Monovalent Cations Mediate Formation of Native Tertiary Structure of Tetrahymena Thermophila Ribozyme

letters

nature structural biology • advance online publication 1

Monovalent cationsmediate formation ofnative tertiary structure ofthe Tetrahymenathermophila ribozymeKeiji Takamoto1,2, Qin He1,2, Stephanie Morris3, Mark R. Chance1–3 and Michael Brenowitz2,3

1Department of Physiology and Biophysics, 2Center for SynchrotronBiosciences and 3Department of Biochemistry, Albert Einstein College ofMedicine, 1300 Morris Park Avenue, Bronx, New York 10461, USA.

Published online 18 November 2002; doi:10.1038/nsb871

The formation of individual tertiary contacts of theTetrahymena L-21 Sca I ribozyme has been monitored byhydroxyl radical footprinting and its global conformationby analytical ultracentrifugation as a function of mono-valent ion concentration in the absence of divalent ions.Advanced methods of data analysis, which allow the hydro-xyl radical reactivity of every nucleotide to be quantified,permit monitoring of each and every structural element ofthe RNA. Monovalent ion-mediated global compaction ofthe ribozyme is accompanied by the formation of native tertiary contacts; most native tertiary contacts are evidentexcept several that are located near where divalent ions areobserved in crystallographic structures. Non-native tertiarycontacts are also observed at low but not high concentra-tions of monovalent ions. In light of recent studies that haveshown that the presence of monovalent ions greatly acceler-ates the Mg2+-dependent folding of the Tetrahymenaribozyme, the present studies suggest that Na+ concentra-tion changes not only the starting position of the RNA on itsfolding funnel but also pushes it deep into the well by form-ing native tertiary contacts and, thus, favoring fast and cor-rect folding pathways.

Although Mg2+ has been long known to be required for thefolding and catalytic activity of the Tetrahymena thermophilagroup I ribozyme1, monovalent cations can compact theribozyme2–5 and accelerate and dictate the predominant path-ways it uses for folding6–12. Here we explore the ability of amonovalent cation (Na+), in the absence of magnesium, to mod-ulate the structure of the Tetrahymena Sca I ribozyme. Hydroxylradical ‘footprinting’ and analytical ultracentrifugation are usedto demonstrate the formation of native and non-native, and dis-ruption of non-native, tertiary contacts by Na+ alone. The impli-cations of these results for the acceleration of rates of folding9,11

and the partitioning of RNA among multiple pathways10 are dis-cussed.

Single nucleotide structural analysisHydroxyl radical (OH•) footprinting titrations of the Sca Iribozyme were conducted as a function of [NaCl] in the absenceof Mg2+. To obtain a comprehensive and objective OH• reactivitymap with single nucleotide resolution, a ‘single-band’ analysisprotocol13,14 was developed and applied to the autoradiogramsobtained for the Tetrahymena ribozyme (Fig. 1a–c). Hydroxylradical footprinting reports the solvent accessibility of individ-

ual nucleotides. Experiments conducted with RNA separatelylabeled at the 3′ and 5′ termini, together with increasing dura-tions of electrophoretic separation, allow almost all thenucleotides of the ribozyme to be quantitatively analyzed(Fig. 1d). The use of the single-band quantitative analysis anddisplay techniques may account for the observation of Na+-dependent effects on formation of specific tertiary contactsthat have previously gone undetected15.

The results of this analysis are summarized in a false-colormap (Fig. 2) whose color mapping is referenced to the lowest[Na+] studied (CE buffer), which was the starting point for bio-chemical analysis of the Tetrahymena ribozyme16–18. The barbelow the Na+ titration (Fig. 2) summarizes the OH• reactivityprofile of the ribozyme folded in the presence of Mg2+, which is

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Fig. 1 Summary of the data analysis procedures. a, A ‘line profile’encompassing the middle ∼ 50% of a lane, defined in the 16-bit digitalimage of an autoradiogram of a gel using ImageQuant (MolecularDynamics). Lane 2 is a region of the Tetrahymena ribozyme in CE buffercontaining 10 mM Na+. Lane 1 is ribozyme in CE buffer containing 10 mMNa+ and 10 mM MgCl2. b, The density profile calculated usingImageQuant and transferred to Origin 6.1 (OriginLab) equipped withtheir Peak Fitting Module. c, Deconvolution of the data in (b) carried outby fitting the peaks to a series of Lorentzian curves, taking care to ensurethat the global minimum was reached in each analysis. The numericalpeak as a function of nucleotide position were used to create the falsecolor image in Fig. 2. d, Schematic representation of the overlappingregions of either 5′- or 3′-labeled ribozyme sequence that were individu-ally analyzed using a sequential series of electrophoresis durations.

