Divalent ions tune the kinetics of a bacterial GTPase center rRNA folding transition from secondary to tertiary structure

Abstract

Folding of an RNA from secondary to tertiary structure often depends on divalent ions for efficient electrostatic charge screening (nonspecific association) or binding (specific association). To measure how different divalent cations modify folding kinetics of the 60 nucleotide E. coli rRNA GTPase center, we combined stopped-flow fluorescence in the presence of Mg²⁺, Ca²⁺, or Sr²⁺ together with time-resolved small angle X-ray scattering (SAXS) in the presence of Mg²⁺ to observe the folding process. Immediately upon addition of each divalent ion, the RNA undergoes a transition from an extended state with secondary structure to a more compact structure. Subsequently, specific divalent ions modulate populations of intermediates in conformational ensembles along the folding pathway with transition times longer than 10 msec. Rate constants for the five folding transitions act on timescales from submillisecond to tens of seconds. The sensitivity of RNA tertiary structure to divalent cation identity affects all but the fastest events in RNA folding, and allowed us to identify those states that prefer Mg²⁺. The GTPase center RNA appears to have optimized its folding trajectory to specifically utilize this most abundant intracellular divalent ion.

INTRODUCTION

The 60 nucleotide (nt) GTPase center RNA (GAC) from 23S rRNA (Fig. 1) must adopt an intricate tertiary structure to be functional (Moazed et al. 1988; Xing and Draper 1996; Holmberg and Noller 1999; Cameron et al. 2002; Helgstrand et al. 2007; Harms et al. 2008; Gao et al. 2009; Voorhees et al. 2010; Sprink et al. 2016). In the ribosome, the GAC is bound by the prokaryotic L11 protein (L12 in eukaryotes); L11 binding requires that GAC adopt its tertiary fold (Blyn et al. 2000). The GAC is also the binding site for the peptide antibiotic thiostrepton (Blyn et al. 2000). GAC nucleotides make specific transient contacts with essential ribosome cofactors during translation (Harms et al. 2008), such that E coli lacking the GAC is not viable. In vivo, Mg²⁺ ions facilitate its transition from secondary structure to tertiary fold (Fig. 1). Previous in vitro experiments have measured its ion-dependent folding that identified a chelated Mg²⁺ ion (Grilley et al. 2007; Leipply and Draper 2011). GAC crystal structures, both free (courtesy of G. Conn) and bound to L11 (Wimberly et al. 1999; Conn et al. 2002), show two common sites of divalent ion association (Fig. 1) that are thought to be essential for proper tertiary structure formation. The critical importance of the GAC to translation motivates efforts to understand how it adopts its tertiary fold.

FIGURE 1.

GAC structures and kinetic folding scheme. (A) Tertiary structure of E. coli GAC, with U1061A substitution (Conn et al. 2002). Divalent ion positions from a superposition of GAC crystal structures (pdb 1hc8, 1mms, 5d8h, 5dar, 4v8p, 4v4q); RNA is 1hc8. (B) Secondary structure from phylogenetic comparisons (Petrov et al. 2014). 2AP positions are labeled in blue. (C) Our model of the divalent ion-mediated (Me²⁺) kinetic trajectory of tertiary folding (Welty and Hall 2016).

Tertiary structure in noncoding RNAs typically involves noncanonical interactions between nucleobases, riboses, and phosphates (Butcher and Pyle 2011). To date, such interactions are virtually impossible to predict de novo, yet they can be intricate (Tinoco and Bustamante 1999; Cruz and Westhof 2009) and intrinsic to function (Mortimer et al. 2014). As negatively charged polyelectrolytes, RNA recruits high concentrations of cations (Misra and Draper 1998; Shiman and Draper 2000; Draper 2008, 2013; Bowman et al. 2012) to screen its phosphates and this charge screening allows RNAs to explore compact conformations which facilitate tertiary interactions (Denesyuk and Thirumalai 2015). Some RNAs can chelate divalent ions to stabilize specific conformations (Conn et al. 2002; Leipply and Draper 2011). Mg²⁺ is the most common divalent cation used for RNA folding, as it can participate in different interactions through its six coordinated waters as well as direct coordination to phosphates.

