Mg2؉-dependent conformational change of RNA studied by fluorescence correlation and FRET on immobilized single molecules
Harold D. Kim*, G. Ulrich Nienhaus†‡, Taekjip Ha*§, Jeffrey W. Orr¶, James R. Williamson¶, and Steven Chu*ʈ
*Department of Applied Physics and Physics, Stanford University, Stanford, CA 94305-4060; †Department of Biophysics, University of Ulm, D-89069 Ulm, Germany; ‡Department of Physics, University of Illinois, Urbana, IL 61801-3080; and ¶Department of Molecular Biology and The Skaggs Institute of Chemical Biology, The Scripps Research Institute, La Jolla, CA 92037
Contributed by Steven Chu, February 9, 2002 Fluorescence correlation spectroscopy (FCS) of fluorescence reso- showed that various cations such as Mg2ϩ,Ca2ϩ,Co3ϩ, and nant energy transfer (FRET) on immobilized individual fluoro- spermidine alone also yield the same folded conformation of the phores was used to study the Mg2؉-facilitated conformational junction (8, 9). Crystallographic studies located 8 Mg2ϩ ions change of an RNA three-helix junction, a structural element that around the junction region that may be involved in stabilizing the initiates the folding of the 30S ribosomal subunit. Transitions of folded form (10). the RNA junction between open and folded conformations resulted When fluorescence resonance energy transfer (FRET) (14, in fluctuations in fluorescence by FRET. Fluorescence fluctuations 15) was applied to single molecules (16), we previously observed occurring between two FRET states on the millisecond time scale conformational changes of individual RNA junctions that con- ؉ ؉ were found to be dependent on Mg2 and Na concentrations. tained shortened helices 20, 21, and 22 (17). In the open Correlation functions of the fluctuations were used to determine conformation, the donor and acceptor are about 8.5 nm apart, transition rates between the two conformations as a function of whereas in the folded conformation they are about 5 nm apart 2؉ ؉ Mg or Na concentration. Both the opening and folding rates based on the three-dimensional structure (10, 11). The large were found to vary with changing salt conditions. Assuming difference in donor–acceptor distance between the open and 2؉ specific binding of divalent ions to RNA, the Mg dependence of folded state makes the two conformations easily distinguishable the observed rates cannot be explained by conformational change ͞ ϩ by their different FRET efficiencies defined as Ia (Ia Id), induced by Mg2؉ binding͞unbinding, but is consistent with a where Ia is the acceptor intensity and Id is the donor intensity. In model in which the intrinsic conformational change of the RNA our previous study, the binding equilibrium and slow dissociation junction is altered by uptake of Mg2؉ ion(s). This version of ͞ of S15 were observed. However, when we used a buffer exchange FCS FRET on immobilized single molecules is demonstrated to be technique with a mixing time of Ϸ10 ms, we were unable to a powerful technique in the study of conformational dynamics of measure the conformational dynamics of the RNA junctions in biomolecules over time scales ranging from microseconds to ϩ response to [Mg2 ] changes. seconds. In this work, we use fluorescence correlation spectroscopy (FCS) (18, 19) and FRET on immobilized single molecules to 2ϩ ϩ onovalent and divalent cations such as magnesium and measure the Mg - and Na -dependent folding rates (kf,obs) and