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Page 2: Monovalent Cations Mediate Formation of Native Tertiary Structure of Tetrahymena Thermophila Ribozyme

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2 nature structural biology • advance online publication

also referenced to the OH• reactivity measured in CE buffer. Theribozyme is annealed and folded in the presence of 10 mM Mg2+

under conditions that fully yield the native, catalytically activeconformation (data not shown). We have classified and mappedthe OH• protections and enhancements on a secondary/tertiarystructural ribozyme representation19 (Fig. 3).

Induction of native tertiary contactsIncreasing concentrations of Na+ induce formation of native ter-tiary contacts in the Tetrahymena ribozyme in the absence ofMg2+ (blue, Fig. 2)20–24. Regions of enhanced OH• reactivityinduced by Na+ are identical to those evident in the Mg2+-foldednative conformation (red, Fig. 2). The close similarity of the OH•

protection patterns in 1.5 M NaCl and 10 mM MgCl2 suggeststhat monovalent cations mediate formation of many elements ofnative structure. Examples of tertiary contacts that are formed in1.5 M NaCl include the nucleotides of the tetraloop–receptorinteraction within P4–P6, the peripheral helix contact P13, theproposed P9–P5 interaction, the OH• protections around P3 andnative catalytic core protections. Formation of P13 in buffercontaining only NaCl has also been observed by dimethyl sulfate(DMS) footprinting10. Nucleotides 265–269 are not protected in10 mM Mg2+ but are at high [Na+]. Thus, monovalent cationscan also induce formation of non-native tertiary structure. DMSmodification studies have shown the formation of the alt-P3alternative secondary structures at <100 mM Na+, with P3 pre-sent at >100 mM Na+ (ref. 10). At [Na+] >300 mM, we infer thatP3 secondary structure is present on the basis of the similaritiesof the OH• reactivity pattern surrounding P3 with that observedat 10 mM Mg2+.

Divalent ion-specific tertiary structureDespite the overall similarity of Na+- and Mg2+-folded RNA, notall of the native tertiary interactions are formed in the presenceof 1.5 M Na+. Protection is absent for nucleotides 302–306 (J8/7)and 99–100 (P3) within the catalytic core and nucleotides167–173 that constitute one-half of the P14 tertiary interaction.(Because our data does not report on the other side of the P14contact in P2, the absence of P14 is inferred.) Protection isabsent within P5c and is barely evident within the A-bulge at1.5 M Na+ (Figs 2, 3). Thus, Na+ mimics some, but not all, of thestructural roles played by Mg2+.

Bound Mg2+ ions are observed in the crystal structure of theisolated P4–P6 domain within P5c and the A-bulge20,21,25,26. Ureadenaturation-hydroxyl radical footprinting analysis of the iso-lated Mg2+-folded P4–P6 domain shows that the P5c and A-bulge protections have elevated stability compared with thosein the rest of the domain12. Phosphothioate substitution27 andbound Fe2+-mediated OH• cleavage studies28 also suggest specifi-cally bound divalent cations in this region. Finally, a Mg2+-dependent secondary structure change has been observed forisolated P5abc by NMR26,29. Together, these results are consistentwith divalent ion-specific stabilization of structure in thisregion. The absence of native contacts in the ribozyme core athigh monovalent ion concentrations in the absence of divalentcation is consistent with the absence of detectable catalytic activ-ity under these solution conditions (data not shown).

Induction of native tertiary ‘exposures’Nucleotide-specific enhancements of OH• reactivity are alsoobserved relative to low-salt reference condition (red, Fig. 2).

