BIOPOLYMERS

VOL. 14,521-542 (1975)

Quasi-Elastic Light Scattering by Calf Thymus DNA and xDNA Irecalled that th(x scattciring vrctor lrrigth is drtcrmincxd by the solution rrfractivc ind(.x 72, the iricidcnt light wavclongth A” and thc scattcring angle 8 :

K

=

(4m/Ao) sin

@/a).

(1)

For the region KR, = 1, thr QLS corrc.latiori function should bc rdatively simplc. For both stiff rodlikr and fl(~xihl(~ coil molwulcs it has b w n showri that the timr-corrclation function should consist o f an c~xponentinl with time constant dcpcndcnt on thc macro~nolcculnrtrnnslatiorinl diffusion cocfficicnt plus a rc.lativc.ly frn- othrr cxponrntials dcpcmdcnt on rotational diffusion or intramolrcular rcdaxation timrs. Expcrimrnt s h a w 521

@ 1975 by John Wiley & Sons, Inc.

522

SCHhIITZ AND PECORA

confirmed these theoric.s.6-10 lcor iiistancc, Huang and Frcdericlig and King ct al. lo have studied intramolccular relaxation of flexible molpculcs (polystyrcws) and cbxtractc.d valuos of the longest intramolecular relaxation time from the light-scattering data. The rcgion in which K R , >> 1 docs not, howvc>r, lcnd itsdf to this relatively simple analysis. l--j l 1 l l a n y intramolecular relaxation processes contribute to thc tinit.-corrclatiori function. Thus, a simple fit of the data to a few cxponcntials may no 1ongc.r hc mmningful. A further complicating fcaturc. for solutions of these huge scmiflcxiblc molecules is that ( ’ v ~ nvery small concmtrations of macromolccul(. result in highly nonidcal solutions so that intc~rmolccularas ~ ~ as 1intramolecular 1 relaxation proccwes may bc important. k’or instancc, Huang and P’rcdcrickz1have found important concentration-dcpendcrit cbffrcts in the seattclring from soiutions of poiystyrcnc of moiccuiar w i g h t -5 X lo7. S o reliable c.xtrapolation procvdurc to zero concmtration has as h-c’t been developed. Polydispersity may also, of c o u w , distort t h r rvsults in these systc.ms.22 N:cwrthclcss, it is hopc.d that thcl QLS tcchniquv may bv used to extract useful information about the dynamics of w r y large scmiflcxiblc molecules in solution. Th(1 prcwnt study d w d o p s tc.chnic1uc.s for studying high-molecular-wight (mol wt = 13-30 million) DXA molcculrs in solution. I n this paper we rcxport on QLS studies on four systcms: calf thymus DKA (CTDNA), CTDSA-acridinc orange (AO) complex, XDNA, and XDNA-protein complex. Since thew is no known predicted form for thc QLS time-correlation function for thrsc systems, one is immcldiatcly faced with the dificult problem of treating the raw data. Previous authors h a w simply fit the QLS timc-correlation function to two cxponcntials plus a basclincxZ4or to the sum of two exponcntials squared plus a baselinc..25 In order to comparc’ our rwults to those of thrsc. authors we h a w trcatcd som(’ of our data by both of thc above mcthods. I n addition, wc have dcvc1opc.d a method that we call asymptotic analysis. I n this method thc logarithm of the correlation function is p1ottc.d as a function of time. for both vary short and very long times. The short-timc analysis is closely rc4atc.d to the cumulant mcthods, which are currently fashionable in t h r analysis of QLS spectra of polydispcrsc ~ y s t c . m s . ~The ~ short-time analysis yields an "average" relaxation time. and a rough mcwmrc. of thc distribution of rclaxation times. Previous authors have found that thc DXA autocorrchtion functions arc each characterized by at least two rdaxation time^.^^-^' Th(1 slowest time results in a diffusion cot.ficicnt an order of magnitudc too small t o be attributed to that of DSA. This is in disagrcemcnt with simple single-chain theories2-5 (dilute solutions), which predict that thr slowest timc appearing in thc spectrum should bc due. to translational diffusion. Schmidt in his study of X l virus D S A attributvd this slow time to scattering from dust.24 From our studim of thc tc.mpcxraturc1, concentration, and ionic strmgth dcpcndenccBs, as w l l as thc, effect of AO on thc CTDXA light-scattering

CALF THYMUS DNA AND XDNA

523

correlation functions, we conclude that t hr slowcst time is in fact associatrd with the DNA and is not a spurious rffect (such as scattering from dust). Thew arc sevrral possible intrrpretations of this long timr. We mention below restricted translational motion and anisotropic diffusion. We find, in addition, that the longest rrlaxation timc for XDSA exhibits a maximum in the thermal transition rrgion similar t o that in calf thymus D S A rcportrd by Schmitx and Schurr. Thc effect is cvcn morr drastic in thc XDSAprotcin system.