Ion-induced RNA folding is mediated by multiple driving forces (Lipfert et al. 2010, 2014). Many RNA molecules undergo rapid compaction or “electrostatic collapse” after mixing with cations of different valences and atomic character (Russell et al. 2000, 2002; Das et al. 2003; Chauhan et al. 2005; Moghaddam et al. 2009; Roh et al. 2010). The earliest folding events can be attributed to electrostatic relaxation, where nonspecific charge screening by cations relaxes single-stranded loop and bulge regions, which allows for better conformational sampling (Bartley et al. 2003). When slower folding events are observed, they are typically attributed to specific ion binding (Gluick et al. 1997; Swisher et al. 2002) or the satisfaction of a conformational search (Pljevaljcić et al. 2005). An early example of time-resolved RNA folding used small angle X-ray scattering (SAXS) to probe the secondary-to-tertiary structure change in the Tetrahymena Group I intron (Russell et al. 2000). This 414 nt RNA has a modular secondary structure that was found to collapse upon addition of divalent ions, then rearrange itself into the correct tertiary fold. The Tetrahymena Group I intron has been a model system for many studies of RNA folding, even though it forms long-lived misfolded structures in vitro. Mutations that prevent or exacerbate misfolding have provided insights into how the RNA uses specific sites during folding, and how ions can modulate its tertiary interactions.

The GAC secondary structure is known from phylogenetic comparisons that also identified eighteen of its sixty nucleotides as invariant among all organisms (Gutell et al. 1992b). Its tertiary structure alone and in co-crystals with the L11 protein and in the context of the ribosome subunit (Gao et al. 2009) is preserved. In vitro solution chemical probing of secondary and tertiary structures of prokaryotic GAC RNAs are consistent with predictions and crystal structures (Leipply and Draper 2011). Biochemical experiments focusing on the E. coli GAC probed its sequence dependence (Ryan and Draper 1991; Lu and Draper 1994, 1995; Draper and Xing 1995), ion dependence (Wang et al. 1993; Bukhman and Draper 1997; Leipply and Draper 2010), and thermal stability (Shiman and Draper 2000; Draper et al. 2001; Leipply et al. 2009), creating a compendium of data on its physico-chemical properties. In E. coli GAC, a single substitution, U1061A, destabilizes the tertiary structure in monovalent ions, and effectively results in a requirement for divalent ions (Mg²⁺) to adopt a stable tertiary structure (Lu and Draper 1994). Its Mg²⁺ requirement allows us to examine how this essential RNA element uses divalent ions to adopt its structure.

We are exploring the kinetic trajectory of the ion-induced conformational change from secondary structure to tertiary fold (Rau et al. 2015; Welty and Hall 2016). We replaced six adenosine nucleobases that crystal structures showed were not involved in hydrogen bonding (Wimberly et al. 1999; Conn et al. 2002) with the fluorescent base 2-aminopurine (Fig. 1). Stopped-flow fluorescence investigations of Mg²⁺-induced folding revealed multiple states along the GAC folding trajectory (Fig. 1; Welty and Hall 2016).

Now, we have examined GAC folding kinetics in the presence of Ca²⁺ and Sr²⁺. An earlier study of the GAC stability in the presence of Ca²⁺, Sr²⁺, and Mg²⁺ identified two binding sites with differential affinities for these ions (Bukhman and Draper 1997) that could affect the states along the kinetic trajectory we proposed (Welty and Hall 2016). Additionally, time-resolved and steady-state SAXS experiments allow us to connect structural insights of conformational ensembles to the mechanistic folding model. Time-resolved SAXS data show a rapid compaction of the GAC within 10 msec after Mg²⁺ addition as seen in other small RNA molecules (Russell et al. 2002; Das et al. 2003; Perez-Salas et al. 2004; Takamoto et al. 2004; Plumridge et al. 2018). Our new results show that initial GAC contacts with divalent ions are electrostatic, but subsequent GAC/divalent ion interactions are ion-specific. The three divalent ions lead to biased subpopulations in the dynamic equilibria of GAC structures within states along folding routes, and reveal how Mg²⁺ ions have a unique role in folding of the GAC.