Fig. 2 A false-color map of the changes in OH• reactivity for the Tetrahymena ribozyme observed as a function of Na+ concentration. The OH• reac-tivity is referenced to the lowest salt concentration analyzed, CE buffer (green). Decreased OH• reactivity (‘protection’) is blue and increased reactiv-ity (‘enhancement’) is red, as shown in the insert to the figure. The bar beneath the Na+ titration shows the ribozyme annealed in CE buffer with10 mM MgCl2 added during annealing of the RNA, which is represented using the same color coding. Data were collected in CE buffer (∼ 10 mM Na+)and 40, 80, 160, 400, 600, 750 and 1,500 mM Na+ by the addition of NaCl. The data underlying the graph were interpolated and smoothed toimprove its visualization.

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nature structural biology • advance online publication 3

These increases in OH• reactivity are typically observed in loopson the outside of the native, Mg2+-folded structure and, thus, arehighly solvent accessible24 (Fig. 3). If the ‘unfolded’ RNA at lowsalt is viewed as an ensemble of structures, it is plausible to viewthese regions as fluctuating between ‘inside’ and ‘outside’ posi-tions. In the presence of cations, they become progressivelylocked outside as the ensemble of partially folded structures con-verges towards the unique native conformation.

Na+-linking folding isothermsThe false-color mapping (Fig. 2) clearly shows the Na+ concen-tration dependence of native tertiary structure formation. Eachof the tertiary contacts can also be represented by a foldingisotherm relating the fractional saturation of the protection to[Na+] (Fig. 4). The Na+-dependent folding isotherms differ dra-matically from the published Mg2+-folding isotherms whoseequilibrium constants are tightly clustered and moderately(P4–P6) or highly (the catalytic core) concerted15,16. To captureboth the concentration dependence and concerted nature of theNa+-folding isotherms in a single measure, the ion concentrationat which they achieve 20% saturation is used to classify the dataand color coding (Fig. 3) to visualize the onset of the transitions.

The behavior of the Na+-dependent folding isothermsobtained by OH• footprinting shows changes that can begrouped within four [Na+] ranges (Figs 2–4). (i) At 30–40 mMNa+, protection to 20% saturation of a proposed contactbetween P9 and P5 is evident as is the tetraloop–receptor withinP4–P6 (green, Figs 3, 4a). Enhanced reactivity of nucleotides381–382 within P9.2 is also observed. (ii) The isotherms for the

P9.1a–P2.1 contact of the peripheral helices (P13) and core ter-tiary contacts reach 20% saturation at 150–300 mM Na+ (cyan,Figs 3, 4b). (iii) A large number of isotherms for protectionswithin P4–P6 and the catalytic core reach 20% saturation by750 mM Na+ (blue, Fig. 3). (iv) Additional native protections(including the A-bulge) show the onset of protection at 1.5 MNa+ but do not fully saturate in our experiments (purple, Figs 3,4c). In aggregate, a high proportion of native tertiary contactsshowing robust protections are observed in 1.5 M Na+ in theabsence of divalent cations.

Some Na+-linked folding isotherms display characteristics notseen in Mg2+-induced folding. For example, OH• protectionappears at intermediate concentrations of Na+ only to vanish asthe monovalent ion concentration increases15. Such transientprotections pertaining to [Na+] are observed in P2.1(nucleotides 61–62, 64–65 and 85–86; Figs 2, 4d). The latter twoprotections are not observed in the presence of Mg2+ and, thus,are presumed to be non-native.

Na+-linked folding isotherms are biphasic at several othersites, including the spatially close protections at the J8/7 side ofP8 (nucleotides 298–300) and J2.1/3 (nucleotides 93–96) andnucleotides 202–203 in a P5–P9 contact. The initial phase ofthese biphasic transitions may represent non-native contactsformed in the electrostatic collapse of these regions, followed byrearrangement to the native conformation at higher concentra-tions of Na+. Thus, titrating the ribozyme with Na+ does notresult in a monotonic march towards a ‘native-like’ ensemble ofstructures. Rather, each salt concentration is a unique mix ofnative and non-native tertiary interactions.

