Biochemistry 1990, 29, 799-8 11 Wagner, G., Kumar, A,, & Wuthrich, K. (1984) Eur. J . Biochem. 114, 315-384. Weaver, D. T., & DePamphilis, M. L. (1984) J . Mol. Biol. 180, 961-986.

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Characterization of the Overall and Internal Dynamics of Short Oligonucleotides by Depolarized Dynamic Light Scattering and NMR Relaxation Measurements? Wolfgang Eimer, James R. Williamson,* Steven G. Boxer, and R. Pecora* Department of Chemistry, Stanford University, Stanford, California 94305- 5080 Received July 10, 1989; Revised Manuscript Received September I , 1989

ABSTRACT: The dynamics of three synthetic oligonucleotides d(CG)4, d(CG)6, and d(CGCGTTGTTCGCG) of different length and shape were studied in solution by depolarized dynamic light scattering (DDLS) and time-resolved nuclear Overhauser effect cross-relaxation measurements. For cylindrically symmetric molecules the DDLS spectrum is dominated by the rotation of the main symmetry axis of the cylinder. The experimental correlation times describe the rotation of the oligonucleotides under hydrodynamic stick boundary conditions. It is shown that the hydrodynamic theory of Tirado and Garcia de la Torre gives good predictions of the rotational diffusion coefficients of cylindrically symmetric molecules of the small axial ratios studied here. These relations are used to calculate the solution dimensions of the DNA fragments from measured correlation times. The hydrodynamic diameter of the octamer and dodecamer is 20.5 f 1.0 A, assuming a rise per base of 3.4 A. The tridecamer, d(CGCGTTGTTCGCG), adopts a hairpin structure with nearly spherical dimensions and a diameter of 23.0 f 2.0 A. The DDLS relaxation measurements provide a powerful method for distinguishing between different conformations of the oligonucleotides (e.g., D N A double-helix versus hairpin structure). Furthermore, the rotational correlation times are a very sensitive probe of the length of different fragments. The N M R results reflect the anisotropic motion of the molecules as well as the amount of local internal motion present. The experimental correlation time from N M R is determined by the rotation of both the short and long axes of the oligonucleotide. The contributions of the various correlation times are given by the relative orientation of the internuclear vector with respect to the main axis and the correlation function for internal motion, if it is assumed that the librational motions decay much faster than the overall reorientational motion. Our results are compared with those from N M R relaxation measurements on other short oligonucleotides with lengths of up to 20 base pairs. Various dynamic models for the reorientation of the internuclear vector are applied to their interpretation. The extent of local internal motion is apparently independent of the length and base sequence of the D N A fragments and gives a significant contribution to the effective correlation time measured by the cross-relaxation rate.

T e biological function of DNA and RNA is most likely determined not only by sequence-dependent properties and static conformation but also by its dynamics. DNA is a semiflexible macromolecule and, due to its length, exhibits a complex dynamic behavior. The local internal motions of DNA have become the subject of increasing interest in recent years. Fast fluctuations in the conformation of DNA may play an important role in transcription and the DNA-protein recognition process. The conformational fluctuations occur on a time scale between l V and lo-'* s and include long-range twisting and bending motions as well as very local fluctuations of small segments about an equilibrium position. Experiments using various types of probes, mainly time-resolved fluorescence polarization anisotropy (FPA) (Genest & Wahl, 1978; Barkley & Zimm, 1979; Millar et al., 1981; Magde et al., 1983), ESR (Bobst et al., 1984; Kao & Bobst, 1985), and 'This work was supported by a grant from the National Institutes of Health (Rot GM27738) to S.B. and a grant from the National Science Foundation (CHE-88-14641) to R.P. Further support came from the NSF-MRL program through the Center for Materials Research at Stanford University. Present address: Department of Chemistry and Biochemistry, University of Colorado, Boulder, CO 80309.

0006-2960/90/0429-799$02.50/0

NMR' relaxation experiments of different nuclei (Early & Kearns, 1979; Bolton & James, 1980a,b; Hogan & Jardetzky, 1980; Mirau & Kearns, 1983; Assa-Munt et al., 1983; Mirau et al., 1985), have been performed to characterize the nanosecond to subnanosecond motions. The fluorescence depolarization measurements show a very rapid initial decay which could be partially resolved by using a picosecond laser setup (Magde et al., 1983). The very fast decay was attributed to the "wobbling" of the intercalated dye molecules (Barkley & Zimm, 1979) with a root mean square fluctuation of about f21'. ESR and NMR studies confirmed the existence of librational motions for the bases and other segments in polynucleotides. The time scale and especially the amplitude for the relaxation processes have been the subject of controversy (HArd, 1987; Schurr & Fujimoto, 1988). For an unambiguous interpretation of NMR and ESR results, it is necessary to provide a precise theory that accounts for the rather complex dynamics of the long DNA fragments, where it is expected that different relaxation modes couple. When collective twisting and bending motions are neglected, the experimental I Abbreviations: NMR, nuclear magnetic resonance; DDLS, depolarized dynamic light scattering; NOE, nuclear Overhauser enhancement.

