Calorimetric and spectroscopic investigation of the helix-to-coil transition of a ribo-oligonucleotide: rA7U7

J. Mol. Biol. (1975) 99, 549-565

Calorimetric and Spectroscopic Investigation o f the Helix-to-coil Transition o f a Ribo-oligonucleotide: rATU7 KE~ZTH J. BR~.SnAVEat$,JVT,TA~M. STURT~.V~T§ AND IGNACIO TINOOO, JR~

~fDeloartment of Chemistry and Chemical Biodynamics Laboratory University of California, Berkeley, Calif. 94720, U.S.A. tDel~artment of Chemistry, Douglass College Rutgers University, New Brunswick, N.J. 08903, U.S.A. §DeTartment of Chemistry, Yale University New Haven, Conn. 06520, U.S.A. (Received 30 June 1975, and in revisedform 10 8eIotember1975) The double-strand to single-strand transition of the self-complementary ribooligonucleotideATU~ is investigated by means of differential scanning calorimetry, equilibrium u.v. melting and temperature-jump spectroscopy. I t is found t h a t these different physical teclmiques provide equivalent means for determining the melting temperature of the transition. The calorimetric experiments provide a value of 99.3 kcal (mol double s t r a n d ) - i for the helix-to-coil transition of ATUT. This represents the first direct determination of the enthalpy change accompanying such a transition in a ribo-oligonucleotide. Ass, mlng all fourteen base-pairs to be equivalent, this corresponds to 7-1 kcal (mol A ' U base-pair)- 1. Comparison with data obtained from polymeric systems permits the conclusion t h a t an A . U base-pair in an oligomer is energetically equivalent to an A . U base-pair in a polymer. The data also appear to indicate t h a t there is no significant variation of the AH with salt concentration. Values are also calculated for ,t0 and AS. Values of AHv.m (van't Heft enthalpy change) are derived from the spectroscopic and calorimetric data and compared with the AH obtained directly from the calorimetric experiment. This comparison reveals t h a t the thermally induced helix-to-coil transition of ATU7 is not a two-state process. Calculations presented in the Appendix indicate t h a t the transition is better represented by a model in which terminal base-pair fraying and intermediate states are taken into account. The relative reliability of the various optical techniques is discussed. I t is noted that AHoal. is in better agreement with the AHv.H. derived from a log c versus l#m plot (c is concentration) than from the slope at the midpoint of an ~ versus melting curve, where ~ is the fraction in single strand. I n addition, it is better to use a sloping rather than a fiat low-temperature baseline to evaluate absorbance vsraua temperature profiles. Further analysis of the data permits the determination of values for s and ~s (or ~). a is the equilibrium constant for formation of an A . U base-pair in an already existing helix and ~8 (or K) is the equilibrium constant for bimolecular helix nucleation by an A. U base-pair. 1. Introduction Our u n d e r s t a n d i n g of the structures a n d the conformational transitions of R N A molecules has been g r e a t l y enhanced b y the synthesis a n d investigation of a v a r i e t y of ribo-oligonucleotides. These compounds are useful models for s t r u c t u r a l features

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£ound in naturally occurring ribonucleic acids. Quantitative thermodynamic d a t a on these model compounds m a y eventually allow prediction of the most stable secondary structure of R N A molecules based purely on their p r i m a r y sequences (Tinoco e~ al., 1973; Borer et al., 1974). To date, the vast majority of the pertinent d a t a have been obtained from optical studies. I n general, experimental melting curves are evaluated b y assuming some model for the conformational transition and then subjecting the optical data to a statistical thermodynamic analysis. Quite often discrepancies result from the use of different physical models for the interpretation of basically consistent data. I n the majority of eases the "all-or-none" model is assumed. However, it is quite possible t h a t this "two-state" model does not adequately reflect the nature of the transition under investigation. Furthermore, the statistical analysis of the optical d a t a usually involves the rather dangerous assumption of a temperature-independent enthalpy change. This paper reports the first direct determination of the energy change accompanying the double-strand to single-strand transition of a ribo-oligonucleotide. (Henceforth, this transition ~ be referred to as a helix-to-coil transition.) The results not only directly provide a model-independent value for the enthalpy change, b u t also allow a test of the all-or-none model for the transition. I n addition, ahsorbance versu~ temperature and temperature-jump studies were carried out. Comparison of the calorimetric and the spectroscopic results permits i m p o r t a n t conclusions on the nature of the transition and the relative reliability of the various optical techniques.