Fig. 3 Structural mapping and classification of the OH• reactivity changes. The color-coding of this figure is based upon the concentration of Na+ atwhich either the protection or enhancement reaches 20% of the maximum change observed as a function of the Na+- against the Mg2+-folded value.(The 20% saturation value was chosen to capture the contribution of both the midpoint and slope of the isotherms in a single value.) Sites repre-sented by two colors indicate the presence of biphasic transitions in the isotherms (for example, nucleotides 93–96). Open rectangles with two col-ors denote transient transitions that appear at the lower concentration and disappear at higher concentrations of Na+ (for example, nucleotides65–67). The regions surrounded by black with colored letters denote nucleotides characterized by greater protection in Na+ than in Mg2+ (for exam-ple, nucleotides 265–269). The arrows show several long-range interactions present in the native folded ribozyme.

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Several conclusions can be drawn from these data. First, themonovalent cation-induced electrostatic collapse of theribozyme3,7,11 includes formation of both native and non-nativetertiary contacts. Second, this process does not proceed in astrictly monotonic fashion. Structural rearrangements fromnon-native to native tertiary contacts are observed. Third, non-native tertiary contacts present at low concentrations of Na+ maybe a source of the kinetic traps that retard Mg2+-induced foldingunder this solution condition16. Because these kinetic traps maybe released in the ensemble of molecules that comprise the ‘ini-tial state’, folding of the RNA may be accelerated in theirabsence11,12,30.

Global and local tertiary correlationsSmall angle X-ray scattering (SAXS)3,10, analytical ultracentrifu-gation11 and gel electrophoresis7 studies have demonstratedcompaction of the Tetrahymena ribozyme with increasing con-centrations of monovalent cations. An analytical ultracentrifu-gation analysis of the L-21 ribozyme was carried out over therange of Na+ concentrations probed by OH• footprinting to cor-relate the formation of local tertiary contacts with changes in theglobal conformation.

Sedimentation (S20,w) and diffusion coefficients (D20,w) aredetermined from a sedimentation velocity experiment. Fromthese quantities, the Stokes radius (RH) and the axial ratio (a / b)were calculated for the ribozyme as a function of [Na+] or[Mg2+]. With divalent cations, compaction of the ribozymeoccurs coincidently with a decrease in the axial ratio, predomi-nantly as a single concerted step with a midpoint of ∼ 0.2 mMMgCl2. A second transition of minimal amplitude is observedwith a midpoint of 7.5–8.9 mM MgCl2 (open circles, Fig. 5).Similarly, two transitions are evident in the Na+ titrations. Themidpoint of the predominant transition is at 39 mM, with thesecond transition at 587 mM (solid squares, Fig. 5). The Na+-mediated transitions are much less concerted than theMg2+-mediated transition. Together, the changes in RH and a / bshow that the ribozyme does not uniformly condense upon theaddition of Na+. The ultracentrifugation results are in overallagreement with small angle X-ray scattering studies conductedover a comparable range of [Na+]3,10,31 (R. Das, I. Millett, R. Russell, S. Doniach and D. Herschlag, pers. comm.).

A model of monovalent ion-induced foldingThe global conformational changes together with the directreports of local solvent accessibility provided by OH• footprint-ing allow a model for the Na+-induced compaction of theTetrahymena ribozyme to be developed. The appearance of theP5–P9 and tetraloop–receptor protections at low concentrationsof Na+ (green, Fig. 3) suggests that the initial compact conforma-tion is stabilized by the formation of specific, native tertiary con-tacts. The presence of the non-native P13 protection as well asthe appearance of the transitions that are transient with [Na+] atthe intersection of P2.1–P3 and P8–J8/7 suggests that specificnon-native interactions also stabilize this compact conforma-tion. The formation of the P5–P9 tertiary contact dramaticallylimits both the size and length of the ensemble of RNA moleculesand, thus, can rationalize the initial compaction observed byultracentrifugation and SAXS.