MATERIALS AND METHODS XDNA XDNA was obtainrd by phenol extraction of purified XCISS7S7 coliphagc. The third rxtraction was twice dialyzed in thc cold (5°C) for 24 hr against 0.02 ionic strength K2HP04,Ill.T h r terminal relaxation timv in thc scwnd complw was compared with thc uncomplcwd DNA in the first expc’rimt.nt to d(1terrnincthc cffcct of thc iritcrcalatrd dye.*

+

Protein Binding by XDNA Contamination of XDSA by p r o t ~ i nmas effected by drawing off part of the interfacial surfacck in the. phmol mtraction proccdurci. Thv contaminated samplc was t h m dialyzed against thr buff er as described above. with Asao/A260= 0.65 for the resulting samplc. Thc sample was hcated to 64°C for 15 min and thvn storcd in t h r cold (5°C) until nckc.dcd. Complex formation of the protvin should occur only XI ith lincw XDSA sincc the cyclic form is unstablc a t 64°C and the ratc of cyciization is very slow a t 5°C.29 S o further characterization of thc samplc was pcrformcld.

Computational Analysis Thc autocorrelation function storcd in the mc1mor-y of th(1 Saicor 43A autocorrclator was plottcsd on 11 X 17-in paper by an .ry rcwrder. Thc function was thcn digitizcd and writtm 011 magndic tap(%with a Calma 302 digitizer. The digitizc.d numhcrs rcprcwnting intcmals of 0.02 in on the plotted graph were then punchcd on computcr cards for functional analysis. Thc original 400 points w r e , by this process of intcqmlation, cxpandcd to approximatcly 700 points. The dclay-time intcwal t bctwcwi succmsivc points for the final set of points was defined by t = 399

x

P/M

(3)

whcrc M is thc number of intcrpolated points and P is thc data-collcction interval. The digitizcd data were thcn fit to thrcc different functional forms: 1) thc sum of two c~xpontmtialssquared plus a basclinv; 2 ) thc sum of two cxponcntials plus a basdin(.; 3 ) what is, in offret, a singlc cxponc~ntialfit (see below). I n all casm, the initial guess paranwtws w r e computrr estimated arid nonlinear lcast squares fit to t h r s p c d i c functional forms until successive values of all paramctcm varied by lcss than 1%.

* These experiments with acridine orange binding were performed a t the University of Washington using an apparatus described p r e v i o u ~ l y . ~ ~

CALF THYMUS DNA AND XIINA

rc.markably closc. Th(x much larger valucx of T? for the CTDXA1-A0 complex ( D I P = 0.01) cannot be explained by concentration depcndcncc alonc since a tmfold changc. (O.G3/0.06S)alters the rotational times by a factor of 1.7S.*j Thc ratio T? (compl(,x, 0.2 mg/ml)/T2 (0.1 mg/ml) = 2.19 must be due. to both conccntration cffccts and extension of the molcculr on binding th(1 dye. Thc niarlwd cffcct of mol(m1ar txtmsion is illustrated in the 0.33-mg/ml data. I t i.; un1il;dy that t h r change in 7 2 upon binding A 0 could bv duc. to dust.

Two-Exponential Plus Baseline Analysis for Calf Thymus and XDNA's If thc rc.laxation timc. 7: is a result of a molecular rclaxation process, then 7 2 should be much slower for XDNA (mol wt 'v 3 1 million)31than for calf

SCHMITZ AND PECORA

528 500usec

v 500usec + 0

200usec

1 B M NaCl , .014rng/ml

1 .0016mg/rnl 1

500usrc

x IOOOusec 2000usrcJ

t

.014rng/ml

LAMBDA DNA 62°C

sin?e/2)

.65

I

I

.I0

I5

Fig. 3. Two-exponential analyses of XDNA data l/A2 vs. sin2(O/2), Eq. (5). The DNA was in 0.02 phosphate buffer, pH 7.8 with one sample having additional salt (0.5 M NaCI). All data were taken a t 62°C where the monomeric linear form of XDNA dominates a t the ionic strength 0.02.