RESULTS

Divalent ion titrations

UV absorbance and steady state SAXS

For all our experiments, we use a variant of E. coli GAC containing the U1061A substitution. Position 1061 is not conserved in GAC sequences; most eukaryotic GAC's have G1061, and some archaea have A1061 (Gutell et al. 1992a). In the background of the E. coli sequence, A1061 destabilizes any tertiary structure that might form in the absence of divalent ions, but has increased stability in the presence of Mg²⁺ (Lu and Draper 1994). Sites of 2AP substitution were selected from phylogenetic comparisons and crystal structures: sites A1067, A1069, and A1061 are not conserved and do not contribute hydrogen bonds to the tertiary fold; A1070 and A1095 are invariant, but do not make tertiary contacts (A1095 contacts cofactors). We assessed secondary and tertiary structure stability for all 2AP constructs by thermal denaturation in UV absorbance measurements, as established by the Draper lab (Ryan and Draper 1991).

To evaluate the role of ions on folding, we compared the change in absorbance and the change in SAXS properties of the GAC during titrations with MgCl₂, CaCl₂, and SrCl₂. Ca²⁺, Sr²⁺, and Mg²⁺ are alkaline earth metal cations that differ in their hydrated radii (4.14, 4.14, 4.28 Å, respectively [Conway 1981]). All have closed-shell electron orbitals, and all are associated with at least six water molecules in solution. Previous studies (Bukhman and Draper 1997) of E. coli GAC U1061G stability in 1.6 M NH₄Cl upon addition of Ca²⁺, Sr²⁺, Ba²⁺, or Mg²⁺, identified two ion binding sites: One site bound tighter to ions with a smaller ionic radius (Mg²⁺ > Ca²⁺ > Sr²⁺); the second site preference was ordered Mg²⁺ > Ba²⁺ > Sr²⁺ > Ca²⁺. Now, we work in a background of 100 mM KCl (K⁺ is more effective than Na⁺ at stabilizing GAC structure [Lu and Draper 1994]) to measure the effects of Ca²⁺ and Sr²⁺ on the kinetics of GAC folding.

First in steady-state experiments, we find that all three divalent cations drive GAC tertiary structure formation, but they are not equivalent. The change in UV absorption upon titration with the ions reveals a progressive decrease in absorbance at 260 nm (Fig. 2A) as the GAC adopts its tertiary structure. We attribute the loss of absorbance to an increase in base stacking and corresponding hypochromicity (Grilley et al. 2007). Mg²⁺ drives the transition to the tertiary structure at lower concentrations than either Ca²⁺ or Sr²⁺. Significantly, the final value of absorbance change is not identical, suggesting that the final folded states of the GAC differ with divalent ion.

FIGURE 2.

GAC tertiary structure ensemble is controlled by divalent ion identity. (A) Percent absorbance change at 260 nm of the GAC RNA upon titration with divalent ions. [GAC] = 2 µM; starting absorbance for each titration is the same within error. Data corrected for dilution with higher concentrations of ions. (B) Calculated Rg from steady-state SAXS measurements upon titration with divalent ions. (C) Kratky profiles from SAXS shows compaction from the extended states in KCl to more compact states in 1 mM divalent ions. [GAC] = 30 µM. All solutions contained 100 mM KCl, 10 mM sodium cacodylate (absorbance) or MOPSO (SAXS), pH 6.5 at 22°C.

Analogous steady-state SAXS measurements provide another measure of the folded tertiary state of the GAC. Titrations of the GAC with each divalent ion show a dramatic difference in the calculated radius of gyration (R_g) of the RNA (Fig. 2B). SAXS profiles are shown as Kratky plots, I × q² versus q (Fig. 2C), to illustrate the evolution of compaction from the extended state. GAC in K⁺ shows a Kratky profile with a low peak and lightly sloping tail, characteristic of extended states. The Kratky profile of a more compact state shows a pronounced peak and a sharper decaying tail at high q. At 1 mM divalent ion concentration, GAC in MgCl₂ is more compact than in CaCl₂, which is more compact than in SrCl₂. For GAC in 1 mM MgCl₂, Rg averaged over 12 measurements taken at 6 beam runs was 21.3 ± 0.5 Å (20.2 Å–21.9 Å). (We note that our SAXS measurements and Rg values for GAC follow very stringent rules developed for analysis [Trewhella et al. 2017].) Please refer to the Supplemental Material for illustrative I versus q data and a Guinier fit for the GAC.) Unfortunately, SAXS experiments were limited to a final 1 mM concentration of ions due to interparticle interference effects at higher divalent ion concentrations. The R_g trend follows the change in absorbance, supporting the interpretation that the folded ensembles of the GAC are not identical for the three ions.

