A 23Na-NMRStudy of Sodium-DNA Interactions in Concentrated DNA Solutions at Low-Supporting Electrolyte Concentration TERESA E. STRZELECKA” and RANDOLPH 1. RILLt

Department of Chemistry and Institute of Molecular Biophysics, The Florida State University, Tallahassee, Florida 32306

SYNOPSIS

Aqueous solutions of DNA fragments with a contour length (500 A ) near the persistence length at DNA concentrations ranging from 10 to 290 mg/mL solvent and a constant supporting electrolyte concentration of 0.01 M (predominantly NaCl) were examined by 23Na-nmrspectroscopy at temperatures of 20,40, and 60°C. Over the higher portion of this concentration range (> 100 mg/ml) the DNA solutions undergo a complex series of transitions between different anisotropic, liquid crystalline phases (T. E. Strzelecka and R. L. Rill, Biopolymers, in press). Counterions in solutions of strong polyelectrolytes are usually described in terms of a two-state model as free or “bound’ (influenced by the electrostatic field of the polyanion ) . The longitudinal relaxation rate ( R1 = 1 / Tl ) at all DNA concentrations decreased with increasing temperature, demonstrating fast exchange between free and bound counterions. R, increased nearly linearly with increasing DNA phosphate/sodium ratio in the isotropic domain until the onset of anisotropic phase formation, in agreement with similar nmr studies conducted at low DNA concentrations. The value of RIb = 194 k 7 Hz obtained for the isotropic phase from 10 to 100 mg DNA/mL at 20°C was in agreement with values reported previously. A nonlinear increase in Rl with DNA concentration was observed upon onset of anisotropic phase formation, indicating an increase in the product of the fraction of bond ions times their relaxation rate ( r * Rl,b). The spectral lineshape of all isotropic samples was Lorentzian. Spectra of anisotropic samples exhibited low magnitude quadrupole splitting of 1400 Hz correlated with appearance of a cholesteric phase with pitch = 2 wm. The magnitude of the quadrupole splitting decreased with increasing DNA concentration at low temperatures and increased with concentration at high temperatures. At all concentrations the quadrupole splitting decreased then increased with temperature. These temperature- and concentration-dependent changes in quadrupole splitting are consistent with an angle between the DNA helix axis and the principal component ( V Z Zof ) the local electric field gradient tensor near the “magic angle” of 54.7”.

INTRODUCT10N DNA molecules in aqueous solutions are highly negatively charged and produce strong electric field 0 1990 John Wiley & Sons, Inc. CCC 0006-3525/90/7-80803-12

$04.00

Biopolymers, Vol. 30,803-814 (1990) * Present address: Department of Biochemistry and Molecular

Biophysics, College of Physicians and Surgeons, Columbia University, New York, NY 10032. To whom correspondence should be sent at the Department of Chemistry.

’

gradients that cause accumulation of small counterions in their vicinity. Interactions with counterions have considerable influence on the conformation and function of DNA-hence many studies of DNA solutions have been devoted to evaluation of the nature of these interactions. DNA solutions are also useful as model systems for general polyelectrolyte behavior, and in some cases counterions may serve as probes of conformational changes DNA molecules undergo in solution. 23Na-nmr is particularly suitable for probing DNA-ion interactions. 803

804

STRZELECKA AND RILL

The sodium nucleus (spin $) possesses a quadrupole moment, which interacts with electric field gradients created by surrounding charges. Since the natural abundance of 23Na is loo%, it is relatively easy to obtain 23Na-nmrspectra in dilute solutions. Extensive prior 23Na-nmrstudies of DNA counterions were conducted on semidilute DNA solutions and were aimed primarily a t testing theoretical models of the counterion distribution about the DNA helix.'-' The counterion condensation model, 'OJ' along with more recent PoissonBoltzmann 12-14 and Monte Carlo treatments, 15-23 have shown that DNA in dilute solutions is surrounded by a layer of counterions that are "condensed" near the polyion surface; hence the Na' population in DNA solutions can generally be divided into free and "bound" subpopulations. Relaxation of 23Naspins is enhanced in the bound state due to quadrupolar interactions with a strong DNA electrostatic field. Unique interpretation of 23Narelaxation parameters in terms of the number and properties of bound counterions has proven difficult. In general, however, the relaxation rate of bound Na' ions (180-220 Hz a t 20°C) is approximately 10 times that of free Na' ions, and the ratio of bound counterions to DNA phosphates ( r ) is estimated to be in the range of 0.5-0.8. The motional correlation time (7,)of the bound N a + ions is on the order of 2-5 ns, and the quadrupolar coupling constant is N 100 KHz ( a t 20°-250C).'~3~5~s There has been only one 23Na-nmrstudy of DNA in a concentrated state-hydrated, oriented DNA fibersz4In this case quadrupole splitting of the 23Na resonance was observed, as expected for a near-solid system.25The magnitude of the splitting was relatively small and varied from N 3400 Hz for DNA fibers parallel to the magnetic field to N 1700 Hz when the DNA fiber axes were perpendicular to the magnetic field. As part of our studies of anisotropic (liquid crystalline) DNA pha~es,'~-~O we have measured 23Na relaxation rates and spectra over previously unexplored semiconcentrated and concentrated DNA regimes, from 10 to 290 mg DNA/mL solvent, over a range of temperatures from 20 t o 6OoC a t a supporting electrolyte concentration of 10 m M (predominantly NaCl) . The apparent product of r * Rl,b, the fractional DNA charge neutralization times the longitudinal relaxation rate of bound counterions, was sensitive to phase transitions occurring in the 100-290 mg/mL DNA concentration range, increasing with increasing concentration. Quadrupole splitting was observed upon formation of the cholesteric DNA phase and exhibited a complex depen-