thymus DNA (mol wt E 15 million).25 This is, indeed, the result found in the present study. I n attempting to fit the autocorrrlation function t o Eq. (4),however, several computations failed t o converge. I n this respect, thc simpler two-exponential form was more successful. The data were fit to C(mt) = A e - m t / A 1+ Be-mt/A'+ G

(5)

where A1 and A2 are characteristic decay times. If the trur spectal form were of the Eq. (4)type and t h r data w r c fit to Eq. ( 5 ) , the times A, and A2 would be a weighted average of t h r times 7, and 7 2 . Furthermore, the ratio ( T ~ / A ~=) 2, would hold if B >> A or TI < < 7 2 . This, however, is not the case for XDNA. Schmidtz4found TI/AZ = 1.75 for N1 DNA a t the ambient temperatuw, which is comparable to our value r 2 / A 2 = 33.1/17.4 E 1.9 at 62°C for XDSA. The sin2 ( 0 / 2 ) dependence of l / A 2 is presented in Figure 3 for data collected at intervals of 2000, 1000, 500, and 200 psrc. It is apparent that all of the data can be represented by the general exprrssion l/Az

=

AK2

+ l/Ao

(6)

in the range of angles reported in this study. It is also quite clear that the parameters A and l / A o are dependent on the rate of data acquisition. This behavior suggests the presence of other relaxation times not represented in the simplified two-exponential analysis. Although conclusions drawn on only two data points (2-mscc data) cannot be conclusive, the 1-2-msec

CALF THYMUS DNA AND W N A

529

TABLE I1 Variation With the Number of Points in Computer Analysis of the Autocorrelation Function ~ ( ~ = t A e) - m t / A 1 + B e - m t / A ? + G Sample

T (“C)

N

Al (msec)

XDNA 0.014 mg/ml 0 . 1 M NaCl

62

CTDNAB 0.1 mg/ml

22

CTDNA2 0 . 1 mg/ml B = O

22

693 643 593 543 484 434 384 334 234 184 484 434 384 334 284

2.46 2.31 2.08 5.62 5.21 5.00 4.78 4.53 2.00 1.73 7.61 7.40 7.07 6.72 6.35

A2

(msec)

17.43 16.51 15.18 111.20 756.60 1217 .OO 651.80 464.60 10.13 8.79

G 0.6048 0.6068 0.6103 0.5124 0.2474 0.1446 0.1667 0.2420 0.6741 0.6783 0.6700 0.6716 0,6740 0.6766 0.6799

relaxation rates taken together arc’ better reprcsentcd by a single line than thc rates obtained from th(. l-*/2-msc.c data. We assume, therefore, that the terminal relaxation times contained in t h r 1- and 2-msec data arc the “true” terminal times in thc relaxation spectrum. It is of interest to point out a t this time the concentration and salt dependences of l / A , exhibited by the ,500-pscc data in Figure 3. The parameter A , n-hich represents an eff ectivc diffusion coefficient, appears to be more DXA-concentration dcpendcnt than the intercept l/AO. The intercept, however, appears to bc more sensitivr to tht. concentration of salt. If the disagreement between longest relaxation times a t diff erent data collection rates is indicative of several relaxation times, thrn a single autocorrelation function should show similar discrepancies for different numbers of points (time scales) used in the analysis. Thc results of such an analysis for ADXA and CTDNA2 are prescmted in Table I1 for data collected a t 200-psec intervals. The erratic behavior of the two-exponential fit is a rcsult of the mutual dependence of the five unlinowns. The rdativclg small change in thc baseline, however, suggrsts a novvl method of analysis. This method appears to bc useful in obtaining unambiguous values of the longest relaxation time regardless of the data-collection interval as well as a weighted-average value of all times in the spcxctrum.

Asymptotic Analysis of ADNA Data The entire sprctrum of relaxation timcs is characterized by a single relaxation time T ~ : where k

=

c - m t / r ~ = ( Cble-mc’rt)k (7) 1 for a heterodyne spectrum and I; = 2 for a homodyncl spectrum.

SCHMITZ AND PECORA

530

LAMBDA DNA

2.4

-

-

2.2

.0016 rng/ml e = 300

.,

22'C t = 59usec

'\

\ \ \

-u I

$ 2.0-

-

.. , \

*

a

0

, ,

\

.

