19F NMR Untersuchung des Konformationsaustauschs mehrerer Zustände im synthetischen Neomycin‐bindenden Riboschalter


 Der synthetische Neomycin‐bindende Riboschalter interagiert mit seinem Liganden Neomycin sowie mit den verwandten Antibiotika Ribostamycin und Paromomycin. Die Bindung dieser Aminoglykoside induziert sehr ähnliche Grundzustandsstrukturen in der RNA, allerdings kann nur Neomycin die Initiierung der Translation effizient unterdrücken. Der molekulare Ursprung dieser Unterschiede wurde auf Unterschiede in der Dynamik der Ligand‐Riboschalter‐Komplexe zurückgeführt. In diesem Artikel kombinieren wir fünf komplementäre fluorbasierte NMR‐Methoden, um die Dynamik der drei Riboschalter‐Komplexe im Sekunden‐ bis Mikrosekundenbereich genau zu quantifizieren. Unsere Daten offenbaren komplexe Austauschprozesse mit bis zu vier strukturell unterschiedlichen Zuständen. Wir interpretieren unsere Ergebnisse in einem Modell, das ein Zusammenspiel zwischen verschiedenen chemischen Gruppen in den Antibiotika und spezifischen Basen im Riboschalter zeigt. Allgemeiner unterstreichen unsere Daten das Potenzial von 19F NMR‐Methoden, komplexe Austauschprozesse mit mehreren angeregten Zuständen zu charakterisieren.



Synthesis of 2-F-ATP
The synthetic access to 2-F-ATP is based on the method published by Santa-Lucia and coworkers [1].Briefly, 2-F-adenosine (500 mg, 1.87 mmol) was dissolved in anhydrous triethylphosphate (5 mL) at room temperature.After cooling to 0 • C, 2-F-adenosine was transformed into the 5'-monophosphate nucleotide by treatment with POCl 3 (2 eq., 349.8 µL, 3,74 mmol) and stirring for 3h at 0 • C.Then, the reaction was quenched at 0 • C by the dropwise addition of sodium hydroxide solution (2M) until pH 4 was reached (controlled by pH paper).The reaction mixture was stirred at 0 • C for one additional hour and then the pH was adjusted to 7 (controlled by pH paper).The reaction mixture was diluted with water and extracted three times with diethyl ether.The monophosphate nucleotide solution was concentrated on a rotary evaporator to a volume of ca. 10 mL and the 2-F-adenosine 5'-monophosphate was then precipitated by the addition of two volumes cold ethanol.After storing the mixture at −20 • C overnight the precipitate was collected by centrifugation at 4 • C, the ethanol/water mixture decanted and the residue dried in high vacuum.The residue was then dissolved in water and further purified by reverse phase chromatography.The final yield was 490 mg (1.41 mmol, 75 %).
The 2-F-ATP was enzymatically prepared by dissolving 490 mg of 2-F-adenosine 5'-monophosphate (1.41 mmol) in 10 mL buffer (50 mM M ATP, 300 mM MgCl 2 , 300 mM KCl and 150 mM Tris-HCI, pH 7.6) in a 50 mL round bottom flask equipped with a magnetic stirring bar.Then, 824 mg phosphoenolpyruvic acid (monopotassium salt, 2.8 eq., 3.95 mmol) was added and the solution degassed by three Ar-flushing/vacuum cycles.Finally, 10 mg DTT, 1000 U myokinase and 300 U pyruvate kinase were added and the flask was stirred under argon atmosphere at 37 • C. The pH was checked after 1h by using pH paper and adjusted to pH 7.6 with 1M NaOH and/or 1M HCl.This procedure was repeated after an additional hour, then the reaction mixture was allowed to proceed overnight.By using 31 P-NMR the reaction progress was monitored and after 16h the reaction was quenched by the addition of 2 volumes of cold ethanol.After storing the mixture at −20 • C overnight the precipitate was collected by centrifugation at 4 • C, the ethanol/water mixture decanted and the residue dried in high vacuum.The residue was then dissolved in water and further purified by reverse phase and weak anion exchange chromatography.The final yield was 350 mg (0.690 mmol, 49 %).