dence on DNA concentration and temperature. Changes in both R1 and the quadrupole splitting at high DNA concentrations are consistent with subtle changes in the counterion distribution, and also proved useful for elaboration of the phase diagram to include the critical concentration for cholesteric phase formation.

Summarizing briefly, relaxation of quadrupolar nuclei is due to interactions of the nuclear quadrupole moment with fluctuating electric field gradients in the immediate vicinity. T h e decay of magnetization to its equilibrium value is not, in general, governed by a single-exponential law. However, in the extreme narrowing limit, when w7, 4 1 ( w is the Larmor frequency and 7 , the motional correlation time), the relaxation rates R1 ( = l / T l ) and R2 ( = l / T z )are equal and

R1 = R2 = ( 2 7 r 2 / 5 ) X 2 ~ ,

(1)

where x is the quadrupole coupling constant defined by

with e the elementary electron charge, Q the scalar quadrupole moment, and e . q ( = V z z ) the main component of the electric field gradient tensor in the laboratory frame. The extreme or near extreme narrowing limit has been found t o apply to semidilute solutions of double-stranded DNA a t moderate magnetic fields ( < 4.2 Tesla) By contrast, when the motional correlation time is long or a t higher fields, the decay of longitudinal and transverse components of magnetization can be described as a sum of two exponentials, Tl is not equal to T,, relaxation is frequency dependent, and the resonance is described ( t o first order) by two superimposed Lorentzians differing in line ~ i d t h . ~ . ' ~ Ions in solutions with charged macromolecules exist in a t least two states: free and bound. If the binding is noncovalent, as in the case of DNA, there is usually rapid exchange of ions between free and bound sites. As defined by nmr criteria, bound ions are sufficiently near the DNA molecule (within = 4 A ) to have relaxation rates much greater than Rf, the relaxation rate characteristic of nuclei in bulk NaCl solution. If the lifetimes of ions in different sites are negligible compared to the relaxation rates a t these sites, and under the extreme narrowing condition, the relaxation rates can be expressed in the form .1-3,536

23Na-NMROF SODIUM-DNA INTERACTIONS

805

is taken over all possible values of OM .25,32 In general, if several types of sites contribute t o quadrupole splitting, and under fast exchange conditions, where pi is the fraction of ions in site i, R , i is the relaxation rate of ions a t this site, and x = 1 or 2.2x375 Measurements of the temperature dependencies of relaxation rates are commonly used t o determine if ion exchange is fast or S ~ O W . In ~ , ~the ~ case of fast exchange the relaxation rates are proportional t o the correlation time 7 c , and since rc decreases with increasing temperature, the relaxation rates also decrease. For a n isotropic solution, where the electric field gradient assumes all directions with equal probability, and under extreme narrowing conditions, the 23 Na-nmr spectrum is a single Lorentzian line. In rigid single crystals (except those with cubic symmetry ) , there are static quadrupolar interactions with anisotropic electric fields that split the resonance into a triplet with relative intensity ratios of 3 : 4 : 3. The frequency separation between the central and side peaks, called the quadrupole splitting, is given by

A

=

X(3 C

O S ~ ~1)/4

(4)

where the summation extends over all sites.

MATERIALS AND METHODS Sample Preparation and Characterization

DNA with a narrow distribution of lengths near the persistence length (500 A ) was isolated from calf thymus nucleosome core particles and characterized a s described previously.28 A set of DNA solutions with concentrations ranging from 10 to 290 mg/mL was prepared in a way that enabled us to control the total and excess Na' c~ncentration.~' DNA nearly free of extra salt was obtained by prolonged dialysis against 0.5 m M N a + buffer. Dialysis was performed under vacuum from a water aspirator in a collodion bag device (Schleicher & Schull) to minimize dilution. The total Na concentration was determined by nuclear activation analysis in the University of Florida Training Reactor facility in Gainesville. After the Na+/phosphiite ratio was determined to be 1 : 1 within error ( C D N A = 0.127 k 0.004 M DNA phosphate and C N =~ 0.129 t 0.003 M ) , aliquots of DNA solution corresponding to total DNA masses of 5, 10, . . . , 145 mg were transferred to microfuge tubes, dried under vacuum, then 500 pL of 0.01 M Na' buffer (9 m M NaC1, 1 m M Na cacodylate, 0.1 m M Na2EDTA, adjusted to p H 6.5 with HCl) were added to each tube, giving a set of DNA samples with excess Na'X- concentration of = 0.01 M . DNA concentrations are expressed here in terms of the unambiguous units of mg DNA/mL solvent unless noted otherwise (e.g., Figure 8 ) ,and are accurate t o f 3%. Concentrations in the more usual units of mg DNA/ml solution are slightly lower and can be calculated assuming a value for the DNA partial specific volume.30 Measurements of the sodium ion activity were made a t 25°C with a n Orion Model p H meter and sodium ion-specific, micro-combination electrode. +

