Molecular
Motions in RNA
and DNA
The Journal of Physical Chemistry, Vol. 83,No. 26, 1979 3359
Molecular Motions in RNA and DNA Investigated by Phosphorus-31 and Carbon-13 NMR Relaxation Philip H. Bolton and Thomas L. James" Department of Pharmaceutical Chemistry, School of Pharmacy, University of California, San Francisco, California 94 143 (Recelved June 29, 1979)
The NMR relaxation behavior of carbon-13 and phosphorus-31 has been investigated to elucidate the conformational fluctuations of RNA and DNA. Measurements of the spin-lattice relaxation time (TI),31P('H) nuclear Overhauser effect, line width, and rotating frame spin-lattice relaxation in an off-resonance radiowere performed for phosphorus-31 in poly(A), poly(1)-poly(C), and calf thymus DNA. frequency field ( A two correlation time model entailing anisotropic rotational wobbling about phosphorus-oxygen bonds in the nucleic acid backbone and long-rangebending motions was capable of simultaneously fitting all four 31Prelaxation parameters quite well at all temperatures in the range examined, 6-40 "C. The rotational wobbling motion has a correlation time of 0.3-0.5 ns for all three nucleic acids and is independent of temperature or salt concentration. The long-range bending motion, however, does depend on temperature, presence or absence of magnesium ion, and single- or double-stranded character of the nucleic acid; the correlation time is on the order of microseconds. Carbon-13 spin-lattice relaxation time and 13C {'HI nuclear Overhauser effect measurements were made for calf thymus DNA. Although the base moiety appears to be immobilized, the ribose moiety possesses a considerable amount of internal mobility. The internal motion correlation times for the ribose carbons are on the order of nanoseconds with motional freedom increasing from l', 3', 4' < 2' < 5', which displays nearly the mobility of the phosphate moiety.
During the past few years there has been growing interest in the conformational fluctuations of biological molecules. The importance of the motion in biological activity is suggested by the very nature of the processes. The transcription and translation of DNA, for example, almost certainly involve a distortion of the double helix as would the specific recognition of base sequences by proteins. The rate and type of chemical modifications of nucleic acids may also be related to the conformational fluctuations. These considerations, as well as others, have lead to theoretical and experimental approaches to investigate the mobility of biological macromolecules.l-1° The examination of the rate of fluorescent depolarization of ethidium bound to DNA showed that the bound drug exhibits reorientation on a time scale comparable to that of the fluorescent lifetime of the drug, about 25 nsa8 Subsequent reinvestigations of the rate of fluorescent depolarization have refined the treatment of the data and indicate that there is internal motion of the bases of double-stranded DNA on a time scale of tens of nanosecond~.~~~ Hydrodynamic studies have shown that polynucleotides do not behave as rigid rods on the whole. The properties of double-stranded DNA can be described in terms of a flexible rod which on the average bends 90° every 160 base pairs, the persistence length of DNA.2J1J2 The flexibility of polynucleotides manifests differences in their physical properties from that predicted on the basis of the rigid rod model. Even relatively short segments of DNA are not properly described by the rigid rod model. In solution it is expected that the fluctuations in the bending of the polynucleotides, and not the overall rotational diffusion, gives rise to the slow motion of the molecules observed by NMR methods. Theoretical investigations of the fluctuations of polynucleotides have indicated that the potential barriers to change in the conformation of the ribose of both RNA and DNA are small.l This indicates that the ribose moiety may undergo considerable motion even in thermodynamically 0022-3654/79/2083-3359$0 1.0010