Msodium play an important role in stabilizing nucleic acid opening rates (ko,obs) of the RNA junction. Conventional FCS on structure in vivo. Specific binding sites for magnesium ions (1) freely diffusing molecules is not applicable if the time scale of have been observed crystallographically in a number of systems, their molecular transition is longer than their diffusion time including tRNA (2), hammerhead ribozyme (3), the P4-P6 across the observation region. Also, impurities, dye degradation, domain of the Tetrahymena thermophila group I intron (4), and or incomplete labeling of one of the FRET pairs can be easily a 5S ribosomal RNA domain (5). Metal ions can also stabilize the identified with immobilized molecules. RNA structure nonspecifically by screening the negatively charged backbone (6). Furthermore, the role of counterions is Materials and Methods critical to understanding protein–nucleic acid interactions (7). Sample Preparation. A Cy3–Cy5 donor–acceptor pair was at- In the case of RNA–protein interactions, the situation can be tached to two ends of the three-helix junction (Fig. 1), and a even more complex when ion-dependent conformational biotin moiety attached to the third helix was used for immobi- changes accompany protein binding. An interesting example is 1 lization on a glass surface. Two coverslips (No. 1 ⁄2, VWR the three-helix junction located in the central domain of the 16S Scientific) were flamed with a propane torch and taped to each ribosomal RNA that is the binding site for protein S15 (Fig. 1). other. The narrow channel between two glasses guided by double Biochemical analysis of the binding of S15 from Bacillus stearo- stick tape was used as a flow cell for microscopy. Glass surface thermophilus has shown that a large conformational change was treated with 1 mg/ml of biotin-labeled bovine albumin occurs in the junction region (8, 9). Two different groups recently (Sigma), 0.2 mg/ml of streptavidin (Molecular Probes) and Ϸ50 solved the crystal structure of the ribo–nucleoprotein complex pM of biotinylated RNA junction, successively. Each step lasted including the junction region and S15 protein (10, 11), and the for 5 min and was followed by washing the flow cell with the structure of the entire 30S subunit has been solved (12, 13). ͞ In the open (unfolded) form of the junction, the three helices standard buffer (10 mM Tris 50 mM NaCl, pH 8). The biotin- 20, 21, and 22 are arranged with nearly equal Ϸ120° angles
between them. The folded form of the junction is formed in the Abbreviations: FRET, fluorescence resonance energy transfer; FCS, fluorescence correlation presence of ions or upon the binding of S15, where helix 21 stacks spectroscopy. coaxially under helix 22, and helix 20 makes 60° angle with helix §Present address: Department of Physics, University of Illinois, Urbana, IL 61801-3080. 22. This unusual structure is stabilized in part by the noncanoni- ʈTo whom reprint requests should be addressed. E-mail: [email protected]. cal base-pairing between C754 and G654. S15 interacts with the The publication costs of this article were defrayed in part by page charge payment. This upper bulge region of helix 22 and the junction region. Solution article must therefore be hereby marked “advertisement” in accordance with 18 U.S.C. studies based on gel mobility of this RNA three-helix junction §1734 solely to indicate this fact.