An order parameter is usually defined as

s = ( ( 3 cos28

-

1))/2,

(5)

where 8 is the angle between the principal axis of the electric field gradient tensor and the magnetic field direction. In liquid-crystalline systems, where there is no rigid lattice, molecular motions usually incompletely average the quadrupolar interaction. Quadrupole splitting in liquid-crystalline systems can be expressed in terms of a n orientation factor and an order parameter,

where Ph is the fraction of bound ions,

where SDis the orientation factor related to the angle HI,, between the liquid crystal director and the magnetic field, and S M =

((3 COS28M

-

1))/2

(8)

where SMis a n order parameter and OM is the angle between the director and the principal axis of the electric field gradient tensor V z z , and the average

23Na-NMR

23Na spectra were obtained a t a frequency of 40.04 MHz on Fourier transform spectrometer built inhouse with wide bore superconducting solenoid and

806

STRZELECKA AND RILL

accessories for solid state applications. Spectra were obtained with a sweep width of -t 2000 Hz and pulse repetition time of 0.3 s. The number of scans varied with total Na' concentration, from 1000 scans for samples with DNA concentrations of 10-100 mg/ mL to 100 scans for higher concentrations. Spectra of isotropic DNA solutions were taken in 5-mm nmr tubes with spinning to eliminate magnetic field inhomogeneities. Spectra of biphasic samples were taken in a specially constructed nmr probe in which the sample was placed horizontally in a receiver coil long enough to contain all of it. T o obtain optimum experimental conditions the magnetic field homogeneity was adjusted until the line width of 1 M N a + buffer was less than 7 Hz for samples in 5-mm tubes and less than 10 Hz for samples in horizontal tubes. Samples placed in the magnet a t 20°C were allowed to equilibrate for a t least 1h before the first spectrum was taken, and a t least 30 min was allowed for samples to attain thermal equilibrium after the temperature was increased t o other set values. Tl relaxation times were measured by the standard inversion-recovery pulse sequence, and TIvalues were obtained by a linear least-squares fit to the logarithm of magnetization versus delay time. Experimental errors in the individual relaxation measurements were estimated to be 3-6%. Ti's were measured a t 20, 40, and 60°C in isotropic samples, and a t 10°C intervals in liquid-crystalline samples. Line widths, integrated peak areas, and peak separations were determined using a line-deconvolution program on the Nicolet-1180 computer. The average line width for free sodium ions was determined to be 6.8 Hz a t 20°C in 1 M N a + buffer. T h e relative error of resonance area determination was usually lower than 1%and the error of the fitting procedure on the order of 1-296.

weakly birefringent, slightly twisted nematic-like phase), and cholesteric phase in coexistence a t 2040°C. DNA solutions with concentrations exceeding N 230 mg/mL were also triphasic, with isotropic, cholesteric, and a higher density phase in coexistence. The 23Naresonances of DNA samples in the concentration range of 10 to N 180 mg DNA/mL were Lorentzian in shape, and no deviations (within a 12% relative error) from a single-Lorentzian line-fit were detected, even though the transverse relaxation rate R2, was 10-15% greater than the longitudinal relaxation rate R1 ( n o t shown). T h e extreme narrowing condition, therefore, does not strictly apply but is a reasonable approximation for analysis of relaxation data. In the near-extreme narrowing limit the changes in signal amplitude obtained in the standard inversion-recovery pulse sequence for measuring TI are expected t o be fit reasonably by a single-exponential accurately reflecting the slowly relaxing c o m p ~ n e n t . ~ ~ ~ ~ ~ ~ The overall longitudinal relaxation rate R1 generally increased with increasing DNA concentration and decreased with increasing temperature (Figure 1) . T h e relaxation rate decrease with increasing temperature demonstrates that exchange between free and condensed or bound counterions is rapid on the nmr time scale a t all DNA concentrations examined. T h e specific dependence of R1 on DNA concentration was complex a t all temperatures, but some interesting features of this dependence can be related, in part, t o the behavior observed by Record, Anderson, and co-workers in semidilute solutions.2,3,5,7,8These features are perhaps best appreciated by examining Eq. ( 3 ) recast in the form

