Phase Transitions of Concentrated DNA Solutions in Low Concentrations of 1 : 1 Supporting Electrolyte TERESA E. STRZELECKA* and R A N D O L P H 1. RlLLt

Urpartmrnt of Chemistry and Institute of Molecular Biophysics, The Florida State University, 1allahclsvae, Florida 32306

SYNOPSIS

Transitions between isotropic and liquid crystalline phases of concentrated solutions of DNA with an average contour length (500 A ) near the persistence length were examined in 0.01 M supporting 1: 1 electrolyte (predominantly NaCl) . A quantitative phase diagram describing the transitions occurring over a DNA concentration range from 100 to 290 mg/ mi, and temperatures from 20 to 60°C was constructed from solid-state ”P-nmr data and examination of the morphologies of the mesophases by polarized light microscopy. Three anisotropic phases were observed in solutions with DNA concentrations of 160-290 mg/ mL: an unidentified, weakly birefringent phase termed “precholesteric,” a true cholesteric phase with pitch N 2 pm, and a third, presumably more highly ordered phase. Comparison with previous studies showed that the critical concentration for anisotropic phase formation and the nature of the phases formed by these DNA molecules are not strongly affected by decreasing the supporting electrolyte concentration from N 0.2 M to 10 m M . There are, however, profound eff’ects of decreasing the supporting electrolyte concentration on the width of the transition from isotropic to totally anisotropic solutions, and the nature of the transitions between phases. Decreasing the supporting electrolyte concentration significantly increases the concentration range of persistence of the isotrophic phase, and results in the formation of triphasic solutions (isotropic and two liquid crystalline phases). Values of the critical DNA concentrations for anisotropic phase formation calculated from the theory of A. Stroobants et al. [ (1986) Macromolecules 19, 2232 to 22381 were found to be significantly lower than the observed values for any reasonable estimate of the effective radius, probably because of the relatively short lengths of DNA fragments examined in the present study. Comparison of the experimentally determined DNA concentrations required for anisotropic phase formation with the values predicted from Flory’s lattice statistics theory, which explicitly considers the rod length, permitted estimation of the effective DNA radius. The estimated radius was inconsistent with effective radii calculated from Poisson-Boltzmann ( P-B ) theory based on a supporting electrolyte concentration of 10 m M , but was in fair agreement with P-B theory assuming that N a + DNA contributes approximately 0.24 Na’ counterions /nucleotide to the effective free sodium ion concentration.

INTRODUCTION Solutions of rod-like molecules and semirigid polymers undergo transitions from the isotropic state to __

C

1990 .John U’iley h; Sons, Inc. CCC 0006-3525/90/1-20057-15 $04.00 Biopolymers. xJol. :i0, 55-71 (1990) * Present address: Department of Biochemistry and Molecular Biophysics, College 01’ Physicians a n d Surgeons, Columbia University, New York. New York 10032. t T o whom correspondence should be addressed.

anisotropic phases when the concentration of rods exceeds a critical value. This behavior was predicted theoretically for uncharged rods by Onsager, Flory2z3and others, and has been observed for many nonelectrolyte polymers, particularly polybenzyl ( Lglutamate) (PBLG 1 .4 Anisotropic phase formation in good solvents is driven by the requirement for minimizing the polymer excluded volume, even when interpolymer interactions are net repulsive.’-3 DNA molecules a few hundred base pairs ( b p ) long behave similarly to rigid rods in aqueous so-

’

57

58

STRZELECKA AND RILL

lutions; hence DNA solutions are expected to separate into isotropic and anisotropic phases when the DNA concentration is sufficiently high. In fact, liquid crystalline phases formed in concentrated DNA solutions have been studied extensively since they were first discovered by R o b i n ~ o nIn . ~ the majority of cases the anisotropic phase observed has been described as cholesteric,6-’8 but a weakly birefringent, “precholesteric” phase, as well as more highly ordered phases, have also been reported. 9~19*20 Since DNA molecules are highly charged and only about 76% of the charges are strongly screened by monovalent counterions, the close approach of DNA helices is hindered by electrostatic repulsion. Onsager proposed that charged molecules should be treated as if they had an effective diameter determined by the extent of the electric double layer surrounding them; however, a description of the “extent of the double layer” is problematic at the high concentrations required for observation of anisotropic DNA phases. The counterion distribution about DNA at distances several Bngstroms from the phosphate charges-the distances pertinent hereseems to be well described for dilute solutions by Poisson-Boltzman ( P-B ) theory of isolated, uniformly charged cylinder^.^^-'^ Although Brian et a1.28 have shown that the effective radii calculated from P-B theory are consistent with the nonideal behavior of semidilute DNA solutions at moderate to high salt concentrations, it is not clear that such calculated radii are pertinent in solutions that are highly concentrated in DNA or dilute in supporting electrolyte concentration such that the effective rod volumes approach (hypothetical) overlap. We describe here the phase behavior of DNA fragments with a contour length (x500 A ) near the persistence length over a DNA concentration range of 100-290 mg Na+DNA/mL solvent and temperature range of 20-60°C at a constant low ( 10 m M ) concentration of supporting 1 : 1 electrolyte (predominantly NaCl) . The phases observed were morphologically analogous to those reported previously for experiments on the same length DNA fragments over a similar DNA concentration range, but conducted at constant Na+ ion activity 2 0.2 M.13z20By contrast to the previous report, the transitions between phases were unexpectedly complex, involving formation of triphasic solutions. The critical concentration for anisotropic phase formation determined here was nearly identical to that found previously, indicating that simple scaling of the effective radius of DNA according to P-B theories of dilute solutions is not appropriate for highly con-

’‘

centrated DNA solutions at low supporting electrolyte concentrations.

