The Fastest Global Events in RNA Folding:
Electrostatic Relaxation and Molten Globule
Formation of the Tetrahymena Ribozyme
Supplementary Material, comprising five Figures.
Rhiju Das, Lisa W. Kwok, Ian S. Millett, Yu Bai, Thalia T. Mills, Jaby Jacob,
Gregory S. Maskel, Soenke Seifert, Simon G.J. Mochrie, P. Thiyagarajan,
Sebastian Doniach, Lois Pollack, and Daniel Herschlag
1
OVERVIEW
In Figure S1, we first present complete sets of small-angle X-ray
scattering (SAXS) Kratky profiles for the time courses discussed in the text. The
remainder of the supplementary material deals with estimates of the radius-ofgyration (Rg) and zero-angle scattering intensity (I0), which are the two
parameters usually extracted in SAXS studies. We discuss below the difficulties
of extracting these parameters accurately from our data using traditional Guinier
fits. We then present a modified, quadratic Guinier approach which appears to be
accurate, although more sensitive to random error than the two-component fit
presented in the main text and in a previous studyS1. Figure S2 summarizes the
accuracy of this approach, and Figures S3–S5 compares two-component fits, Rg
values, and I0 values for all collected time points.
2
SUPPLEMENTARY METHOD: Quadratic Guinier fits.
Radius-of-gyration (Rg) and zero-angle scattering intensity (I0)
measurements from SAXS data allow one to monitor the size and weightaveraged molecularity (e.g., monomer vs. dimer vs. aggregate), respectively, of
the probed ensemble of molecules. The second derivative of a SAXS profile
extrapolated to zero scattering angle is exactly proportional to the mean squared
radius of gyration. S2; S3. In practice, the radius of gyration (Rg) for compact
molecules is generally estimated by a “Guinier fit” of the SAXS data at lowest
scattering angles to a Gaussian shape. S2; S3 A plot of log I(s) vs. s2 in the low-s
region is fit to a straight line:
log I(s) = log I0 – (2Rg)2/3 s2.
(S1)
Unfortunately, the more extended conformations of the Tetrahymena ribozyme
are so large that their expected SAXS profiles do not fit to Gaussian profiles
except in the region s < 0.003 Å–1, which is not accessible in our current
beamline geometries. See, e.g., blue line in Figure S2a.
We find, however, that a “quadratic” Guinier approximation successfully
fits the profiles in the experimentally available low-angle range s = 0.003 –
0.007 Å–1 (see red line in Figure S2a):
log I(s) = log I0 – (2Rg)2/3 s2 + constant (s2)2.
(S2)
3
To empirically test the accuracy of this approximation, Rg and I0 values estimated
from such three-parameter fits were compared to actual parameters for a
thousand random conformations of a coarse-grained model of the ribozyme
(presented in a previous studyS1).; see Figures S2b and S2c. The accuracy is
better than 5% for each conformation, whereas the traditional “linear” Guinier fit
consistently underestimates both Rg and I0 by up to 35%.
Alternative methods of Rg estimation, based on an indirect transform
techniquesS4–S7, are also being investigated; preliminary results (not shown) with
these techniques yield Rg values consistent with those from the quadratic
Guinier fit described above.
4
SUPPLEMENTARY RESULTS
Radius-of-gyration and two-component fits display the same compaction events
In the main text, we have presented two-component fits over a large
scattering angle region, rather than Rg estimates, to carry out quantitative time
constant fits of compaction events.
Figures S3 and S4 shows that the time course behavior of the radius-ofgyration is qualitatively consistent with the compaction behavior monitored by
two-component fits, but with greater scatter in the estimated Rg values than in the
two-component fits. There are three reasons for the increased scatter: (i) the
requirement of fitting an extra parameter compared to a standard “linear” Guinier
fit lessens the precision of the Rg estimate; (ii) high backgrounds (due to parasitic
scattering in the beamline) in the low s region; and (iii) the low number of
averaged detector pixels in the low s region. Furthermore, all of these difficulties
are exacerbated in our fastest timepoint data set from the continuous-flow setup,
which did not probe scattering angles as low as the stopped-flow setup; the Rg
estimates for the fastest timepoints have much larger errors (up to ± 50%) and
are not shown.
Probes of aggregation
Figure S5 displays I0 values estimated from the quadratic Guinier fits,
which are proportional to the weight-averaged molecularity of the RNA in
solution, S2; S3 and thus provide a sensitive test of time-dependent multimerization
5
or aggregation. For all time courses, fitted I0 values are constant within error
(~10%) for time points less than one second, indicating that aggregation is
negligible for the early compaction events that are the focus of this study. As a
further control for aggregation, several timepoints shorter than 100 milliseconds
were remeasured for the quintuple mutant time course in 10 mM Mg2+ with RNA
concentrations of 4 mg/ml, 2 mg/ml, and 1 mg/ml in the continuous flow setup
and yielded SAXS profiles that were identical, within error (compare open circles,
squares, and triangles in Figure S3). On time scales longer than one second,
there may be a modest aggregation in the Mg2+ and Na+ time courses [Fig. S5 a–
c]. These time courses show a modest ~25% increase in I0, and the quintuple
mutant time course displays an increasing radius of gyration (Fig. S4b) on long
timescales.
