J . Phys. Chem. 1988, 92, 6836-6841
6836
*H NMR of DNA Liquid Crystals: Structural and Dynamical Aspects R. Brandes and D. R. Kearns* Department of Chemistry, University of California, San Diego, La Jolla. California 92093-0342 (Received: May 27, 1988)
We report the observation of a 2Hspectrum of deuteriated DNA fragments, organized in a cholesteric liquid crystal. To account for our observations,we propose that there is rapid rotation of the DNA molecules about their long axis (correlation time I 1 ps) but greatly restricted end-over-end tumbling. From an analysis of the liquid crystal spectrum, it was concluded that the static tilt angle of the purine bases is > 2n6, the two outermost peaks coalesce to a single peak located at their average resonance frequency, as shown in Figure 3D. The line widths then depend on 6 according toi7
z
u l j 2 = (aT2)-'
+ ( ~ / 2 ) 6 ~ k ~= -(7rT2J1 '
(sa)
For even faster motion, such that
Figure 3. Spectral effects of molecular motion on different time scales (see text). (A) Static case. (B) Jump rate k, > ( 2 7 4 . (E) Extreme narrowing limit.
-
and base tilt amplitude, if high-quality experimental spectra can be obtained. The choice of a Gaussian distribution for (3 is reasonable but arbitrary, and for comparison, calculations based on a square distribution function were also carried out. In Figure 2B, the spectra calculated by using these two distribution functions are compared for (e) = 90'. Similar line shapes can be obtained except in the center of the spectra, where the square distribution has a lower intensity. This is also expected since the Gaussian function allows for a larger angular deviation from the mean than does the square distribution. The effect is similar for (e) = 75' as shown in Figure 2C, although the difference between the two distributions is smaller. The center part of the spectrum might, therefore, be poorly fit if an incorrect distribution function is assumed. Motional Effects. It will be of interest to consider how molecular motion, on different time scales, affects the 2H spectral shapes of D N A in the solid, liquid crystalline, and liquid states. A generally applicable analysis would allow for a distribution of possible DNA orientations, but for simplicity, consider the spectrum of a collection of DNA molecules, statically aligned with only two helix axis orientations characterized by fit and (3*, with respect to the magnetic field. The spectrum of an equally populated mixture would consist of four peaks of equal amplitude, as shown in Figure 3A. The slitting, 6, between the two outermost peaks is calculated from eq l a and l b (with 60 = 0' and (e) = go'), according to
where
< lPil < 90°, i
(2b) and the line widths are assumed to be determined only by the transverse relaxation time, T2, according to 0
v1/2
= 1, 2
= (aT2)-'
T2-I >> ( ~ ~ / 2 ) 6 ~ k , - ' (5b) the line widths are once again independent of the exchange rate (Figure 3E). The total spectral splitting, Av, is here calculated from eq l b (with Bo = 0' and (e) = 90') by substituting (3 = '/2((31 + (32). Two important conclusions can be drawn from the above considerations. First, motions in the intermediate exchange regime can substantially reduce T2, and might even render the NMR signal (FID) unobservable if T2, is much shorter than the delays in the quadrupolar echo sequence.'O Note also that an increased splitting 6 will cause an even larger reduction in T , since the signal will be spread out over a larger spectral region. Therefore, a larger motional amplitude (i.e., larger jump angle, p2 - PI), corresponding to a larger change in frequency, 6, produces a shorter T2,in the intermediate exchange regime. Second, a short T2, could be obtained in either the slow or fast exchange regime.
Results The 2H N M R spectra obtained from DNA samples with concentrations 0.25 and 0.13 g/mL are shown in Figure 4,parts A and B, respectively. In the 0.25 g/mL sample, the spectrum has a splitting between the resonances, Au, of -42 kHz, and since TZe 60 ps, the peaks are homogeneously broadened by at least -5 kHz. The intense (truncated) central component in these two spectra is caused by residual HOD in the deuterium-depleted water solvent. Because the purine deuteron has a shorter spin-lattice relaxation time (-0.04 s) than does the water deuteron (0.22 s), the shortest possible (due to instrumental limitations) pulse repetition time of 68 ms was used to suppress the water resonance. A further improvement was obtained by collecting an additional spectrum using a longer repetition time of 700 ms to obtain a spectrum where the water signal was not suppressed. This latter spectrum was thereafter used, with appropriate scaling, to subtract the residual water signal in the spectrum obtained with the shorter repetition time. As can be seen in Figure 5, the water resonance is efficiently suppressed in this difference spectrum, and the signal-to-noise is only slightly worse. The spectrum of the diluted DNA sample was collected with identical parameters as were used for the 2-fold more concentrated sample (except for a smaller number of acquisitions). Nevertheless, no signals from the DNA could be observed (Figure 4B). The results of the spectral simulations of the spectrum in Figure 5, using (8) = 90°, 85", 80°, and 75', are shown in Figure 6, parts A-D and Table 11. As is evident in Figure 6A,B, (e) = 90' or 85' would be consistent with the experimental spectrum, whereas 80°, or less, produces inferior fits (Figure 6C,D). The poor fit of the central portion of the spectra may in part be caused by the use of a Gaussian distribution function in the calculation.