EXPERIMENTAL DNA Isolation and Sample Preparation DNA fragments with a most probable length of 500

A (146 base pairs) and a narrow distribution about this length were isolated from nucleosome core particles as described previou~ly.’~ A set of Na’DNA solutions with concentrations ranging from 10 to 290 mg DNA/mL solvent was prepared in a way that permitted control of the total and excess Na’ concentrations. Essentially salt-free DNA was obtained by prolonged dialysis against 0.5 m M Na’ buffer, performed under vacuum from a water aspirator in a collodion bag device (Schleicher and Schull) to minimize dilution. The total Na+ concentration in the DNA solution after dialysis was measured by nuclear activation analysis of diluted aliquots of DNA solution. Nuclear activation analyses of DNA samples were performed by standard procedures in the University of Florida Training Reactor facility in Gainsville. The DNA phosphate concentration was determined from the absorbance at 260 nm of a quantitatively diluted aliquot using an extinction coefficient of 6600 M-‘ (nucleotide) cm-’. DNA samples were prepared from a dialyzed DNA solution with 0.127 M (20.004 M) concentration of phosphate and 0.129 M( k0.003 M ) concentration of Na’. Aliquots of DNA solution containing total DNA masses of 5,10, . . . , 145 mg were transferred to microfuge tubes and thoroughly dried under vacuum in a Speed-Vac centrifugal concentrator ( Savant Instruments, Inc.) , then 500 pL of 10 m M Na+ buffer ( 9 m M NaC1,0.5 m M sodium cacodylate, 0.3 m M NaN3, 0.1 m M NazEDTA, adjusted to pH 6.5 with HCI) were added to each tube, giving a set of 29 DNA samples with concentrations of 10, 20, . . . , 290 mg DNA/mL solvent and an excess NaX concentration = 10 mM. Errors in the concentrations are estimated to be 2 3%. These concentrations differ from the usual convention according to the equation C’ (mg DNA/mL solution) = C (mg DNA/mL solvent) [ V/(g,U, V ) ] where , Vis the solvent volume, gD is the DNA weight, and UD is the DNA partial specific volume. The partial specific volume of DNA in highly concentrated solutions is not known, but the calculation of C’ is relatively insensitive to errors in UD. Unless stated otherwise,

+

PHASE TRANSITIONS OF DNA SOLUTIONS

the concentrations indicated below and in the figures are in terms of the unambiguous C (mg DNA/mL solvent). Values of C' were calculated where necessary for UD = 0.55 cm3/g. Microscopy

Samples of DNA solutions were placed on a slide (cleaned by prolonged soaking in concentrated nitric acid), covered with a coverslip and sealed with Permount (Fisher Scientific Co.), then observed through crossed polarizers with a Nikon OptiphotPol microscope under 3200 K tungsten-halide illuminati~n.'~?~' 3'P-NMR Spectroscopy 31

P-nmr spectra were taken on nonspinning samples a t a phosphorus frequency of 61.28 MHz using a n in-house constructed multinuclear Fourier transform spectrometer, equipped with wide-bore superconducting solenoid and quadrature detector, modified for solid-state applications. Gated proton decoupling was used during data acquisition only. Spectra were taken with a sweep width of f5000 Hz and pulse repetition time of 12.5 s; 100 scans were collected for each spectrum. Temperature was controlled by a thermocouple to within k l " C . Each sample was equilibrated for 1 h a t 20°C in the magnet before the first spectrum was taken. Spectra a t higher temperatures ( 30-60°C) were taken after a t least :30 min from the time of temperature change. Resonance areas were obtained using a line-deconvolution program on the Nicolet-1180 computer. The relative error of resonance area determination was usually lower than 1%, and the error of the fitting procedure on the order of 1-296. Equilibration of the DNA solutions is of potential concern because phase changes of PBLG and similar polymers with axial ratios 2 50 are extremely slow. Increasing the equilibration time of these DNA solutions did not change the spectral shape, or the areas of isotropic and anisotropic resonances within error, indicating t h a t equilibration was complete. A few experiments repeated two months after the first yielded identical results. Furthermore, microscopic examination showed that phase changes occurred rapidly and reversibly with temperature changes, yielding a stable texture within minutes after perturbation (see also below). Sample textures were stable for prolonged periods in the absence of drying. Presumably the length homogeneity and small ef-

59

fective axial ratio of this DNA greatly facilitate phase changes. DNA samples were placed in 1.5 mL cylindrical tubes, cut down in such a way that 500 pL of solution filled them without creating air bubbles. Since the anisotropic phase tended to settle to the tube bottom, it was necessary to place tubes horizontally in a specially constructed nmr probe in which the receiver coil contained all of the sample. Phase Diagram Construction from 3'P-NMR Data

Solid-state 31P-nmr spectra of DNA solutions can be used to determine the phase diagram boundaries for isotropic to liquid crystalline transitions that take place in concentrated DNA solution^.'^ When the DNA solution is isotropic, only a single Lorentzian resonance is observed, and the line width increases modestly with increasing DNA concentration as the anisotropic phase boundary is app r ~ a c h e d . ' ~ In , * ~the biphasic solution, where the isotropic and anisotropic phases coexist, the 31P spectrum is a superposition of two resonances: a relatively sharp resonance corresponding to the isotropic phase, and a broad resonance of the anisotropic phase. The line shapes of liquid crystalline phase resonances observed in this study were always Gaussian, although in previous studies a t higher supporting electrolyte concentrations a narrower asymmetric resonance was sometimes ~bserved.'~;~' The phase state of each sample used for nmr experiments was examined by polarized light microsCOPY. Phase diagrams for isotropic to liquid crystalline phase transitions in polymer solutions are usually presented in terms of the polymer volume fraction vs temperature. In the case of DNA solutions, determination of the appropriate DNA volume fraction is not straightforward; however, since knowledge of the effective DNA radius, which includes the condensed counterion atmosphere, is required. Theoretical estimates of the effective DNA radius a t various ionic strengths assume dilute DNA solutions and therefore are suspect for considerations of concentrated solutions. In a concentrated solution, a change in the effective radius may take place when the DNA helices are forced t o lie close to each other. The procedure adopted here was to express the phase diagram in terms of DNA concentration ( m g / m L ) vs temperature for a given ionic strength, and then, by comparison with theoretically predicted phase diagrams, estimate the effective DNA radius and volume fraction.