0 1990 American Chemical Society

800 Biochemistry, Vol. 29, No. 3, 1990 results indicate a rather large amplitude of about 35” and in some cases even larger values. Taking into account the long-range fluctuations, Schurr and Fujimoto (1988) estimated the amplitude of the local motion of bases to reduce to =loo. A knowledge of the extent of internal motion and the overall molecular reorientation is also an important precondition for determining the structure of oligonucleotides by 2D NMR (Wuthrich, 1986; Borgias & James, 1988) in solution. There is experimental evidence that the structure in a crystal or fiber differs significantly from the conformation of very short DNA fragments in solution. For B-DNA, X-ray crystallography data (Saenger, 1984) indicates that the base planes are oriented nearly perpendicular to the helix axis; the tilt angle varies mostly between 0 and 5’. On the other hand, linear dichroism spectroscopic studies (Edmondson & Johnson, 1985, 1986, 1987) and electric dichroism measurements (Hogan et al., 1979) of the conformation of polynucleotides in solution predict a tilt angle that may be even greater than 25O and depends on the base-pair sequence. These findings have been questioned (Lee & Charney, 1982; Charney et al., 1986), and it is still not clear whether or not the structural parameters in solution differ from those in crystals. A large-amplitude internal motion would complicate any structure determination using distance information obtained from 2D NMR spectroscopy. Criticism in this direction has already been raised on the basis of the experimental finding of some very large librational amplitudes of the bases. A better understanding of relaxation mechanisms within DNA fragments is therefore essential for the justification of the complex structure determination procedures. Depolarized dynamic light scattering (DDLS) and NMR cross-relaxation studies are combined here for the first time to characterize the overall and internal motions of a set of small DNA fragments. The shapes used for calculating hydrodynamic properties of the oligonucleotides can be approximated as axially symmetric bodies such as ellipsoids or cylinders. DDLS spectra are determined by the reorientational motion of the symmetry axis of the oligonucleotides, which is the end-over-end rotation. The size of the cylindrical molecules can be calculated from a knowledge of the experimental rotational diffusion coefficient. A theory for the translational and rotational diffusion coefficients of cylindrically symmetric molecules with a large length-to-diameter ratio was developed by Broersma (Broersma, 1960a,b; 1980) almost 30 years ago. This theory is, however, not applicable to the transport coefficients of short cylinders. A more recent hydrodynamic model by Tirado and Garcia de la Torre (Tirado & Garcia de la Torre, 1979, 1980) overcomes this problem and gives expressions for D the translational and 8 the rotational diffusion coefficient of rodlike molecules in the range 2 < p 5 30, where p = L / d , the length to diameter ratio. The hydrodynamic behavior of relatively long DNA fragments (p = 25) is well described by this theory (Tirado et al., 1984a). For low values of p the theory also gives good agreement with experimental data (Tirado et al., 1984b). Furthermore, the hydrodynamic theory can be used to calculate an effective rotational correlation time for a rigid, anisotropic molecule, where motions about the different axes have to be considered. The NMR cross-relaxation experiment monitors the reorientation of the cylindrical molecules about both the long and short molecular symmetry axes (Huntress, 1968). In the NMR experiments three different correlation times contribute to the measured effective correlation time for a cylindrically symmetric molecule. The relative contributions of these times depend on the orientation of the internuclear vector whose