-
(3)
However, if the DNA jump between the two orientations PI and p2, with a jump rate k, and a corresponding lifetime at the
(1 7 ) Harris, R. K. Nuclear Magnetic Resonance Spectroscopy; Pitman: Massachusetts, 1983. (18) Spiess, H. W.; Sillescu, H. J . Magn. Reson. 1981, 42, 381-389.
The Journal of Physical Chemistry, Vol. 92, No. 23, 1988 6839
2H N M R of DNA Liquid Crystals n
A
,2 ,
*oooo
,
,
20000
,
,
, 0
n
,
,
,
,
-20000
40000
Hz
/ 4000C
I
I
20000
0
'
I
-2I)oco
--iocco
tJ2
Figure 5. Deuterium NMR spectrum of *H-labeledDNA at a concentration of 0.25 g/mL. This spectrum was obtained by subtracting out the residual HOD signal in the spectrum shown in Figure 4A (see text).
-
40000
20000
0
-20000
-40000
HZ
Figure 4. Deuterium NMR spectra of 2H-labeledDNA obtained with a quadrupolar echo sequence. (A) DNA concentration 0.25 g/mL
(80000 scans). (B) DNA concentration 0.13 g/mL (33392 scans). TABLE 11: Optimized Parameters Obtained from Simulations of the Experimental Spectrum of Deuterium-Labeled DNA in the Liquid Crystalline State
(e), deg
up, deg
75 80 85 90
5fl 6fl 14* 1 16.5 f 1
l&,l,deg 30.0 f 0.5 35.8 i 0.5 37.4 f 0.5 36.8 f 0.5
quality of fit" poor (no fit) poor good
good
"See Figure 6. A more appropriate function would have a larger contribution of helix axis orientations away from the average value of (e), (e) (compare with Figure 2B).
Discussion In the concentrated DNA sample, a liquid crystal f ~ r m e dand ,~ a ZH spectrum was relatively easy to observe. We were unable to observe any DNA resonances from the 2-fold more dilute DNA sample, and this is consistent with earlier failures to obtain spectra from deuteriated RNA duplexes.1° These observations might seem surprising in view of our earlier study where we found that as a solid DNA sample is increasingly hydrated, the resonances start to disappear when the hydration level exceeds 13.4 H,O/nucleotide? a level of hydration that is much lower than that present in the liquid crystal. This collection of observations can be explained as follows. At low hydration levels, the bases of solid DNA execute small, high-frequency librational fluctuations that only marginally affect the spectral splitting but contribute to the spin-lattice relaxation.' At a hydration level above -13 H20/nucleotide, the DNA molecules execute larger amplitude torsional motion^.^ This new component of motion is probably due to lower frequency collective DNA motions, since the spin-lattice relaxation rate does not change abruptly at this level of hydration.' For the ZHsignal to disappear, the transverse relaxation time, T,, must be shorter than the sum of the delays, T~ + = 80 ps, in the quadrupolar echo sequence and, as discussed above, this arises when the rotational diffusion rate is comparable to the quadrupolar interaction strength. For example, a diffusional isotropic correlation time T~ 1 ps results in a predicted relaxation time T,, 10 ps.I9
-
-
(Note, in reality, the FID decays nonexponentially when 7;' (3/4)r($qQ/h), with a faster decay for short times.) Apparently, the correlation time (and amplitude) of the DNA twisting motion causes a significant reduction of T2, in the more heavily hydrated DNA fibers. With even higher levels of hydration, the DNA spectrum disappears completely, and this can be explained by the onset of large amplitude bending motions on the appropriate time scale. To account for the observation of an N M R signal from DNA in the heavily hydrated liquid crystalline sample, the following two conditions are proposed to be met. (i) The DNA molecules spin rapidly about their own axis so that the spectrum is cylindrically averaged. This requires an axial rotation correlation time, T~~