60

STRZELECKA AND RILL

T h e phase diagram boundaries corresponding to

Ci and C,( Ci is the DNA concentration a t which the anisotropic phase first appears and C, is the concentration at which the last amount of isotropic phase vanishes) were determined as introduced prev i ~ u s l y ’and ~ elaborated here. The fraction of molecules present in each phase was determined from the relative areas of the isotropic and anisotropic phase 31Presonances. Let Ni be the number of molecules in the isotropic phase of volume Vi = (1 - a )V, and N,the number of molecules in the anisotropic phase of volume V, = aV, where a is the fractional volume of anisotropic phase and V is the total solution volume. T h e DNA weight concentrations in each phase are given by Ci = N ~ M / N A ,1( - a ) V

and

c, = N,M/N*,aV

(1)

-

where M i s the DNA molecular weight (97 l o 3 Daltons) and N A v is Avogadro’s number. For any overall DNA concentration C in the biphasic region a t a given temperature:

c = (1- a ) C , + ac,

(2)

The fractions of molecules in each phase are obtained from nmr data, namely

Equations ( 7 ) and (8) were used previou~ly,’~ when data were limited. These can be generalized to the case in which data are available f x several DNA concentrations in the biphasic regicjn to

and Cf, = -CC,/(C,

- C,)

-

C,Ca/(C, - Ci)

(10)

Both Cfi and Cf, are linear functions of the total DNA concentration C in the biphasic region, and plots of Cfi or Cf, vs C ( a t a given temperature) yield intercepts of C = C, or C = Ci, respectively, when f ; or f a are zero. The above discussion assumes a biphasic equilibrium between isotropic and anisotropic phases. Below we show that a n additional anisotropic DNA phase forms in several cases before the isotropic phase disappears. In these cases the plots exhibit downward curvature and the local slope is a function of the total DNA concentration. The extrapolated limits as f i or f a approach zero provide reasonable estimates of C, or Ci in these cases since the curvature is small.

R ES ULTS Combining Eqs. ( 2 ) and ( 3 ) yields the relations

(1 - a ) C i = Cfi

and

a C a = Cf,

(4)

T h e fractional volume in the anisotropic phase a is unknown, but when two phases are in equilibrium the DNA concentration of each phase is expected to remain constant a t a given temperature. In this case, for two different total DNA concentrations, C1 and C2, a t a specific temperature,

and

Eliminating a1 and a2 yields the relations

Polarized light Microscopy

The lowest DNA concentration ( C ) a t which a n anisotropic phase could be observed unambiguously was 160 mg DNA/mL solvent. Samples with DNA concentrations of 160-190 mg/mL were nearly transparent and quite viscous. When viewed microscopically between crossed polars these samples exhibited heterogeneous textures. Most commonly observed were weakly birefringent patterns of widely spaced, concentric fringes of roughly circular or oblate shape, sometimes coexisting with small spherulites (Figure 1 A ) . Viewing of these weakly birefringent areas a t higher magnification occasionally revealed inversion walls characteristic of a nematic mesophase (Figure 1B). This phase appeared analogous to the phase previously observed and termed “ p r e c h o l e ~ t e r i c . ”The ~ ~ molecular organization in this phase has not been determined unequivocally, but our observations to date are most consistent with a very slowly twisting cholesteric with pitch > 10

PHASE TRANSITIONS OF DNA SOLUTIONS

61

Figure 1. Polarized light microscopy of liquid crystal textures observed in 160-170 mg/ mL DNA solutions in the precholesteric phase. ( A ) Weakly birefringent, roughly oblate patterns of widely spaced fringes on dark isotropic background (170 mg/mL, original magnification 1OX). ( B ) Region displaying a “thread-like’’ texture due to inversion walls superimposed on birefringent fringes as in A ( 160 mg/mL, original magnification 20X).

pm. We cannot rule out the possibility of a phase similar to the “blue phase” of small molecules in which the molecular organization twists slowly in more than one dimension, as suggested by Livolant.lg Microscopic textures of large pitch phases may be misleading when the sample thickness is less than the pitch, and measurements were made with relatively thin specimens ( N 5 p m ) . A true cholesteric phase with a pitch of approximately 2 pm first appeared a t a DNA concentration of 180 mg/mL as small spherulites or globules exhibiting the characteristic regular pattern of fringes with N 1 pm spacings (Figure 2A, B ) . As the DNA concentration increased, islands of the cholesteric phase appeared and grew larger, coexisting with the precholesteric and isotropic phases until the DNA concentration reached 230 mg/mL. Within the cholesteric islands the texture was generally homeotropic, with occasional oily streak striations ( Figure 2 C ) . A similar cholesteric organization was

noted previously, 13*20and the cholesteric packing of this phase has been confirmed by electron microscopy3’ and optical diffraction measurements.31 Thermal melting of the cholesteric phase proceeded through formation of small isotropic areas that increased in size with increasing temperature. At the border between the cholesteric and isotropic phases there was a region of the weakly birefringent phase (Figure 2A). Changes in sample morphology with temperature were rapid. The time interval from the moment when the temperature was increased to the moment when major changes in the texture took place was on the order of 1-3 min. Anisotropic phase formation on cooling was equally rapid, with the weakly birefringent phase appearing within a few minutes from the time heating was terminated (data not shown, see Ref. 3 2 ) . At a DNA concentration of 230 mg/mL a small amount of precholesteric phase appeared to be present, but a third anisotropic phase was detected. Some

