The dispersion of the hyperchromic effect in thermally induced transitions of nucleic acids

J. Mol. Biol . (1962) 5, 587-610

The Dispersion of the Hyperchromic Effect in ThermallyInduced Transitions of Nucleic Acids

GARY FELSENFELD AND GEORG~NA SANDEEN

Laboratory of Molecular B iology, National Institute of Arthritis and MetabolicDiseases, National I nstitutes of Health , Bethesda 14, Maryland, U.S.A.

(Received 3 May 1962)

The increase in optical absorbance in the ultraviolet light band which occurswhen nucleic acids are heated has been shown to have a different functionaldependence upon temperature at each wavelength, because there is a correlationbetween the denaturation temperature of a denaturing unit and its absorptionspect rum . The dep endence of the median temperature (Tm) of absorbanceincreas e upon wavelength is plotted to give an optical denaturation-dispersioncurve characteristic of the nucleic acid. It is shown that the magnitude of thedispersion in native calf thymus DNA is much greater than in native T4 phageDNA, eit her before or afte r shearing of the phage DNA. This result givesinformation about t he composit ion of denaturation " nuc lei " in the phageDNA molecule.

Multiple wavelength data are also analysed to give separa t e curves showingthe degree of denaturation of adenine-thymine (A-T) base pairs and guaninecytosine (G-C) bas e pairs as a function of t emperature. It is sh own that innative calf thymus DNA the valu es of Tm for A-T and G-C pairs are withina few degrees of on e another, but that in reheated denatured calf thymus DNAthe values of Tm are widely separate d . The shape of the A-T and G-C curves inthe denatured DNA is sh own to be interpretable in terms of structural modelspreviously proposed by other investigators. A similar analysis of S-RNAdenaturation shows that the st ruct ure of S-RNA is different from that ofdenatured calf thymus DNA. It is concluded that t he longest regions of orderedstr uct ure in S-RNA consist of some sequenc es relatively pure in G-C base pairs,and other sequences rela ti vely pure in A-U base pairs.

1. IntroductionThe thermal denaturation of DNA has been defined principally in terms of changesin viscosity, optical rotation, or optical absorbance which occur when native DNA isheated (Thomas, 1953, 1954; Rice & Doty, 1957; Doty, Boedtker, Fresco, Haselkorn& Litt, 1959). Of these, the most commonly employed has been the measurement ofthe optical absorbance increase at the absorption maximum, in the neighborhood of260 tssp: It has usually been assumed that such a measurement completely describ esthe denaturation process; analyses of over-all base composition and of heterogeneity'lith respect to base composition have been made, using the parameters of the"melting curve" (Marmur & Doty, 1959).

In this paper, it is shown that the optical absorban ce method can be extended togive additional information about the denaturation process by making measurementsnot only at 260 mp' but also at other wavelengths throughout the region in whichthe nucleic acid absorbs. The method depends upon the fact that adenine-thymine(A-T) base pairs, which differ from guanine-cytosine (G-O) base pairs in their effect

38 587

588 G. FELSENFELD AND G. SANDEEN

on DNA denaturation temperature, also differ in their contribution to the absorptionspectrum. The dependence of absorbance upon temperature is, consequently, differentat each wavelength. The "dispersion curves" ofdenaturation temperature as a functionof wavelength are shown to be a sensitive measure of the contribution to the denaturation behavior made by heterogeneity of base composition. Methods are presentedfor analysing the data quantitatively, and the technique is used to obtain informationabout denaturation heterogeneity in native and denatured calf thymus DNA, intactand sheared T4 bacteriophage DNA, soluble RNA and the synthetic polynucleotides.

2. Experimental(a) Materials

Calf thymus DNA was isolated from fresh thymus glands in the manner previouslydescribed (Kay, Simmons & Dounce, 1952; Felsenfeld & Huang, 1961). This preparationhad a protein content of 0'5%, determined by Dr. Maxine Singer by the method of Lowry,Rosebrough, Farr & Randall (1951) ; its median sedimentation coefficient at a concentrationof 10-4 M (monomolar concentration) in 0·1 M-NaCl, pH 6'8, was 23·4 s, corrected to 20°C.

T4 DNA was prepared by the method of Mandell & Hershey (1960). At a concentrationof 10-4 M, in 10-4 M-cacodylate buffer, pH 6·6, 0·1 M-NaCl, the median sedimentationcoefficient (at 31,410 rev.fmin) of several preparations varied from 57·8 to 43·6 s, correctedto 20°C. According to Rubenstein, Thomas & Hershey (1961), the largest value of Scorresponds to a molecular weight distribution containing a large proportion of intactmolecules comprising the entire contents of the bacteriophage. (The nucleic acid concentration used in these measurements is slightly higher than that used by Rubenstein et al.,1961.) All of these DNA preparations showed the same denaturation dispersion behavior;they are referred to collectively as "unsheared T4 DNA". Shearing was accomplished byforcing the DNA solution through a glass capillary. Under the conditions employed, themedian sedimentation coefficient of the sheared preparations varied from 23·0 to 25·2 s,corresponding to a mean molecular weight about one-fifth that of the intact molecule(Rubenstein et al., 1961). Glass capillary was used for these experiments because it wasfound that standard hypodermic needles ordinarily used for shearing introduce smallamounts of metal ion contamination. In low ionic strength solutions (0,001 M-NaCl) thiscontamination can cause an elevation in Tm of almost 20°C, and even at 0·1 ionic strengthan effect of the ionic contamination upon the denaturation curve shape is observed.Addition of 10-4 M-EDTA is sufficient to abolish all of these effects but tends to interferewith absorbance measurements at short wavelength. It is therefore of importance tocarry out the shearing in non-metallic systems if accurate denaturation studies are to beperformed.

All DNA preparations except those passed through metal hypodermic needles wereunaffected in their melting behavior by the addition of small quantities of EDTA (of theorder of 10-4 M), indicating that divalent ions such as MgH, Mn2+ and BaH were notpresent in amounts sufficient to affect Tm . Dialysis of the T4 DNA against 1 M-NaCI toremove polyamines resulted in lowering ofTm measured in 0·002 M-NaCl, 0·001 M-cacodylatebuffer by about 2°C, but there was no change in the dispersion. The lowering of Tm maybe attributable either to loss of polyamines or to some damaging effect of the additionalpreparative steps. Results presented in this paper were obtained with T4 DNA notdialysed in this manner.

The synthetic polyribonucleotides were purchased from Miles Laboratories, Inc. Thepoly d(AT) was the gift of Professor R. Baldwin. The yeast S-RNA was a gift of Dr.GiulioCantoni. It was prepared by slight modification of the method of Monier, Stephenson &Zamecnik (1960).