,

\

1.8 -

'\

' 0 '\

0

L-

0.

.

0.

1.6-

0 '\

0.

0

L

I

I 200

I

I

I

I

I

600

400

rn

Fig. 4. Asymptotic analysis, shoretime limit.

As shown in the Appendix, we have the asymptotic expressions for the homodyne spectrum

for mt/r

> 1, where T, is the slowest relaxation time in the spectrum. Equation (10) assumes that there is a wide separation between T, and the faster relaxation times of the system. A plot of 1 / versus ~ ~ m for the 0.0016-mg/ml solution of XDNA is presented in Figure 4. The data appear to have a slight curvature, which means that the intercept depicted in the graph ( ( 1 / ~ )-2.32 X psec-l) represents a lower limit with a possible error of no more than -25% (Appendix). The variance of the spectrum of reciprocal times as computed from the slope is ((1/?) - ( 1 / ~ ) = ~ ) 4.4 x l o p 9 ~ S ( Y - ~ which , further suggests the presence of several relaxation times. It should be pointed out that polydispersity could also contribute t o this value.23 We note without ' 4.3 mscc, which is slightly less than further comment that ( l / ~ ) - N 2~~ N 4.92 msec obtained in thc two-exponential analyses of the high-salt and DNA-concentration data (Tablc 11).

CALF THYMUS DNA AND XDNA

DNA

LAMBDA

v denatured

500usec

native

lOOusec

x native

200usrc

0

53 1

.0016 mg/ml /

22oc

/

e = 30

/

/ / /

/ 0

1.0

/

UI 0

/

/

/

/ /

.8

/ /

/ /

.6

- 7/-

,‘

4

I

/

- -- //

0

I

.5

0 x

/XNX

- - -v -- v

//’ -0.-

00

I 1.0

I

1.5 ( I/N) x

I 2 .o

I 2.5

lo3

Fig. 5 . Asymptotic analysis, long-time limit. Plots of the reciprocal of TN, the “best fit” single relaxation time characterizing the first N points of the autocorrelation function vs. 1 / N for XDNA a t 22°C.

We now focus our attention on the 1/rCversus l / m plot in Figure 5. The curvature in the 100-psec data of native DNA is again indicative of other relaxation modes not accounted for in the In b, term. The apparent absence of curvature in the 200-psec data indicates that the faster modes have sufficiently decayed t o negligible contributions in the data range covered. Using t = 399 X 200/667 = 118 psec in Eq. (lo), we obtain from the slope a value b, -0.06. A value of -0 for the slope in the denatured DNA data indicates that, a t 500-psec data-collection intervals, only the slowest mode contributes significantly to the normalized autocorrelation function in the time range of the computation; that is, b, -1 in the normalized function. The intercept indicates that the terminal relaxation time is -1.5 timcs faster for the denatured DKA compared to the native DNA. This relatively small contraction a t this low ionic strength (-0.02) is consistent with sedimentation data.32 Plots of 1 / versus ~ ~ l / m for data collected a t loo-, ZOO-, and 1000-psec intervals of the 0.014-mg/ml solution of XDNA in 0.02 phosphate buffer are shown in Figure 6. Linear extrapolation of the 100- and 200-psec data

532

SCHMITZ AND PECORA LAMBDA oNQN 62OC

8.35 .014 mg/ml

,. .

,.,, ’

*’

.*’

,,

Fig. 6. Comparison of data collected a t different rates, asymptotic long-time analysis. Plots of t,he reciprocal of T N the “best fit” single relaxation time charact,erixing the first N points of t,he autocorrelation function versus I / N for XDNA a t 62°C. The average asymptotic time constant for the collection int,ervals 100, 200, and 1000 psec a t 35” ~ 32. ) f 3 see-’. scattering angle is ( l / ~‘u