62

PHASE TRANSITIONS OF DNA SOLUTIONS

textures of this phase resembled multiple-domain walls characteristic of a nematic mesophase, while others were similar to platelet or mosaic textures observed in smectic or columnar samples20333 (Figure 3 ) . The cholesteric phase predominated in the 230 mg/mL sample, but was partially replaced by the third phase as the DNA concentration increased (Figure 3 ) . The nature of the high concentration phase and the order of this phase transition are unclear. Focal-conic fan textures such as those associated previously with a smectic-like or columnar phase” were not observed; however, careful microscopic and optical diffraction studies of highly concentrated DNA samples in 0.2-0.3 M 1: 1supporting electrolyte have shown recently that the transition from cholesteric to a more highly ordered phase occurs through an intermediate phase where the cholesteric pitch gradually unwinds from N 2 pm to > 5 pm prior to appearance of focal-conic fans.31 The textures we observed at DNA concentrations > 250 mg/mL in 10 m M NaX (Figure 3) were similar to those of the above intermediate phase. Rapid temperature-dependent changes were also observed in the 290 mg/mL sample, without formation of the weakly birefringent precholesteric phase with increasing temperature (not shown, see Ref. 3 2 ) . In some cases the uniformly dark areas present at lower temperature became progressively brighter when the temperature was increased, indicating that they were not isotropic but corresponded to parts of the sample with a planar or homeotropic alignment. Some small regions remained dark, however, supporting nmr evidence that the isotropic phase did not totally disappear until the DNA concentration exceeded 290 mg/mL (see below).

Solid-state 3’P-NMR Data The line shapes of anisotropic phase resonances were purely Gaussian, whereas the line shapes of isotropic phase resonances were Lorentzian, as confirmed by a line-deconvolution procedure.32The observed line widths of anisotropic phases did not ex-

ceed 14 ppm, much less than the nearly 200 ppm line width obtained from powder patterns of solid B-form hydrated DNA (Refs. 34-36 and unpublished observations), indicating that the motional dynamics of DNA molecules were not totally dampened by formation of the anisotropic phase. Interpretation of the observed line widths in terms of molecular dynamics requires proof that the resonances are homogeneous, since a Gaussian resonance in a nonhomogeneous system is an envelope of many narrow Lorentzian lines. Two experiments were performed to determine whether the lines observed in our DNA solution were homogeneously broadened. In the first “hole-burning,’ experiment, a narrow frequency band near the tail of the broad resonance was irradiated by a selective pulse and then the signal was collected after the usual 90” observe pulse. If the resonance is homogeneous, the total resonance intensity will decrease, whereas in the case of nonhomogeneous broadening one ( o r a few) of the narrow resonances a t the frequency of the weak pulse will be saturated and disappear, forming a “hole” in the spectrum. The second experiment was a spin-echo experiment in which the values of the delay times between pulses were varied. If the resonance is homogeneous, then for values of the delay times longer than T2 the resonance will disappear, whereas if it is a collection of narrow lines it will not. The results of both experiments for the 290 mg/mL sample demonstrated that the line was homogeneous (data not shown, see Ref. 32). If no other processes contributed to resonance broadening, the increased line widths could be related to the mobility of DNA molecules in the anisotropic phase. However, the degree of magnetic alignment of DNA molecules also affects the line width. As reported previously,13the line width attributed to the anisotropic phase fluctuated with concentration, presumably due to changes in the degree of magnetic ordering (data not shown). Changes in the line width were accompanied by changes in the separation 6 between the isotropic and anisotropic resonances, which showed a rather

Figure 2. Polarized light microscopy of 180-200 mg/mL solutions showing mixed isotropic precholesteric cholesteric phases. ( A ) Region of the 190 mg/mL sample showing development of areas of cholesteric spherulites or globules from the weakly birefringent precholesteric areas (original magnification 40X ) . ( B ) Globule of cholesteric phase with well-developed 1 Fm fringe pattern on isotropic background (180 mg/mL, original magnification 40X ). ( C ) Precholesteric regions (broad fringe patterns) and islands of cholesteric phase with bright “oily streaks” are superimposed on isotropic background (200 mg/mL, original magnification 1OX ) .

+

+

63

64

STRZELECKA AND RILL

A

B

C

D

Figure 3.