In contrast, calculating Rg from the co-crystal structure (PDB ID 1HC8, after stripping off the L11 CTD) gives a value of 17 Å using the program CRYSOL (Svergun et al. 1995). This difference implies that crystallization may inhibit some of the freedom of configurational motion in solution that allows the GAC to sample alternate conformations.

Previously, Grilley et al. (2007) also used SAXS to compare the envelopes of folded and unfolded GAC-U1061A. In a solution of 40 mM K⁺ and 1 mM Mg²⁺ at 15°C, they calculated (with GNOM) Rg = 18 Å, and without Mg²⁺ Rg = 23–25 Å (40–150 mM K⁺). The lower monovalent concentrations (40 mM KCl + Mg added) can lead to repulsive interactions at SAXS concentrations of nucleic acids, which could be misconstrued as lower Rg (Pabit et al. 2009, 2013), accounting for the disagreement between our values. In our experiments, we collected data at several GAC concentrations in several salt conditions (please see the Supplemental Material) to arrive at conditions where the data were consistent. We also used in-line and in-lab Size-Exclusion Chromatography (SEC) SAXS to probe for micro-aggregates that would inflate the Rg values. Although our value of Rg = 21.3 ± 0.5 Å for GAC in its tertiary fold is larger than the Grilley value, the trends from extended to compacted volume in the presence of Mg²⁺ are the same.

Fluorescence

For fluorescence experiments we utilized six individual constructs in which one Adenosine was replaced with 2-Aminopurine (2AP-GAC) (Dellinger et al. 2011). We have previously shown by thermal denaturation that these substitutions do not significantly alter GAC stability (Rau et al. 2015) (the GAC has a characteristic UV absorbance profile upon thermal denaturation). 2AP fluorescence reports local environmental changes (Jean and Hall 2001; Rachofsky et al. 2001; Rist and Marino 2001; Hall and Williams 2004; Sarkar et al. 2009), which in the GAC we have found are sensitive to the conformational change from secondary to tertiary structure (Welty and Hall 2016). Ion titrations of each 2AP-GAC showed that tertiary folding reaches equilibrium in Mg²⁺ and Ca²⁺ by 3 and 5 mM, respectively, whereas 100 mM Sr²⁺ is required. A comparison of the percent fluorescence change at each site in the presence of 5 mM and 100 mM Me²⁺ shows a consistent increase or decrease of fluorescence (Fig. 3). We interpret these data to indicate that local structural changes of the GAC are similar for the three divalent ions, and that its tertiary fold has formed.

FIGURE 3.

The RNA folds upon addition of divalent ions (Mg²⁺, Ca²⁺, Sr²⁺). Titrations of 2AP-GAC fluorescence for (A) 2AP-1061 and (B) 2AP-1070 are shown. Other sites are analogous.

Folding kinetics

Stopped-flow fluorescence

The time-trace of 2AP-GAC fluorescence for each 2AP site after addition of each divalent ion is shown in Figure 4. Concentrations of each added divalent ion were selected from titration experiments to ensure that saturation was reached (all stopped-flow fluorescence traces at all ion concentrations are shown in Supplemental Fig. 6A–C). Note that the shape of the fluorescent time-trace from several 2AP-GAC constructs varies with different divalent ions. Transitions in the presence of Mg²⁺ appear later in the timecourse, and the trace from 2AP-GAC 1061 is the most idiosyncratic. All traces collected with the same divalent ion at a given concentration were globally fit to the sum of three exponentials (Eq. 1),

$$y=y_0+A_1{e}^{-t/{\tau }_1}+A_2{e}^{-t/{\tau }_2}+A_3{e}^{-t/{\tau }_3}$$ (1)

which successfully reproduced the data, with the exception of AP1089, which has different transition times. The amplitudes differ with each 2AP site, but the rates are common to each. The resulting observed rates (k_obs = 1/τ) partition into three timescales: 1–20 msec, 20–200 msec, and >200 msec (corresponding rates 1–50 sec⁻¹, 0.1 to 4 sec⁻¹, and 0.01 to 0.15 sec⁻¹), which are plotted for each ion in Figure 5.