gives an interccpt n ~ 2 higher 0 ~ ~than the lOO-ps(>cdata. Thcsc linearly extrapolated values for the longest relaxation times for the three data sets are in much better agreement than those obtaincd from conventional analysis (Figure 3). The 20% discrepancy can be explained by comparing thc slopes of the plots, which, in general, arc’ rcprescntcd by B(7nt) at a jixecl angle (cf. Appendix). If these functions arc constant, as infcrrcd by Eg. (lo), thcri the ratios t’B(mt)/tB(mt’) = R(t,t’) should bc simply thc ratios of collection intervals t’/t. Wc find, however, R(lOO,200) 2 I S , R(200,1000) N 4.4,and R(100,lOOO) ‘v 7.S. It is vvidcnt from thv gcricral definition of B(mt) that fastcr modcs are prcsmt whow amplitudrs h a w decayed a t the longer timc intorvals. That is, for a fixed ~ i u n t b e rof points in two autocorrelation functions of two diffcrmt collcction intcmds, the fractioiz of points in which t hc fastt.r modcs h a w significant contributions is snzaller for the larger collrction timcl intcmml. Indwd, the largwt discrepancy occurs \\ith t h r wid& timc scyaration ~ ( l O O , l O O O ) / l O = 0.7s compared to thc, smallest separation of timc intwvals R( 100,200)/% = 0.90.

CALF THYMUS DNA AND XDNA LAMBDA

533

DNA

62" C 2 0 0 usec .5M N a C l .014 mg/ml

1

I

I

I

Fig. 7. Scattering vector dependence of long-time asymptotic values l / ~Eq. ~ ,(11). The effective diffusion coefficient A = 0.24 X 10-8 cm2/sec (62°C) is an order of magnitude smaller than that obtained on extrapolation of the data of Iteinhert e t al. to 30 million mol wt.

The sin2 (8/2) deprndence of the intcnept 1 / is~illustrated ~ in Figure 7 for 0.004-mg/ml DiVA in the phosphatr buffrr with 0.3 111 SaCI, which apprars to be of t h r form 1 / =~ A~K 2

+ l/Ao

(11)

wherc K is the scattering vrctor and A is an effective diffusion coefficient. The observation that both t h r slope and intcrcppt of the plot in 1Ggurc. 7 are comparable to thc valurs obtained in the conventional plot of t h r 1000- and 2000-pscc data of E'igurc 3 gives additional support to the asymptotic method of analysis.

Transition Region Asymptotic analysis was carrkd out for XDNA and protein-contaminatrd XDNA through the thermal transition rc.gion. It is apparent from Figurc. 8 that the slowest rrlaxation time. of XDSA exhibits a maximum in its thermal profile in t h r latcr stages of thrrmal dcnaturation. This behavior is consistrnt with t h r data of Schmitz and Schurr on calf thymus DKA.2s Although thc molecular w i g h t of XDSA is almost twicr that of CTDNA, the XDSA concrntration is almost 50 timrs morr dilutr, hence t h r degree of aggregation is not as c>xtrnsivv. It is char from E'igurc. 9 that thv prrsencc of protein dTastically affects the thermal bchavior of the slowrst rrlaxation timc. in thc transition rrgion. Comparcl thc A280/A260 ratio of XDXA-protrin of 0.63 with t h r 0.53s ratio of XDSA (E'igurc S). Thus

534

SCHMITZ AND PECORA LAMBDA DNA

,0016 mg/rnl

.02 ionic strength 500 usec

73°C

87°C ln N

0 -

84OC

X

1 Fig. 8. Thermal transition of XDNA, asymptotic analysis. The scattering angle is 30”. TN is the “best fit” single relaxation time characterizing the first N points of the autocorrelation function.

the protein must have a higher affinity for denatured DNA than for native DNA. This increased affinity observed in the present study is consistent with the nmr measurements of Gabbay ct al.33for proteins containing aromatic rings. It may be possible that minutch quantities of protein could cause the aggregation of XDNA indicated in Figure 8. This prospect seems unlikely, however, since it requires a sharp alteration of the protein affinity to explain the maximum in the thermal profilc. Furthermore, Rimai ct al.4 obscrvcd an increase in the relaxation time. of RKase through the transition region, which they attributed to aggwgation. A significant difference in their study, however, was the corresponding increase in t h r reduced viscosity, which lead to eventual precipitation. Seithcr of these events 0ccurrc.d in the uncomplcxcd studies.