Eimer et al. relaxation is being studied with respect to the main symmetry axis of the cylinder. In addition, any internal motion of the internuclear vector in the molecular frame also contributes to the spectral density. Assuming that the librational motions of the bases take place on a much faster time scale than the overall motion, the internal motion affects the relative contributions of the three rotational correlation times, Le., has an influence on the amplitude factors. To characterize the internal motion of DNA, long fragments with a length of more than 100 base pairs have usually been studied. This has the disadvantage that the relaxation mechanism for such long molecules is in general complex. The fragments are relatively flexible, and therefore, besides local internal motions of the bases and the backbone, collective twisting and bending motions also have to be considered. This makes a straightforward interpretation of the experimental data more difficult. To mitigate this complication, we have studied the very short oligonucleotides d(CG)4 and d(CG)6, 8 and 12 base pairs long, for which collective motions are likely to be less important. These molecules are well approximated by cylinders. Furthermore, we have studied d(CGCGTTGTTCGCG), which adopts a specific hairpin structure (Williamson & Boxer, 1989). Under these conditions the molecule is almost spherical and the overall reorientational motion should be different from that of the corresponding helical duplex molecules. DNA has been found to exist in several different conformations in vitro and in vivo. These include, A-, B-, and ZDNA as well as bent or hairpin structures. The biological importance of some of the conformations has not yet been clarified. It is, however, of great interest to develop spectroscopic methods that can identify conformational differences of DNA oligomers to facilitate the study of possible structure-activity relationships. In the following we show that DDLS is a very powerful tool for distinguishing between the duplex and hairpin DNA forms. In addition, it can be used to measure small changes in DNA length such as those that might occur by intercalation. In contrast to FPA and ESR experiments, no introduction of a label molecule or a chemical modification of the bases is necessary in the case of DDLS. Thus, any uncertainty about possible structural changes upon chemical modification and the orientation of the transition moment (FPA) or hyperfine principal axes (ESR) is avoided. The interpretation of DDLS experimental results is relatively straightforward. The line width of the depolarized spectrum directly gives the reorientational relaxation time of the rotation about the short symmetry axes. Any pair correlation effect, which might occur because DDLS is a coherent process, can be accounted for by performing the measurements as a function of concentration. In general, NMR relaxation experiments have the disadvantage that the spectral density and therefore the relaxation rate depends on P,the inverse sixth power of the internuclear distance. Often r is not known and may change during the reorientational motion. This problem was avoided in our experiments because we followed the buildup of NOE from the H6 to the H5 of the cytosine bases. The position of the protons is fixed within the aromatic ring, and their distance is well-known. For a rigid cylindrical body the effective correlation time that determines the spectral density can be calculated by using Woessner’s formalism (Woessner, 1962). To account for local internal motion Lipari and Szabo (1982a,b) have proposed a general theory that they call a “model-free approach”. The assumption is that the internal motion is much faster than the overall reorientation and that

Overall and Internal Dynamics of DNA

Biochemistry, Vol. 29, No. 3, 1990 801

the decay of the internal motion is characterized by a single exponential. In this model the information about the fast component of the relaxation parameter in a NMR experiment can be described by a “generalized order parameter” S,which reflects the spatial restrictions of the internal motion, and an internal correlation time qnt,which characterizes the frequency of the motion. S2 is the asymptotic value of the normalized internal autocorrelation function for t = a. It is also possible to construct dynamic models for the internal motion, derive the correlation function, and obtain more information about the geometric restrictions of the motion. One approach is the diffusion in a cone model (Lipari & Szabo, 1981), for which Wang and Pecora (1980) have calculated the time correlation functions. Another model assumes that the system undergoes overdamped librational motions (Schurr & Fujimoto, 1988; Schurr, 1984) about an equilibrium position in harmonic polar and azimuthal potential wells. We have applied all three models to our data and give a comparison of the final results. In the following section, a brief summary of some of the relevant underlying principles of DDLS and NMR cross-relaxation experiments is given to show the strengths and weaknesses of each technique and how they may be used to complement each other in studying the dynamics of short DNA fragments. THEORY For rigid molecules both spectroscopic methods, DDLS and NMR relaxation, monitor directly or indirectly the time dependence of a stochastic variable R, which is a function of the orientation angles D of the molecules. The time dependence of R ( t ) is characterized by its time autocorrelation function

= (R(t)R(O)) (1) where the the angular brackets indicate an ensemble average. The stochastic variable R that determines the time correlation function in a given experiment, for example, the polarizability tensor a in DDLS or the dipolar interaction between two nuclei in NMR relaxation experiments, may be expressed in terms of linear combinations of the Wigner rotation matrices of J = 2 with coefficients containing the spherical tensor components of the particular stochastic variable in the molecule-fixed frame. These molecule-fixed spherical tensor components are time independent for rigid molecules. The Wigner rotation matrices express the time-dependent transformation of R from the molecule-fixed frame to the laboratory-fixed frame. The correlation functions of interest for our experiments are thus linear combinations of time correlation functions of the form

c(t)= ( D(2)*k,m

[%F(o)l

D(2)k,m [%F(t)l )

(2)

where DLF denotes the Euler angles that specify the orientation of the molecule in the laboratory-fixed system. The relevant linear combinations consist in general of a sum of five exponentials

c(t)= EA, m

exp-(t/7,)