(b ) Measurements

Optical measurements were carried out in a Zeiss model PMQ II spectrophotometer,using a thermostatic cell holder manufactured by Zieler Instrument Company, Boston,Mass. The holder permits thermostatic control of four cells, with a maximum measured

DI SPE R SI ON OF T H E HYPER CHR OMI C EFFECT 589

t emperature differ en ce of about 0'05 °0 among the four po sitions . The temperature wascon t rolled with a H aa ke model F circulat ing bath and measured with a Vict ory Engineer ingCompany model 51A35 glass-imbedded bead the rmistor. The thermist or was positioned inthe wat er " b la nk " optical cell a bove t he ligh t path. This rectangular cell had a 1 em pa thlength and was eq uipped with ground glas s st oppered closure . The glass stoppe r wasreplaced by a machined DuP on t Teflon st opper with a hole dr illed to accept the thermistorleads. The thermi stor was held in place, and t he stopper sealed, by applica tion of acoating of General Elect r ic Com pany RTV -60 or RTV-90 silicone rubber compound . Thism ateri al , whe n hardened , makes a vapor -t ight seal but is easily remo ved whe n the cellmust be disas sembled. The other cells con t a ined the samples and a control consisting ofsolven t alone . These cells had ground glass stoppers, with a film of Dow- Corning silic onegrease on the stoppers, and were also sealed with the R TV silicone rubber compound. Theseal was stro ng eno ugh to hold the stopper in place against t he pressure gene rated in t hevery small a ir space left above the solu t ion ; this ai r space was sma ll enoug h to makenegligible the errors caused by evaporat ion of solvent and its subsequent conde ns ationon the walls of the ai r space. The deposition of air bubbles on the optical surfaces a t highert emperatures was prevented by bubbling water-saturated h elium th rough all solutionsjust before filling the cells to remove di ssolved air. H elium , unlike nitrogen and oxygen ,has a positive temperature coefficien t of solubility.

The thermistor was h eated in an oven at about lOooO for one week, before calibrationagainst a Bureau of Standards calib rat ed mercury thermometer. The resistance of thethe rmist or was measured with a Wheatstone bridge having 50,000 ohm and 5000 ohmfixed resistor arms (General R adio Comp any, ± 0·05%) and an Electroscientific Industries10,000 ohm (± 0·03%) decade resistance bo x as the variabl e arm. The bridge re sistancevalues were chosen to limit th e curren t t h ro ugh the thermistor, so t hat direct heatingeffects never introduced an erro r as great as 0·01DC. The voltage source of the bridge wasa 1·4 v mercury dry cell with a variable voltage attenuator ; t he detector was a H oustonInstrument Company mod el M-IO d .c , am p lifier with output connected t o a ± 100 m icroampe re m eter. Tempera t ur e can be read to ± 0·01 DC with th is device.

Typical denat urat ion curves contained between 15 and 20 observat ion t emperatures .Thermal equi librium was always attained b efore readings were taken, and some of thesereadings were checke d to ascertain that a steady state of op ti cal absorbance had al so beenreach ed in t he time in t erval used between readings at successive t em pe ratures .

The slit width of the m on och romat or was k ep t fixed , usu all y at 0·15 m m, through outthe experimen t . Adjustmen t of t he solven t blank absorbance to zero was accomplish edwith the sensitiv ity control alone. This assured, with minimum effort , that the slit widthus ed at any given wavelength was t he same at all tem pera tures.

(c) Calcu lations

Values of the median temperature of denaturat ion, T rn- wer e calcula t ed by mathematicalinterpolation between t he two point s on eithe r side of the 50 % absorbance increase point .All data were corrected for thermal expansion ofthe solution, using the expansion coefficien tof water. Changes in solvent abs orbance with temperature were also taken into account.

In a number of experiments, di spersion curves were calc ulated using not only the m ediandenaturation temperature, Too , but also another qu ant ity, the mean denaturationtem perat ure, T. This quantity is defined as

T maxT= ~ T j LlA j ,

T j= T o

Aooax-Ao

where ~A j is the absorbance change in the n eighborhood of tem perature T j, and Tmax,To. A max• A o a re the h igh est and lowest values of temperatu re and their correspondingabsorbances. T appears to be a m ore satisfactory quanti t y t han Tm for characterizing thedenatura t ion curve arising from a h et erogeneous di stribut ion of m olecules, since eacht emperature is weighted wit h the a bso rbance change occurring in it s neighborhood.Accurate calcula t ions of If' clearly require the recording of a large number of points in t hedenaturation region.


(d) OomputationThe computations of A-T and G-C denaturation curves described in the Appendix were

performed by a Minneapolis-Honeywell 800 computer, using an algebraic compiler programwritten by the authors. Though most of the calculations and corrections described in theprevious paragraph were carried out manually, the data for S-RNA were entirely processedwith the computer, using a program written by Mr. John Shaw.

55

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FIG. 1. Absorbance increase at three wavelengths as a function of temperature in a mixture ofpoly (A+ U) and poly (I+C), 0·033 M-NaCl, 0·005 M-cacodylate buffer, pH 6·5.• (dotted line)260 mJL; 0240 mJL; D. 230 mI"

3. ResultsIf a solution containing a mixture of the synthetic polynucleotades.] poly (A+ U)

and poly (1+0), is heated, the absorbance at 260 m/-, rises with temperature in themanner shown in the dashed curve of Fig. 1. In the absence of further information,

100o:----,-------.--------,-----,-~=

such a curve probably would be interpreted in terms of denaturation of a single,reasonably homogeneous, component. Only when curves obtained at other wavelengthsare compared with the 260 m/-, result does it become clear that there is more than onecomponent involved (Fig. 1). If the median temperature for the absorbance increaseis defined, in the customary manner, as the "melting temperature" (Tm ), then thedifference between Tm(A) and Tm(260) can be plotted as a function of the wavelength,A, to give the "melting point dispersion curve" shown in Fig. 2. The dispersion curveshows that the value of Tm determined at 230 m/-, is 3·1°0 higher than that at 260 txu».

This is easily explained by the observation that the melting temperature of poly(1+0) is about 3·4°0 higher than that of poly (A+ U) under these conditions. At230 m/-" poly (A+ U) undergoes almost no absorbance change when heated, while thepoly (I + 0) changes considerably. The inverse is true at 260 uu». Thus, the dispersionvalue at 230 tsu« is a direct measure of the melting point difference between the twocomponents.

t Abbreviations: Poly (A+U) is the two-stranded complex of polyadenylate homopolymer andpolyuridylate homopolymer. Poly (I + C) is the two-stranded complex of polyinosinate homopolymer and polycytidylate homopolymer.

DISPERSION OF THE HYPERCHROMIC EFFECT 591

Though this model system is an extreme example, the same kind of behavior is tobe expected from any heterogeneous nucleic acid, since the denaturation temperatureof a DNA molecule depends upon its G-C mole fraction (Marmur & Doty, 1959).

3.0

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270260230220 240 250i\ (mjL)

FIG. 2. Dispersion curve for the poly (A+ U)-poly (1+0) experiment of Fig. 1.

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Temperature (OC)

FIG. 3. Absorbance increase at three wavelengths as a function of temperature in calf thymusDNA, concentration 1·65 X 10-4 M, dissolved in 2 X 10-3 M-NaOl, 5 x 10-4 M-cacodylate buffer,pH 6·5. 0220 mu ; b. 260 mu ; 0290 mu

The results presented in Figs. 3 and 4 for calf thymus DNA show a pronounced meltingpoint dispersion. The shape of the dispersion curve is in qualitative agreement withthat predicted from the relative contributions of free adenosine, thymidine, guanosineand cytidine to the absorbance at each wavelength, assuming that the contributionof each nucleoside to the hyperchromic effect is proportional to its absorbance. Thedispersion curve has approximately the same shape whether calculated from T or Tm ·

100


This reflects the observed similarity in the DNA denaturation curve shapes at allwavelengths under these conditions. Though T and Tm are not equal, Tm - T is thesame (about 1·5°C) at all wavelengths. This is not necessarily true for other polynucleotide systems, or under other conditions.