RESULTS

where r is the fraction of bound sodium ions per nucleotide phosphate, and ( P ) and ( N a ) are the molar concentrations of DNA phosphate and total sodium ions, respectively. If Rb, Rf, and r are independent of concentration, then the observed relaxation rate should increase linearly with the ratio ( P )/ ( N a ) . Bleam et aL5 observed a linear dependence over a range of temperatures from 6 to 33"C, and a range of ( P )/ ( N a ) of about 0.01-0.7. The latter range was obtained by increasing the NaCl concentration in DNA solutions maintained with ( P ) x 15 m M , corresponding to a DNA weight concentration of about 5 mg/mL. Van Dijk et al.' also observed a linear relationship between R1 and NaCl concentration a t a constant DNA concentration of

Spin-Lattice Relaxation

Samples with DNA concentration of 10-120 mg/ mL were isotropic a t room temperature by optical and nmr criteria, whereas samples with DNA concentrations > 130 mg/mL contained increasing amounts of optically anisotropic (liquid-crystalline ) phase. The phase behavior of these solutions was complex and temperature dependent, and is described in detail in Ref. 32 (see also below). Summarizing briefly, DNA samples with concentrations in the range of x 130-230 mg/mL were bi- or triphasic, with isotropic phase, precholesteric phase ( a

807

23Na-NMR OF SODIUM-DNA INTERACTIONS

_i 160

I

I

I

Figure 1. Dependence of the overall 23Nalongitudinal relaxation rate R , on DNA concentration (mg DNA/mL solvent)at20(A),40(A),and6O0C(0)(toptobottom).

Arrows indicate DNA concentrations at which various anisotropic phases appeared in solution as indicated by 31P-and 23Na-nmrspectroscopy and polarized light microscopy. The I1 refers to the precholesteric phase, I11 to the 2 pm pitch cholesteric phase, and IV to the high-density phase. See Ref. 32 and Figure 8 for more details on these phases. (Note that phase boundaries Figure 1 and Figure 8 appear slightly different since they are expressed in different concentration units.) about 33 mg/mL over a wide range of ( P ) / ( N a ) , but small deviations from the predicted dependence were observed a t a DNA concentration of N 66 mg/ mL (0.2 M nucleotide ) .Analogous plots of our data obtained by increasing the DNA concentration from 10 to 290 mg DNA/mL solvent while maintaining constant supporting electrolyte concentration exhibited two distinct regions (Figure 2). In the first region corresponding t o the isotropic phase, from 10 to about 120 mg/mL, R, was approximately linear with ( P ) / ( N a ) ratio; thus in these solutions the product r ( Rl,b - Rl,f) remained nearly constant, as observed for moderately dilute DNA solution^.^^^ The small deviation from linearity may be related to pretransition ordering phenomena, as suggested

-

by Van Dijk et al.,’ who noted a small anomaly in the dependence of R1 on NaCl concentration a t a DNA concentration of 0.2 M (nucleotide). It should be noted t h a t the 30% increase in R1 in this region from ( P )/ ( N a ) = 0.75 t o 0.97 was due solely to the increase in Na’ DNA concentration. Since the DNA concentrations reached here were much higher than those utilized by Bleam et al.,5 the values of ( P ) / ( N a ) were also much higher. The presence of a small excess of NaCl in the “desalted” DNA sample would shift the curves horizontally t o slightly lower ( P )/ ( N a ) and decrease the maximum value of ( P ) / ( N a ),but would not change the fundamental shape of the curve in any concentration range. In the second region, above x 120 mg/mL, a sharp increase in R1 with increasing DNA concentration or ( P )/ ( N a ) was noted upon onset of anisotropic phase formation. This abrupt departure of the dependence of Rl on ( P ) / (N a ) from the linear response a t lower DNA concentrations is most consistent in general terms with a n increase in the product r.Rl,b for the anisotropic phase. A more specific interpretation is not possible because the overall relaxation rate is dependent on the number and populations of different Na’ ion states, and the relaxation rates of these states determined by the quadrupole coupling constants and the correlation times T,, for motions relative to the electric field gradients in each state.25 Some limits on the maximum values of r and Rl,b for the anisotropic phase can be estimated by retaining the two-state model and assuming that Rl,f is independent of DNA concentration. An estimate

iJ 2oo

JP 0 Odmo

0

0

0

0 00 3 &

0

0 0 0

0

0

I

I

.78 81

I

.84

1

I

60”

9-

0

20 .75

8 40”

I

I

I

.87 -90 .93 .96 .99

P/ NA Figure 2. Dependence of the overall 23Nalongitudinal relaxation rate R1 on the ratio ( P ) / ( N a )of the concentrations of DNA phosphate to total sodium ions at 20,40, and 60°C (top to bottom). Arrows indicate the points corresponding to a DNA concentration of 100 mg/mL.