4284–4289 ͉ PNAS ͉ April 2, 2002 ͉ vol. 99 ͉ no. 7 www.pnas.org͞cgi͞doi͞10.1073͞pnas.032077799 Downloaded by guest on September 29, 2021 ϩ ϭ at time t . Applying the initial condition, Nm(t) N and ϩ solving for Nn(t ) by using Eq. 4 leads to N ͑t ϩ ͒ k k ͑ ͉ ϩ ͒ ϭ n ϭ ͩ␦ Ϫ nͪ Ϫ ϩ n P m, t n, t ͑ ͒ mn e , Nm t [6] ␦ where mn is the Kronecker delta. If Im is the observable measured from a single molecule in state m, the autocorrelation of I can be derived from Eq. 1 as
2 2 ͑ ͒ ͑ ͉ ϩ ͒ ImInP m P m, t n, t ͗I͑t͒I͑t ϩ ͘ m ϭ 1 n ϭ 1 Ϫ ϭ Ϫ 2 1 1 ͗I͑t͒͘ 2 ͑ ͑ ͒͒2 ImP m Fig. 1. The secondary structure of a modified 16S ribosomal RNA junction. m ϭ 1 Bases in bold light gray are conserved above 95% across all known eubacterial sequences. On folding, rotation of helix 22 by 60° toward helix 20 decreases ͑ Ϫ ͒2 I2 I1 k1k2 Ϫ the donor–acceptor distance from 8.5 nm to 5 nm, and the FRET efficiency ϭ ͑ ϩ ͒2 e . [7] increases markedly. Based on the crystal structure, it is likely that C754 switches k1I1 k2I2 base pairing from G587 to G654 in this transition. We assume that the donor (acceptor) signal fluctuates in an folded anticorrelated manner between two intensity levels Id and open folded open ylated end of an RNA junction then forms a specific binding to Id (Ia and Ia ). We further assume that two rate coeffi- the surface through the streptavidin linker. cients, the observed folding and opening rates, kf,obs and ko,obs apply to both signals. Applying these assumptions to Eq. 7, the Correlation of Fluorescence Intensities. Information on stochastic autocorrelations for donor and acceptor signals and the cross- processes underlying the fluctuations is contained in correlations correlation between the two signals become of fluorescence fluctuations. Even for shot-noise-dominated Ifolded 2 fluorescence fluctuations, rate constant for the fluctuations can ͩ a Ϫ ͪ open 1 be extracted with high accuracy by counting a large number of Ia ko,obs Ϫ AC ͑͒ ϭ e , [8] photons. The autocorrelation AC( ) of a signal I(t) is defined by a Ifolded k 2 k ͩ a ϩ o,obsͪ f,obs open ͗␦I͑t͒␦I͑t ϩ ͒͘ ͗I͑t͒I͑t ϩ ͒͘ Ia kf,obs ͑͒ ϭ ϭ Ϫ AC ͗ ͑ ͒͗͘ ͑ ͒͘ ͗ ͑ ͒͗͘ ͑ ͒͘ 1, [1] I t I t I t I t Iopen 2 ͩ d Ϫ ͪ ͗ ͘ ␦ folded 1 where I(t) is the time average of I(t), and I(t) is the difference Id kf,obs Ϫ ͗ ͘ AC ͑͒ ϭ e , and [9] of I(t) from I(t) . Similarly, the cross-correlation CC( )oftwo d Iopen k 2 k ͩ d ϩ f,obsͪ o,obs signals is defined by folded Id ko,obs ͗␦I ͑t͒␦I ͑t ϩ ͒͘ ͗I ͑t͒I ͑t ϩ ͒͘ ͑͒ ϭ d a ϭ d a Ϫ ͑͒ ϭ Ϫ͓ ͑͒⅐ ͔͑͒1/2 CC ͗ ͑ ͒͗͘ ͑ ͒͘ ͗ ͑ ͒͗͘ ͑ ͒͘ 1. [2] CC ACa ACd , [10] Id t Ia t Id t Ia t where the apparent rate coefficient is the sum of kf,obs and To obtain correlation functions in terms of transition rates, we folded Ͻ open folded Ͼ open ko,obs. It is assumed that Id Id and Ia Ia for an consider a two-level system composed of N identical molecules anticorrelated fluctuation. The two-state approximation holds with state 1 and state 2. The master equation that governs the valid if the correlations decay exponentially with a single rate stochastic dynamics of the system is constant. Two parameters, the decay time of the exponential and the amplitude of the exponential at ϭ 0, can be obtained from d ͑ ͒ Ϫ ͑ ͒ ͩ N2 t ͪ ϭ ͩ k1 k2 ͪͩN2 t ͪ ͑ ͒ ϩ ͑ ͒ ϭ each correlation function. ͑ ͒ Ϫ ͑ ͒ and N1 t N2 t N, dt N1 t k1 k2 N1 t BIOPHYSICS [3] Single-Molecule Measurements. A confocal scanning microscope system was used to excite and