PHASE TRANSITIONS OF DNA SOLUTIONS

65

360

280

“200

I I

60 120

40

I 180

I

1

1

I

200

220

240

260

1 280

+

C (mg DNA/ml solvent) Figure 4. The separation 6 between anisotropic and isotropic resonances as a function of DNA concentration C (mg DNA/ml solvent) a t 20 ( A ) , 30 (O), 40 (A),50 (V),and 60OC ( 0 ) .Note the sharp increase a t a concentration of = 220 mg/mL.

complex behavior as functions of temperature and DNA concentration (Figure 4 ) . In general, narrowing of resonances with increasing temperature was accompanied by a n increase in the separation of the two resonances, indicating increased magnetic alignment of DNA molecules in one or both anisotropic phases. Changes in the 31P-nmr line width therefore cannot be interpreted simply in terms of

either magnetic alignment or motional dynamics of DNA molecules. TI relaxation times determined for several samples with DNA concentrations in the range of 130290 mg/mL showed only a small decrease from 2.5 s for the 130 mg/mL sample to 2.45 s (?3-T,%) for the 290 mg/mL sample. These values are only slightly shorter than those obtained for dilute DNA

Figure 3. Microscopic textures of DNA samples with concentrations exceeding 230 mg/ mL (original magnifications 20X ) . ( A ) Region of cholesteric oily streaks in the 290 mg/ rnL sample with the cholesteric planes oriented parallel to the viewer by a magnetic field. ( B ) Neumatic-like inversion walls in another region of the 290 mg/mL sample. ( C ) Platelet or mosaic-like texture in a region of the 280 mg/ml sample. Note the sharp angles on the “platelet” edges, which were not observed in the precholesteric or cholesteric phases. ( D ) Very heterogeneous texture of 240 mg/ mL sample with isotropic holes, cholesteric oily streaks, inversion walls, and platelets.

66

STRZELECKA AND RILL

s o l u t i ~ n s Since . ~ ~ ~the ~ ~longitudinal relaxation of phosphorus nuclei is dominated by fast internal motions of the DNA backbone, that TI did not change significantly when the solutions underwent transition from the isotropic to fully liquid crystalline phase suggests that the backbone phosphate motions were not strongly affected by the formation of anisotropic phases. Phase Diagram for Isotropic to Liquid Crystalline Transitions

Critical concentrations for the appearance of anisotropic phase ( Ci) and disappearance of the isotropic phase (C,) were determined from the intercepts of plots according to Eqs. (10) and (11)from the nmr data obtained from samples with DNA concentrations of 180-290 mg/mL (Figure 5 ) . These intercepts divide the phase diagram into three principal regions indicated by solid lines in Figure 6: isotropic, isotropic anisotropic, and fully anisotropic. Plots of Cfa or Cfi vs C at 20-40°C exhibited obvious curvature, however, and could be best fit with two straight lines (Figure 5 ) , suggesting that the

+

$

n L

200

\

0

E

v

b

rc

160 120 -

X

0 80

-

40

-

+

isotropic anisotropic region should be divided into two subregions. The inclusion of such a division was supported by microscopic observations, which showed that in the lower concentration region, e.g., the range of 160 to N 220 mg/mL at room temperature, the isotropic, precholesteric, and cholesteric phases coexisted; while in the range of DNA concentrations of 240-290 mg/mL, the isotropic, cholesteric, and unidentified third anisotropic phase defined another triphasic region. The position of this division, indicated by a dashed line in the phase diagram (Figure 6 ) was determined from the intersection points of the two straight line segments. This position agrees well with both microscopic observations and the increase in separation of the isotropic and anisotropic resonances, which reached a plateau at approximately 220 mg/ml ( 20-40°C). A fourth boundary is tentatively included in this diagram as a dotted line at the low-concentration side of the isotropic to anisotropic boundary. The approximate position of this boundary was determined on the basis of the 31P-nmr resonance line shape: the sample was considered fully isotropic when the 31Presonance could no longer be fit as a

PHASE TRANSITIONS OF DNA SOLUTIONS

50

I

n

0

0

U

I-

40i-

30k I

I

oc i I

I

I

I

80

I60

240

320

C’ (mg DNA/ml SOLUTION) Figure 6. T h e phase diagram for isotropic t o liquid crystalline phase transitions for DNA solutions in 0.01 M Na’ buff‘er. Concentrations ( C ’ ) are expressed in mg D N A / m L solution. Region I is isotropic; region I‘ is isotropic but exhibits a higher viscosity a n d broader 31P resonance t h a n in region I; region I1 is biphasic (isotropic precholesteric); region I11 is triphasic (isotropic precholesteric t cholesteric) ; region IV is triphasic (isotropic + cholesteric higher order p h a s e ) , a n d region V is fully higher anisotropic (probably a mixture of cholesteric order phases until very high concentrations are reached).

+

+

+

67

only modestly dependent on temperature. The phase transitions of DNA solutions in 1 : 1 supporting electrolyte described here and p r e v i ~ u s l y ” ~are ’~~~~ qualitatively consistent with the behavior expected for rods when interactions range from repulsive to very weakly attractive in that ( a ) relatively high concentrations are required for phase separation, ( b ) the concentration range from isotropic to fully anisotropic phases is relatively narrow, and ( c ) the temperature dependence is modest. For these reasons and because the accessible temperature range is small for DNA, we continued the practice adopted p r e v i ~ u s l y and ’ ~ attempted to fit the critical concentrations for anisotropic phase formation ( Ci) to Flory’s t h e ~ r y , assuming ~’~ that the charged DNA molecules can be replaced by effective hard-core rods that include the counterion atmosphere, and that interactions between rods are negligible. According to Flory, the volume fractions of rods with axial ratio x in the isotropic phase ( v,) and in the anisotropic phase ( u ; ) in a n athermal solution with the two phases in equilibrium are determined by

+

and superposition of two resonances with a relative error lower than 3 % . Samples with DNA concentrations from 100 to 150 mg/mL were highly viscous and exhibited a n abnormal line shape a t the lower temperatures, although there was no microscopic or other evidence for formation of a n anisotropic phase. This ahnormal line shape could be due to gelation, as reported by Fried and Bloomfield under somewhat similar condition^,^^ or the consequence of “pretransition” clustering of DNA molecules analogous to phenomena observed with other polymer systems.