Further increases in [Na+] from 300 to 750 mM results in pro-gressive organization of P4–P6, the catalytic core and the periph-eral helices. Formation of these native tertiary contacts correlateswith the second global compaction transition observed by ultra-centrifugation (Fig. 5). Additional increases in the [Na+] to1.5 M seem to ‘tighten-up’ the ribozyme structure. Overall, theseresults suggest that Na+ drives formation of an ensemble of com-pact and spatially constrained structures stabilized by bothnative and non-native contacts that converges to more native-like structures with increasing [Na+]. This absence of severallocal tertiary contacts between ribozyme folded with Na+ com-pared with Mg2+ is reflected in the difference in global confor-mation evident at high [Na+] and [Mg2+] (Fig. 5).

Implications for the kinetics of foldingThe time-dependence of both tertiary contact formation andcompaction of the Tetrahymena ribozyme upon Mg2+-initiatedfolding have been measured at low [Na+]; tertiary structureforms at least five times more slowly than global compactionunder this experimental condition17,31. Thus, the search for

Fig. 4 Examples of the Na+-dependent folding isotherms derived fromthe data summarized in the false-color map of Fig. 2. Each isotherm rep-resents the averaged protection for the indicated nucleotides as a func-tion of Na+ concentration (Fig. 2). a, For the P4–P6 tetraloop, Na+

20% =103 mM and nH = 1.2; b, core region, Na+

20% = 131 mM and nH = 0.9; c, A-Bulge, Na+

20% = 829 mM and nH = 4.0; and d, the transient transitionat P2.1, Na+

20% = 22 mM and 333 mM, and nH = 2.0 and 3.8.

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contact partners occurs within a constrained conformationalspace.

Monovalent cations not only condense RNA4 but also alter thepredominant pathway of its folding7,10. Compaction per se can beargued not to facilitate fast and error-free folding but, rather, theelimination of non-native contacts and/or the formation ofnative contacts in the ensemble of RNA molecules is responsible.The present data argue for contributions from both mechanismsand suggest that the time lag of stable tertiary structure forma-tion behind global compaction will diminish as the monovalentcation concentration increases.

Substantial acceleration of the early steps of folding for boththe isolated P4–P6 domain9,11,30 and the L-21 ribozyme(T. Uchida, Q.H., C.Y.R., M.R.C. and M.B., submitted) isinduced by increases in the Na+ concentration from ∼ 10 to200 mM. The formation of native tertiary contacts and thedestabilization of non-native tertiary contacts occur over this[Na+] (Fig. 2). A prediction of these data is that a progressivelysmaller subset of Mg2+ folding transitions will be observed as[Na+] is increased.

For the catalytic core, numerous short- and long-range inter-actions present at high Na+ concentrations will restrain theensemble to a small number of native-like populations. The P3rather than alt-P3 secondary structure is dominant above300 mM NaCl10, eliminating a well characterized kinetic trap32,33.These structures and contacts are predicted to favor direct fold-ing. Although the above-described interactions should facilitatefolding of the catalytic core, the structure surrounding J8/7 isnon-native in the absence of Mg2+ and P1 is apparently notdocked to J9/7. Thus, the contribution of kinetic traps to Mg2+-dependent folding of the catalytic core cannot be discounted evenwhen a large fraction of the native tertiary structure is present.

In summary, the ensemble of structures present at high con-centrations of monovalent cation are predicted to be committed

to fast and correct folding because of the high probability of for-mation of native tertiary contacts. Thus, increases in monova-lent ion concentration induce structural changes that causefolding to commence, not only from different locations alongthe edge of folding funnel, but also from deep within it.However, Na+ cannot effectively substitute for all Mg2+ ions;Mg2+ is required for the formation of key catalytic core interac-tions that allow catalysis to occur.

MethodsEquilibrium titrations. The L-21 Sca I ribozyme fromTetrahymena thermophila was transcribed by T7 polymerase and 5′or 3′ end labeled with 32P as described34–36. The labeled RNA in CEbuffer was heated to 95 °C for 2 min and annealed by slow coolingto room temperature. Aliquots of the RNA were equilibrated at42 °C in CE buffer to which the indicated concentration of NaClwas added. Fe-EDTA-mediated Fenton chemistry was used to gen-erate OH• (refs 18,37–39). The RNA samples were footprinted at42 ºC for 2 min and processed for electrophoresis as described16.Following electrophoresis, the gel was imaged using a phosphorstorage plate that was scanned by a Storm 800 PhosphorImager(Molecular Dynamics).