FIGURE 4.

GAC tertiary folding kinetics. (A–C) Traces from stopped-flow fluorescence experiments show each 2AP-GAC RNA response to addition of each divalent ion at [Me²⁺] = 20 mM (top: Mg²⁺, middle: Ca²⁺; lower Sr²). 1061, blue; 1067, green; 1069, lavender; 1070, yellow; and 1095, gray. Each data trace is superimposed with its global fit from Equation 1. Traces have been offset to an ending value of 1 A.U. for comparison. (D–F) Traces replotted to show the rapid (∼1 msec) 2AP fluorescence changes upon addition of divalent ions. Traces have been normalized to percent fluorescence change, with the starting value (without Me²⁺) equal to 100%.

FIGURE 5.

Global observed rates calculated from exponential fitting to Equation 1 as a function of divalent ion concentration (1/τ_n = k_n,obs, n = 1,2,3). k_1,obs (left) is the most rapid observed rate; k_2,obs (middle) corresponds to the transition with the largest amplitude; k_3,obs (right) is the slowest rate. Mg²⁺, ▪; Ca²⁺, X; and Sr²⁺, Δ.

This analysis reveals that GAC folding in Mg²⁺ is consistently different than in either Ca²⁺ or Sr²⁺, revealing new insight into the mechanism of its ion-induced folding. The first transition with observed rate k_1,obs is the most rapid. As we previously noted (Welty and Hall 2016), k_1,obs for Mg²⁺ addition decreased with increased concentration of ion. This is a signature of a rate-limiting kinetic step that precedes a binding event (Galletto et al. 2005; Vogt and Di Cera 2012). For the GAC interaction with Mg²⁺, that kinetic step corresponds to conformational changes of the RNA that occur before Mg²⁺ binds. In contrast, k_1,obs in the presence of Ca²⁺ and Sr²⁺ increase with increasing ion concentrations, which is also consistent with an induced-fit mechanism (in the limit of rapid equilibrium); while perhaps not intuitively obvious, the analytical relationship has been demonstrated (Vogt and Di Cera 2012). In the induced-fit mechanism, Ca²⁺ and Sr²⁺ would associate with the GAC and “force it” to adopt a conformation. Both signatures are examples of conformational selection (Vogt and Di Cera 2013; Chakraborty and Di Cera 2017), but the mechanisms are distinct.

Observed rates of subsequent GAC folding transitions (k_2,obs and k_3,obs) are consistently slower in the presence of Mg²⁺, and are sensitive to the specific ion. We can interpret these data in terms of conformational ensembles: Mg²⁺ reduces rates of conformational sampling, while Ca²⁺ and Sr²⁺ allow more rapid sampling possibly due to weaker association. As a consequence, different ions preferentially stabilize different conformations in the ensembles.

Time-resolved SAXS

In our time-resolved fluorescence experiments, GAC in 100 mM KCl without divalent ion is mixed with a solution of MgCl₂, CaCl₂ or SrCl₂ in 100 mM KCl at various concentrations. The dead time of the mixer is ∼1 msec, so events that occur more rapidly cannot be directly observed. However, at the first detectable timepoint (∼1 msec), we observe that all 2AP-GAC fluorescence intensities have changed from their starting values in KCl (when the GAC has only secondary structure). In Figure 4D–F, that starting fluorescence value is designated as 100%. Dotted lines indicate the jump of fluorescence intensity upon mixing with divalent ion solution. The trend at each site is independent of the specific divalent ion, although its amplitude is ion concentration-dependent.

We previously proposed that the rapid event in the fluorescence experiments was due to a rapid initial global compaction of the GAC upon Mg²⁺ addition (Welty and Hall 2016). Now, we use time-resolved SAXS to measure the scattering properties of the GAC during Mg²⁺-induced folding. (Similar experiments in the TR-SAXS flowcell with CaCl₂ yielded unusable results caused by interparticle association, and the required Sr²⁺ concentration is too high for the apparatus.) Time points (0.01, 0.03, 0.05, 0.1, 0.3, and 1 sec) corresponded to analogous fluorescence measurements. Rg was calculated at each timepoint (Fig. 6A) from Guinier analysis; representative Kratky profiles are shown (Fig. 6B). TR-SAXS data show that the RNA forms a more compact state within 10 msec of the addition of divalent ions. Kratky profiles continue to evolve up to 1 sec approaching the final state (t = ∞) at Rg of ∼22 Å, comparable to the steady-state value of 21.3 ± 0.5 Å in 1 mM MgCl₂. We conclude that indeed the fluorescence change that occurs in <1 msec in our stopped-flow fluorescence experiments is due to a global compaction of the GAC.