2. M a t e r i a l s a n d M e t h o d s

Ca) S y ) a h e ~ o,f (~4p)~(up)6u A mixture of (Ap)n oligomers was obtained by limited alkaline hydrolysis of poly(A). This mixture of oligomers was treated with alkaline phosphatase in order to remove the 3' terminal phosphates. The various chainlengths were then fractionated on a DEAE Sephadex A25 co],~mn by elution with a linear gradient of 0 to 0.3 M-NaCI in 7 M-urea (TomllnRon & Tener, 1963). The desired (Ap)eA peak was identified by paper chromatography and the appropriate tubes were pooled. The U residues were added to the 3~ end of the (Ap)eA by reaction with UI)P in the presence of primer-dependent polynucleotide phosphorylase. A small amount of radioactive UDP was included in order to facilitate subsequent peak identification. The conditions for this reaction were approximately those described by Thach (1966). Maximization of the product resulting from the addition of 7 U residues was found to occur by allowing the reaction to proceed for about 4 h at 37°C. The reaction product (a mixture of ATUn co-polymers) was fractionated on a DEAE Sephadex A25 colnmn by elution with a linear gradient of 0 to 0.3 M-NaC1, 0.01 M-formate, 7 M-urea, adjusted to p H 3.4. The desired A~U7 peak was identified by digesting a small amount of the first few peaks with RNase A. The hydrolysis product was separated by paper chromatography and the radioactive Up/U ratio was determined thus revealing the chainlength of the peak (Martin e~ aL, 1971). In order to avoid any contamination from ATUe or ATUe only the central fraction of the ATU7 peak was pooled. Desalting was accomplished by using 1 M-triethy|arnlne bicarbonate to elute the sample from a 50 ml DEAE Sephadex A28 colnmu. A rotary evaporator was used to remove the eluting salt. Final traces of the triethylamine bicarbonate were removed by several washes with methanol. Passage through a Biogel P2 eo]nm~ completed the desalting process.

T H E H E L I X - T O - C O I L T R A N S I T I O N OF rATU~

561

(b) _ ~ 6 m s n ~ All measurements reported in this paper were carried out in a buffer system consisting of 1 ~[-NaCI, 0.01 z . s o d i u m phosphate, a n d 10-4 ~-sodinm EDTA, adjusted to p H 7. The concentration of the oligomer was spectrophotometrieally determined using the 25 a n d 60°C extinction coefficients (~) per monomer reported b y Borer (1972) for A6Ue. Considering t h a t the • value per monomer of A4U4 is essentially identical to t h a t of A6Ue, we assume t h a t the extinction coefficient per monomer for ATU~ is very nearly equal to t h a t reported for AsTEs. Triplicate determinations on the ATU7 stock solution led to a n average calculated concentration of 4.38 x 10- 4 ~ in single strand. This ATU7 stock solution was used for all calorimetric a n d equilibrium u.v. experiments reported here. After each experiment the hypochromicity of the solution was checked in order to be certain t h a t no significant degradation of the oligomer h a d occurred. The percentage hypoehromicity of the A~U7 was found to be 22 at 260 nm. This is in good agreement with the range of values of 22~/o a n d 24~/o found b y Martin e~ ~ . (1971) for the series of AnTJn copolymers, where n = 4 to 7. The differential scannlng calorimetry was carried out a t Yale University on a n i n s t r u m e n t which has previously been described in detail (Danforth et ~ . , 1967; Tsong e~ ~ . , 1970). There are 2 p l a t i n u m cells, one of which serves as the reaction cell while the other serves as the solvent reference cell. I n a given transition experiment, one obtains d a t a at temperature intervals of 1 rnin on the total energy fed back to the reaction cell. These data (along with the k n o w n concentration of the solute) permit the construction of a n enthalpy (mol- ~) v e r s ~ temperature curve as shown in Fig. 1 a n d a specific heat verona temperature curve as shown in Fig. 2. E q u i l i b r i u m u.v. absorbance melting curves were measured a t 260 n m using a n automarie recording spectrophotometer (Gilford Instruments). The temperature was increased continuously at a rate of 13 deg. C/h b y means of a motor-driven thermoregulator. Use of a 0.2 m m pathlength cell allowed these curves to be deterrn~ned at the same concentration as t h a t of the calorimetric experiment (4.38 X 10- 4 ~ in single strand). The temperature-jump experiments were performed on a n apparatus t h a t has been previously described b y Eigen & de Maeyer (1963) a n d Gralla & Crothers (1973). These relaxation experiments were carried out on a single diluted sample of the ATU~ stock solution (10.8 X 10- e ~ i n single strand) in the same buffer as t h a t used for the calorimetric a n d the equilibrium u.v. melting studies. We t h a n k Professor D. M. Crothers for the use of this instrument. 120

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FzG. I. Ca]orimetris enthalpy v s r ~ temperature transition curve for rATU~ in 1 ~-Na +. The strand oonoentration is 4.38 x 1 0 - ' ~.