Analytical ultracentrifugation. Sedimentation velocity experi-ments were performed at 20 °C using a Beckman Optima XL-I ana-lytical ultracentrifuge, An-60 Ti rotor and Al-Epon/Charcoalcenterpieces at 30,000g. The Tetrahymena ribozyme at 71.4 nM(8.96 µg ml–1) was folded under the same conditions as describedabove with indicated concentrations of either NaCl or MgCl2. Thesedimentation boundaries were directly fit as dc / R using SVED-BERG40 to determine the sedimentation and diffusion coefficients, Sand D, respectively. The observed values were normalized to stan-dard conditions at 20 °C in water. The Stokes radius, RH, and axialratio, a/b, were calculated using Sednterp41,42 assuming υ = 0.53 cm3

gm–1 and hydration = 0.59.

Footprinting data analysis. The relative densities of the bandsrepresenting each reaction product were determined by singleband analysis following a published protocol43. The gel images areconverted to lane profiles using ImageQuant (Molecular Dynamics)that are fit to a series of Lorentzian curves using the Peak FittingModule within Origin v6.1 (OriginLab). Iterations are run until thefidelity of fitted peak profile reaches at least 99.9% of original pro-file. The fitted peak areas are assembled as a two-dimensionalmatrix. Each column (lane) is ‘standardized’ by dividing the peakarea values by single or averaged ‘standard’ bands16,43–45. (Standardbands on a gel electrophoretogram do not vary as a function of theexperimental parameter being probed in a series of footprintingreactions and correct for variation in the amount of sample loadedonto each lane of a gel.)

The preceding published protocols have been automated byanalysis software that determines and uses the most appropriatereference bands. The principle underlying the automated system isthat the standard deviation of the peak area of valid standardbands is minimal compared with bands whose peak area varies withthe experimental parameter being assayed. The algorithm sequen-tially calculates the standard deviation for a set of bands and thenranks them by a ‘score’ that is equal to the ‘global standard devia-tion of matrix’ multiplied by the ‘mean value of standard deviationsof matrix row element’. The standardized matrix is then ‘normal-ized’45 to the reference lane with the lowest salt concentration by

Fig. 5 Values of the Stokes radius and axial ratio (RH and a / b, respective-ly) derived from sedimentation velocity experiments conducted in CEbuffer to which the indicated [NaCl] or [MgCl2] was added. The transi-tions were modeled as the sum of two Hill equilibria. For the MgCl2 titra-tion (open circles), the midpoints of these transitions are 0.2 and 7.5 mMfor RH and 0.2 and 8.9 mM for a / b. For the NaCl titration (solid squares),the midpoints of these transitions are 39 mM and 587 mM for RH and28 and 582 mM for a / b.

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division. The details of these procedures and the software devel-oped to streamline these procedures will be described elsewhere.Sets of individual analyses were averaged and combined to yieldthe two-dimensional map of the entire ribozyme using KyPlot v2.0β(K. Yoshioka, Japan).

The Na+-dependent folding isotherms were generated using asummation over protection values from the single band analysis(Fig. 2). The integrated density, ρi, as a function of [Na+] was scaledto the fractional saturation of the protection (ρi – ρlower) / (ρupper –ρlower), where ρlower and ρupper are the lower and upper limits of thetransition curves determined from the CE buffer (‘unfolded’) andMg2+-CE buffer (native) lanes, respectively16,44,45. The isotherms werefit by single or multiple-transition Hill equations46.

AcknowledgmentsWe thank D. Herschlag and R. Russell for pre-publication discussion of theirresults. This work was supported by grants from the National Institute of GeneralMedical Sciences and the Biomedical Technology Program of the Division ofResearch Resources.

Competing interests statementThe authors declare that they have no competing financial interests.

Correspondence should be addressed to M.B. email: [email protected]

Received 21 May, 2002; accepted 16 October, 2002.

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