FIGURE 6.

The GAC has a rapid response to addition of divalent ions. (A) TR-SAXS continuous mixer allows us to follow the change in Rg of the GAC as a function of time in the presence of Mg²⁺. (B) Kratky plots for t = 0, t = 30 msec, t = 300 msec, t = steady state along the trajectory.

Numerical modeling of folding kinetics

The initial interaction of the GAC with divalent ions (<1 msec) is not described by Eq. 1. This in part led to our working model (Welty and Hall 2016) of the folding kinetics in the presence of Mg²⁺ that included six states (Fig. 1). In our model, the secondary structure (2°) transitions to intermediates I₁ and I₂ upon addition of divalent ion in <1 msec. Association of a single stoichiometric ion leads to I₃, which then samples conformations to result in a final ensemble that includes I₃, I₄, and the tertiary fold (3°). More complex kinetic mechanisms, both nonlinear and those with additional states, were unable to better fit the data.

Now, with three divalent ions, Mg²⁺, Ca²⁺, and Sr²⁺, we describe all states along the folding trajectory analyzed by metaheuristic optimization algorithms (Hastie et al. 2009) to determine any similarities in their kinetic mechanisms (see Supplemental Material). While our kinetic scheme describes GAC folding in the presence of all three divalent ions, the analysis notably reveals that ion interactions with the RNA result in different rate constants and equilibrium populations (Table 1; Fig. 7).

TABLE 1.

Rate constants along the GAC folding trajectory

FIGURE 7.

Apparent equilibrium constants (K_n) and calculated rate constants (k_n) for GAC tertiary folding. *K1 and *K3 reflect bimolecular interactions between RNA and ions (s⁻¹mM⁻¹). k_n is forward rate constant; k_−n is reverse rate constant. (**) Upper limit values. Slower rates do not change the quality of fit.

The first GAC transition (<1 msec) is not divalent ion-specific (K₁; k₁, k₋₁ are identical), suggesting that the ions are there to neutralize phosphate charges and allow a close approach of chains. Significantly, rate constants k₋₄ and k₋₅ for Mg²⁺ are uniquely slow. These slow reverse rates effectively drive the GAC forward to its final conformation (3^o in Fig. 1), as they limit its backward sampling of previous states. In contrast, the rate constants k₋₄ and k₋₅ in Ca²⁺ and Sr²⁺ are equal to or more rapid than their respective forward rates, and as a consequence, the final state of the GAC in these divalents will contain substantial populations of I₃, I₄, and 3° ( Fig. 1). The critical ion property that alters these rate constants cannot be ascertained from our experiments. Ion charge density, hydrated radius, number of associated waters, polarizability, or ease of dehydration may all contribute. Curiously, the rate constants could reflect the difference in ion binding affinity of these three divalent ions (Bukhman and Draper 1997) [site one affinity: (Mg²⁺ > Ca²⁺ > Sr²⁺); site two affinity: (Mg²⁺ > Sr²⁺ > Ca²⁺)] noted in equilibrium binding experiments with the GAC.

Here we must introduce a caveat regarding the interpretation of intermediates in the kinetic model of GAC folding (Fig. 8). Classically, these intermediates have been associated with specific structures that undergo conformational changes along a path. As articulated by Dill and Chan, in their perspective on protein folding (Dill and Chan 1997), these intermediates are in fact ensembles of conformations. Distributions of conformations can be broad, and conformations are not restricted to a particular intermediate state. The concept of a rugged folding funnel seems made for descriptions of RNA folding: GAC folding has a “bumpy landscape” with its corresponding multiple state kinetics.

FIGURE 8.

A conceptual model of GAC folding. From left: Starting from the secondary structure (State 1), an ensemble of conformations is present upon addition of divalent ions (States 2 and 3); a stoichiometric Me²⁺ ion can bind to some structures, leading to formation of tertiary interactions (including base triples) that staple the hairpins together; the three-way junction is collapsed to form a triloop (States 4,5,6). Blue stars correspond to two sites in crystal structures where divalent ions are located.