RNA sample preparation
2F-A modified RNAs were synthesized via in vitro transcription using T7 polymerase and synthetic single-stranded DNA templates with a double-stranded promotor region.For transcription 4 mM commercially available cytosine-, guanosine-and uridine-5'-triphosphate (Merck) and 4 mM 2F-adenosine -5'-triphosphate were used.RNA transcripts were purified by preparative urea PAGE according to standard protocols and desalted via PD-10 columns (GE Healthcare).To obtain monomeric hairpin forms, RNAs were folded by heating to 95 • C for 10 minutes followed by injection into 10 equivalents of ice cold water.Concentration and buffer exchange into NMR buffer (25 mM potassium phosphate pH 6.2, 50 mM potassium chloride) was performed using Vivaspin concentrators (MW cutoff 3000 Da, Sartorius).
Sample concentrations varied between 215 and 1200 µM.NMR samples were titrated with 1 to 1.5 equivalents of commercially available neomycin, ribostamycin or paromomycin (Merck) and binding of the ligand by the RNA was followed via the disappearance of fluorine resonances of the free RNA in 19 F NMR spectra.

ITC experiments
Isothermal Titration Calorimetry (ITC) experiments were carried out on a MicroCal iTC200 instrument (Malvern Instruments).Measurements were performed at 37 • C using samples prepared in buffer containing 20 mM Na-cacodylate, 200 mM NaCl, 10 mM MgCl 2 , 1 mM spermidine, pH 6.8.For measurements with ribostamycin as ligand 10 µM 2F-A modified neomycin riboswitch in the sample cell and 100 µM ribostamycin in the injector syringe were used.Experiments with paromomycin were done using 30 µM RNA and 300 µM ligand solution.After an initial delay of 120 seconds, an initial injection of 0.2 µL was followed by 19 injections of 2 µL at intervals of 180 s and at a stirring speed of 750 rpm.For all measurements, the reference power was set to 11 µcal −1 .Thermograms were processed and analyzed using Origin 7.0 software (OriginLab) and thermodynamic parameters were obtained from a curve fit to the data using the one-site binding model.All measurements were repeated three times and the reported K D values are the average of these experiments.

NMR spectroscopy
Assignment spectra in figure S1 were recorded on a 600 MHz Bruker NEO NMR spectrometer equipped with a nitrogen cooled 1 H/ 19 F [ 13 C, 15 N] TCI probehead.All 19 F EXSY-exchange, CEST, CPMG, on-resonance and off-resonance R 1ρ experiments were recorded on a 500 MHz Bruker NEO NMR spectrometer equipped with a triple resonance TCI H&F-C/N-D nitrogen cooled probehead, with the proton coil tuned and matched to the 19 F resonance frequency of 470.59 MHz.Data were acquired with a recycle delay of 1.0-1.5 s without 1 H decoupling during the acquisition.The carrier frequency was -51.0 ppm for the 1D spectra and adapted to the resonance of interest for all on-resonance experiments.90º pulse lengths were calibrated individually for all samples and temperatures and were typically between 12.8 µs and 13.2 µs.Spectra were processed with the NMRpipe software [2] and analyzed with Python and Matlab scripts.Datasets were typically acquired as triplicates to infer experimental errors of all datapoints.EXSY: 19 F-19 F EXSY spectra were acquired as pseudo-3D experiments with an acquisition time of 8.5 ms in the indirect dimension (F1) and mixing times of 1, 2, 5, 10, 25, 50, 75, 100, 150, 200, 400 and 700 ms.Spectra were processed with NMRpipe using exponential window functions with 50 Hz line broadening in both dimensions and converted to plain text using the NMRpipe pipe2txt.tclscript.Each spectrum was globally fit with in-house Matlab scripts using four two-dimensional lorentzian functions, in which two parameters for peak positions were used along each dimension and two line widths (Γ L1 and Γ L2 ) were used.Based on these backcalculated spectra the peak volumes were calculated as where a is the scaling parameter of the lorentzian peak function L, and Γ x and Γ y are the full width at half maximum parameters along the direct and indirect dimension: CEST: 19 F-CEST experiments were acquired as pseudo-2D experiments using 140-156 offset frequencies spaced between 25-200 Hz and centered around the resonance of interest (Figure S11).In brief, a low power pulse is applied at a stepped frequency offset specified by an fq1list, followed by an anti-ringing element.1D spectra were extracted and converted to text format data with the NMRpipe scripts readROI and pipe2txt.tclscripts, respectively.Peak intensities were subsequently integrated and analysed with Matlab scripts.CEST fields were calibrated following the determination of B 1 amplitude distributions from Guenneugues [3].
To avoid offset effects in the relaxation dispersion, the 19 F carrier frequency was set to the maximum of the respective peak in the 19 F 1D spectrum.

Analysis of NMR data 1.5.1 CEST data analysis
In the analysis of CEST data, we extended the procedure introduced by the Kay group [5] from a 2-state exchange to 3-state and 4-state exchange.In this approach, the intensities are numerically calculated using the Bloch-McConnell equations, which are modified by the presence of the CEST field ω CEST .For convenience, we ordered the equations by the components {x, y, z} instead of the states {a, b, ..., n}.The equations can be assembled from the relaxation matrix R, the chemical shift matrix C, the CEST field matrix O and the exchange matrix K.The latter is given by where the diagonal elements are given by and detailed equilibria are given by If all transverse relaxation rates R 2,i and longitudinal relaxation rates R 1,i are assumed to be identical , the diagonal relaxation matrix can be written as with obvious modifications if any of these rates are treated individually (i.e. if they are fixed or included as separate parameters during minimization), which was not the case in the present work.
The offset δ i of state i from the low power CEST field ω CEST connects the x and the y components of i as Finally, the CEST field ω CEST enters as For a 2-state exchange a ⇀ ↽ b in the presence of a transverse ω CEST field, the recasted Bloch- McConnell equations can thus be written as a time evolution equation for the vector ⃗ With explicit consideration of the relaxation back to the equilibrium populations M j eq , the final equation for the vector with the evolution matrix (13) where the equilibrium magnetizations M i eq are given by the populations p i .The intensity of the ground state a after saturating with ω CEST at a given offset δ CEST for a time T CEST can then be directly calculated with a matrix exponential (expm in MATLAB) from the starting magnetization ⃗ M 0 = [E/2, 0, 0, 0, 0, M a z , M b z ] T (where M i z are given by p i ) with the projection on the ground state ⃗ M proj = [0, 0, 0, 0, 0, 1, 0] T as Similar equations with (n + 1) × (n + 1) matrices A can be formulated from the above set of equations for n = 3 states (yielding a 10 × 10 matrix) and n = 4 states (yielding a 13 × 13 matrix).Of note, the same equations can be used to calculate the intensity of any other state i by projecting the time-evolved magnetization onto this state.In our case, we used projections on the L1 and the L2 state for analysis of the NEO-and PAR-bound riboswitches (main text, Figure 3 and Figure 5).

CPMG data analysis
Analysis of CPMG data followed a similar explicit calculation based on the Bloch-McConnell equations.For a 2-state exchange, the full evolution matrices between the π-pulses are given by Effective transverse relaxation rates R 2,e f f of an observable state i as a function of the CPMG frequency ω CPMG /2π can then be calculated as The evolution matrices B and B show, that transverse and longitudinal magnetization components are not mixed if pulse imperfections and evolution during the pulses are neglected.As a consequence, the matrix equations can be reduced to the evolution of transverse magnetization.For 3-site and 4-site exchange, the matrices can be expanded in a straightforward manner.