6
Figure S1. To prevent clutter in Figure 2 of the main text, only selected time
points were presented. Here, we show the Kratky profiles [s2•I(s) vs. s] for all
timepoints smaller than ten seconds, and for every third time point greater than
ten seconds. Data collected in the continuous flow mixer have been extended to
lower scattering angles with a quadratic Guinier extrapolation (gray lines; see
Supplementary Material Method) to facilitate comparison with data from the
stopped-flow mixer.
7
Figure S2.
Figure S2. (a) Guinier plot of calculated SAXS profile (squares) for an extended
state of the ribozyme, based on a coarse-grained model of the Tetrahymena
ribozyme1; see inset. A linear fit (blue line) of the region s = 0.003–0.007 Å–1 is
inadequate to fit the data, but a quadratic fit (red line) reasonably reproduces the
8
low-s portion of the profile. (b) Comparison of radius-of-gyration estimates to
actual radius of gyration for 1000 conformations of the coarse-grained model,
based on linear (blue circles) and quadratic (red crosses) Guinier fits. (c)
Estimates of scattering intensity at zero scattering angle, compared to the true
value of one, from linear (blue circles) and quadratic (red crosses) Guinier fits..
9
Figure S3. The fractional component in the folded state P F (see Figure 2b) is
plotted for each time course in Figure S1. Solid circles are time points from the
stopped-flow set-up; open circles from the continuous-flow set up. Open squares
and open triangles in (b) are repeated time points at two-fold and four-fold lower
RNA concentrations, respectively. Curves are shown as guides to the eye; in (a)
and (b), the curve fit through time points shorter than 1 second have fastest time
constants coincident with those shown in Figure 2b of the main text. Time points
greater than one second have been binned to avoid clutter. Horizontal error bars
display time ranges of data acquisition for each exposure; vertical error bars
10
display 1 standard error of fits estimated from intrinsic scatter in the profiles (for
times < 1 sec), or scatter in PF for repeated data points (> 1 sec).
Singular value decomposition analysis (not shown) verifies that timepoints
faster than one second from all timecourses can be adequately represented by
two components. S1 For greater times, however more components are required,
S1
and the displayed PF values do not accurately represent attainment of the
native state. For example, in (c), PF values in 1 M Na+ approach unity, although
the final state is not identical to the native state in 10 mM Mg2+, as can be seen
from the Kratky plot (Figure S1c), the radius-of-gyration value (Figure S4c), and
previously published SAXS and chemical footprinting experiments. S8; S9
11
Figure S4. Radius-of-gyration estimates using a quadratic Guinier approximation
(see Supplementary Material Method) in the region s = 0.003–0.007 Å–1 of SAXS
profiles from the stopped-flow setup. Also shown are Rg estimates for static
SAXS profiles of the Tetrahymena ribozyme for the initial state without Mg2+
(green line), and for the folded native state with 10 mM Mg2+
(red line). Time points greater than one second have been binned to avoid
clutter; error bars as in Figure S3. All data are from stopped-flow setup.
12
Figure S5. Estimates of I0, scattering intensity extrapolated to zero scattering
angle, using a quadratic Guinier approximation (see Supplementary Material
Method) in the region s = 0.003–0.007 Å–1 of SAXS profiles from the stoppedflow setup. If the RNA remains unimolecular during folding, the I0 value is
expected to stay constant (green line). Time points greater than one second have
been binned to avoid clutter; error bars as in Figure S3. All data are from
stopped-flow setup.
13
Supplementary Material References
S1.
Russell, R., Millett, I. S., Tate, M. W., Kwok, L. W., B. Nakatani, B.,
Gruner, S. M., Mochrie, S. G., Pande, V., Doniach, S., Herschlag, D. &
Pollack, L. (2002). Rapid compaction during RNA folding. Proc. Natl.
Acad. Sci. USA 99, 4266-71.
S2.
Doniach, S. (2001). Changes in biomolecular conformation seen by small
angle x-ray scattering. Chem. Rev. 101, 1763.
S3.
Feigin, L. A. & Svergun, D. I. (1987). Structure analysis by small-angle xray and neutron scattering (Taylor, G. W., Ed.), Plenum Press, New York.
S4.
Moore, P. B. (1980). Small-angle scattering. Information content and error
analysis. J. Appl. Cryst. 13, 168-175.
S5.
Svergun, D. I. (1992). Determination of the regularization parameter in
indirect-transform methods using perceptual criteria. J. Appl. Cryst. 25,
495-503.
S6.
Russell, R., Millett, I. S., Doniach, S. & Herschlag, D. (2000). Small angle
X-ray scattering reveals a compact intermediate in RNA folding. Nat.
Struct. Biol. 7, 367-70.
S7.
Fang, X. W., Thiyagarajan, P., Sosnick, T. R. & Pan, T. (2002). The ratelimiting step in the folding of a large ribozyme without kinetic traps. Proc.
Natl. Acad. Sci . U S A 99, 8518-23.
14
S8.
Russell, R., Zhuang, X., Babcock, H. P., Millett, I. S., Doniach, S., Chu, S.
& Herschlag, D. (2002). Exploring the folding landscape of a structured
RNA. Proc. Natl. Acad. Sci .U S A 99, 155-60.
S9.
Takamoto, K., He, Q., Morris, S., Chance, M. R. & Brenowitz, M. (2002).
Monovalent cations mediate formation of native tertiary structure of the
Tetrahymena thermophila ribozyme. Nat. Struct. Biol. 9, 928-33.
15