•3.0

2.0

o

220 250 260 270 280 290

" (mj.L)

FIG. 4. Dispersion curve for the calf thymus DNA experiment of Fig. 3. T m (260 mf-L) = 56·28°C.T (260mf-L)=57·79°C.• t.Tm ; 0 ss:

+ 0.10r--,---,---,---,-----,

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-0.10

270A

FIG. 5. Dispersion curves of poly (A+U) .&, and poly d(AT)O. Poly (A+U) absorbance at260 mf-L (1 em), 20°C = 0·744 in 0·033 M-NaCl, 2·5 x 10-4 M-cacodylate buffer pH 6·5.T m (260 mf-L) = 49·36°C. Poly d(AT) absorbance at 260 rnu, 20°C = 0,925, dialysed against0·1 M-NaCI. T m (260 mf-L) = 60·58°C.

The results presented thus far do not prove that all of the dispersion of calf thymusDNA arises from correlation of melting point with base composition. It is also possiblethat certain portions of the absorption spectrum of an ordered polynucleotide mightbe affected preferentially by some preliminary structural changes occurring attemperatures just below Tm . This hypothesis can be tested by studying a polynucleotide with only one kind of base pair. Examination of the dispersion accompanyingthe melting of poly (A+U) suggests that the hypothesis is not correct (Fig. 5), since

DISPERSION OF THE HYPERCHROMI C EFFECT 593

the value of Tm is independent of wavelength, within the limits of error which areabout ±0'06°C at all wavelengths shown for these polymers. In Fig. 5 is shown alsothe dispersion curve of poly d(AT), which is similar to that of poly (A+ U) inmagnitude. Data below 240 mfl- and above 270 mfl- have been omitted from Fig. 5because of the small magnitude of the hyperchromism at these wavelengths. Theuncertainty in determination of Tm becomes greater with decreasing magnitude ofabsorbance change per degree temperature rise, so that, although the dispersion valuescan be measured for poly d(AT) at 220 and 230 mfl- (+0'03°e and -0·12°erespectively), estimated limits of error are ± 0·07 at 220 mfl- and ± 0'09 °e at 230 txu».

Further evidence in favor of the proposed explanation for DNA dispersion can beobtained by examining th e denaturation of calf thymus DNA at pH 3·1 to 3·3 andat pH 10·5. Under the conditions used for these experiments (Figs. 6 and 7) the

+ 0.4

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FIG. 6. Dispersion curves of calf t hymus DNA, about 10-( M. in 0·2 M-NaCI, buffered at lowpH. • 0·01 sr-acetate buffer, pH 3,3 , T m (260 mIL) = 50·43 °C; 0 0·01 :II-glycine buffer,pH 3,1, T m (260 mIL) = 42·29°C.

spectra of the native DNA are not very different'] from that obtained for native DNAat pH 7. After denaturation, however, the spectra are quite different, since the bases(adenine and cytosine at low pH, guanine and thymine at high pH), are liberatedfrom hydrogen bonding and able to gain or lose protons relatively easily. Thedispersion curves shown in Figs. 6 and 7 are different from each other and from thepH 7 curve; the differences are in agreement with qualitative predictions based uponthe spectra of the free bases at low and high pH, assuming that molecules with higherA-T content have lower denaturation temperatures.

These observations make it appear likely that all of the melting point dispersion ofDNA arises from the relation between the contributions of base pairs to melting pointand to absorption spectrum.

tIn 0·2 M·NaCI at pH 3·0 the DNA absorbance at 290 mIL is increased, relative to a pH 7 DNAsolut ion , by about 25 % of the total increase observed when the pH 2·9 solution is heat-denaturedand then cooled. Dove, Wallace & Davidson (1959) have studied the titration of cytosine innative DNA dissolved in 0·1 M·NaC!. A larger fraction of the cytosine groups is protonated atpH 3·0 in 0·1 M·NaC1 than in 0·2 M·NaC!.

594 G. FELSENFELD AND G. SANDEEN1.5 r-----,----,------,,-----.-----,

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FIG. 7. Dispersion curves of calf thymus DNA in 0·2 M·NaOI buffered at high pH.0, .0'5 M-carbonate buffer, pH 10·5; D, • 0·5 M-glycine buffer, pH 10'5. T m (260 mu), incarbonate : 45·09°0, 47'71°0; in glycine: 75'65°0, 67'89°0. The value of T m is very sensitive tosmall pH changes in this region. The large difference between T m in glycine and in carbonatearises from the larger decrease of pH in glycine, compared to that in carbonate, as the t emperatureis raised.

(a) Artefacts

IT the measurement of dispersion is to provide accurate information about thedenaturation mechanism, the possible existence of certain artefacts must be considered.For example, in studying the denaturation of poly (A+U) by absorbance methods,one is observing not only the absorbance increase resulting from the reaction poly(A+U) -e-poly A+poly U, but also further absorbance increases arising from changesin the liberated poly A and poly U within and beyond the temperature range inwhich poly (A+ U) dissociates. In order to make accurate measurements of thedenaturation of poly (A+U) it is therefore necessary to measure also the absorbancechange with temperature of separate poly A and poly U solutions under identicalconditions, and to obtain the true absorbance change, liE, attributable to poly (A + U)denaturation by use of the equation

liE = liE' -f(LiEu+LiEA), (I)

where liE' is the observed absorbance change, f is the fraction of poly (A+U)denatured, and liEu and LiEA are the absorbance changes in separate poly A andpoly U solutions of the same concentration present in the poly (A+U) solution. Thevalue off is a function of liE and it is necessary to solve for f algebraically. Since thepurpose of the correction is merely to remove the temperature dependence of lOA andlOU' the values of liEu and Li€A may be referred to any convenient starting temperature,To (for which Li€A = liEu = 0 by definition). This correction has been applied to thepoly (A+U) data presented in Fig. 5. It has a relatively small effect upon the dispersioncurve, and in this case changes Tm at most by a few hundredths of a degree. In thefollowing section, however, it will be shown that the same correction, applied to calfthymus DNA, results in somewhat larger changes of Tm at 290 mJL.

A second kind of artefact may occur when denaturation is carried out at low orhigh pH. IT the pH of the solution is near the pK of one or more of the bases, then


there will usually be a change in the degree of ionization of these bases with temperature, arising from the fact that ti.HiOnizatlon i= O. If a buffer is employed, then therewill be a change in the degree of ionization of the bases if the values of ti.HIOnizatlon

for buffer and base differ. Since ionization of the bases affects the spectrum, thedependence of optical density upon temperature will contain a contribution that doesnot arise from the denaturation process. Since the spectral changes accompanyingionization are different from those accompanying denaturation, an error will appearin the dispersion curve. The results presented in Fig. 7 show that this error may belarge. In this case, measurements were made in the presence of two buffers differingin their enthalpies of ionization (Edsall & Wyman, 1958): glycine buffer (10,550 calmole<) and carbonate buffer (3603 cal mole'<). Since the starting pH and the ionicstrength were the same in both experiments, the differences in the dispersion curvesare most reasonably attributed to the effect of temperature on ionization. Despitethese differences, the main features of the two curves are similar and the curveshape at wavelengths above 260 mft is invariant. At low values of pH (Fig. 6), theeffect of buffer choice appears to be smaller, though this may be in part the result of asmaller difference between the enthalpies of ionization of the buffers in this case.