808

STRZELECKA AND RILL

of the maximum possible R1,b for the anisotropic phase can be calculated in this case assuming that the fractional counterion binding r remains invaria n t with DNA concentration. The assumption of constant r with DNA concentration is consistent with the observation that the apparent sodium ion activity coefficient measured at 20°C remained approximately constant in the range of 0.25-0.30, very close to the value predicted by Manning's theory, over the DNA concentration range from 30 to 290 mg/mL (data not shown). These activity measurements cannot be directly related to the fraction of bound sodium ions as defined by nmr criteria, but the insensitivity to anisotropic phase formation suggests that some fraction of sodium ions remain free a t the highest DNA concentrations. Assuming constant r , the fraction of free ions was calculated for each sample from the formula:

where n, is the molar concentration of added Na' buffer, np is the DNA concentration in moles of nucleotide phosphate, n is the total Na' concentration, and a value of 0.25 was taken for the contribution of each DNA nucleotide to the free sodium ion concentration based on 23Na-nmrdata of Anderson et aL2 More recent studies5s7 set a lower limit on r . Based on measured values of the 23Na relaxation rate in 0.01 M NaCl of Rf = 22 Hz a t 20°C, 17 Hz a t 40"C, and 15 Hz a t 60"C, we calculated values of the apparent R1,b a t all DNA concentrations and temperatures ( Figure 3 ) . Apparent R1.b values in isotropic solutions a t all temperatures were nearly constant from 10 to 100 mg DNA/mL, increasing by only about 5%. The small increase may be related to pretransition ordering effects, as noted above. Average values of Rl,b over this range were 194 k 7, 113 f 4, and 66 5 Hz a t 20, 40, and 60"C, respectively. T h e average Rl,b calculated a t 20°C is in excellent agreement with previous estimates of 180-220 H z . ' - ~ ,A ~ t higher DNA concentrations, after onset of anisotropic phase formation, Rl,b rose rapidly until a plateau was approached a t x 200-220 mg DNA/mL. The averages of Rl,b calculated over the plateau region concentrations of 220-290 mg/mL were 256 f 10, 163 f 8, and 103 k 5 Hz a t 20, 40, and 60"C, respectively, corresponding to approximately 32, 44, and 56% increases in R1,b relative to the isotropic phase. The assumptions of constant Rl,f and r = 0.75 over the whole DNA concentration range set the above as approximate upper bounds on Rl,b in the

*

300

c

I

"0oo0" oooooooooooo""

2

0

100

200

300

[DNA] (mg/ml) Figure 3. Dependence of the apparent longitudinal relaxation rate of bound sodium ions Rl,b,on DNA concentrationat20(A),40(A),and6O0C(0) (toptobottom). Rl,b values were calculated from the known supporting electrolyte and DNA concentrations assuming constant Rl,fand fractional sodium ion binding, r = 0.75 (see text).

cholesteric DNA phase a t the temperatures investigated. A decrease in the assumed constant r value would increase the apparent R1,b. The assumption of constant R1, with DNA concentration is unlikely to be strictly true a t the highest DNA concentrations because of a n expected increase in the local electrostatic field as the DNA molecules become closely packed in the anisotropic phase. In the extreme, if all ions experience the same average field, then all are formally considered bound, and r = 1. In this regard it is interesting to note that the limiting values of R1 a t all temperatures were approximately equal to the estimated R1.b values in the isotropic phase. Quadrupole Splitting 23

Na-nmr spectra of highly concentrated DNA samples exhibited quadrupole splittings with complex dependencies on temperature and DNA concentration (Figures 4-7). The quadrupole splitting decreased with increasing concentration a t 20 and 30"C, decreased and then increased with concentration a t 40", and progressively increased with concentration a t 50 and 60°C (Figures 4 and 5 ) . At a given concentration the quadrupole splitting decreased with increasing temperature to a minimum of zero, then increased. The temperature a t which A = 0 was dependent on DNA concentration and

23Na-NMR OF SODIUM-DNA INTERACTIONS

809

A

A

IDNAI rng/ml

2 A

230

L

200

- 1 7 . 5 ppm

+ 1 7.5 ppm

- 1 7 . 5 ppm

+ 1 7 . 5 ppm

Figure 4. DNA concentration dependence of the quadrupole splitting of the 23Naresonance of anisotropic DNA samples a t 20 ( A ) and 6OoC ( B ). Note that the quadrupole splitting decreased with increasing concentration at 20°C, but increased with concentration at 60°C, although the intensities of the satellite peaks increased with concentration in both cases.

4 0 0 1

I

I

I

I

I

200

220

240

260

280

[DNA]

I * 300

Img/mll

Figure 5. DNA concentration dependence of the 23Na , ( A) 50 ( V ) , quadrupole splitting at 20 ( A ) , 30 (0140 and 60°C ( 0 ) .

i

20

30

40

50

60

t I'CI

Figure 6. Temperature dependence of "Na quadrupole splittingfor210(A),230(0),250(A),270(V),and290 mg DNA/mL ( 0 )samples.