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FIG. 2. Calorimetric heat capacity curve for rAvU7 in 1 M-I~Ta+ . The strand concentration is 4.38

x I 0 - 4 z~.

(c) Tre~ment of t h e

data

I n order to derive c a n ' t Hoff enthalpy values from either the optical or calorimetric data, the experimental curves (shown i n Figs 1 a n d 5) m u s t be converted into = v e r s ~ t melting curves, where ~ represents the fraction in a single strand. This conversion is accomplished b y assnm~ng t h a t the fractional change i n either enthalpy or absorbance a t a n y temperature is proportional to the extent of reaction at t h a t temperature. Thus a value of ~ can be obtained at a n y temperature b y simply taking the ratio of the distance between the 2 baselines a n d the distance between the lower baseline a n d the experimental curve. I n such a treatment, the melting temperature (~m) is defined as the temperature a t which ~ equals 0.5. E v a l u a t i o n of the resulting ~ v e r ~ s t curve allows one to calculate the c a n ' t Hoff cnthalpy change for the transition. The details are described below. W h e n 2 strands of a self-complementary molecule (i.e. AvUT) combine in a n all-or-none fashion to form the fully bonded helix, the equilibrium constant m a y be written as

K

-/2

=

(1

--

cc)2CT '

(1)

where GT is the total strand concentration and ~ represents the degree of conversion of the initial into the final state. The variation of this equilibrium constant with temperature provides a means for determlnlng the c a n ' t Hoff enthalpy (AHv.~.) according to the expression: 01n K 0~

~Hv.H. --

RT s

"

(2)

Equations (1) a n d (2) can be combined to yield the following expression for the c a n ' t Hoff enthalpy change accompanying a helix-coil transition for self-complementary strands.

~Sv... = 6R~m(a ~/o ~),=.

(3)

Thus, if the slope of a n ~ vsrsus t plot is evaluated a t the melting temperature, the v a n ' t Hoff enthalpy change accompanying the transition can be calculated from equation (3). I t should be emphasized t h a t the exact value of AHv.~. determined b y this method will depend upon the choice of the pre- a n d post-transition baselines assigned to the absorbance versua temperature curve. The results presented i n a later section illustrate this point.

THE

HELIX-TO-COIL

TRANSITION

O F rATU7

558

3. R~ults (a) Oalorimetrio and spectrosco'trio melting temperatures A melting temperature based upon the calorimetric data can be obtained from either Figure 1 or Figure 3. In Figure 1, the tm is defined as the temperature at which the experimental curve bisects a vertical line drawn between the extrapolated baselines. In Figure 3, t m is simply the temperature at which ~ equals 0.5. Analysis of either of these curves leads to a tm value of 45.5°C for the helix-to-coil transition of ATU7 in 1 ~-NaC1. A melting temperature based upon the spectroscopic data can be obtained from the u.v. melting curves shown in Figure 4. Curve A represents the u.v. melting curve derived from the absorbance versus temperature profile by assuming a fiat lowtemperature baseline (also referred to as a pre-baseline). Curve B represents the

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F i e . 3. Fractional completion of t h e transition as a function of temperature. D a t a for this curve wore derived from t h e calorimetric e n t h a l p y versus t e m p e r a t u r e profile (Fig. 2).

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FIG. 4. Fractional completion of t h e t r a n s i t i o n as a function of t e m p e r a t u r e . D a t a for these curves were derived from t h e o.D. versus t e m p e r a t u r e profile (Fig. 6). ( O ) D a t a o b t a i n e d from Fig. 5 using a fiat pro-baseline; ( $ ) d a t a o b t a i n e d from Fig. 5 using a sloping pro-baseline (0.2% per dog. C).