A more obvious demonstration of the error caused by the temperature dependenceof ionization is provided by heating a solution of poly U alone at a starting pH of 9·7in glycine buffer or in carbonate buffer. In the carbonate buffer, the optical absorbanceat 240 txu: rises with increasing temperature and the absorbance at 260 mft falls. Inglycine buffer the inverse occurs. These changes are predictable from the absorptionspectra of neutral and ionized uridylic acid. The enthalpy of ionization of the glycinebuffer is greater than that of uracil, while the enthalpy of the carbonate buffer is less;the degree of ionization of uracil therefore changes in opposite directions in the twobuffers as the temperature is raised. The method could permit a simple evaluation ofthe enthalpy of ionization of the base.

(b) Denatured calf thymus DNA

It was shown above that the temperature dependence of absorbance of the complexpoly (A+ U) contains a contribution from absorbance changes of its dissociatedcomponents. Similarly, DNA may undergo further absorbance changes with increasingtemperature beyond its point of denaturation. If a solution of calf thymus DNA in0·11 M-NaCI, 0·006 M-cacodylate buffer, is heated beyond the denaturation pointuntil no further absorbance change occurs, cooled (there is no "renaturation", Doty,Marmur, Eigner & Schildkraut, 1960) and then heated again, it is found that partof the absorbance change during the second heating occurs in the temperatureregion in which the original denaturation took place. Unfortunately, knowledge ofthe second heating curve does not permit an exact correction to be made: thecomposition of the denatured material used in the second heating is that of the entireDNA sample, while the composition of the denatured component during the originaldenaturation process changes with increasing temperature, starting with moleculesof highest A-T content and gradually including molecules of higher G-C content asthe temperature is raised. Thus, a correction based on the second heating may resultin subtraction of contributions from G-C-rich denatured molecules not actuallypresent at the same temperature in the first heating. The approximate correctionremains useful, however, because it is small except in the latter stages of denaturation,where the error in the correction itself becomes small. It should be noted that the


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FIG. 8. Dispersion curve for calf thymus DNA, 2·01 X 10-4 M, in 0·109 M-KaCI, 0·006 M-cacodylatebuffer, pH 6·5. T m (260 mfL) = 83·98°C (uncorrected), 83·29°C (corrected). 0 Dispersion correctedfor contribution of denatured DNA; • Uncorrected.

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FIG. 9. Dispersion curve for denatured calf thymus DNA, reheated. DNA concentration2·04 X 10-4 M, in 0·109 M-NaCI, 0·006 M-cacodylate buffer, pH 6·5. T m (260 mu) = 61·53°C.T (260mfL) = 60·25°C.• t.Tm ; 0 sr.


correction for DNA becomes small at low ionic strength (Fig. 4) because the dependenceof absorbance upon temperature in denatured DNA becomes small. The results ofsuch a correction are shown in Fig. 8, compared with the uncorrected dispersion curvefor native calf thymus DNA in 0·11 M-NaOI, 0·006 M-cacodylate buffer. The correctionwas determined using equation (1) in the manner described above. The correcteddispersion curve deviates significantly from the uncorrected curve at 290 tnp:

The behavior of denatured calf thymus DNA upon re-heating is of interest not onlyas the basis for the above correction, but also because of its relation to the partlyordered structure which has been postulated for the denatured material and whichis supposed to be destroyed as the temperature is raised (Doty et al., 1959). Studiesof denatured calf thymus DNA in 0·11 M-NaOI, 0·006 M-cacodylate buffer, pH 6·5reveal a much larger dispersion (Fig. 9) than that observed with any native DNA.The "disordering" reaction in this case takes place over the entire temperature rangefrom room temperature (or below) to nearly 100°0. The slope of the absorptiontemperature curve is therefore small and the quantity T is a much more satisfactoryparameter than Tm for evaluation of dispersion curve properties. In this case theresults obtained with T differ considerably from those obtained with Tm but it is clearthat with the use of either parameter a large amount of dispersion is revealed. Thecause of this dispersion will become clear in the presentation of (d) Analysis of data.

(c) T4 bacteriophage DNA

Since the dispersion successfully reveals denaturation heterogeneity in calf thymusDNA, a heterogeneous nucleic acid, it is of interest to investigate the behavior of ahomogeneous nucleic acid, the DNA of T4 bacteriophage. It has already been

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FIG. 10. Dispersion curves for T4 DNA, about 10-4 M. 6. 0·2 M-NaCl, 5 x 10-4 M-cacodylatebuffer, pH 6·5. T m (260 mIL) = 85·21 0C; 0 0·2 M-NaCl, 0·05 M-carbonate buffer, pH 10·5.T m (260 mIL) = 49·03°C. The dotted line shows, for comparison, the dispersion of calf thymusDNA, 0·109 M-NaCl, 0·006 M-cacodylate buffer, pH 6·5.

shown (Beer & Thomas, 1961) that T4 DNA, when partly denatured by heat in thepresence of formaldehyde, forms regions of opened strands within an otherwiseundenatured DNA molecule. The question remains whether these loops occur atspecial sites, presumably of abnormally high A-T content, and whether such sitescomprise a large part of the DNA molecule.

The dispersion curve of a preparation containing unsheared T4 molecules which areassumed to be largely intact (see Experimental) is shown in Fig. 10. The dispersion is


an order of magnitude smaller than that of calf thymus DNA under similar conditionsand is only slightly larger than the estimated limit of precision of measurement.Since the dispersion is smallest at high ionic strength, the experiments were repeatedat much lower salt concentration (Fig. 11). Again, the dispersion is about an order of

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FIG. 11. Dispersion curve of T4 DNA, about 10-4 M. O. f'c. 10-3 M-NaCI, 5 x 10-4 M-cacodylatebuffer, pH 6'5, Till (260 miL); 0 57'02°C; f'c. 57·30°C. The dotted line shows, for comparison, thedispersion of calf thymus DNA under the same ionic conditions.

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•

260 270 280

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FIG. 12. Typical dispersion curves of T4 DNA, sheared (open symbols) and unsheared (solidsymbols). 0, .; O•• ; 0·001 M-NaC!. 0·001 M-cacodylate buffer, pH 6·5; s, ... 0·2 M-NaCI.0·001 M-cacodylate buffer, pH 6·5. The preparation represented by circles is an example of theextreme of "scatter" encountered in this experiment.

magnitude smaller than that of calf thymus DNA. Finally, the experiment wasrepeated in carbonate buffer at pH 10·5. Since the base compositions of T4 DNA andcalf thymus DNA are nearly the same (it is assumed that hydroxymethylcytosineand cytosine have reasonably similar absorption spectra) the effect of high pH shouldbe to produce the rather large dispersion at 280 and 290 mp. seen for calf thymusDNA in Fig. 7. The results of Fig. 10 demonstrate once again that T4 DNA has amuch smaller dispersion than calfthymus DNA. It should be noted that the correction


for absorbance changes in the denatured component cannot be applied in the case ofT4 DNA because it is not possible to isolate this component. Under conditions ofhigh ionic strength, where the correction might be important, renaturation occursupon cooling (Marmur & Lane , 1960).