DISCUSSION The autocorrelation function of XDNA contains a t least two relaxation modes whose time constants diffcr by an order of magnitude. The values of the time constants apprar to dcpend on the rate of data acquisition in the conventional angular analysis of the data. This behavior strongly suggests that the two time constants are actually representative values of a manifold of relaxation modes. The relative contribution of each component in the manifold is, therefore, dependent on its extent of decay in thc time range under analysis. E’or cxamplc, assume the autocorrdation function contains 1000 points and the fastest mode decays to givc. a negligible contribution aftm 100 points. Data are now taken at a faster rate and the

CALF THYMUS DNA AND XDNA LAMBDA DNA

+

33.5

PROTEIN

8.350

o 200usec, 36OC 5 0 0 u s e c , 62OC

v 500 usec, 71°C

5

10

15

20

25

3

( I / N ) x 10

+

Fig. 9. Thermal transition of AlINA protein sample, asymptotic analysis. The scattering angle is 35". TN is the "best fit" single relaxation time characterizing the first N points of the autocorrelation function.

fastest mode givw a significant contribution up to the 300th point of thc 1000-point autocorrclation function. Thc characteristic timc in tht. first exaniple is slower than in the second example bccause thc fastest modr is significant in 10 and 50%, respectively, of the data. One can, of course, use more rxponmtial functions in analyzing the autocorrelation function. The difficulty in this procedure, h o n c v r , is dctcrmining t h r ?lumber of c.xponmtia1 functions. I:urthtmnorc, thc tendency of nonlinear least squares analysis of tn-o clxponcmtiali having siniilar tim~ coiistaiits is either 1) an attempt to approxiniate both functions as a singl(, exponclntial or 2 ) t o rxchange continually the t n o scts of parameters b(1twecw the matrix locations of thc two modes with no convergence. We can, howcvcr, perform asymptotic analysis of the data t o obtain values of the slo~vcstrclaxation timc constant(s) and the average initial timc constant. I n this analysis, t h r autocorrelation function is clraracterzxed by a singlr timc constant 1 , ' ~ ~ .Thc varianccl of the manifold of timc constants can bc computed from t h r plot of l / r cversus 111 at thc initial decay of the autocorrelation function, whcrc 112 is the point number. In thc longtime limit, deviations from lincaritj. of vm-sus 1,'m arc' anothcr indication of additional relaxation modes. The data for thc 0.0016-nig/ml XDSA concentration a t W 0 C and scattcring angle of 30" wwe analyzed by thc asymptotic method. Thc avcmgc initial time constant ( l / ~ )was found to br 232 sec-l with thc smallcst (i.cl., longest relaxation timcl) componmt bring 32 wc-'. Thc standard

SCHIIITZ AND PECORA

536

deviation (Appendix) of thv spectrum of timo constants x i s computtxd from tlic lincw portion of t,hc l / r c v(mus 111 plot, rcwdting in :t valuc. of -67 s ~ c - l . This asymptotic analj in t h r short-time, limit :tiid thc curvature in thc l / r c versus l/m plot. :it th(. long-timv limit supports thc hypotho that scvcml rclnxation modw contributcx to thc spectrum of scattcvd light. Thc results of th(>acridinv orang(' binding by calf thymus I I S A cqwrimcnts strongly support thch assignmmt of thv Iongost rchxation modp to thc DXA. This assigniiicmt is furthvr supported by th(1 ionic strmgth arld DSA concmtration c.ff(lcts on thv Iongost rc,l:isation timo. Sinrcl is roughly lincar in K 2 ,whet-(>K is thv scattwing vcctor [Eq. ( l ) ] ]the. molccwlar diffusion cocfficimt I), niay bc wtimattd from th(x quantity A in Eq. (11) by using thc relation 11,

zz

A/2

(12)

for a homodync spectrum (I'igurcl 7). Corrocting th(. valucl of 11, for (presumably) monomc.ric lincsar XDSA obtained at G2-20°C, n-(1 find D, (20OC) -0.5 X lop9 cm2/we for th(>0.014-nig/ml data. Itcinc,rt c.t al,35 studied thc molccular-\v(-ctightdopcmhicc~of th(. translational diffusion coc4fic.ic.nt in the w i g h t rang(>1-20 million. On c.xtrapolrtting thrir data. to 30 million, it is found that the cqc>ctcd diffusion coefficicwt is approximately 0.S X cm2/svc a t 20°C. D, is, thc~rc.forc1,:i,pproximatc>ly 13 tinics snzaller than thc projc.ctcd valuo in Itc~inc~rt's data. This is, curiously, approximatdy th(1 samc as thc1 ratio of thv long- mid short-tinw constants of tho quasi-elastic light-scnttc.ring data. Thc tinw romputcd from the. intercept of thc K 2 plot in 1;igurc. 7 givcbs L: valucb O.OGG see. W r can compar(' this timc: with that for thc longmt intrarnolccular mod(, as prcdictvd by tho Rouse-Zimm mod(l13G in both thc frctct-draining and iioiifrc.o-draining limits: 7,

=

BAT7 [ ~ ] ~ / T ~ R T

(1.3)

T,

=

AT?