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corresponding u.v. melting curve in which the low-temperature baseline is taken to have a slope of 0 . 2 ~ per deg. C. The tm as determined from curve A is 45°C while t h a t determined from curve B is 47°C. This range of 2 deg. C probably represents a reasonable upper limit for the error in tm introduced b y the selection of different low-temperature baselines for evaluation of an absorbance versus temperature curve. The good agreement between the spectroscopic and the calorimetric melting temperatures is important to note. These results represent the first direct evidence t h a t these two different physical techniques in fact provide equivalent means for determining the melting temperature of thermally induced transitions in ribooligonucleotides. This is a matter of considerable importance since m a n y of the 'thermochemical analyses of optical melting curves depend upon the value of the melting temperature. Since the temperature-jump experiments were carried out at much lower concentration, it is not possible to compare directly the tm value derived from t h e relaxation experiments with those determined b y equilibrium techniques. Nevertheless, it should be noted t h a t a t= of 33.8°C can be calculated from the differential melting curve shown in Figure 6 t. This value is consistent with the t= values for ATU 7 as determined b y Martin d al. (1971). (b) Calorimetric enthalpy data Figure 1 shows one of the calorimetrically determined transition curves. T h e enthalpy change at the tm is given b y the height of the vertical line between the two extrapolated baselines. The slopes of the pre-and post-transition baselines were set to correspond to an excess heat capacity of 52.6 cal deg -1 mo1-1 as suggested b y the experimental heat-capacity curve (see Fig. 2). This treatment resulted in an enthalpy value of 100.8 kcal (reel double strand)- x for the transition. A second calorimetric run resulted in a closely agreeing value of 97.8 kcal (mol double strand)-1. An average calorimetric value of 99.3 keal (reel double strand) -~ was assigned to the helix-to-coil transition of ATU 7 (see Table 1). I f one assumes all fourteen base-pairs to be equivalent, then each A . U base-pair contributes 7.1 kcal m o l - L The calorimetric data can also be used as a basis for calculating v a n ' t H e f t enthalpies. Conversion of the two experimental zJH versus t curves into ~ versus t curves allows calculation of zJHv.m values from equation (3). The first two entries in Table 2 are based upon such a calculation. I t should be noted t h a t even though TABLE 1

Calorimetrically ddermined enthal~y changes Experiment no. 1 2 Average

4H, sl. (at ~ =tm) (keal reel- 1) 100.8 97-8 99.3

~fThe t~ is not simply the maximum in the curve but rather must be calculated using a van't Heft treatment (see Gralla & Crothers, 1973).

THE

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TRANSITION

O F rATU7

565

TABL~ 2 Calculated van't Ho ff enthal/l~J changes E n t r y no.

Method of analysis

ABv.jz , (keal m o l - z)

1

Evaluation of slope a t $= of melting ourve derived f r o m / I H versz~s ~ o u r v e 1

66.5

2

Evaluation of slope a t t= of melting curve derived f r o m / I H v e r s u s ~ o u r v e $

79.8

3

E v a l u a t i o n of slope a t t= of melting curve derived from o.D. v e r ~ $ curve using a fiat pre-baseline

57.4

4

Evaluation of slope a t tm of melting ourve derived from o.D. v s r a u a t o u r v e using a sloping pre-baseline

70.3

5

E v a l u a t i o n of differential melting ourve obtained from t e m p . - j u m p d a t a

78.3

the two calorimetric experiments result in closely agreeing values for the total enthalpy change, small differences in the overall shapes of t h e / I H v e r ~ t curves significantly affect the calculated values for the van't Heft enthalpies. (c) Equilibrium u#raviolc$ melting data Figure 4 shows the ~ versus t melting curves derived from the experimentally determined absorbance versus temperature profile (Fig. 5) using different lowtemperature baselines. Evaluation of these two curves by means of equation (3) results in ziHv. m values that differ by almost 20% (entries 3 and 4 in Table 2). Thus, in contrast to the small effect on the value of t=, the calculated van't Heft enthalpy data are significantly affected by the choice of the low-temperature baseline. !.00 0 ('4

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FZO. 5. Equilibrium absorbanoe v e r ~ t e m p e r a t u r e transition ourve for rATUv in 1 ~r-Na + . The s t r a n d oonoentration is 4.38 × 10- 4 ~r 37

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(d) T env~erature.jwnp data The final van't Heft enthalpy value in Table 2 is based upon temperature-jump experiments. Temperature-jumps of 3 to 4 deg. C were carried out over a temperature range of 5 to 4()°C and monitored at 266 nm. Plate I shows a typical oscilloscope trace of the change in percentage transmission versus time. In each experiment one slow and one very fast relaxation effect was observed. Analysis of the oscilloscope trace allowed the determination of the fractional absorbance change associated with each of these two effects. We assume that the slow effect corresponds to the co-operative component of the transition, while the very fast effect could be due to a variety of phenomena, including singie-strand unstacking and/or end-effects ("fraying"). These fast effects probably correspond to the processes that give rise to the sloping pre- and post-baselines found in the integral melting curve. The important point is that the temperature-jump technique allows one to resolve kinetically these two effects and thereby permits the construction of a differentiated melting curve that corresponds only to the slower co-operative component of the transition (see Fig. 6). This allows an analysis of the transition that 60 50-

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Average temperature (°C) FIG. 6. Differential t h e r m a l t r a n s i t i o n profile d e t e r m i n e d b y t e m p e r a t u r e - j u m p for rATU~ a t 1 M-Na + . T h e f a s t effect h a s b e e n s u b t r a c t e d o u t a n d o n l y t h e slow effect is s h o w n . T h e s t r a n d c o n c e n t r a t i o n is 10.8 × 10 - e M.