810

STRZELECKA AND RILL

decreased with increasing DNA concentrations (Figure 6 ) . The observed quadrupole splittings were very small, less than 400 Hz at 20"C, compared to values of the order of a few thousand Hz in some micellar systems and up to 100 kHz in ionic crystals. The magnitude of A depends on the quadrupole coupling constant and the overall order parameter S [Eq. ( 4 ) 1. In addition, quadrupole splitting will occur only for those sodium ions experiencing the anisotropic field, hence will depend on the fraction of bound sodium ions in the anisotropic phase. The overall order parameter S can be separated into two components: SD,related to the angle between the liquid crystal director and the magnetic field, and S M , related to the average orientation of the principal component of the electric field gradient tensor with respect to the director [ Eq. ( 6 ) 1. Estimates of the minimum values of the order parameter S M were obtained with the assumptions that only one type of bound site for sodium ions contributed to quadrupole splitting, and that the sample was homoge-

I

'0

. I * '

I

I

I*

F3001 4oob

Q

200

I

I

200

I

220

[DNA]

1

240

I

260

I

280

I

300'

(mg/ml)

Figure 7. Top to bottom: Dependence of the fraction of DNA in the anisotropic phase, f a ; the 23Naquadrupole splitting, A; and the percent of the total 23Naresonance intensity represented in a side peak; on DNA concentration (mg/mL solvent) at 20 ( A ) , 30 ( O ) ,and 60°C ( 0 ) .

Table I Values of the Minimum Order Parameter ISMI Estimated for Some Anisotropic DNA Samples"

190 210 230 250 270 290

10.3 f 0.6 8.6 f 0.5 6.8 f 0.4 6.0 f 0.4 5.7 f 0.3 4.0 f 0.3

8.0 f 0.6 6.3 Ifr 0.5 4.6 k 0.4 3.7 f 0.3 2.8 5 0.2 0.0

-

4.8 k 0.2 2.5 k 0.2 1.6 f 0.2 0.0 2.7 5 0.2

a Estimated from the quadrupole splitting assuming SD= -I/ 2 and all bound 23Na+ions ( r = 0.75) contribute to the splitting.

neous and perfectly aligned. Quadrupole splitting did not appear until the cholesteric phase formed as judged by polarized light microscopy.29~30 A homogeneous cholesteric DNA phase aligns with the director perpendicular to the magnetic field direction,28,33-37 in . which case 8D = 90" and SD= -4. Estimates of S M were calculated using values of the quadrupolar coupling constant from Van Dijk et al? of x = 94 kHz at 20"C, 93 kHz at 30"C, and 72 kHz at 60°C for calf thymus DNA in 0.2 M NaCl (Table I ) . All estimates of ( SM)were in the range of 110.10-3, indicating that (8,) is near the angle of 54.7". A value of (8,) near 54.7" is also consistent with the complex changes in quadrupole splitting observed concurrent with changes in the fraction of anisotropic phase caused by increasing DNA concentration or temperature. For example, despite the fact that the relative area of the side peak increased with increasing fraction of liquid crystalline DNA phase, indicating an increase in overall sample order (Figure 7 ) , the quadrupole splitting decreased over the same DNA concentration range at 20 and 30"C, and decreased then increased at 40°C (Fig. 5 ) . Since the decreases in quadrupole splitting were not accompanied by the loss of side peak or total signal intensity, they must be attributed to passage of 8 M through the "magic angle" of 54.7". Relationship of Quadrupole Splitting to the Phase Diagram

Previously we took advantage of the sensitivity of the DNA 31P-nmr resonance line width to anisotropic phase formation to determine the critical concentrations for the appearance of anisotropic phase ( Ci) and disappearance of isotropic phase ( C , )

23Na-NMROF SODIUM-DNA INTERACTIONS

81 1

DISCUSSION

v

40

t

30

t

2o 101

0

'

'

80

1

'

160

'

I

240

'

I

320

8

1

Concentration (mg DNA/ml Solution) Figure 8. Phase diagram for transitions of DNA solutions between different phases determined as described in Ref. 32, elaborated to include the critical concentrations for formation of the cholesteric phase as determined from the areas of the side peaks of the 23Naresonance. Region I is the isotropic phase. There are four distinct regions of anisotropic phases: 11, isotropic precholesteric; 111, isotropic precholesteric cholesteric; IV, isotropic cholesteric + higher order; and V, cholesteric higher order. The lightly dashed line (far left) denotes a region (1') where the 31Presonance broadened modestly and the solutions became very viscous, but there was no evidence for an anisotropic phase.

+

+

+

+

+

as functions of DNA concentration and temperat ~ r e . "We ~ ~were ~ not, however, able to clearly distinguish the critical concentrations for appearance of the cholesteric phase, which was preceded by appearance of the anisotropic precholesteric phase. Microscopic analyses of samples near room temperature showed that quadrupole splitting of the 23Naresonance occurred only when cholesteric phase was present. The area of a side peak was approximately linearly related to DNA concentration up to a concentration when a plateau was approached near the maximum of 30% of the total resonance area expected for fully liquid-crystalline samples. The maximum area observed in all cases was about 1015% less than the theoretical limit (30% of the total area 1, suggesting that a small percent of sodium ions did not experience an anisotropic field gradient (Figure 7 1 . Because quadrupole splitting of the 23Na resonance was characteristic of the cholesteric phase, we were able to determine the temperature dependence of the critical concentration for appearance of the cholesteric phase from the extrapolated concentration where the side peak area reduced to zero. The elaborated phase diagram is shown in Figure 8.