(14)

[7]0/

(0.586)R1'(4.04)

rcspcctivdy. Assuming t.hc reduccd viscosity of 140 dl/g is a good approximation for t h r intrinsic viscosity [ q ] o and using :t molccular w i g h t L!I = 31 million, we have, at W"C, r , = 0.041 scc arid r , = 0.051) see. Employing the t,c.mI)c,raturci-viscosity corrctction factor to O.OG6, th(1 corrcsponding timc at 25OC would hc -0.12 s w . This valuc is compared to the prcdictt.d valuc, in thc Callis-Davidso~i~~ c~mpiricnlcxpr(wion, rCD

=

5 X 10-14

A(/l.BO*.l

(15)

lor f U' = 31 million, we find for r C D t,ht. valuw 0.27, 0.05, 0.00s scc for the exponents 1.7, l.G, and 1.5, rcspc.ctivcly. It is apparmt that thc. intcrccpt gives a timc that is comparablr to th(. slowwt timc c,xpc.ctcd from tho Ilousc;-Zimm thoory or thc Callis-Davidson c.mpirica1 cxprmsion. This rough agrecnicmt is probablj- fortuitous. i\'cwc,rthclcss th(. possibility romains that thv longcxst rchxation time. contains :i compoiwnt from a long1ivc.d intramolccular mod(..

CALF THYRIUS DNA AN11 XI>NA

ri37

If the longc’st relaxation timc is not due to siniplc translational diffusion of single DKA m o I ( d m , what is its origin‘? W r bdicvcx it must ark(, from intcrmolccular intwactions. Using a typical D S A concmtration of 10 pg/ml, onc finds that thc avcxragc distanw bet\wc>ncmtclrs of mass is approxirr;latoly 1G,000A. Ir, to doduccx a more dctaikd mcxchanism for t h r longclst relaxation timv. One possible mc.chanism is t h a t somo mol(~cu1warc trapped in a position for a timc by their ~wighborsarid thcn diffusc. away. A similar mc.ch:tnism has bwn invoked t o c.xplain scattering from g d s arid concentrated I)olymc,r solutions.2519 On(. may view this mc,ch:tnism as tht. formation of tcxmporary “iiggregatvs,” which thcn bred; apart. As mmtioncd carliclr, thc drop in th(. rc.duccd viscosity prior to 3S”C (1;igiu-v 2 ) is assumc.d to bc a rcmilt of dissolution of aggregates. Unlcss t h r visconivtclr is iiismsitivc. to furthcr dissolution of aggrc.gatc.s, or if furthcr dissolution doc>snot occur, thc platmu region (5So-GSoC) is ncwwary (but, of coursc, not conclusive.) cvidmcc. that the XDSA is in its monomeric linvar form. The “lifctimc~” of thc aggrc>gatvin thv QLS data must nccwsarily b(1 ICSS than th(. timv rcquircxd in the viscosity vxporimmt. W r can intcvyret the. longc.st rdaxation timc as c.ithcr due. to diffusion of an “aggrcyatcx,” or pwhaps thc lifetime. of thc aggregatcx. This modcl can also b(>uscd to explain thr behavior of th(1 longest rc.laxation timr in th(. transition region. In the (Larly transition region, formation of small loops and somv unwinding from thc ends presumably occurs. Latca in the, transition rty$on, how-c.vc>r, at least o11c cmd of the molcculc has undcrgonc. cxtcnsivcl dmaturation. It is in this r q i o n of the. transition that the bound countwions ar(1 rdcascd into the s o l u t i o ~ i . ~Cons(.”~~~ qumtly, both thc increased clcctrostatic repulsion bctn-ecn phosphate. groups and contour Icngth of the dcnaturcd rcgion makcs reunion of the two complcmcntary strands an unfavorable cvmt. As a result of t h r proximity of nciighboring molecules, intc.rmolccular intc.ractions bcgin t o play a niorcl important role. Although the naturc of the intc~rmolccular intcwictions cannot br dvduced from thc prcsmt data, tht. possibility of associations b r t w w i complementary haws of nr4ghboririg molcculrs cannot br rulcd out. Rcccnt studies by l ’ r i t ~ h a r don ~ ~13. coli D S A dmaturation indirwtly support thv fcasibility of base-bas(. intclractions. Bridly, th(. two strands of sheawd E . coli DS,4 i v ( w cross-linlwd n i t h thc rcxduccd form of mitomycin c. Trc>atmmt n-ith vcnom I’hosphodicstcrast. rmulttd in cross-linked samples a t thc duplcx tmmini with singlr-strandcd 5’ polynuclcotid(, chain ends. Thcsc cross-1inkt.d samplcs 1% cr(’ thcri isolated and scparatcd into compositionally homogcmwus fractions by drnsity-gradimt