On-resonance and off-resonance R 1ρ data analysis
For the analysis of rotating frame relaxation data, we initially followed the approach of Trott and Palmer [6].In brief, for the first-order linear differential equation ( 11) describing a 2state exchange (with the CEST field ω CEST replaced by the spin lock field ω SL ), the general solution is given by where ⃗ l n are proportional to the eigenvectors of the evolution matrix A, and λ n are the corresponding eigenvalues.The least negative real eigenvalue λ lnr is an estimate for R 1ρ : The approach can be extended in a straightforward way to analyze difficult exchange topologies involving more than two states, by computing the eigenvalues of the corresponding evolution matrix.In agreement with the finding, that only two of the six eigenvalues in a 2-site exchange are real [6], we find that three out of nine and four out of twelve eigenvalues are real for 3-site and 4-site exchange for the exchange regimes encountered in this study.
The eigenvalues for an n-state system can be obtained by inverting the corresponding 3n × 3n dimensional matrix.In practice, we used the MATLAB eig function to calculate all eigenvalues, and retained the least negative real one.We note that an alternative approach has been formulated, in which the problem is reduced by Schur matrix decomposition to the calculation of characteristic polynomials of 3 × 3 matrices [7].
In our case, the 3-state and 4-state exchange processes of the PAR-bound riboswitch under saturating and non-saturating conditions include the slow exchange between two substantially populated states, L1 and L2.Under these conditions two eigenvalues become similar in amplitude and the eigenvalue approach breaks down.However, we find that the decay of the spin-locked magnetization for the parameters obtained in our case still hardly deviates from a mono-exponential decay (which is not necessarily the case).We therefore turned to a direct numerical approach [8] and calculated the magnetization for the experimental time points t i as where in which the tip angle is given by the the spin lock frequency ω SL and the offset Afterwards, we approximated R 1ρ by explicitly fitting the decay to a mono-exponential function exp −R 1ρ t .We note that it is also possible to directly compare experimental intensities to numerical back calculations without assuming a mono-exponential decay, and that this approach becomes obligatory in decidedly non-monoexponential decays.In these cases it follows that relaxation of the spin-locked magnetization can not be characterized by a single variable R 1ρ .

EXSY data analysis
EXSY data were numerically analyzed with a matrix approach.For a 4-site exchange, the autopeak intensities I ii and cross peak intensities I ij,i̸ =j after a time T EXSY can be calculated from the starting intensities I 0 with a matrix exponential as where In practice, we calculated the full evolution matrix of the 3-site and 4-site exchange, respectively, as exemplified in matrix (15) for a 2-site exchange, and only considered the longitudinal part of the magnetization.Of note, it is not necessary to know the initial intensities of states k ̸ = i, j not involved in the exchange i ⇀ ↽ j under consideration in order to obtain the autopeak and crosspeak intensities I ii , I ij , I ji and I jj .

Estimation of experimental errors
Experimental errors were determined from replicates.For experimental data points D exp,i of replicate i, the error was calculated as with the mean experimental value Due to the small replicate size (typically triplicates), errors of individual datapoints can heavily underestimate the true experimental error, which subsequently skews the data fitting.
In order to prevent such bias, we introduced minimal errors σ j min for all experiments j, based on σ CEST min = 0.005 [normalized intensity] (29) (34)

Fit optimization procedure
Experimental data were numerically fitted with the approaches described above by minimization of a combined χ 2 , which sums up the contributions χ 2 j of the datasets j under consideration with In practice, we used the MATLAB function fminsearch to implement the minimization.

Model selection
For exchange scenarios with n > 2, the general scheme in which all states directly exchange with each other might not be justified by the experimental data, although it will necessarily yield the same or a lower χ 2 , due to the additional parameters k ij ex compared to any reduced model.In order to avoid this caveat of overfitting, we used three criteria (reduced χ 2 = χ 2 ν , Akaike information criterion (AIC) and Bayesian information criterion (BIC) ) to evaluate, which exchange topology should be chosen to fit the data.
where N is the total number of data points and K is the number of fitting parameters in a given model.We then used the differences in AIC and BIC values (∆AIC i , ∆BIC i ) from different models i to calculate normalized likelihood estimates (weights w AIC i , w BIC i ) for each model [9,10], i.e. models that are more likely according to AIC (BIC) have lower AIC (BIC) values and larger AIC (BIC) weights:

Estimation of exchange parameter uncertainties
To estimate errors in the parameters (populations, exchange rates, etc.) extracted from the fitting of NMR data (CEST, CPMG, etc.) 500 cycles of Monte Carlo simulations were carried out.In each cycle, each data point was randomly varied according to its standard variation, with minimal values given in section 1.5.5.These randomly varied datasets were then numerically fitted, with starting parameters randomly varied around their optimum value.Finally, standard deviations were calculated from the distribution of optimal solutions obtained from all runs.