It is of interest to compare the above results with those obtained when the T4 DNAhas been broken by shearing into molecules about one-fifth the size of the intactmolecules . In Fig. 12 it is shown that there is no large change in the amount ofdispersion. Similar results are obtained at high pH in carbonate buffer.

(d) Analysis of data

Though the dispersion curve is a convenient way of summarizing the denaturationdata, it does not derive the maximum amount of information from them. It has beensuggested by Professor N. Davidson that the data could be analysed more satisfactorily if it was assumed that

(2)

where ~A is the change in absorption at any wavelength A and temperature T,€AT and €GC are the average molar extinctions ofthe free nucleosides (A+T) and (G+C)respectively as a function of A, XAT and X GC are the mole fractions of A-T and G-Cbase pairs respectively, and fAT andfGC are the fractions of A-T and G-C base pairsdenatured at any temperature; h is a constant independent of A and T.

The assumption involved in writing equation (2) is that the hyperchromicitycontributed by denaturation of a base pair is always proportional to the free nucleosidespectrum of the pair, with the same constant, h, at each wavelength. Though thisassumption is not correct, it usually provides a reasonable first approximation tothe "exact" solution described below, with the advantage that it is possible to solvefor fAT andfGc as functions of temperature by simple graphical methods. For example,if both sides of equation (2) are divided by EAT' X AT and if

is plotted against€GC'XGC

EAT,XAT

the slope of the line determined by the points is proportional to fGc. The proportionality constant is found by use of the data at high temperature, for which fGC = 1.The values of fAT may be found by a similar method.

When this graphical method is used it becomes clear at once that equation (2) isnot entirely satisfactory, since the points never lie on a straight line, and some kindof estimate of "best fit" must be made. However, if equation (2) is written in the form

(3)

where PAT and PGC are arbitrary functions of A and X unrelated to the free basespectra, it is apparent that the equations may be solved in a more general manner,since XAT and X GC are constants for a given nucleic acid, and measurements at mvalues of Aand n values ofT yield m(n-l) values of ~A, but generate only 2(m+n-l)unknowns. For the usual values of m and n the solutions are overdetermined and withthe use of a digital computer it is possible to find such solutions (see Appendix).


There is an infinite number of choices of values of fJ and f which will satisfy equation(3) for a given set of LiA(.:\, T); four independent parameters must be fixed to determinea unique solution. Two of these are provided by the requirement that fAT = fGC= 1at the highest temperature. The other two may be, for example, values of fJAT atany two wavelengths. The method used in choosing these values is discussed in theAppendix. It must be emphasized, however, that the resulting A-T and G-C meltingcurves are relatively insensitive to the values of fJAT chosen. Furthermore, thepossible choices of fJAT are severely circumscribed by the physical requirements ofthe system. Thus, in the case of native calf thymus DNA (Fig. 13), if the ratio

100

•90

80

70"~ 60::>..,0c

'"" 501:!'"~ 40s:

30

20

10

<II

30 35 40Temperature (0C)

FIG. 13. Separated A-T and G-C denaturation curves for the calf thymus DNA experiment ofFig. 3. 0 A-T; • G-C.

fJAT(250 mu) :fJAT(260 mu) is chosen too small, the corresponding G-C melting curvemay exhibit maxima and minima, rather than increasing monotonically as one wouldexpect. Certain choices of the fixed parameters may result in some values of fAT orfGC which are much greater than 1, which is also physically unreasonable. The regionof acceptable values of the parameters is sufficiently small that the shapes of themelting curves presented below can be determined semi-quantitatively withoutfixing these parameters precisely. Though it is possible in the case of extreme choice ofparameters that the separation of the A-T and G-C curves might be nearly twicethat shown in Fig. 13, the approximate parallelism' of the curves is in every casepreserved. Similar preservation of relative shapes is found for the other nucleic acidsamples discussed below.

The only assumptions implicit in equation (3) are the linear relationship betweenhyperchromism and degree of denaturation, and the reduction of the absorbanceincrease to the sum of two independent processes. There is further discussion of thejustification for these assumptions at the conclusion of the Appendix. The results ofthe machine computation show that the error in fitting the experimental values ofLiA(.:\,T) with equation (3) is ofthe order of!%(see Appendix). One ofthe advantages


of th e method is that whatever choice of the two f3 parameters is made, the resultingunique solution is always one of the " best fit" solutions for the data.

The data presented in the previous section have been analysed with the use ofequation (3). In Fig. 13 are presented the A-T and G-O denaturation curves of calfthymus DNA at low ionic st rength. It will be seen that there is approximately a 5°0difference between the values of Tm (A-T) and Tm (G-C). The separation of Tm valuesis quite small compared with the separation of 41°0 found in the ideal homopolymersof A-T and G-O (Marmur & Doty, 1959).

100

90

80

70...... ----" ~

~ ...» >B 'l ....0

--....

c

-- "" ---o 50 / "... /c /"t' / " A40 /

~ /

" A/30[- /

! / AI

20L // A

10 L / /A

A

I A

55 60 65 70Temperature (O()

FIG. 14. Separated A-T and G-C denaturation curves for denatured ca lf thymus DNA,reheated, corresponding to the dispersion curve shown in Fig. 9. Open symbols, A-T. Closedsymbols, G-C. Curves are shown for sev eral choices of paramet ers (see Appendix). 0 , • Lowestvalue of R (0 '834), 76% of maximum possible A-T and G-C base pai rs re-formed ; 6. , A Highestvalue of R (0'838), 76% of maximum possible A-T and G-C base pairs re-formed. Dotted line:A-T curve for R = 0,834, assuming 100 % of G-C pairs re-formed. The A-T curve for R = 0·838and 100% G-C re-formed lies between the dotted line and the line through the open triangles.The G-C curves, a function of R only, are the same as those for the solid circles and trianglesre spe ctively.

The analysis of re -heated denatured calf thymus DNA presents a completelydifferen t result, as shown in Fig. 14. In this case it must be remembered that thedegree of "denaturation" is arbitrarily set equal to zero at the lowest temperat ure ,and to 100% at the highest temperature. This rest rict ion causes both curves to havethe same origin, but does not fix the temperature at which the curves approach100% denaturation, provided that this te mperature is less than t he maximumtemperature used. The A-T and G-O curves of denatured calf thymus DNA divergewidely at low temperatures ; the largest separation of temperatures, a difference ofabout 30°0, occurs at about 40% denaturation. The separation at 50% denaturation,f1Tm , is about 27°0. The separation continues to decrease as the temperature is raised;in the region where the original denaturation occur red , the separation is of the samesize as in undenatured DNA. This analysis shows that, at lower temperatures, themelting behavior of G-O and A-Tis " decoupled" , so that the separation of denaturation temperatures approaches that found when G-O and A-T are complete ly


1001 ~ I

I / 0

90~- /0 0I P 0

80~ / 00/

7+b 0 •

0 0-0 •e

601 •.3

0 •c~ 50.., •c

"~ 40~

30

20

10

45 65 100

Temperature (Oel

FIG. 15. Separated A-U and G-C denaturation curves for yeast S-RNA in 0·005 M-NaCI,0·003 M-cacodylate buffer, pH 6·5. S-RNA concentration 1·25 x 10-& M. Open symbols, A-U.Closed symbols, G-C. Curves are shown for two models (see Appendix). 0, • No interactionbetween G-C andA-T, lowest value of R (0,715); 6., A No interaction, highest value of R (0'800);D, • Interaction between G-C and A-T, highest value of R (0'785); 6., • Interaction, lowestvalue of R (0'715)

30

o

25

60Percentdenatured

FIG. 16. The separation of A-T and G-C denaturation curves, in degrees, as a function of theper cent of A-T or G-C denatured. A Denatured calf thymus DNA, reheated (Fig. 14); • S-RNA(Fig. 15).


independent of one another. The interpretation of this finding in terms of denaturedDNA structure is discussed below.