where y is the disorientation index. The ratio y / x is relatively insensitive to rod length, and y = 0.1610.167 for x = 10-20. These equations were solved numerically for trial axial ratios, setting the interaction parameter XI = 0 for the athermal case, and iterated t o obtain the best-fit axial ratio. The assumption of XI = 0 is inconsequential since the predicted dependence of u2 on XI is very small when Comparison with Flory’s Theory rod interactions are net r e p u l ~ i v e . ~The , ~ ~best-fit -~~ Flory’s theory based on lattice s t a t i s t i ~ s ~ ,treats ” ~ ~ - ~ ~ axial ratio was then used to calculate the effective radius of the equivalent spherocylinder.7 The efthe molecules as hard rods, with interactions between rod segments described (in the most recent fective diameter can be viewed as the minimum disversion) in terms of a Mayer-Saupe p ~ t e n t i a l . ~ ’ - ~ l tance of approach between two DNA molecules actA narrow hiphasic region between isotropic and aning as hard noninteracting rods. isotropic phases is predicted for noninteracting or The effective radius of DNA a t infinite dilution repulsively interacting rods. The critical concentrain 10 m M 1 : 1 electrolyte calculated from the data tions for isotropic t o biphasic, and biphasic to fully of StigterZ4was 78 A. This radius predicts an effecanisotropic, phase formation in this case are pretive volume fraction well exceeding 1.0 for DNA dicted to be strongly dependent on axial ratio but concentrations above 100 mg/mL, and hence cannot

’’

68

STRZELECKA AND RILL

be appropriate. An effective DNA radius of 21-22 A was calculated to best fit the critical concentration (Ci) of 131 ( f 6 ) mg D N A / m L solution for the isotropic t o biphasic transition observed a t 20°C. This effective radius is in fair agreement with the value of 28 A calculated by Stigter for a n ionic strength of O.lM, assuming a physical DNA radius of 1 2 8, and a n effective charge of -0.73 e/phosphate. Assumption of a 10 A physical DNA radius would reduce the effective radius to x 25 Az4. An ionic strength of 0.1 A4 is close to the effective free sodium ion concentration in the 131 mg DNA/mL solution assuming that DNA contributes the fraction of counterions predicted by Manning's condensation theory," i.e., CNa,free N ( C / M , , ) (1 - 0.76) 0.01 N 0.105 M , where M,,, is the average nucleotide molecular weight x 330. The calculated effective DNA radius decreased with increasing temperature because the critical concentrations for anisotropic phase formation increased (Figure 6 ) . T h e fitted value of 21-22 A for the effective DNA radius a t 20°C corresponds to an effective DNA axial ratio ( L / D ) of N 11.5. The corresponding effective DNA volume fraction at the boundary corresponding to first appearance of the anisotropic phase is 0.62. T h e effective radius calculated from Flory 's theory t o fit the critical concentration for anisotropic phase formation a t 20°C is only in fair agreement with the effective radius calculated according to Stigter for a n ionic strength of 0.1 M . It is of interest to note, however, that broadening of the 31Presonance and a n unusual increase in solution viscosity was first noted a t a concentration of 93 (t5)mg DNA/mL solution, although the solutions exhibited no birefringence indicative of a n anisotropic phase. T h e effective radius corresponding to this concentration that best fits Flory's theory is 27-28 A, precisely in agreement with the Stigter radius for a n ionic strength of 0.1 M .

+

Comparison with the Theory of Stroobants et aL4*

Onsager first theoretically predicted the ordering of rod-like, nonelectrolyte solutes and proposed that polyelectrolytes could be treated as effective particles with a diameter including the ion double layer.' Stroobants e t al.42 have expanded Onsager theory to explicitly include the ion double layer and the influence of twisting caused by interactions between closely spaced charged rods. This twisting effect increases the critical concentration for phase separation above that predicted based on the effective diameter alone. Results of numerical calculations of

the dependencies of the concentrations in the isotropic and anisotropic phases on the twisting parameter ( h , see below) have been tabulated ( Table I11 in Ref. 42). The theoretical phase diagram boundaries, given in terms of the reduced concentrations ci and c,, are also approximated by ci =

3.290( 1 - 0.675h)-'

(13)

C, =

4.191 (1 - 0.730h)-'

(14)

and

where the reduced concentrations are related to the number density of polyelectrolyte (c') via the effective cylindrical excluded volume, beR= ( x / 4 ) L 2DeR by

where L is the length of a molecule, DefTis its effective diameter, and c' is the number density of polyelectrolyte in solution. T h e parameter h , which reflects the electrostatic interaction between polyelectrolyte molecules, is given by

where K is the Debye screening parameter, and DeE can be calculated from the following formula:

D e f f = D [ l + ( l n A ' + y + l n 2 - ~ ) / D ] . (17) D is the hard-core DNA diameter, y is Euler's constant, and A' is given by

Q is the Bjerrum length and

r

=

l / K O (R , ) .