detect fluorescent-labeled single where N (t) and N (t) are the number of molecules in state 1 and 1 2 RNA junctions as described (17). Donors were directly excited state 2, and k and k are transition rates to state 1 and state 2, 1 2 with an argon laser (Coherent, Santa Clara, CA) at 514 nm, and respectively. The solution to this equation is fluorescence was collected through an oil immersion objective ϫ͞ k k (Achroplan 100 1.25 oil; Zeiss) and detected at the donor ͑ ͒ ϭ ͩ ͑ ͒ Ϫ m ͪ Ϫt ϩ m Nm t Nm 0 N e N, [4] emission maximum (590 nm) and acceptor emission maximum (675 nm) by two photon counting modules (SPCM-AQ, EG & G Optoelectronics, Vaudreuil, Quebec). The surface density of where ϭ k ϩ k and m ϭ 1, 2. The long-time equilibrium 1 2 RNA junction was adjusted so that the fluorescent spots were probability P(m) of the system is then given by well separated from one another. ͑ ͒ One-step photobleaching was used to confirm the presence of Nm t km P͑m͒ ϭ lim ϭ . [5] single molecules, and photons from a number of different dye N t 3 ϱ molecules had to be collected to achieve good statistics for correlation analysis. In our experiment, the excitation laser We now calculate the conditional transition probability P(m, intensity at 514 nm was kept at Ϸ10 W/m2, and oxygen in t͉n, t ϩ ) that a molecule in state m at time t, will be in state n solution was depleted by use of an enzymatic oxygen scavenging
Kim et al. PNAS ͉ April 2, 2002 ͉ vol. 99 ͉ no. 7 ͉ 4285 Downloaded by guest on September 29, 2021 Fig. 2. Fluorescence autocorrelations AC() calculated over 5 orders of magnitude of time. Autocorrelation curves in A and B are fitted with 2 exponentials [A1exp(Ϫ͞t1) ϩ A2exp(Ϫ͞t2)], and autocorrelation curves in C and D are fitted with 3 exponentials [A1exp(Ϫ͞t1) ϩ A2exp(Ϫ͞t2) ϩ A exp(Ϫ͞t )]. (A) AC() of Cy3 dyes attached to RNA junctions, directly excited 3 3 Fig. 3. Fluorescence fluctuations of donor (green) and acceptor (red) signals at 514 nm, in the absence of Cy5 acceptors. A ϭ 0.42, t ϭ 1.1 s, A ϭ 0.058, 1 1 2 at different [Mg2ϩ]. Similar traces were seen with Naϩ.(A) [Mg2ϩ] ϭ 30 M. (B) t ϭ 15 s. (B) AC() of acceptor Cy5 dyes from S15-bound RNA junctions. The 2 [Mg2ϩ] ϭ 140 M. (C) [Mg2ϩ] ϭ 400 M. (D) Fluorescence signals of donor and fluorescence emission of Cy5 dyes arises because of high FRET from the directly acceptor from an RNA junction, locked in the folded conformation by S15 excited Cy3 dyes. A ϭ 0.076, t ϭ 7.4 s, A ϭ 0.2, t ϭ 180 s. t is much slower 1 1 2 2 2 protein. than the relaxation time of Cy5 in the presence of oxygen, which was mea- sured to be on the order of Ϸ1 s (20). However, the triplet-state lifetime of Cy5 might be dramatically lengthened in the absence of oxygen, a very configuration, giving high FRET efficiency (17). The autocor- effective triplet-state quencher. For example, the triplet decay rate of rhoda- Ϸ mine 6G in aqueous solution equilibrated with argon atmosphere was re- relation amplitude of Cy5 is shown in Fig. 2B. The 100- s ported to be 2.5 msϪ1, 1,000-fold lower than the 2.5-sϪ1 decay rate in relaxation time may indicate that Cy5 has a slower triplet-state oxygen-equilibrated solution (21). (C) AC() of donors at [Mg2ϩ] ϭ 140 M. relaxation time than Cy3. The observation that Cy5 photo- ϭ ϭ Compared with A, a third exponential process is apparent. A1 0.40, t1 2.1 bleaches faster than Cy3 is consistent with this difference. ϭ ϭ ϭ ϭ ϩ ϩ s, A2 0.073, t2 78 s, A3 0.2, t3 7.8 ms. (D) AC( ) of acceptors at When Mg2 or Na was introduced, an additional relaxation 2ϩ [Mg ] ϭ 140 M. Compared with B, a third exponential process is apparent. feature appeared in both donor and acceptor correlations (Fig. ϭ ϭ ϭ ϭ ϭ ϭ A1 0.19, t1 2.1 s, A2 0.25, t2 210 s, A3 0.14, t3 7.5 ms. 2 C and D), which is well separated in time from the relaxation processes intrinsic in the dye molecules. We identified this decay system, 0.1 g of -D(ϩ) glucose, 0.25 mg of glucose oxidase with the reversible conformational change of the RNA junction. Fluorescence time traces from single RNA molecules were (Roche Molecular Biochemicals), 0.5 l of catalase (Roche 2ϩ ϩ Molecular Biochemicals), and 10 lof-mercaptoethanol in 1 obtained at various concentrations of either Mg or Na , with ϩ an example shown in Fig. 3. At the midpoint concentrations, 130 ml of the standard buffer. Minimum of 50 mM of Na was kept 2ϩ ϩ in the buffer to prevent RNA junctions from denaturing. Under M for Mg and 350 mM for Na , the overall times spent in the these conditions, the Cy5 usually photobleached faster than the open and folded conformations become equal and the fluores- Cy3, with approximately 50,000 photons detected during its cence fluctuation is maximized. 6 We plotted the histogram of the FRET signals from a single lifetime. Typically Ϸ10 photons were collected from Ϸ50 mol- ϩ RNA junction at [Mg2 ] ϭ 140 M using different time bins in ecules to calculate correlation. Fig. 4. With typically 3 ϳ 4 photons detected from a single To capture the potentially fast conformational dynamics of the molecule per millisecond, an optimal time bin partially resolves RNA junction, the rising edge of pulses from the avalanche the two FRET levels. At a 1-ms bin width, FRET distribution is photodiode was detected with a 100-ns clock signal (PCI-MIO- not resolvable due to low signal-to-noise in each bin. As the time 16E-4, National Instruments, Austin, TX). This acquisition method created data files storing the arrival times of single photons with 100ns resolution. With this method of recording, (i) the time resolution is limited by the speed of the clock board, (ii) the calculation of correlation functions can be performed much faster, and (iii) the same amount of information can be stored in much more compact form. Results and Discussion Fluorescence fluctuations of donor (Cy3) and acceptor (Cy5) dye molecules can be characterized by the intensity autocorre- lation function. A Cy3 dye attached to the RNA junction in the absence of a corresponding Cy5 FRET partner shows two Fig. 4. Histograms of the FRET efficiencies at different widths of the time 2ϩ ϭ relaxation times (1.1 s and 15 s) (Fig. 2A). These relaxations bins. A fluorescence time trace of a single RNA junction obtained at [Mg ] 140 M was binned in 1 ms, 5 ms, and 25 ms. FRET efficiencies were calculated may be tentatively identified as a combination of a trans–cis for each binned point over the whole trace. Their numbers are shown in a isomerization and triplet-state relaxation (20). To mimic a histogram as a function of the FRET efficiencies at 1-ms bin width (A), 5-ms bin situation of direct excitation of Cy5, S15 protein (3-h off rate) width (B), and 25-ms bin width (C). At Ϸ5-ms bin width, a bimodal distribution was attached to the junction so that the molecule is in the folded of the FRET efficiencies appears.