stable, double helical structures. There have been recently a number of NMR investigations of the conformational fluctuations of nucleic acid^.^-^ The advantage of the NMR method lies in its sensitivity to motions over a wide range of times. Proton NMR offers the ability to monitor several points of the nucleic acid structure but suffers in the ability to interpret the relaxation mechanisms unambiguously. Phosphorus-31 NMR offers the observation of a single readily assignable resonance and the relaxation mechanisms can be identified by examining the relaxation parameters at different magnetic field strengths. Phosphorus-31 NMR is limited, of course, by only monitoring a single point of the nucleic acid structure. Carbon-13 NMR offers the advantages of monitoring several points of the nucleic acid structure as well as having a well-defined relaxation mechanism. The drawback is the very low sensitivity of natural abundance carbon-13 NMR. This can be overcome, in part, by the use of a modern wide-bore spectrometer. The carbon-13 NMR data presented here complete the set of readily available NMR data which can be obtained for polynucleotides. Comparison of the results of the NMR and other methods allows a consistent picture of the conformational fluctuations of nucleic acids to be constructed. The local flexibility of the phosphate group is the greatest, followed by the 5' position of the ribose. The internal motions of the ribose ring show some variation from site to site, but all are slower than the 5' position. The internal motion of the aromatic bases appears to be much slower than that of the ribose. The lack of motion of the bases is attributed to steric constraints caused by the presence of neighboring bases. The NMR results support a model for the overall motion of nucleic acids as being that of a flexible rod. The fluctuation of the long-range bending of the nucleic acids gives rise to an approximately isotropic reorientation of any given magnetic dipole-dipole interaction on a time scale of microseconds. In contrast to the local motions, the overall motion is sensitive to salt and temperature. 0 1979 American Chemical Society
3360
The Journal of Physical Chemistry, Vol. 83, No. 26, 1979
Theory The discussion below is concerned with the relation between the NMR relaxation of the carbon-13 and phosphorus-31 nuclei of nucleic acids and molecular motion expressed in terms of spectral densities and correlation times. The spin-lattice relaxation time T1, the spin-spin relaxation time T,, the nuclear Overhauser effect NOE, and the rotating frame spin-lattice relaxation time in the presence of an off-resonance rf field Tlpoffare given in terms of the spectral densities J J w ) for dipolar coupling to a hydrogen by13J4 1 - = K [ J o ( ~ -HWI) + 3Ji(w1) ~ J ~ ( W H WI)] (1) T1
(3) 1 - -1 - K[sin2 8,(2JO(we)~] +-
TlpOff
T1
(4)
Bolton and James
with A = l /4 (3 COS' 4 - 1)'
B = Y4(sin224)
K=
20r6
(5)
where the subscript I is for either carbon or phosphorus and subscript H is for hydrogen, yI and yH are the gyromagnetic ratios, wI and wH are the angular Larmor frequencies, and r is the internuclear distance. The other terms in TlpOff(eq 4) are given as follows:14 Oe = tan-l (yIH1/2~uoff) we = 2 a v o f f / C O S Oe
(6)
(7)
we is the
angular precession frequency about the effective field vector He created by application of the rf field of strength H1at a frequency voff o f f - r e ~ o n a n c e : ~ ~
The expression for TlpOffin eq 4 is valid only for the condition that the H1 field is applied far off-resonance:14 voff 2 ~ ( Y I H ~ / ~ T )
(9)
The steady state magnetization along the effective field He results from the competition between T1 and TlpOff relaxation:14
Tlpoff Me, = M O P (10) T1 where Mo is the magnetization in the absence of the offresonance field a t equilibrium and Meffis the magnetization in the presence of the off-resonance field at equilibrium. The ratio