We have extended measurements of the overall longitudinal relaxation rate of 23Naions in Na+ DNA solutions to DNA concentrations much higher than examined previously. In general terms, much of the behavior described for semidilute DNA solutions holds remarkably well up to DNA concentrations exceeding 100 mg/mL solvent. The limit of rapid exchange of Na+ ions between free and bound states remains valid over temperatures from 20 to 60°C and DNA concentrations up to 290 mg DNA/mL solvent. The overall relaxation rates R 1 , measured by Van Dijk et al.' for calf thymus DNA solutions (31 mg/mL solution) at 37.65 Hz, agreed well with our results at 40.04 Hz and a DNA concentration of 30 mg/mL (114 vs 132 Hz at 20"C, 70 vs 79 Hz at 40"C, and 45 vs 49 Hz at 60°C). The two-state model of counterion binding was applied to estimate the values of the relaxation rates of bound ions in the isotropic and liquid crystalline phases. Surprisingly, the product of r * Rlvbremained nearly constant up to concentrations exceeding 100 mg/mL, when obvious phase separation began. The overall relaxation rate increased abruptly upon phase separation. In terms of the two-state model, this nonlinear rise in R1 with increasing ratio of DNA phosphate to sodium concentration indicates a corresponding rise in r * Rl,b. If r and R1,f (the relaxation rate of free ions) remain invariant with DNA concentration, then R1.b must be greater in the anisotropic phase than in the isotropic phase. The calculated increase, assuming r = 0.75, is modest (1.3-fold at 20°C to 1.6-fold at 60°C) compared to the N 10-folddifference between the relaxation rates of free and bound ions in dilute solutions. Alternatively, part or all of this increase may be due to an increase in the fraction of Na' ions bound. In either case a perturbation of the ion atmosphere upon anisotropic phase formation is indicated-a constant fraction of "bound" ions may move closer to the DNA, hence experience an altered electrostatic field, and/or a larger fraction of counterions may move sufficiently close to the DNA ( N 4 A ) on average to be relaxed by the DNA electrostatic field. Alternatively, relaxation may be enhanced by rapid exchange of counterions between DNA molecule^.^ The interpretation of quadrupole relaxation data in polyelectrolyte solutions is hindered by the lack of theory linking the nmr behavior of counterions to their physical behavior in solution. Two theories of nmr relaxation of counterions in dilute polyelectrolyte solutions have been proposed, 38,39 but their applicability to concentrated solutions of polyions

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is limited. As suggested by Van Dijk et al.,' the most likely processes causing 23Narelaxation in DNA solutions are correlated motions of sodium ions and DNA phosphate groups, and local counterion diffusion. The DNA backbone is subject to fast internal motions on a time scale of 0.5-2 ns.40-42A Monte Carlo simulation of the Na+-DNA-water system l5 indicated that the average distribution of sodium ions is strongly correlated with the configuration of the sugar-phosphate backbone, and that the counterions form a double helix external to the cylindrical volume determined by the phosphate groups. A molecular dynamics simulation of the structure of hydrated Na' ions around the DNA helix43showed an arrangement of ions similar to that predicted by Clementi and Corongiu,15 but about half of the sodium ions were closer to the N7 group of guanine than t o the phosphates. Under conditions that were equivalent to the fully hydrated B-DNA, the sodium ions were found to be bridged by water molecules, forming a hydrated bound pair, which in turn formed a bridge between the phosphate group and the guanine N7. Klein and Pack16 examined the distribution of counterions around the DNA helix by finding an iterative solution to the set of equations coupling the electrostatic potential and average spatial charge density around DNA. They also estimated the magnitude of local electrostatic potentials and fields induced a t the nuclei of the DNA molecule. Results for the ionic strength of 0.01 M NaCl showed the presence of negative E, components of the electric field a t 03', C5', 05', and Ol'positions of the sugarphosphate backbone. A substantial negative E, component was also found a t the N7 position of guanine and the N6 position of adenine. These results indicate that the spatial correlation between Na' ions, the phosphate groups, and the guanine N7 observed in Monte Carlo simulations 15-23*42 are a consequence of a strong negative field around these groups. The sodium ion correlation times estimated for dilute DNA solutions are of the order of 2-5 n ~ . ~ , ' If the sodium ions remain spatially correlated to phosphate groups at least partially during the internal DNA motions, then this correlated motion could be driving 23Na relaxation.' We have determined that the motions of the DNA phosphates as monitored by the 31PT1are not strongly affected by an increase in DNA concentration above that required for phase separation (unpublished observations). The maintenance of a fast phosphate correlation time may explain, in part, why the relaxation rates of bound ions in the anisotropic phases