Thermodynamic analysis
Thermodynamic parameters for the detailed equilibrium between two states i and j were obtained from analysis of the equilibrium constant K eq,ij as well as forward and reverse rates (k ij , k ji ) for {CEST, CPMG, EXSY}-datasets between 293 K and 303 K. First, K eq,ij was fit according to The values obtained for the change in entropy ∆S ij and in enthalpy ∆H ij were subsequently used as constraints in the fit equations where k B is the Boltzmann constant (1.38 × 10 −23 J K −1 ) and h is the Planck constant (6.626 × 10 −34 J s), ∆S ij and ∆H ij are the differences in entropy and enthalpy between state i and state j, ∆S ‡i→j and ∆H ‡i→j are the entropy and enthalpy differences between state i and the transition state between i and j, ∆S ‡j→i and ∆H ‡j→i are the entropy and enthalpy differences between state j and the transition state between i and j, and the transmission coefficient κ was assumed to equal one.

Side note on the exchange topologies of n-state systems
Data analysis of NMR experiments that probe dynamics in the range of microseconds to seconds is based on the assumption, that the exchanging system adopts n distinct states.
A state i is characterized by a chemical shift δ i , a population p i , other parameters such as relaxation rates R i 1 and R i 2 , and exchange rates k ex,ij = k ij + k ji with any other state j.For n = 1, only the ground state (GS) is populated (p GS = p a = 1), for n = 2, a single excited state exchanges with the ground state with an exchange rate k ex,ab , for n = 3 there are two excited states with three exchange rates k ex,ab , k ex,ac and k ex,bc .In general, for n-site exchange, there will be a total of n • (n − 1)/2 exchange rates from which it follows directly, that there are 2 n•(n−1)/2 different (not necessarily fully connected) topologies [11].The number of distinct topologies for distinguishable states (e.g.distinguishable by their chemical shift) without disconnected states can be calculated by graph theory and is equal to the number of labeled, connected graphs.For a graph with n nodes, the number of connected labeled graphs C n is given by the recurrence relation [12] We note, that the number thus derived not only singles out the position of the ground state with the highest population, but also counts two topologies as distinct, where the minor states interchange their position in the graph.This view is appropriate in situations, where not only the ground state, but also all excited states can be labeled, e.g. by their chemical shift, as derived from off-resonance experiments (CEST, off-resonance R 1ρ ).In contrast, it has been argued that only the ground state is specified ('labeled') in the graph, which shifts the problem from testing more topologies to the problem of attributing the correct chemical shifts to the excited states [11].
The resultant numbers of different exchange topologies for n states (n vertices or nodes in graph theory) are given in table S1.For four states, all 38 possible labeled, connected graphs corresponding to unique topologies of 4-state exchange systems are given in Figure S10 # states 1 2 3 4 5 6 # topologies (fully labeled) 1 1 4 38 728 26704 # topologies (ground state labeled) 1 1 3 11 58 393 Table S1: Number of exchange topologies for n states, given by the number of connected, labeled graphs according to equation ( 47), and for topologies, in which only the ground state is labeled [11].

Supplementary Figures
Figure S1: Assignment of 19 F resonances in the neomycin-sensing riboswitch. 19F spectra of (a) the U4C A24G double mutant in the free riboswitch, (b) the A17C mutant in the free riboswitch, (c) the wild type sequence free riboswitch, (d) the wild type riboswitch in the presence of RIO, (e) the A17C mutant riboswitch in the presence of RIO and (f) the U4C A24G double mutant in the presence of RIO.Note that the A16 resonance is shifted in the A17C mutant.The upfield shoulder of the A16 resonance in the free riboswitch arises from a slow exchange process of A24.In addition, the resonance of A24 is broadened in the unbound riboswitch due to dynamics in the helix, which were not included in our analysis.
-   S3.   Values and uncertainties of the exchange processes are summarized in table S6, the extracted thermodynamic properties are summarized in table S9.S4, the extracted thermodynamic properties are summarized in table S9.S7.
and k A−L3 as well as equilibrium constants K eq,L1−L2 , K eq,L1−L3 , K eq,L1−A and K eq,L3−A as a function of inverse temperature T −1 .Values and uncertainties of the exchange processes are summarized in table S7, the extracted thermodynamic properties are summarized in table S9.