SCHMITZ AND PECORA

538

centrifugation or hydroxylapatite chromatography. Melting profiles, which are essentially free of effects due to end unwinding and strand separation, were then determined for the various composition fractions. Although the T , dependence on composition was in agreement with theory (i.e., linear with G C content), the breadths wcrc not narrow. I n fact, the transition breadths in some fractions even cxcceded that obtained for the unfractionated DNA. Furthermore, the compositional distribution of T,’s was narrower than the breadth of the unfractionated sample. These observations are in contrast with current the0ry,~3which suggests the total width of the compositionally heterogeneous D K A results from a succession of narrow-width profiles of compositionally homogeneous regions in the DNA. T o explain the observed breadths, out-of-register interactions were proposed. That is, bond formation and breakage of the kth base within a loop on strand 1 did not always occur with the kth base on strand 2 , but could also interact with the j t h base of the same loop. It is a simple matter to extend this model to include neighboring molecules when thc probability of the two complementary strands to reunite is greatly reduced. At constant chemical potential, thc formation of intermolecular bonds could aid in the dissolution of intramolecular bonds to compensate for the decrease in entropy. Another possible origin of the slowest relaxation mode should be mentioned. According t o recent computer calculations of equilibrium dimensions, flexible polymer molecules in solution may not be s p h ~ r i c a I . ~ ~ - ~ ~ Thus, there should be diff erent translational diffusion times parallel and perpendicular to the longest axis of the molecule. The longest relaxation time could arise from the slower translational diffusion time perpendicular to the longest axis of the molecule. These separate diffusion modes could become even more important if intermolecular interactions hinder rotation of D N A molecules. Jamieson and Presley4’ recently reported observations of anisotropic diffusion by polyacrylamide. The two relaxation times observed in the low-ionic-strength data coalesced into one a t high ionic strength. Since the molecular dimensions were smaller a t the higher ionic strength, they concluded that intermolecular interference, or inability to rotate, was responsible for the two modes of diffusional relaxation. It seems reasonable to consider that a similar mechanism is preventing rotational relaxation about the smaller axis of the DNA-molecule. It should be pointed out, however, that at least two relaxation modes persist in D S A even a t high salt concentration ( 2 J l NaCl)24or low DIYA concentration (0.0016 mg/ml). We have, a t this time, found no evidence that the two modes will coalesce, as reported for the polyacrylamide data. I n any case, these comments are highly speculative. Aluch more work on the theory and experiment of QLS on large molecules of this typc is needed. It is hoped that some of the methods used here will be further developed and applied to the study of other systems exhibiting multiple modes of relaxation.

+

CALF THYMUS DNA ANI) XIINA

539

APPENDIX ASYMPTOTIC ANALYSIS OF QLS AUTOCORRELATION FUNCTIONS Assimie t h at the autocorrelation function is composed o f several exponentials: C(kl)

=

AF(nlt)

+G

(A11

F(nlt)

=

C aie - mt/rL

(A21

where

for a heterodyne experiment or F(n1t)

=

(Cbje-mt'+

( C h,,c-mr'I)

=

(A3

t j

for a homodyne experiment, where we have defined b,j = b,bj and l / r L j = T h e constant. A is a normalization factor: A

=

1/7i

+ I/.;. (A41

l/F(O).

Set t h e correlation fliriction equal t o a single exponential C(nit)

= e-mt'7r

+G

(A51

where rc is a characteristic time and ,-mt/r,

=

A F (ni1).

(A6)

If P(mt) consists of more than one exponential, T~ will vary st.rongly with time. For convenience, we define the relative amplitudes b, such that A = 1 . We now expand t,he exponent.ia1 as the infinite series

where the double indices have been redefined and rondetised to one if F(ni/j is given by Eq. (A3). Substituting Eq. (A7) into Eq. (AG), taking t h r natural logarithm of both , noting 0; = 1, we find sides of the resulting equation, solving for I / T ~and

C 3

where x,

=

nit/r,.

Asymptotic Limit: x,