S-RNA. The A-U and G-C melting curves of amino acid acceptor RNA (S-RNA)isolated from yeast are shown in Fig. 15. Again, the degree ofdenaturation is arbitrarilyset equal to zero at the lowest temperature, and 100 %at the highest. Unlike thecurves for denatured DNA, however, the A-U and G-C curves of S-RNA continueto diverge with increasing temperature. The separation of the two curves as a functionof fraction of material denatured is compared in Fig. 16 with that of denatured DNA.The curves for the two polynucleotides are clearly different.

TABLE 1

Hyperchromic spectra(normalized with respect to the maximum of each spectrum)

Native calf thymus Denatured calf thymus S-RNA§" (miL) DNAt DNAt poly

A-T G-C A-T G-C A-V G-C d(AT)

220 0·50 0·72 0·46 0·88 0·07 0·58230 0·32 0·56 0·34 0·49 0·14 0·56240 0·56 0·68 0·57 0·59 0·48 0·96 0·42250 0·89 0·62 0·83 0·70 0·80 1·00 0·80260 1·00 0·87 1·00 0·89 1·00 0·79 1·00270 0·82 1·00 0·88 1·00 0·89 0·84 0·60280 0·34 0·81 0·44 0·75 0·46 0·84290 0·06 0·31 0·05 0·43 0·07 0·38

Ratio of A-Tor A-V toG-C at 260 miL 2·02 1·97 1·64

t Corresponds to curves of Fig. 13.t Corresponds to open and closed circle denaturation curves of Fig. 14.§ Corresponds to open and closed triangles of Fig. 15.

Spectra. The values of fiAT(;>") and fiGc(;>") obtained from the analysis of equation (3)are the hyperchromic spectra] of the average A-T and G--C base pair, multipliedby the concentration of each. They are shown in Table 1. Though some error is presentin these values, there is no doubt that the hyperchromic spectrum of A-T in nativecalf thymus DNA is somewhat different both from that of the free bases and thatobserved in poly dAT, a result which would be expected on the basis of recent theoriesof the hyperchromic effect (DeVoe & Tinoco, 1962).

4. DiscussionThe preceding results demonstrate that it is possible, with suitable corrections, to

use the variation in absorbance with temperature at a series of wavelengths toseparate from one another the contributions of A-T and G-C base pairs todenaturation. Though corrections must sometimes be made, they are no different inprinciple from the corrections necessary for accurate interpretation of any single"melting curve", whatever the method used to obtain it. For example, continuedtemperature-dependent changes in the properties of poly A and poly U strandsseparated by heating will probably produce errors in optical rotation or viscositymeasurements, as well as in absorption measurements, used to follow the denaturation.

t The hyperchromic spectrum is the difference between the denatured and native spectra.

39

604 G. F E L S E N F E L D AND G. S A N D E E N

The quantitative separation into A-T and G-C denaturation curves reveals that innative calf thymus DNA, the denaturation behavior of A-T and G-C base pairs isclosely coupled ; the interspersion of G-C and A-T pairs brings the mean meltingtemperature of th e A-T up , and that of the G-C down, from their values in thehomopolymers.

The partly ordered st ructure of denatured calf thymus DNA does not behave inthis manner when the temp erature is raised. This is probably becau se the structureconsists of regions of va ry ing lengths of hydrogen-b onded base pairs, randomlyformed and separated by disordered regions in the manner suggeste d by Doty et al.(1959). The disordered regions insulate the ordered regions from one another so thatthe transition is less cooperat ive. The A- T and G-C denaturation curves are mostwidely separated at the lower temperatures. This is to be expected, since the hydrogenbonded regions being disrupted at these temperatures must be rather short and ,therefore, are capable of accommodat ing a rather wide variation in the ratio of G-Cto A-T base pairs. (It is assumed, for simplicity, that only the conventional pairingoccurs.) The effect of this variation in base composition among independent shortordered regions is to produce a large dispersion and a large separat ion of the A-T andG-C curves, approaching that ofthe homopolymers. At higher temperatures, however ,only longer hydrogen-bonded regions are stable and these probably have imposedupon them, in proportion to their length, the requirement that their base compo sitionapproach that of the native molecules. This reduces the likelihood of a large excursionfrom the mean base comp osition of the nucleic acid and the separation of the A-T andG-C denaturation curves accordingly approaches that of native calf thymus DNA athigh t emp eratures.

The curves for S-RNA can be obtained, to a first approximation , by inverting thoseof denatured DNA. This mean s that the longest regions of ordered stru ctur e have thelargest deviations from the mean in base compo sition. This is t he opposite of what onewould expect to find in a randomly re-formed st ruc t ure , as exemplified by denaturedcalf thymus DNA. From the melting point separat ions, it appears that the longestregions mu st consist of sequences of relatively pure G-C, melting independently ofother sequences of relatively pure A- D. The independence of melting might arise ifthese ordered regions were sepa rated from one another by random coil regions, or ifthey occurred in separate molecules. The st ructure would be consistent with theobservation of McCully & Cantoni (1962a) that sequences of G-C base pairs adj acentto other G-C base pairs occur with greater than random frequ ency in rabbit liverS-RNA, and with the more detailed structure proposed by McCully & Cantoni(1962b).

The data for T4 DNA have not been resolved into separate curves, since thedispersion is not much larger than the smallest amount det ectable by present methods.It appears that the regions undergoing denaturation at the lowest temperature inT4 DNA, if they are regions of unusual base composition , mu st comprise a relativelysmall fra ction of the ba ses. The alternative is that the initiating regions have a basecomposition not markedly different from the mean. If a gaussian distribu tion ofconcent rations of independently melting regions is assumed , t he half-width of thedistribution curve can be est imated, since it is possible to show that, to a firstapproximation, the difference between values of Tm at any two fixed wavelengths isproportional to a2 , the square of the standard deviation of the distribution ofindepend ently denaturing units with respect to base composit ion (assuming a gaussian


distribution). If it is assumed that the melting point dispersion of calf thymus DNAarises principally from heterogeneity among molecules and that the dispersion arisingfrom intramolecular denaturation heterogeneity is small compared to this, then themeasurements of calf thymus DNA serve to calibrate the dispersion method, sinceSueoka (1961) has measured the value of a2 for the base composition distribution ofcalf thymus DNA. The assumption that the melting point dispersion of calf thymusDNA arises principally from intermolecular heterogeneity is probably not entirelysatisfactory, since the dependence of dispersion upon ionic strength shown in Fig. 4and Fig. 8 suggests that there is intramolecular heterogeneity of denaturation. Thisobservation is closely related to the findings of Dove (1962), who reported that thechange in breadth of optical density denaturation curves with change in ionicstrength was not accompanied by a corresponding change in the slope of the curverelating Tm to the average mole fraction of G-C content in a series of DNA preparations.