(3)

where the sum is over m = 0, f l , and f2. The T, for rigid cylindrically symmetric molecules is given in terms of 8, and e,,, the rotational diffusion coefficients for the reorientation about the short and long axes of the cylinder, respectively: 1/7,,, = 68, m2(eI1- €Il). The 7”s are the same for both spectroscopic techniques, but the amplitude factors A , are specific for the DDLS and the N M R experiments and are responsible for the differences in the experimental information obtained from them. In the case of DDLS the time autocorrelation function of the scattered light electric field is determined by the labora-

+

tory-fixed yz component of the polarizability tensors (Y of the molecules (Berne & P a r a , 1976). For asymmetric molecules, the DDLS correlation function consists of up to five exponentials. The amplitude factors are a function of the elements of the polarizability tensor a and the rotational diffusion tensor 0. For symmetric top molecules, however, azz(=all) > ayv = a,.. (=aI), and the correlation function corresponding to eq 3 reduces to a one-exponential form given by SvH(q,r) = ANf12(1 +/n) exp-

[:(%)I

(4)

where 0 (=ail - aL)is the optical anisotropy of a molecule, A is a constant, N is the number of molecules, 7, is the reorientational correlation time for a single molecule, and f and g are, respectively, the static and dynamic correlation factors. In general, SVH(q,t)includes information about dynamic correlations in orientation and position between all pairs of molecules through the static and dynamic correlation factors fand g. It has been found for many symmetric top molecules that the dynamic correlation factor gN 98%. The DNA fragment d(CGCGTTGTTCGCG) was synthesized by the phosphoramidite method. Details about the preparation are given elsewhere (Williamson, 1988). The experiments were performed in a phosphate buffer (50 mM sodium phosphate, 100 mM NaCl, 2 mM EDTA, and 0.1% NaN,) at pH 7.0 (for H20). DDLS Experiments. A depolarized dynamic light scattering apparatus similar to one whose detailed description is given elsewhere (Eimer, 1987) was used. The light source was an argon ion laser (Spectra-Physics, Model 2000) operating in single mode at X = 488.0 nm. The scattered light was collected at a scattering angle of 90' in the VH geometry and frequency analyzed by a piezoelectrically driven Fabry-Perot interferometer (RC-110, Burleigh Instruments). A set of 750-MHz confocal mirrors was used to allow the analysis of slow relaxation processes on the order of nanoseconds. The typical

Overall and Internal Dynamics of DNA finesse was about 80-90. The detection system consists of a photomultiplier tube (EMI, Model 9865), an amplifier discriminator (SSR 1105), and a data acquisition and stabilization unit (DAS-1, Burleigh Instruments). Because of the low intensity of the depolarized scattered light, at the beginning of each scan a small portion of diffuse, unscattered light (incidence angle = 180°) was passed through the interferometer for stabilization purposes. Thereafter, 2 orders of scattered light were collected. The measuring and reference beam are controlled by a shutter system (Newport, Model 845). Data analysis was performed on a microcomputer (Universe 68, Charles River Data System). All spectra were deconvoluted by using an iterative method (van Cittert, 1931), using the spectrum of the unscattered light mentioned above as the instrumental function. In some cases, due to the influence of dust, the spectrum of the depolarized light contained a narrow line with a half-width at half-height equal to that of the instrument. Nevertheless, a deconvolution with two Lorentzians gave the reorientational correlation time of the oligonucleotides. The amplitude of the narrow component was less than 10%. N M R Experiments. All measurements were performed on a GE GN-500 spectrometer at 500 MHz. NMR samples were prepared by lyophilization of a known amount of oligonucleotide from H20, the appropriate buffer solutions were added, and the sample was exchanged for D 2 0 by repeated lyophilization from 99.8% D20. The samples were finally dissolved in the original volume of 99.996% D 2 0 in a glovebag under nitrogen. The samples of d(CG), and d(CG)6 contained 50 mM sodium phosphate, pH 7.0, 100 mM NaCl, and 2 mM EDTA. The sample of d(CGCGTTGTTCGCG) contained 35 mM sodium phosphate, pH 7.0,70 mM NaCl, and 5 mM EDTA. Cross-relaxation rates were determined by measuring the time dependence of the NOE. Five spectra were recorded in an interleaved fashion, one as a control with no irradiation and four with selective saturation of one resonance with incremental irradiation times. The irradiation times were chosen, depending upon the oligonucleotide and temperature, such that the magnitude of the largest NOE in a series was