4286 ͉ www.pnas.org͞cgi͞doi͞10.1073͞pnas.032077799 Kim et al. Downloaded by guest on September 29, 2021 As stated in Materials and Methods, the observed folding and opening rates, kf,obs and ko,obs, can be extracted from the two fit parameters, and the correlation amplitude at ϭ 0 using the open͞ folded folded͞ open experimentally determined ratios Id Id and Ia Ia . open open The intensities, Id and Ia are taken from intensity mea- surements at low-salt condition where the junction is in open folded folded state, and Ia and Id are taken from measurements with S15 bound to the junction. The fluorescence properties of donor and acceptor may slightly vary with ion concentration. For example, the individual fluorescence intensities of Cy3 and Cy5 at fixed emission wave- lengths varied up to 10% over the range of Mg2ϩ and Naϩ in our measurements. It is also possible that the FRET efficiency at a fixed distance changes with varying ion concentration. Because open͞ folded there is no direct way to accurately determine Id Id and folded͞ open Id Id as a function of ion concentration, we let them float up to 15% around the estimated values. ͞ With the unknown variable ko,obs kf,obs, and the variables, open͞ folded folded͞ open Id Id and Ia Ia , partially constrained as discussed above, the two equations for ACa(0) and ACd(0) can be solved ͞ for the range of ko,obs kf,obs. The value of at each concentration is taken as the average of ’s obtained from ACa( ), ACd( ), and CC( ). Individual rate constants, kf,obs and ko,obs, are then ͞ calculated from and ko,obs kf,obs. 2ϩ ϩ The overall dependence of kf,obs and ko,obs on Mg and Na is shown in Fig. 6. The rates, kf,obs and ko,obs are equal at [Mg2ϩ] ϭ 140 M, in agreement with our previous result (17). ϩ 2ϩ The effects of Na and Mg on kf,obs and ko,obs are similar, except for the 2,500-fold larger equilibrium constant. Both cations accelerate the folding rate of the open form and reduce the unfolding rate of the folded form. Folding due to a simple bimolecular reaction (Fig. 7A) be- tween the RNA junction and cations cannot explain our data. In such a model, ko,obs would be identical to the dissociation rate of an ion, which should not depend on concentration. Therefore, a different approach to the conformational change should be considered to explain the Mg2ϩ dependence of the opening rate. We start from relaxing the constraint that ion exchange be coincidental with the actual conformational change of the RNA junction. Assuming that ion exchange is much faster than the confor- mational change, open and folded junctions will be equilibrated between ion-bound and ion-free forms with binding constants KO and KF, respectively. For simplicity, we assume that n ions bind cooperatively (i.e., any sequential binding is not time- resolved in our experiment) so that junctions exist either in the Fig. 5. Correlation functions obtained at [Mg2ϩ] ϭ 120 M. The autocorre- ion-free form or in the form bound with n ions. These two lations of donor and acceptor signals are fitted separately with a single different forms connected by KO or KF are not distinguishable by exponential [A1exp(Ϫ͞t1)]. Cross-correlation is calculated in both lag direc- means of fluorescence. More properly, the value of n should be tions and fitted with a symmetric single exponential centered at ϭ 0. These taken as the Hill coefficient, the maximum possible value of representative correlation functions are the time-weighted-average of indi- which is equal to the number of binding sites. BIOPHYSICS vidual correlation functions of single RNA molecules. The correlations for ϭ In such a four-state model as sketched in Fig. 7B, the observed 0 are not considered. This treatment of the data effectively ignores the faster conformational changes can occur via two pathways, one be- relaxation rates. Two parameters are determined from each correlation func- (0) (0) tion Ϫ, the sum of k and k and AC (0), AC (0), or CC(0), the correlation tween ion-free forms, O and F and the other between f,obs o,obs a d ion-bound forms, O(n) and F(n). With k (0), k (0), and k (n), k (n) amplitudes at ϭ 0. (A) A1 ϭ 0.14, t1 ϭ 6.5 ms. (B) A1 ϭ 0.14, t1 ϭ 6.5 ms. (C) f o f o A1 ϭϪ0.13, t1 ϭ 6.5 ms. denoting such transitions between ion-free forms and n ion- bound forms, the observed folding rate (kf,obs) and observed opening rate (ko,obs) are given as