The use of Sueoka's value of a2 thus permits estimation of a lower limit for the widthof the distribution of independently melting units in T4 DNA. Since the dispersion ofT4 DNA is everywhere about 0·1 as large as that of calf thymus DNA under similarconditions, the standard deviation of the distribution is about one-third as great inintact T4 DNA as in calf thymus DNA. Geiduschek (1962) has concluded from thelack of agreement between the observed denaturation curve of T2 DNA and thatcalculated from the theory of Zimm (1960) that some intramolecular melting heterogeneity is present. A qualitative estimate of the effect of introducing the degree ofmelting heterogeneity deduced above suggests that it is sufficient to account for theobservations of Geiduschek.

The insensitivity ofT4 DNA dispersion to shearing shows that breaking the moleculedoes not affect the distribution of independently melting units. At worst, the limits oferror of the denaturation dispersion measurement might permit an increase of 100%in the magnitude of the denaturation dispersion to escape detection. (In almostevery experiment, the dispersion of sheared and unsheared solutions of the samepreparation agreed more closely than the dispersions of two different unshearedpreparations.) This would mean that whatever the standard deviation of the originalT4 distribution, it could not be more than ~2 times as great in the sheared material.The fact that breakage creates no units possessing melting properties markedlydifferent from those of intact DNA may mean that the mean base composition of eachof the pieces is the same as that of the intact molecule. However, it is also possiblethat the breaks have occurred in such a way that they have little effect upon theindependently melting regions existing in the intact molecule. This result thus providesan upper limit for heterogeneity of mean base composition of the fragments in thesheared preparation. If the calf thymus DNA heterogeneity is assumed to ariseentirely intermolecularly, the value of a for the sheared T4 DNA preparation is about2% in G--C composition.

On the basis of the preceding examples, it seems reasonable to conclude that theanalysis of optical dispersion of denaturation provides a sensitive and useful toolfor examining the mechanism of denaturation, the relationship of variation in basecomposition and ionic conditions to the control of this mechanism, the hypochromismof A-T and G-C base pairs in naturally occurring polynucleotides and perhaps, also,the beginning of a physical method for studying the composition of ordered sequencesin nucleic acids.


5. Appendix(a) Mathematical methods

(The authors are indebted to Dr. Norman Shapiro, Computation Branch, N.I.H.,for the following mathematical analysis.)

Equation (3) may be written in the form

(4)or in the form

where ~ is an n x 2 matrix representing the values of f3AT and f3GC at each of n wavelengths, and f is a 2 x m matrix representing the values of fAT and fGe at each of mtemperatures. a is the n x m matrix of observed absorbance increases, LlA(A, T).

If the values of all the elements f3A and f3G in equation (4) were known, the solutionfor the elements fA andfG would be straightforward. In this case, the digital computeris provided with a trial set of f3A and f3Gand tie equations are solved for t, and fG'The sets offAandfG so obtained are used to solh, in turn, for a new set of f3A and f3G'always normalizing so that at the end of each cycle, fA = fG = 1. At the completionof each cycle the parameter T2 is computed,

T2 = 'Zi,j(aij-f3AifAj-f3GJGj)2

where the sum extends over all i and j. In all of the experimental situationsinvestigated so far, this iterative method appears to result in convergence toward asolution. The condition for ending the computation is that T2 should not change insuccessive cycles. When this condition is met in the case of calf thymus DNA, thevalue of

[T2 ] t

'Zi,j(ai j )2

is about 10-2. The resulting set of solutions for the matrices ~ and f generate thematrix a with errors of the order of 1%. These solutions are not unique, since

~G-IGf= a = Wf'where G is a non-singular 2 x 2 matrix, and

(~G-l) = W, (Gf) = f'.

However, if any two linearly independent elements of Ware specified, G is uniquelydetermined, since two elements of f' are already fixed at unity. In practice, thecomputer is programmed to solve for the transformation matrix G given the twoelements of~' (usually the hyperchromic spectral constants of A-T at 250 and 260 mu],and the computer's solution for ~ and f. The transformation is then applied to thecomputer's solution for ~ and fto yield the unique solution possessing the two specifiedelements of~/. Both a and T2 are clearly invariant under this transformation.

(b) Choice of the fixed elements

As stated earlier, the general shape of the A-T and G-C melting curves can bedetermined without any very specific choice of the two fixed elements. Nevertheless,it is desirable to attempt a rational selection of these values. This has been done by


making use of the observation of Marmur & Doty (1959) that there is, to a goodapproximation, a linear relationship between hypochromism at 260 m/-, and basecomposition in a series of natural and synthetic polynucleotides. DeVoe & Tinoco(1962) defined hypochromism as the difference in absorbance between the freenucleosides and the helix, divided by the free nucleoside absorbance. They plotted theresults of Marmur & Doty introducing a 10% correction for the conversion fromfree base to random coil. Assuming a linear relationship, and expressing changes inabsorbance as the difference between random coil and helix, the equation of the linemust be

(6)

where M is the difference in absorbance, at 260 m/-" between random coil and helixfor a given polynucleotide solution of monomolar concentration CT , ET is the molarfree base absorbance at 260 m/-" LiAAT and LiAGC are the values of LiA for samples ofpolymer containing pure A-T and pure G-C respectively at concentration CT , EATand <oc are the corresponding free base molar absorbances, and XGC is the molefraction of G-C base pairs. By definition, (LiA(260 mu) == LiA(A, T) of equation (3),with fAT =foo = 1),

where YAT and YGC are the true contributions at concentration CT of the A-T andG-C pairs to absorbance increase in a DNA with mole fraction of G-C equal to X oo.

It follows that

YAT+XGdYGC-YAT) = LiAAT+XGc{LiAoo_ LiAAT}.ET EAT EGC EAT

(7)

(8)

From the form of equation (7), it is clear that YAT and YGC must be functions of X oosince ET is a function of X Gc' If it is assumed that the dependence of YAT and Yooupon X GC is linear, with no quadratic terms in X oo and if the ratio of zero to firstorder coefficients in X oo is the same for both.] then

AAT A ooYAT = ET'--; Yoo = ET·--·EAT Eoo

Values computed for YAT(260) and yoo(260) of calf thymus DNA from these equationsgive a predicted value of M (260 miz) within 0'5% of that observed, using values of

and

plotted by DeVoe & Tinoco (1962), and values of EAT and EGCfor the ribosides or deoxyribosides taken from Beaven, Holiday & Johnson (1955).

Measurement of the hypochromism of several DNA samples reveals that thehypochromism at 250 m/-, is in every case almost identical with that at 260 mu. This

t Though the linear coefficients derived here are somewhat different in algebraic form fromthose derived for the nearest neighbor interaction model discussed below, the numerical values ofthe coefficients for the two models differ very little.


is true for a range of base compositions extending from 33% to 100% A-T.Consequently, whatever analysis applies to YAT (260) applies equally well to thevalue of YAT at 250 ttu». It follows that

YAT(250)YAT(260)

,sAT(250),sAT(260)

ET (250)ET (260) . (9)

The use of equation (8) to fix ,sAT (260), and of equation (9) to fix ,sAT (250), makespossible the choice of a unique solution for the matrices ~ and f.