are not greatly different from the values obtained in very dilute DNA solutions. Quadrupole splitting of the 23Na resonance occurred upon appearance of the cholesteric phase. The absence of quadrupole splitting in the precholesteric phase must be due to motional averaging in this lower density phase. We have observed very rapid motions of the nematic director in this phase on a macroscopic scale by videomicroscopy (D. Van Winkle, M. Davidson, and R. L. Rill, unpublished data). Fortuitously, however, this distinction between the two phases permitted elaboration of the previous phase diagram3' to include the critical concentrations for cholesteric phase formation. Interpretation of the quadrupole splitting data in molecular terms is also difficult because the components of the electric field gradient tensor around the DNA helix are unknown. The maximum absolute magnitude of the 23Na quadrupole splitting of the cholesteric phase (which aligns with the director perpendicular o the magnetic field) was about 20% of the magnitude of quadrupole splitting reported ( 1700 Hz ) for DNA fibers oriented perpendicular to the magnetic field.24The quadrupole splittings observed for DNA in both cases are significantly smaller than splittings observed in solutions of cylindrical micelles of anionic detergents, 25 suggesting that the order parameter SM,for DNA is intrinsically smaller than for micellar systems. Assuming that a single class of counterions contributes to quadrupole splitting in the cholesteric DNA phase, it was possible to estimate the absolute values of the order parameter S M , describing the averaged orientation of the principal axis of the electric field with respect to the liquid crystal director. The magnitude of ( S M ) was calculated to be of the order of lop3for all anisotropic samples. The order parameter calculated for DNA fibers using the value of A = 1700 Hz in the perpendicular orientation, X = 94 kHz, and assuming that the fraction of bound ions r = 1,was (S,) N 4 lo-', which is about ten times larger than the values estimated for the anisotropic solutions and corresponds to the angle OM = 53.3". The corresponding values of OM for liquid crystalline samples were 54.7-54.4", suggesting that over a wide range of concentrations up to the hydrated fiber state OM changes by only about 1". The smaller quadrupole splittings observed in the liquid crystal phases, relative to DNA fibers, can be attributed, in part, to a lower degree of orientation of the director with respect to the field, since all solutions exhibiting quadrupole splitting were bi- or triphasic (see Ref. 30 and Figure 8 ) . The effects of variations in the macroscopic orientation of the liquid-crystal phase

-

23Na-NMR OF SODIUM-DNA INTERACTIONS

with respect to the magnetic field on the quadrupole splitting are expressed in terms of S D [ Eqs. ( 6 )( 9 ) 1 , which was set equal to -4 in the above calculations of S M . Decreasing the magnitudes of SD would increase the magnitudes of calculated S M values, but would not explain the complex temperature or concentration dependencies of the quadrupole splitting because the overall sample order increases with increasing DNA concentration, and decreases with temperature. There are two main contributions to the order parameter SM. One is the variation or mosaic spread of molecular orientations with respect to the local liquid crystal director due to molecular motions. Increased molecular motions in the cholesteric DNA phase may also contribute to the difference between the quadrupole splitting observed in this phase relative to hydrated DNA fibers. It seems unlikely, however, that molecular disorientation accounts for the small quadrupole splitting observed for both fiber and liquid-crystal states in view of the unusual variation of the quadrupole splitting of the liquid-crystalline DNA with DNA concentration and temperature. Two main tendencies were apparent. At the lower temperatures the magnitude of the quadrupole splitting decreased with increasing DNA concentration as the fraction of cholesteric phase increased, while at any given DNA concentration the quadrupole splitting first decreased to zero then increased with increasing temperature. Both behaviors suggest a change in sign of SMand are contrary to the expected effects of changes in molecular motions on the quadrupole splitting, since molecular motions are expected to decrease with increasing concentration and to increase with increasing temperature. Likewise, both behaviors are contrary to effects of concentration and temperature on the overall sample order. The most consistent interpretation of these data, therefore, is that the angle between the principal axis of the DNA electric field gradient tensor V,, and the liquid crystal director, hence the DNA helix axis, is near the magic angle of 54.7". The above comments assume that there is only one type of bound counterions contributing to the quadrupole splitting, and that the quadrupole coupling constant x is unchanged with increasing DNA concentration. In principle, however, the bound ions in each phase could have different values of x and the order parameter SM,and the observed quadrupole splitting in such a system would be affected by exchange of counterions between phases. Given the complexity of the phase behavior of DNA a t this low supporting electrolyte concentration,3oand discrepancies between various theoretical descriptions

813

of the DNA counterion atmosphere, 15-23 and hydration layer, precise interpretation of these quadrupole relaxation data and quadrupole splittings in molecular terms is not possible. Nonetheless, the changes noted in 23Naspectra and relaxation behavior with DNA concentration are indicative of subtle changes in the counterion atmosphere close to the DNA with increasing concentration and phase separation, and are consistent in general terms with more intimate association of counterions with the helix. More information may be available from studies of DNA samples with higher supporting electrolyte concentrations, which exhibit a simpler phase behavior (T. E. Strzelecka and R. L. Rill, in progress). We are grateful to Dr. Richard Rosanske and Dr. Tom Gedris for their assistance with nmr measurements, to Michael Waley from the University of Florida Training Reactor Facility in Gainesville for help with the nuclear activation analysis of DNA samples, to Michael Davidson for technical assistance, and to Dr. Timothy Cross for discussions on nmr data. This work was supported in part by NIH grant GM37098.

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Received August 14, 1989 Accepted April 18, 1990