R = M e f f / M o= Tlpoff/T1
(11)
is experimentally determined as the ratio of the intensity of the resonance in the presence to that in the absence of an off-resonance field. The calculation of the spectral densities for random anisotropic reorientation about an axis undergoing isotropic reorientation was developed by Woessner15 and has been applied to macromolecules.16~17This approach gives the spectral densities:
=
[1/70
rc = [ l / r o
+ 1/(6~i)]-~
+ 2/(3ri)]-l
C = Y4(sin44) where 4 is the angle between the carbon (or phosphorus)-hydrogen (I-H) internuclear vector and the axis of the internal rotation, 7i is the correlation time for reorientation of the internuclear vector about the axis of internal rotation, and T~ is the correlation time for isotropic reorientation of the axis of internal rotation. The relaxation of carbon-13 nuclei which are directly bonded to a hydrogen can be considerably solely in terms of dipolar relaxation. However, for phosphorus the contribution of the chemical shift anisotropy to the relaxation must be considered. The contribution of the chemical shift anisotropy to the relaxation of the phosphorus in nucleic acids can be determined by use of (1/Ti)cBa
h2YI2YH2
TB
= 2/j~p'A~'[Ji(~)l
(13)
where Au is the chemical shift anisotropy, and it is assumed that the chemical shift tensor is axially symmetric.17 The contribution of the chemical shift anisotropy can be directly determined by observing the relaxation of the phosphorus-31 at different magnetic field strengths. As presented in the Discussion, the chemical shift anisotropy makes little contribution at 40.5 MHz to the phosphorus-31 relaxation, about 109'0, but at 81 MHz the contribution is about 35% (see Table 111). The 31PNMR data at 40.5 MHz give essentially the same results whether or not the chemical shift anisotropy is included. The line width is considered to be the least reliable indicator of molecular motion due to the chemical shift inequivalence of the different nuclei. Examination of the phosphorus-31 spectrum of low molecular weight poly(1)-poly(C) has shown that there are two peaks of equal intensity with a splitting of about 15 Hz at 40.5 MHz. For the high molecular weight samples examined in this investigation, line widths are much larger than the chemical shift inequivalence which is estimated to be about 15 Hz for both poly(1)-poly(C) and calf thymus DNA. For carbon-13 nuclei the chemical shift inequivalence is more difficult to estimate since the ribose and aromatic carbons experience substantial ring current shifts. Estimation of the magnitudes of the chemical shift inequivalence is not straightforward. Furthermore, we do not have any reliable data from model systems on which to base an empirical estimate; thus, the line width information from the carbon data is not used. The correspondence between molecular motions and local and overall correlation times is necessary in interpreting the NMR relaxation data. The persistence length of DNA can be used to estimate the energy needed to bend a given length of DNA to a particular radius of curvature according tol1,l2J8 E = (ahT/4)(d/r2)
(14)
where the persistence length a is 60 nm so (akT/4) 8.5 kcal nm/mol, d is the length of a DNA molecule, and r is the radius of curvature. As illustrated in Figure 1, the energy needed to induce reorientation of the I-H vectors by bending of DNA is quite small. While Figure 1 only indicates bending of DNA in the plane of the drawing,
The Journal of Physical Chemistry, Vol. 83, No. 26, 7979 3361
Molecular Motions in RNA and DNA 300 base pairs
E = ( 8 5kcal)(l/r2) I= length-l00nm r = r o d i u s of curvature
I
r r 15 n m Ew4kcal
Flgure 1. Schematic drawing of the reorientation of the phosphorus-hydrogen (or carbon-hydrogen) internuclear vectors, indicated by the arrows, induced by long-range bending of RNA or DNA. The drawings indicate the orientation of the vectors for different radii of curvature of a 300 base pair segment of polynucleotide.