(19)

R, is a reduced distance from the polyelectrolyte and KOis the zero-order modified Bessel function. R , is defined in the following way: for R 2 R, the reduced potential rF/ = KO(R )/ K O (R, ) , i.e., for R 2 R, the Debye-Huckel approximation for the electrostatic potential is used. T h e value of R, is determined from the condition to(R,) = vQ,where tois the reduced charge density calculated from formulas of Philip and Wooding43 and VQ is the reduced charge density of DNA. The contribution from DNA to the Debye parameter was taken into account by using the effective

PHASE TRANSITIONS OF DNA SOLUTIONS

69

Table I Values of Parameters Used in Calculations of Theoretical Phase Boundaries from the Theory of Stroobants et al.42

20 30 40 50 60

7.12 7.20 7.30 7.40 7.50

4.188 4.235 4.294 4.353 4.418

0.1280 0.1298 0.1384 0.1471 0.1536

salt concentration (in number of ions per unit volume ) :

n

+ 0.24%

=

(20)

where no is the 1 : 1 electrolyte concentration and np is the DNA concentration calculated from =

NA,C'/M

with C' being the DNA concentration in mg/mL solution. Calculated values of the parameters Q, vQ, K , R, , I', D e w ,and h are given in Table I; and predicted critical concentrations for phase transitions are given in Table 11. Comparison of these data with the experimentally determined phase diagram shows the critical concentrations for anisotropic phase formation are only 50-6096 of the experimental values a t all temperatures.

DISCUSSION We have found that the phase transition behavior of concentrated DNA solutions in the presence of a low, nearly constant concentration of 1: 1electrolyte Table I1 Temperature Dependence of the Phase Boundaries Predicted According to Stroobants et al.42

20 30 40 50

60

3.669 3.667 3.658 3.649 3.643

4.718 4.715 4.702 4.690 4.681

58.9 59.5 61.9 64.2 65.9

75.8 76.5 79.6 82.5 84.7

Reduced concentrations according to Eqs. (11)and (12). Concentrations in mg DNA/mL solution calculated according to Eq. ( 1 3 ) using the effective diameters given in Table I. a

2.362 2.385 2.478 2.573 2.644

13.62 14.00 15.63 17.48 19.02

51.1 50.6 48.5 46.6 45.37

0.1530 0.1523 0.1490 0.1458 0.1435

( NaX) is related to but more complex than observed in prior s t ~ d i e s . " . ~We ~ . ~ previously ~ examined phases formed when the DNA concentration was decreased while keeping the sodium ion activity approximately constant a t 0.21 M by addition of 0.3 M NaCl to a 350 mg/mL DNA solution. The supporting electrolyte concentration increased from approximately 50 t o 200 m M as the sample was diluted through the anisotropic region of the phase diagram (from 350 t o 130 m g / m L ) . In this case we observed the phase termed "precholesteric," a n unambiguously cholesteric phase with pitch = 2 pm, and a more highly ordered columnar or smectic T h e phase transitions are represented by a simple sequence of alternating monophasic and biphasic solutions: isotropic + isotropic precholesteric + precholesteric + precholesteric cholesteric + cholesteric + cholesteric higher order + higher order. The net isotropic + anisotropic phase transition occurred over a narrow concentration range, (C, - C i ) = 35 f 5 mg/mL, the observed ratio of concentrations in the anisotropic to isotropic phases ( 1.25 t 0.05) agreed well with the prediction according to Flory ( C,/Ci = 1.27), and the effective radius calculated t o best fit Flory's theory (22.3 8, a t 20°C) was consistent with the value of 21 A calculated by Stigter for a supporting electrolyte concentration = 0.2 M . The behavior of concentrated DNA solutions a t a constant supporting NaCl concentration of 1M also appears to follow this pattern ( Strzelecka and Rill, manuscript in preparation). Although the phases observed in the present study appeared analogous to those described previously, there are three new qualitative features of the phase diagram determined here. The phase transition sequence is more complex and includes triphasic regions. The microscopic and nmr evidence suggests that the sequence is isotropic + isotropic precholesteric + isotropic precholesteric cholesteric + isotropic cholesteric higher order + cholesteric higher order. In addition, the region between the fully isotropic and fully anisotropic phases is much broader (C,/C, = 1.95), and the

+

+

+

+

+

+

+

+

+

70

STRZELECKA AND RILL

temperature dependence of the phase diagram boundaries is stronger. The observation that the DNA concentration required for initial formation of anisotropic phase in 10 m M supporting electrolyte was approximately the same as that in 0.2 M supporting electrolyte shows that anisotropic phase formation is relatively insensitive to supporting electrolyte concentration when this concentration is low (I 0.2 M ) . The bestfit scaled radius of 21-22 A calculated from Flory's theory for the observed phase transition of DNA in 10 m M supporting electrolyte a t 20°C is inconsistent with the effective radius (78 A ) calculated from P B theory a t this supporting electrolyte concentration in dilute DNA solutions, but it is in fair agreement with the values of 25-28 A calculated from P - B theory if one assumes that the effective counterion concentration is = 0.1 M , i.e., that the DNA contributes approximately 0.24 moles sodium ions per mole DNA nucleotides, in accord with Manning's counterion condensation theory." The degree of agreement worsens a t higher temperatures since the effective radius calculated from P-B theory is not very temperature sensitive. Some pretransitional changes in the DNA solutions were evident, however, a t a DNA concentration corresponding, in terms of Flory's theory, to a n effective radius of = 28 A. Our results in this regard agree with those of Brian et al.,7 who previously noted that scaling of the effective DNA radius according to P - B theory, in combination with scaled particle theory, provided a good description of the dependence of the osmotic pressure of semiconcentrated DNA solutions on DNA concentration (determined by equilibrium sedimentation) when the supporting electrolyte concentration was 0.2 M or above, but not when the supporting electrolyte concentration was only 0.005 M . T h e critical concentration for anisotropic phase formation of 102-107 mg/mL determined for = 200bp length DNA in 0.2 M NaCl by Brian et al.7 is also in good agreement with the value of N 130 mg/ mL determined here and in our previous study13 when account is taken of the inverse length dependence of the critical concentration for rods of modest axial The theory of Stroobants et al.,42which explicitly takes into account the increase in critical concentrations expected due to twisting of the nematic phase by electrostatic repulsions, consistently predicts values of the DNA concentration required for the phase separation that are about 50% lower than the experimental values for any reasonable choices of the effective DNA radius. One of the reasons for this discrepancy may be the fact that Onsager the-