does not depend upon the pre-and post-baseline extrapolations encountered in equilibrium melting curves. However, it should be emphasized that the van't Hoff LJH calculated exclusively from the slow component of the differentiated melting curve only corresponds to the co-operative part of the transition and therefore does not include any energy contribution due to rapid end-effects. Depending upon the particular system studied, end-effects may or may not be significant. For ATUT, this matter is examined in greater detail in the Appendix. The shape of the differential melting curve shown in Figure 6 is typical of a highly co-operative transition and generally reflects the hyperchromism which accompanies the conversion of an ordered double helix to disordered single strands. Similar behavior has been previously observed by Craig d al. (1971) and Gralla & Crothers (1973). The van't Heft enthalpy change for the transition can be evaluated from this curve by the method of Gralla & Crothers (1973) and results in a value of 78.3 keal mol-z, It should be emphasized that no baseline extrapolations were necessary

PLATE I. O b s e r v e d r e l a x a t i o n signal a t 266 n m for t h e m e l t i n g of A 7 U 7 in 1 M-NaC1. T e m p e r a t u r e j u m p e d f r o m 32.1°C to 35-8°C. T h e h o r i z o n t a l s e n s i t i v i t y is 20 m s / c m . T h e v e r t i c a l s e n s i t i v i t y is 20 m V / c m for t h e u p p e r t r a c e a n d 10 m V / c m for t h e lower trace. T h e s h o r t signal n e a r t h e lower left c o r n e r r e p r e s e n t s t h e b a s e l i n e before t h e t e m p e r a t u r e - j u m p . E x t r a p o l a t i o n of a s e m i l o g a r i t h m i c plot o f t h e slow a b s o r b a n c e c h a n g e v e r s e , s t i m e a l l o w e d p a r t i t i o n i n g of t h e t o t a l a m p l i t u d e ( 100 m V ) i n t o 48 m V for t h e slow effect a n d 52 m V for t h e f a s t effect. T h e a b s o r b a n c e o f t h e s o l u t i o n is 1.4 a t 260 n m a n d 50°C.

[fadng p. 556

THE HELIX.TO.COIL

TRANSITION

OF rAvU7

5M

for determining this van't Hoff enthalpy change. It is of interest to note that this enthalpy value is more consistent with the ~Hv.H. value derived using a sloping rather than a fiat pre-baseline (see Table 2). This lends support to the selection of a sloping pre-baseline for the evaluation of equilibrium u.v. melting curves. In snmmary, inspection of Table 2 reveals that, depending upon the experimental technique and method of analysis employed, the calculated van't Hoff enthalpies can vary by as much as 20%. However, the important point is that in all cases the calculated van't Hoff enthalpies are considerably lower than the calorimetrically determined enthalpy (see Table 1). The significance of this disparity is discussed in a later section.

(e) Thermodynamic laarameter8 (i) Caleula*ion oI K(tm), s(t=) and fl According to the all-or-none approximation, for an equilibrium of the form 2 M ~ - D~,

(4)

where M is the single strand and DN is the fully bonded filmer with N base pairs, the equilibrium constant can be written as

K

=

fi8N,

(5)

where the formation of the first base-pair between the single strands has an equilibrium constant of ~a and all subsequently formed base-pairs have all equilibrium constant of a. It is of interest to determlne values of fl for helices of different base-composition since this parameter should give us some insight into the nature of the helix initiation process. As can be seen from equation (5), knowledge of K and * at a given temperature is required for the determination of ft. The value of K at the melting temperature can be determined readily from equation (1). At the melting temperature, ~ is equal to 0.5. Thus at tin, equation (1) reduces to

K,m -- 1/o~.

(6)

Since the total strand concentration GT in these experiments is 4.38×10 -~ M, K~= is equal to 2.28 × 10 ÷ 3 ~ - 1 at t m = 45-5°C.

In the notation originally developed by Zimm & Bragg (1959), 8 represents the equilibrium constant for adding one base-pair to an already existing helix. The general method for calculating, makes use of polymer data and involves a simple van't Hoff treatment with a temperature-independent enthalpy change. For this calculation, the t~ of poly(A)-poly(U) at 1 ~-NaC1 is taken to be t ~ = 78°C (Kr~kauer & Sturtevant, 1968) and the enthalpy change is assigned the average calorimetrically determined value of 7.1 kcal (tool base-pair)-1 reported here. These data are used to calculate 8 at the t= of the oligomer by ma~ing use of the following van't Hoff expression: ~H log *tin = 2.3R { 1/tin - - 1/t=~}.

(7)

This treatment results in a n , value of 2.83 at t= = 45.5°0. These values o f , and K at the melting temperatures can be used to caleulafo ft.