bending can also occur perpendicular to this plane. Although the actual long-range bending of DNA in solution will be much more complicated than that shown in Figure 1,the drawing illustrates that the bending of DNA will give rise to essentially isotropic reorientation of the I-H vectors. Calculations based on eq 14 suggest that approximately 2-4 kcal/mol (activation energy) are required for reorienting a given I-H vector by bending. This indicates that the rate of reorientation is about 105-107e l . This estimate leads to a correlation time for overall reorientation of the I-H vectors due to bending of DNA of about 10-7-10-5 s. This is in reasonable agreement with a more detailed analysis.2 We note that reorientation of I-H vectors due to rotational diffusion of DNA is much slower than that which arises from the bending motion. The rotational diffusion time for a DNA molecule with a molecular weight of a few million is on the order of 10-5-10-4 s.ll Thus, overall reorientation of the P-H vectors observed in the NMR relaxation experiments will be primarily due to bending of the DNA molecules rather than to rotational diffusion. It is presumed that the same situation occurs for doublestranded RNA. The internal motion of a P-H vector is illustrated in Figure 2. Rotation about the P-0 bond induces a change in the orientation of the P-H vector with an angle of rotation of about 40' with respect to the rotation axis. The internuclear phosphorus-hydrogen distance is about 0.26 nm. The interpretation of the NMR relaxation data is not particularly sensitive to small changes in the angle of rotation (f5O) or in the proton-phosphorus internuclear distance (f0.02 nm). A recent investigation of the phosphorus relaxation of deoxyoligonucleotides has employed an effective angle of internal rotation of 60°.4 However, effective angles of internal motion near 54.7', the dipolar magic angle, are not consistent with the experimental results (vide infra). Rotation about the 0-C bond as shown in Figure 2 will also contribute to relaxation of the phosphorus-31 and induces changes not only in the angle of a P-H vector but in the internuclear distance as well. Rotation about the c-0 bond is neglected in the calculations as it cannot be distinguished from rotation about the P-0 bond by the NMR relaxation data. Thus, the internal motion correlation time deduced from the NMR data may include some contribution from motion about the C-0 bond, although the carbon-13 NMR results suggest that
" 03
s i d e view of bond being rotated
v i e w along the rotated bond
Figure 2. (A) Angles and distances pertinent to the internal motion of the phosphorus-hydrogen internuclear vector. Rotation about the P-0 bond, 6, induces reorientationof the P-H vector with an effective angle of internal rotation of 40°, angle 4 , with respect to the rotation axis. The internuclear phosphorus-proton distance is 0.26 nm. The orientation and distances are assumed to be equivalent for the 3', 5', and 5" protons which assumption appears reasonable on the basis of molecular models and X-ray crystallography data. (B) Internal motion at tetrahedral carbons of ribose reorientingthe carbon-hydrogen internuclear vector. Similar motions occur at the other ribose carbons. Rotation about the C-C bond, as indicated, reorients the C-H vector with angle of internal rotation 4 of 70.5' (or 109.5') with respect to the axis of rotation. The C-H distance is taken to be 0.109 nm.
the motion of the ribose is slower than that of the phosphate (vide infra). The distances and angles were measured from a Dreiding model in the conformation derived from X-ray studies.le The internal motion of the carbon-hydrogen vectors is somewhat more complicated. Figure 2B depicts some of the motions which might be expected to occur for a nucleotide unit of DNA. It is seen that use of a single internal correlation time to describe the local motion may be too great of a simplification. However, since we are primarily interested in differences in local mobility, the interpretation of the local motion in terms of a single correlation time is probably adequate. The carbon-hydrogen distance is taken in all cases to be 0.109 nm. The angle of internal motion is in all cases assumed to be 70.5O which is the supplement of the tetrahedral angle. As was the case for phosphorus, small changes in this angle will not seriously affect the interpretation of the carbon-13 results. However, angles of internal motion near the magic angle, 54.7', can be eliminated on the basis of the NMR results.
Results and Discussion Phosphorus-31 NMR Relaxation. The phosphorus-31 data monitor the molecular motion of a single site of the polynucleotides. The interpretation of the phosphorus-31 data is instructive in choosing a model to fit the NMR relaxation data. Attempts to fit the data for poly(A) (see Table I) to a model first involved describing the conformational fluctuations of poly(A) in terms of a single isotropic motion. At neutral pH, poly(A) is known to form a single stranded helix which melts in a noncooperative fashion. Theoretical values of the relaxation parameters
3362
The Journal of Physical Chemistry, Vol. 83, No. 26, 1979
TABLE I: Phosphorus-31 NMR Relaxation Parameters of Polynucleotides at 40.5 MHz AVl,*,
Bolton and James
TABLE 11: Internal and Bending Motion Correlation Times of Polynucleotides Determined from Phosphorus-31 NMR Relaxation Dataa
temp, "C
T , ,s
NOE
6 8 12 20 40
1.6 1.56 1.52 1.54 ND
Poly(A)a 1.26