DISCUSSION

There is not a single tertiary structure of the GAC RNA. Instead, there is an ensemble that is best modeled as a dynamic equilibrium of folded states (I₃, I₄, and 3°). Indeed, previous work has shown that sequence variants of the GAC exhibit different stabilities under thermal denaturing conditions depending on the associated divalent ion (Bukhman and Draper 1997). This suggests two possible hypotheses: First, that the RNA has unique conformational states for each ion; Second, that the RNA accesses the same folded states but in different ion-specific proportions. Because our data sets from each ion can all be modeled by the same kinetic mechanism, we propose that there is ion-specific stabilization of different states within a common ensemble.

Other studies of RNA folding have arrived at similar conclusions. For example, observation of the flux of intermediates in the ion-dependent folding pathway of the Tetrahymena Group I intron RNA, and dynamic equilibria of RNAs observed using single molecule experiments (Heilman-Miller et al. 2001; McDowell et al. 2010; Wan et al. 2010; Suddala et al. 2015) are consistent with our second hypothesis. Specifically, Tetrahymena Group I intron was shown to undergo electrostatic collapse, also referred to as electrostatic relaxation or compaction, as the first response to divalent ions (Russell et al. 2000, 2002; Das et al. 2003). Previous studies have used equilibrium ion titrations to measure RNA tertiary folding, the more sophisticated of which typically invoke either cooperative folding mechanisms (Fang et al. 2002; Behrouzi et al. 2012; Strulson et al. 2014) or the partial ion interaction coefficient framework (Record et al. 1978). The assumptions and complications of these approaches have been discussed by Lipfert et al. (2010, 2014). If an RNA tertiary structure is composed of multiple states in a dynamic equilibrium with similar spectroscopic signals, then standard binding density functions will not accurately describe the ion associations. Our kinetics experiments reveal the presence of ion-dependent transitions that equilibrium experiments cannot see.

Dissecting RNA tertiary folding trajectories can prove challenging and has only been attempted for a few RNA molecules (Deras et al. 2000; Ralston et al. 2000; Keller et al. 2014). The difficulty arises in trying to define often short-lived intermediates that are very difficult to identify and quantify. Previous attempts have utilized a range of time-resolved techniques such as footprinting (Sclavi et al. 1998; Silverman et al. 2000; Shcherbakova et al. 2004), scattering (both X-ray and neutron) (Russell et al. 2000; Das et al. 2003; Perez-Salas et al. 2004; Moghaddam et al. 2009; Roh et al. 2010; Pollack 2011), as well as fluorescence (Chauhan et al. 2009; Haller et al. 2011; Buskiewicz and Burke 2012; St-Pierre et al. 2014; Frener and Micura 2016). Our experiments directly observe continuous changes in the orientations and stacking of the 2AP nucleobases (local events) as well as changes in the global conformational ensemble observed via SAXS during the transition from secondary structure to tertiary folds.

Separating the effects of nonspecific ion association and specific ion binding to nucleic acids is a complex and nontrivial problem. In the context of equilibrium RNA folding the energetic contributions of nonspecific association and binding are linked, and not independently measurable. Examining the kinetics of folding can help disentangle both effects by attempting to discover discrete binding events. Discrete binding events behave according to mass action laws, however nonspecific interactions, such as counterions with polyelectrolytes, do not (Wyman and Gill 1990). It is possible that there are nonspecific ion association effects that mimic stoichiometric binding to the GAC; however, this is unlikely due to the consistency of the model when accounting for three different cations at varying concentrations.

The identity of the ion alters both uni-molecular reactions (conformational changes) and bi-molecular reactions (discrete ion binding). The model in Figure 1 has two ion binding/unbinding steps; if the nature of nonspecific interactions were identical across all three cations, then only these rate constants would change. However, all rate constants, aside from k₁/k₋₁, are modulated differently by each cation. These findings further support the hypothesis that the GAC “binds” each of these ions, although it does so with different affinities. Binding could be chelation, hydrogen bonding, and/or polarization; the differences could account for affinities and rate constants. Our data indicate that folding rates and equilibrium populations of RNA can be tuned by ion identity.