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In the notation of Z l m m & Bragg (1959), ~ represents the dlrnluufion of the equilibrium constant a for forml.g the firstbase-pair between two complementary single strands. Using the values determ;,ed for Ktm and stm in equation (5), ~ can be calculated to be 1.1X 10 -8 M-1 at 45.5°C. Comparison of fl with previously reported values is presented in the Discussion. Sche~ler eta/. (1970) have proposed an alternative formulation for the thermodynamic parameters. They reason that an isolated base-pair should be thermodYnamically different from a stacked base-pair. Therefore, they suggest that one should not express the equilibrium constant for forming an isolated base-pair (helix nucleation) in terms of the equilibrium constant for helix propagation. Instead they propose assigning the equilibrium constant K for forming an isolated base-pair in an intcrmolecular reaction. In their treatment, K is expressed in units of A8 per molecule and simply replaces the ~a term of the conventional formulation. One advantage of using K rather than ~s is that its temperature dependence is simpler to interpret than that of ft. We obtain a value of K = ~s ---- 3-1 x 10-8 M-1, which corresponds to a value of 5.2 A 8 per molecule for ATU7. (ii) Cal~lo~ion of ~dG and .'t8 for formation of an A . U base-pair In the previous section, s was determined to be 2.83 at t = 45.5°C. This value can be used to calculate AG ° in accordance with the equation A G ° = --RTlns. This treatment leads to a value of --0.66 kcal tool- 1 for the standard free energy change accompanying the formation of an A . U base-pair at 45.5°C. Using the integrated form of the van't Hoff equation and the calorimetrically determined AH reported here, ZG ° can be calculated at 25°C. A value of --1.1 kcal per tool of A . U base-pair formed is obtained. This compares favorably with previously reported values (Tinoco et uL, 1971; Borer eta/., 1974). The entropy change can be calculated from the value of AG at 45.5°C and the calorimetrieally determined enthalpy change using the equation AG

=

AH

--

tAS.

This results in a value of --20.2 cal deg -1 mol -x for the formation of an A . U basepair, which compares well with the value of --23 cal deg-1 (mol base-pair)-1 reported by Rawitscher e$ a/. (1963) and the value of --23.5 cal dog -1 (mol base-pair) -1 reported by Borer d al. (1974). 4. D i s c u s s i o n

(a) The entha/py change It is of interest to compare the enthalpy of formation of an A . U base-pair reported here with values reported by other investigators. It should be noted that all previous calorimetric studies have been carried out on polymeric systems. The results of these earlier calorimetric investigations are s-mmarized in Table 3. These values are in generally good agreement with the 7.1 kcal (mol base-pair) -1 (or 7.6 kcal (mol stack) -1) found in this investigation. Such direct comparisons are important in any attempt to determine whether A . U base-pairs in short helices (such as are found in tRNA) behave slml]arly to the A . U base-pairs of poly(A).poly(U). Significantly,

ti59

T H E H E L I X - T O - C O I L T R A N S I T I O N OF rAvU~

TABL~ 3 2¢e,m~a

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~ o r i m e t r i o 8tudie.s on pelymerio systems

AH Reaction

Method

Conditions

Real (mol A . U

Reference

base-pair)- x Poly(A)+poly(U)-~ Poly(A) .poly(U)

~#i~ng Calorimetry

0.11 z~-K+ t~ = 58°C

7.6

Poly(A) .poly(U)-~ Poly(A)+poly(U) Poly(A) .poly(U)-> Poly(A)-[-poly(U)

Heat capacity Calorimetry Heat capacity Calorimetry

0.06 ~¢-Na+ t~ ----49°C 0.018zc-Na+ tm ----44"5°C

6.8 7.38

Rawitseher st aL (1963); Ross & Seruggs (1965) Neuman & Aekerman (1967) Krakauer & Sturtevant (1968)

based upon the results reported here, one can conclude t h a t an A . U base-pair in an oligomer of chaiulength 14 has essentially the same energy as t h a t of an A. U basepair in the polymer. Further comparisons can be made with published enthalpy values indirectly derived from optical studies. Martin d al. (1971) have spectroscopically studied the helix-to-coil transition of AnU n where n varies from 4 to 7. These authors made use of the all-or-none model in order to analyze their optical data. T h e y converted their absorbance versus temperature profiles into melting curves and used equation (3) to calculate the v a n ' t Hoff enthalpy change for the transition. This method of analysis resulted in a value of +5-5 kcal (reel A . U base-pair) -1. However, the v a n ' t H e f t enthalpy change can also be obtained from the concentration dependence of the t m according to the expression: 11~' = llt + -~Z~Hv... In ol~',