͑ ͒ ͑ ͒ ϩ bin is increased to 5 ms, a bimodal distribution emerges, whereas k 0 ϩ k n ⅐͑K ͓Mg2 ͔͒n a 25-ms time bin completely smears out the bimodal distribution. ϭ f f o kf,obs ϩ ͑ ͓ 2 ϩ ͔͒n and [11] If the raw data are put into 1-ms time bins as shown in Fig. 5, 1 Ko Mg ͑ ͒ ͑ ͒ ϩ the average correlation functions are well fitted by a single k 0 ϩ k n ⅐͑K ͓Mg2 ͔͒n exponential function with the same decay rate, implying that the ϭ o o F ko,obs ϩ ͑ ͓ 2 ϩ ͔͒n . [12] anticorrelated donor and acceptor fluctuations are driven by the 1 KF Mg same stochastic process. This finding further supports the idea that conformational changes of the RNA molecules cause the We used the nonlinear least square fitting routine from ORIGIN observed fluorescence fluctuations on this time scale. (Microcal Software, Northampton, MA). To judge how well the
Kim et al. PNAS ͉ April 2, 2002 ͉ vol. 99 ͉ no. 7 ͉ 4287 Downloaded by guest on September 29, 2021 Fig. 7. Schemes for Mg2ϩ-dependent conformational change of the RNA junction. O(0) and F(0) are ion-free, open and folded junctions, and O(n) and F(n) are open and folded junctions bound with n Mg2ϩ ions. (A) In bimolecular reaction scheme, the opening rate should be Mg2ϩ-independent. (B) In this extended model scheme, it is assumed that n number of Mg2ϩ ions bind (0) (n) (0) (n) cooperatively to the junction. kf (kf )and ko (ko ) are folding and opening rates for ion-free (ion-bound) junctions. KO and KF are binding constants for binding one Mg2ϩ ion to the open and folded junctions, respectively. Thus, (1) (0) 2ϩ (1) (0) 2ϩ KO ϭ [O ]͞([O ][Mg ]) and KF ϭ [F ]͞([F ][Mg ]). Fluorescence fluctua- tion occurs as a result of conformational change between O forms and F forms with two observed rate constants, kf,obs and ko,obs. In the case where the folded form of the junction can be bound with more Mg2ϩ ions than the open form, (n ϩ nЈ) a fifth state F is introduced with additional binding constant KFЈ. Similar (nϩ1) (n) 2ϩ to KO and KF,KFЈ ϭ [F ]͞([F ][Mg ]).
It is also possible that different number of Mg2ϩ ions are bound to different conformations of the RNA junction. One such case is that more cations bind the folded form to stabilize the RNA structure with closer proximity of negative phosphates (22). Assuming that the folded junction can take additional nЈ Mg2ϩ ions, the reaction scheme should allow a transition be- (n) (nϩnЈ) tween F and F and ko,obs becomes
͑ ͒ ͑ ͒ ϩ k 0 ϩ k n ⅐͑K ͓Mg2 ])n ϭ o o F ko,obs ϩ ͑ ͓ 2ϩ n ϩ ͑ ͓ 2ϩ n͑ Ј͓ 2ϩ nЈ , 1 KF Mg ]) KF Mg ]) KF Mg ]) [13] Ј Ј where KF is the binding constant for binding additional n ions (n) to F . For example, if n is fixed to 4 as determined from kf,obs, Eq. 13 fits the data at nЈϭ1 (result not shown), suggesting that ϩ ϩ Fig. 6. The overall dependence of [Mg2 ] and [Na ] on the observed folding an additional Mg2ϩ further stabilizes the folded form of the and opening rates. The error bars show errors propagated from the 15% open͞ folded folded͞ open junction. However, it should be mentioned that because of inaccuracy introduced in Id Id and Ia Ia and the SD of among 2ϩ the poor precision of the data, it is very difficult to determine the three values from ACa(t), ACd(t), and CC(t). (A) ko,obs as a function of [Mg ]. The phenomenological fits based on Eq. 12 with n ϭ 1 to 4 are shown, where stoichiometry in these model schemes. Also, the cooperativity of n is defined to be the number of Mg2ϩ ions that bind collectively to the folded binding represented by n might not be the same over the whole ϭ (0) ϭ Ϫ1 (n) ϭ Ϫ1 ϭ 2ϩ junction. For example, at n 2, ko 0.604 ms , ko 0.007 ms and KO range of Mg . Ϫ1 2ϩ 0.026 M .(B) kf,obs as a function of [Mg ]. The phenomenological fits based It is likely that any reaction scheme based strictly on a ϭ 2ϩ on Eq. 11 with n 1–4 are shown. kf,obs increases rather steeply with [Mg ] stoichiometric binding mechanism cannot properly completely up to the equilibrium constant and plateaus at higher [Mg2ϩ]. For example, at ϭ (0) ϭ Ϫ1 (n) ϭ Ϫ1 ϭ Ϫ1 F describe ion–nucleic acid interaction. Besides unique sites that n 4, kf 0.015 ms ,kf 0.061 ms and KF 0.04 M .