Figure S10:
Connected, labeled graphs with four nodes and three to six edges, corresponding to the unique topologies of a 4-state exchange system with states i = {a, b, c, d} distinguishable (labeled) by their chemical shift ω   Table S8: Error analysis of exchange in the unsaturated PAR-bound riboswitch between 293 K and 308 K. χ 2 is the error-weighted sum of squared residuals (eq.( 36)), χ 2 ν is the reduced χ 2 (eq.( 37)), AIC is the Akaike Information Criterion (eq.( 39)), BIC is the Bayesion Information Criterion (eq.( 38)), N is the total number of data points, K is the number of parameters in a model, ∆AIC and ∆BIC are the difference in AIC (BIC) of the current model compared to the model with a minimum AIC (BIC), and w AIC and w BIC are the model weights according to eqs. ( 40 ba I ca I da I ab I bb I cb I db I ac I bc I cc I dc I ad I bd I cd I dd

Figure S2 :
Figure S2: CEST data for the RIO-bound riboswitch at different temperatures.CEST profiles at 293 K, 298 K, 303 K and 308 K from A17 at B 1 fields of 12.8 Hz, 25.7 Hz and 51.3 Hz with data (circles with errorbars) and fits that use a model in the absence of exchange (293 K, 298 K) and a 2-state exchange model (303 K, 308 K) (solid line).The resonance positions of L2 and L3 are indicated above the CEST spectra.The insets show a zoom of the CEST profiles in the region of the L3.Values and uncertainties of the exchange processes are summarized in tableS3.

Figure S3 :
Figure S3: CEST, EXSY-exchange and CPMG data for the PAR-bound riboswitch (cont.).CEST profiles, EXSY-exchange data and CPMG curve of the A17F2 resonance at (a) 293 K, (b) 298 K, (c) 303 K and (d) 308 K, together with the parameters obtained by a least-square fitting routine.Values and uncertainties of the exchange processes are summarized in tableS6.

Figure S4 :
Figure S4: Temperature dependence of exchange processes in the PAR-bound riboswitch.Populations (p L2 , p L3 , left) and exchange rates (k ex,L1−L2 , k ex,L1−L3 , middle) as a function of temperature T. Right: Logarithmic rate constants k L1−L2 , k L1−L3 , k L2−L1 and k L3−L1 as well as equilibrium constants K eq,L1−L2 and K eq,L1−L3 as a function of inverse temperature T −1 .Values and uncertainties of the exchange processes are summarized in table S6, the extracted thermodynamic properties are summarized in tableS9.

Figure S5 :
Figure S5: A three-state exchange in the unsaturated RIO-bound riboswitch.(a) CEST profiles at 293-308 K from A17 2F at B1 fields of 12.8 Hz, 25.7 Hz and 51.3 Hz with data (circles with errorbars) and the fit from the 2-state (293 K, 298 K) and 3-state (303 K, 308 K) exchange model (solid line).The resonance positions of L2, L3 and A are indicated above the CEST spectra.The insets show the CEST profiles in the region of the L3 state.(b) temperature dependent populations of the unbound riboswitch (p A ) (c) temperature dependent exchange rates between the L2 and A (k ex,L2−A ) (d) logarithmic plot of the rates k L2−A , k A−L2 and K eq,L2−A = k L2−A /k A−L2 .Values and uncertainties of the exchange processes are summarized in tableS4, the extracted thermodynamic properties are summarized in table S9.

Figure S6 :
Figure S6:[ 19 F-19 F]-EXSY spectrum of the unsaturated PAR-bound riboswitch at 303 K with a mixing time of τ = 75 ms.In addition to the L1-L2 cross peaks, weak L1-A cross peaks are visible.Note that the L1-A cross peaks were not used in the fitting of the data as the intensities are too low to be accurately quantified.

Figure S7 :
Figure S7: ITC titrations of the 2FA-labeled neomycin-binding riboswitch.ITC thermograms for ligand binding at 310 K show that the 2FA-labeled riboswitch retains a higher affinity towards RIO (a) compared to PAR (b)

Figure S8 :
Figure S8: CEST, EXSY-exchange and CPMG data for the unsaturated PAR-bound riboswitch (cont.).CEST profiles, EXSY-exchange data and CPMG curve of the A17F2 resonance at (a) 293 K, (b) 298 K, (c) 303 K and (d) 308 K, together with the parameters obtained by a leastsquare fitting routine.Values and uncertainties of the exchange processes are summarized in tableS7.

Table S9 :
Summary of thermodynamic parameters for the three-site and four-site exchange in the unsaturated RIO-bound riboswitch and the saturated and unsaturated PAR-bound riboswitch at 303 K