(8)

where c and 0' represent concentrations. A plot of I/t= versus log o should be linear with a slope equal to 2.3R/AH. B y using this method of analysis, Martin d ¢g. obtained a value of 7.6 kcal (reel A . U basepair)-x. I t should be emphasized t h a t both methods for evaluating the optical data (log o versus 1/tin and (0a/0t)~m) are based upon a two-state model. The fact t h a t the two methods of analysis result in significantly different values of AHv.H. is a m a t t e r t h a t requires further investigation. However, it is of interest to note t h a t the calorimetric data reported here are consistent with the v a n ' t H e f t enthalpy derived from the concentration dependence of the melting temperature. Additional important information can be derived b y a more detailed comparison of the results of this investigation and the data of Krakauer & Sturtevant (1968) on poly(A).poly(U). These workers found an aTparent temperature-dependent enthalpy change for the transition of poly(A).poly(U) ~- poly(A) + poly(U) which could be described b y the equation AHtffi = --0.073 tm2. However, since they studied the transition as a function of sodium ion concentration, it was not possible to separate the effect of the cation concentration on AH from the e f f e c t of temperature on AH. As a result, one could not conclude whether a true temperature dependence was being observed for the enthalpy.

560

K. J. BRESLAUER

ET

AI,.

However, we can make a direct comparison of enthalpy changes for poly(A) •poly(U) in 0.018 M-Na + (tm = 44.5°C) and ATU7 in 1 M-Na + (tin = 45"5°C). The value of 7.38 kcal (tool A . U base-pair)-1 for poly(A)-poly(U) is close to the value of 7.1 kcal (tool A . U base-pair) -1 for ATUT. This comparison suggests that at constant temperature there is no significant variation with salt concentration of the enthalpy change associated with the formation of an A . U base-pair. Bloomfield et aL (1974) came to a similar conclusion by compiling and comparing previously published results on calorimetric mixing experiments with calorimetric heat capacity measurements at various salt concentrations and comparable temperatures. (b) Heat capacity Bloomfield et al. (1974) tabulated published data on the heat of forming a poly(A). poly(U) helix from poly(A) and poly(U) single strands at various temperatures. I t appears that the reaction has a significant heat capacity. This conclusion is not supported by the present investigation. Examination of Figure 2 indicates t h a t the heat capacity of the initial and final states is approximately equal, so that ACT (change in heat capacity at constant pressure) for the reaction is probably quite small. This is consistent with the ACT value o f - - 8 4 - 6 ca] deg -1 tool -1 reported by Krakauer & Sturtevant (1968) for the helix-to-coil transition of poly(A), poly(U) at 0.018 M-Na + and 44.5°C. However, analysis of the AC T by this technique is subject to some uncertainty due to the difficulty in accurately measuring the slopes of the low- and high-temperature regions of the curve. Therefore, additional calorimetric heatcapacity measurements should be carried out over a range of concentration in order to investigate more directly the possibility of a temperature dependent enthalpy change. Nevertheless, if we assume t h a t Krakauer & Sturtevant were observing a temperature-dependent AH, then their reported value of 8-20 kcal (tool base-pair) - 1 at 58.2°C (and 0.104 M-Na +) can be used in conjunction with the data reported here to determine a value for AC T. This approach results in a calculated AC~ of 864-35 cal deg- x tool- 1. In this connection the recent calculations of Levine (1974) are of interest. He assigned AC T values of 0, 30, and 50 cal deg- 1 tool- 1 to the helix-coil transition of the AnUn oligomers studied by Martin et al. (1971). He found t h a t the assignment of these heat capacities did not significantly affect the A H values calculated from either the slope of the transition or the concentration dependence of the tm. (e) Nature of the transition The calorimetric results provide an important means for testing the validity of the all-or-none model (Sturtevant, 1969). I f the van't Hoff enthalpy differs significantly from the calorimetric enthalpy, then the all-or-none model is an inadequate representation of the transition. Agreement of the van't Hoff enthalpy with the calorimetric value is a necessary and sufficient criterion for the validity of the two-state model. I t should be clear that the existence of any significantly populated intermediate states would lead to a broadening of the optical melting curve and a reduction in (da/clt) t ffitin. This reduction in the slope of the melting curve will, according to equation (3), result in a lower calculated value for the van't Hoff enthalpy. Thus, in general, any departure from two.state behavior will lead to a reduced ZJHV.H., so