(C) ko,obs ( ) and ϩ ϩ 2 kf,obs (E) as a function of [Na ], Fits with n ϭ 2–4 are shown. take up integral number of Mg ions, an RNA structure has diffusing ions accumulated around its negatively charged back- bone and is stabilized through delocalized electrostatic screen- model agrees with the data, we used the 2 function weighted by 2ϩ ing. Quantitative models for ion screening and the electrostatic the uncertainties in the data. For Mg , ko,obs is best fitted with ϭ Ն ϭ potential of RNA molecules have been suggested based on n 2, whereas kf,obs can be fitted with n 4. Fits at n 1–4 are ϩ shown in Fig. 6A. For Na , the best fit to ko,obs is obtained with nonlinear Poisson–Boltzmann theory (23, 24), but these models ϭ 2ϩ n 3, and similar to the Mg case, the optimal n for kf,obs cannot have yet to be used to calculate the energy landscape of the RNA be well determined. junction affected by electrostatic screening.
4288 ͉ www.pnas.org͞cgi͞doi͞10.1073͞pnas.032077799 Kim et al. Downloaded by guest on September 29, 2021 A simple, qualitative argument based on such a screening In conclusion, we applied FCS at the single-molecule level to mechanism can also account for the data. The two-state model determine rate constants for conformational changes of an RNA for the RNA conformational change tells us that the open and molecule over a range of concentrations of Mg2ϩ and Naϩ. The folded conformations of the RNA junction are thermodynami- RNA conformational change was approximately a two-state cally stable. In the absence of screening ions, because of the fluctuation, but the ion dependence of rates could not be high-repulsive interaction between the two negatively charged explained by simple ion binding models because the opening rate arms of the junction, the open conformation is much more stable was greatly dependent on ion concentration. The results pre- than the folded conformation. In the presence of screening ions, the open state, the transition state, and the folded state of the sented in this paper suggest that an RNA molecule in the folded conformation is greatly stabilized by interacting with Mg2ϩ.Naϩ RNA junction are all energetically lowered. However, the folded 2ϩ state with the highest density of negatively charged phosphates is shown to be capable of replacing the role of Mg at 2,500-fold is preferentially lowered compared with the more extended open higher concentration. With this 16S ribosomal RNA junction as state. Therefore, with increasing cation concentration, the a model system, we demonstrated that FRET technique com- folded conformation becomes more favored. Change of rate bined with FCS can find its application in probing millisecond or constants with increasing ion concentration can be understood faster conformational dynamics of biomolecules at the single- in association with the transition state as well. molecule level. In reality, however, it is most likely that the observed RNA conformational change is a result of both specific binding and This work was supported by the National Science Foundation, Air Force diffuse binding͞screening. The x-ray crystallography studies Office of Scientific Research (S.C.) and National Institutes of Health ϩ have found 3 Mg2 ions localized near the junction region (10), Grant GM53757 (to J.R.W.). H.D.K. received support from a Stanford and these ions are good candidates for specifically bound ions. Graduate Fellowship, and J.W.O. received support from the Cancer ϩ The question of whether the multiple Mg2 ions determined by Research Fund of the Damon Runyon–Walter Winchell Foundation. our phenomenological model correspond to the ones found in G.U.N. acknowledges generous financial support from the Volkswagen the crystal structure requires further investigation. Foundation.
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Kim et al. PNAS ͉ April 2, 2002 ͉ vol. 99 ͉ no. 7 ͉ 4289 Downloaded by guest on September 29, 2021