'

ory, on which is based the theory of Stroobants et al.,42is strictly applicable only to rods with very large axial ratios ( L D ) . For longer rods the critical concentration required for phase separation is significantly lower than for short rods, decreasing approximately inversely with length a t least t o lengths approaching 2000 In general, the problem of taking into account finite and small rod lengths would require difficult evaluation of the third virial coefficient and end effects. Inclusion of the effects of finite flexibility of the DNA rods would also increase the predicted critical concentrations4* ( Odijk, personal communication). In summary, the critical concentration for anisotropic phase formation and the nature of the phases formed by DNA molecules with contour lengths approximately equal to the persistence length are not strongly affected by decreasing the supporting electrolyte concentration from N 0.2 M to 10 m M , probably due to counterion contributions to the total sodium ion activity. There are, however, profound effects of decreasing the supporting electrolyte concentration on the width of the transition from isotropic to totally anisotropic solutions, and the nature of the transitions between phases. Decreasing the supporting electrolyte concentration significantly increases the concentration range of persistence of the isotropic phase, and results in the formation of triphasic solutions. It is of interest to note that Flory's lattice statistics theory predicts broadening of the biphasic region and admits the possibility of triphasic solutions when the solvation parameter becomes positive, i.e., when polymer segment-segment interactions in solution become net favorable. This connection with Flory's theory appears unlikely in the case of DNA since Lerman, Frisch, and c o - ~ o r k e r shave ~ , ~ shown ~ rigorously that DNA interactions in semiconcentrated isotropic solutions remain net repulsive up to the critical concentration for anisotropic phase formation. Oosawa has suggested that fluctuation interactions between counterion clouds of closely spaced polyelectrolytes could provide a n attractive interaction, 46 but Monte Carlo calculations on close hexagonally packed charged rods suggest that this effect does not yield a net positive interaction between rods neutralized with monovalent counterions.47 Stroobants e t a1.12,48,49 recently described Monte Carlo simulations of a system of hard (uncharged) spherocylinders and showed that transitions from isotropic -+nematic smectic columnar ordering are predicted even for particles with axial ratios as low as two. Simulations of this type for polyelectrolytes may provide better insights into

+

- -

PHASE TRANSITIONS OF DNA SOLUTIONS

mechanisms of DNA ordering and the behavior of the DNA counterion atmosphere in crowded solutions of modest length DNA molecules. 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 Gainsville for help with the nuclear activation analysis of DNA samples, to Michael Davidson for technical assistance, and to Dr. Timothy Cross for discussions of nmr data. This research was supported in part by grant GM37098 from the National Institutes of Health.

REFERENCES 1. Onsager, L. (1949) Ann. N Y Acad Sci. 51,627-659. 2. Flory, P. J. (1956) Proc. Roy. SOC.(London) Ser. A 234, 60-73. 3. Flory, P. J. (1956) Proc. Roy. SOC.(London) Ser. A 234, 73-89. 4. Miller, W. (1979) Ann. Rev. Phys. Chem. 29, 219. 5. Robinson, C. (1961) Tetrahedron 13, 219. 6. Bouligand, Y . & Livolant, F. ( 1984) J.Phys. 45,18991923. 7. Brian, A. A., Frisch, H. L. & Lerman, L. S. (1981) Biopolymers 20, 1305-1328. 8. Livolant, F. (1984) Eur. J. Cell Biol. 33, 300-311. 9. Livolant, F. & Bouligand, Y. (1986) J.Phys. 47,18131827. 10. Livolant, F. (1986) J. Phys. 47,1605-1616. 11. Rill, R. L. (1986) Proc. Natl. Acad. Sci. U S A 83,342346. 12. Stroobants, A., Lekkerkerker, H. N. W. & Frenkel, D. ( 1987) Phys. Rev. A 36, 2929-2945. 13. Strzelecka, T. E. & Rill, R. L. (1987) J. Am. Chem. soc. 109, 4513-4518. 14. Senechal, E., Maret, G. & Dansfeld, K. (1980) Znt. J. Biol. Macromol. 2, 256-262. 15. Maret, G. & Dransfield, K. ( 1985) in Topics in Applied Physics, ( Herlach, F.) ,Ed., Springer Verlag New York, pp. 143-204. 16. Brandes, R. & Kearns, D. R. (1986) Biochemistry 25, 5890-5895. 17. Iizuka, E. & Kondo, Y. ( 1979) Mol. Cryst. Liq. Cryst. 51, 285-294. 18. Iizuka, E. ( 1978) Polym. J. 10, 237-253. 19. Livolant, F. J. (1987) Physique 48, 1051-1066. 20. Strzelecka, T. E., Davidson, M. W. & Rill, R. L. (1988) Nature 331,457-460. 21. Manning, G. S . (1978) Q. Rev. Biophys. 11,179-246. 22. Le Bret, M. & Zimm, B. H. ( 1984) Biopolymers 23, 271-285.

71

23. Schellman, J. A. & Stigter, D. (1977) Bwpolymers 16, 1415-1434. 24. Stigter, D. (1977) Biopolymers 16, 1435-1448. 25. Mills, P., Anderson, C. F. & Record, M. T., J r . ( 1985) J. Phys. Chem. 89, 3984-3994. 26. Mills, P. M., Paulsen, M. D., Anderson, C. F. & Record, M. T., Jr. (1986) Chem. Phys. Lett. 129, 155-158. 27. Murthy, C. S., Bacquet, R. J. & Rossky, P.