(i) Native calf thymus DNA (Fig. 13). The preceding analysis, applied to calf thymusDNA, gives a value of 0·85 for the ratio R = ,sAT (250)/,sAT (260). The value of fJAT (260)is 3360 per mole. The analysis of experimental data reveals that there is no way ofchoosing a ratio, R, between 0·80 and 0·87 which will result in values of fao increasingmonotonically with temperature. The smallest value of R which results in satisfactorybehavior of the functionfao is 0·89 and this is used to obtain the curves of Fig. 13.The corresponding spectral values are shown in Table 1. It is also possible to calculatedenaturation curves corresponding to the approximate upper limit of the ratio R. Thislimit is determined for fixed ,sAT (260) by requiring that all of the hyperchromicspectral coefficients for A-T be positive. This is a somewhat arbitrary requirement,since it is possible that ,sAT (290), for example, might be a negative number. If it isnegative, however, it is almost certainly small in magnitude compared to ,sAT (260), sothat the choice of ,sAT (290) = 0 as an approximate "cut-off" point is appropriate.

(ii) Denatured calfthymu8 DNA (Fig. 14). If it is assumed that the ratio of A-T toG-C base pairs re-formed in denatured calf thymus DNA is the same as that in thenative molecule, then, from M (260), it may be calculated that 0·76 of all A-T andG-C pairs are re-formed. Using the same calculation of ,sAT (260), and the samerestrictions upon the behavior of fao and ,sAT discussed above, it is found that0·83 < R < 0,84, in close agreement with the predicted value, R = 0·85. Results arealso shown in Fig. 14 for the extreme case that all of the G-C bonds re-form, a ratherunlikely possibility. There is almost no change in the restriction upon R, and thedenaturation curves change very little.

(iii) Soluble RNA (Fig. 15). To begin the calculation, it is assumed that the maximumformation of hydrogen bonded A-U and G-C occurs. Unusual bases are excluded fromthis pairing, as are one adenine and one cytosine which are the two terminal bases(Hecht, Stephenson & Zamecnik, 1959; Preiss, Dieckmann &Berg, 1961). Two modelsare possible for the evaluation of ,sAU (260) and of R: either the one described abovemay be used, or in view of the conclusions with regard to S-RNA structure drawn inthis paper, it may be assumed that no interaction between AU and GC occurs, so thatYAU = ~AAU and YGC = ~AGc' The latter model may appear the more reasonable inthis case; in any event the denaturation curves predicted are quite similar for eithermodel. Using the "no-interaction" model, one computes that the absorbance changecorresponds to 96% of the maximum hydrogen bonding originally assumed; withthe base-interaction model, it is 100%. Employing the usual criteria for f and ~A theexperimental limits of R are approximately 0·71 < R < 0·80 for both models. Thevalue of R calculated from the model without interactions is 0·76; the base interactionmodel gives R = 0·91. Denaturation curves are plotted for the extreme values of Rfor both models. The lines have been drawn through the points for the no-interactionmodel at R = 0,80, slightly higher than would be expected if interactions werealtogether absent.


(iv) Some assumptions. In the case of S-RNA and in that of denatured calf thymusDNA, it has been assumed that all of the regions of ordered structure are long enoughso that the hyperchromism is dependent only upon the base composition. Thisassumption appears warranted for S-RNA; if a large fraction of the bases contributedless than the full hyperchromism, more base pairing would be required to accountfor the observed hyperchromism than is theoretically possible. In the case of calfthymus DNA some error is possible; this would affect the shape of the denaturationcurves at low values off, but would be unlikely to cause major changes.

It is assumed in equation (3) that one can treat the hyperchromism arising fromdenaturation as the sum of two separate processes involving "average" hyperchromiccontributions from A-T and G-O base pairs. Thus, it is assumed that the opening ofan A-T or G-O pair contributes a hyperchromism which is not very dependent uponits environment in the molecule. Since the results given in Table 1 and in the precedingdiscussion show that there is some dependence of fJAT and fJGC upon the base composition, a calculation was undertaken to determine the effect of this variation upon thevalues of fAr and fGc. In this calculation the matrix elements used in determiningthe curves of Fig. 13 were divided into two approximately equal groups, with datafrom the low-temperature half of the denaturation curve in one group and data fromthe high-temperature half in the other. The two groups of data were then analysedseparately and the values of fJAT' fJGC' fAT andfGc determined by the usual methods.The two halves presumably contain data for DNA molecules differing considerablyin mean G-O content, and the calculated values of fJ varied at a few wavelengths byas much as 15% of the values given in Table 1. The new values offAT andfGc' however,were relatively insensitive to these changes and the predicted denaturation curvesagreed well with those shown in Fig. 13. Similar results were obtained when the dataof Fig. 14 were analysed in this manner. The largest factor affecting the denaturationcurves in the case of native DNA is the change in the range of values of R giving"acceptable" solutions; dividing the data in half makes possible choice of a slightlylower value of R.

It may be concluded both from the above result, and from the fact that the approximation suggested by Davidson (equation (2)) gives qualitatively excellent agreementwith the results of solution of equation (3), that the assumptions implicit in equation(3) are reasonably satisfactory. It has been suggested to the authors by Dr. S. Lifsonthat a more rigorous approach to this problem would be to express ~A as the sum ofcontributions from loss of nearest-neighbor interactions. Assuming a randomdistribution of base pairs, it is possible to derive a simple expression for ~A as afunction of X GC in terms of three interaction terms for AT-AT, GC-GO and AT-GOneighbors. In the case that the AT-GO term is the mean of the AT-AT and GO-GOterms, the expression reduces to equation (3), although fJAT and fJGC are not necessarilythe hyperchromic spectra of the A-T and G-O base pairs. It must be concluded thatthis is a reasonable first approximation; further study should permit evaluation of thecorrection term.

Finally, it must be pointed out that the behavior of the AT-rich and GO-richregions of DNA may be seen qualitatively, without recourse to mathematical analysis,by inspection of the spectral data. In the case of denatured calf thymus DNA, forexample, it is clear that the absorbance at 290 mfL rises very little compared to thatat 260 mfL in the low temperature region, but rises rapidly at higher temperatures.The curves of Fig. 14 are a somewhat more quantitative expression of this basic fact.


We are grateful for the advice and early collaboration of Professor Peter H. von Hippel,and for the use of his laboratory during the first stages of this investigation. The invaluable contributions of Professor Norman Davidson are also gratefully acknowledged.We wish to thank Dr. Norman Shapiro for his assistance in the mathematical analysisand Mr. Robert Brunelle and Mr. John Shaw for assistance in computer programming.We are indebted to Professor Robert Baldwin for his gift of poly d(AT), to Dr. GiulioCantoni for his gift of yeast S-RNA, to Dr. Maxine Singer for protein analyses, and toDrs. Jon Applequist, Robert Baldwin, Martin Gellert, Shneior Lifson and Philip Rossfor good advice.

REFERENCES

Beaven, G. H., Holiday, E. R. & Johnson, E. A. (1955). In The Nucleic Acids, ed. byE. Chargaff & J. N. Davidson. New York: Academic Press.

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The dispersion of the hyperchromic effect in thermally induced transitions of nucleic acids

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