In cells, the GAC will be surrounded by K⁺ and Mg²⁺ ions, both of which are preferred for its folding. Because it is a small autonomous structural element, it can adopt its secondary structure as it is being transcribed. After its final stem has formed, it can fold into its tertiary structure, and the folding trajectory that we describe here is a plausible model. In prokaryotes, the L11 protein could be present; L11 can bind to the GAC before it folds, and might be thought of as a (nonessential) chaperone.

MATERIALS AND METHODS

All GAC RNAs containing a single site 2-aminopurine were chemically synthesized by Agilent (Dellinger et al. 2011). GAC molecules were also transcribed using T7 RNA polymerase by run-off transcription (Milligan et al. 1987). All RNAs were purified by denaturing gel electrophoresis and dialyzed against 0.2 M EDTA, then against deionized distilled water. Solutions were lyophilized to concentrate the RNA, which was stored at −20°C until needed. To fold GAC into its secondary structure in buffer (no divalent ions), solutions were heated at 65° for 30 min and cooled to room temperature on the bench top (Leipply and Draper 2011). All experiments were performed in a buffer background of 10 mM sodium cacodylate and 100 mM KCl at pH 6.5. All stock solutions were passed through 0.45 µm cellulose nitrate filters and stored in the plastic reservoir (Nalgene).

Equilibrium fluorescence measurements were collected at 2 µM 2AP-RNA on a Photon Technology International spectrofluorometer at 20 ± 0.1°C. Samples were excited at 305 nm, and emission was measured at 368 nm wavelength. Absorption measurements were taken on a Cary 100Bio absorption spectrophotometer. Stopped-flow measurements were made on an Applied Photophysics SX-20 stopped-flow spectrometer 20 ± 0.1°C. RNA concentration for stopped-flow fluorescence was 100 nM (final), and for absorbance, 2 µM. Stopped-flow data were averaged and normalized with MATLAB (MathWorks), and globally fit using the originPRO (OriginLab Corp) software package. The basis for application of genetic algorithms to determine rate constants is detailed in the Supplemental Material.

All RNAs used in SAXS experiments were transcribed with T7 RNA polymerase (Milligan et al. 1987). Buffer conditions for SAXS experiments were 10 mM MOPSO, 100 mM KCl, pH 6.5. Divalent ions were added to the RNA immediately prior to the SAXS measurements or mixed within the flow cell for the time-resolved SAXS (TR-SAXS) measurements. For static SAXS measurements, RNA concentrations were 30 and 60 µM and for TR-SAXS, 75–100 µM GAC.

All SAXS data were collected at the Cornell High Energy Synchrotron Source (CHESS). Steady state SAXS measurements were made using the BioSAXS setup at the G1 beamline (Supplemental Fig. S1) with x-ray energy of 9.924 keV and a beam size of 250 µm². Liquid samples were loaded in a 1.5 mm quartz capillary and the samples were oscillated to avoid radiation damage. Measurements were made using the Pilatus 100K detector over 20 sec with a 1 sec integration time. Time resolved SAXS (TR-SAXS) measurements were collected at the same G1 beamline with a home-built continuous flow mixer setup (Supplemental Fig. S4) using 11.18 keV x-rays that passed through a 50 µm scatterless pinhole. In the continuous-flow mixer setup, GAC in buffer and 100 mM KCl flows in the inner channel, and buffer with 20 mM MgCl₂ and 100 mM KCl flows in the outer channel. Mixing was facilitated by coaxial diffusion of Mg²⁺ ions into the sample as described previously (Pabit and Hagen 2002; Calvey et al. 2016; Plumridge et al. 2018). To collect TR-SAXS images, the flow cell was moved with respect to the x-ray beam to coincide with a particular mixing time point (Supplemental Table S1). Buffer background profiles were collected by turning off the sample flow. TR-SAXS experiments used an Eiger 1 M detector. All SAXS data were processed using BioXTAS RAW (Hopkins et al. 2017) and in-house MATLAB scripts. The reported radii of gyrations (Rg) were calculated from a Guinier Analysis (Supplemental Fig. S3), and the Kratky profiles, plots of I × q² versus q, are shown to emphasize shape changes in the high-q region. More information on the SAXS experiments and the TR-SAXS flow cell are in the Supplemental Material.

SUPPLEMENTAL MATERIAL

Supplemental material is available for this article.