THE

HELIX-TO-COIL

TRANSITION

OF rAIU~

{161

t h a t AEv.H. < AEca,, provided there is no intermolecular co-operation as in a phase transition. In the transition under investigation, the calculated van't Heft enthalpies range from 57 to 79 kcal mol- z with the temperature-jump value of 78 kcal mol- z probably being the most reliable. This should be compared with the average calorimetric value of 99.3 kcal (reel double strand) - z. Clearly Atto=I. > AHv.H.. This demonstrates t h a t the thermally induced helix-to-coil transition of ATU 7 in 1 M-NaC1 is not a two-state process. Further evidence in support of this conclusion comes from a comparison between experimental melting curve derived from the calorimetric data and a melting curve calculated on the basis of the all-or-none model (see Fig. 7). Examination of Figure 7 reveals that the experimental melting curve is a good deal broader (less co-operative) than the melting curve calculated on the basis of the two-state model. This comparison further supports the conclusion t h a t the transition is not a two-state process. I00 o 9O o "~ 80 zo

//

/

f

~

f

~ 60 .E 50

.~ 40 o 50 2O IC 0

I0

20

30

40

50

60

70

80

Temperoture (°C)

(

(

FzG. 7. Comparison of t h e experimental melting curve derived from the calorimetrie d a t a ; see Fig. 3) a n d t h e melting curve calculated on the basis of the 2-state model

).

In this connection it is of interest to note the recent results of Borer et a l (1974). These investigators used nuclear magnetic resonance in order to study the melting behavior of the serf-complementary ribo-oligonucleotide A2GCU2. Their results clearly indicate t h a t the terminal A . U base-pairs melt before the internal A . U base-pairs. I f this behavior is general, then perhaps the terminal A . U base-pairs in ATU 7 are melting prior to the more co-operative disruption of the internal base-pairs. Temperature-dependent nuclear magnetic resonance studies are being carried out in order to examine this possibility. A more quantitative treatment of such end effects is given in the Appendix. (d) H d i x initiatio¢ In order to compare the helix initiation parameter determined in this work with values reported in the literature, it will be useful to speak in terms of the product of fl and 8. In the notation of Scheffler e~ aI. (1970), this product can be represented as x and has units of/13/molecule. For the fl and 8 values found in this investigation (fl = 1.1 × 10 -a M-z and 8 ---- 2-83), f18 (or K) equals 3-1 x 10 -3 M-z (or 5.2 A3/molecule). This compares favorably with the K value of 7 21a per molecule reported by Scheflter et al. (1970) for the monomer-dimer equilibrium of d(TA)N.

~62

K. ~. B R E S L A U E R

ET

AL.

R e c e n t l y , Appleby & Kallenbach (1973) derived thermodynamic data on the A,U, system by fitting calculated melting curves with experimental results and tatrlng into account singie-strand stael~iu~. They found a 8s value of 7.6 X 10 -8 ~-1. Levine (1974) used a standard statistical thermodynamic approach and varied J H and 8s (or K) in order to bring into agreement the calculated and experimental melting curves for A,Un where n varied from 4 to 7. Although he did not find a unique fit, he reports an average 88 value of 0.78×10 -8 M-1 when the enthalpy change is taken to be 7.0 kcal (tool base-pair)-1. Craig et aJ. (1971) used temperature-jump kinetics to study the helix-to-coil transition of A,Un molecules at 0.25 M-Na +. They report an average 88 of 2.5 × 10- 3 M - 1 which is essentially independent of temperature from ll.I°C to 21.3°C. This is in good agreement with the value of 3.1 × 10 -3 M-1 determined in this work at 45.5°C. In this connection it should be noted that if the enthalpy change accompanying helix initiation (the AH for the intermolecular formation of the first base-pair) is taken to be zero, the 8~ values should not exhibit a temperature dependence. This is generally thought to be the case for bimolecu~r helix initiation in which base-water hydrogen bonds are exchanged for base-base hydrogen bonds. The net energy change for such a differential hydrogen bond should be quite small. The reasonably good agreement found here for 8s values determined at different temperatures would appear to support this physical picture. 5. Conclusion The calorimetric results reported here provide the first direct measure of the enthalpy change accompanying the helix-to-coil transition of a ribo-oligonucleotide. Significantly, this euthalpy value was found to be consistently greater than the van't Hoif enthalpies derived from the spectroscopic and calorimetric data by application of the all-or-none model. This allowed the conclusion that the helix-tocoil transition of ATU7 involves more than just two states. In fact, based upon the calculation presented in the Appendix, the transition can be better represented by a model in which the terminal base-pairs are specifically destabilized rather than by the standard intermediate-state model. In general, calorimetric results such as those reported here should help lead to improved intermediate-state models for interpreting conformational transitions in nucleic acids b y providing a model-independent parameter with respect to which theory can be normalized. The comparison between the calorimetric and spectroscopic enthalpy values also allowed important conclusions to be reached regarding the best methods for evaluating optical data on transitions in which intermediate states are significantly populated. Furthermore, the data indicate that u.v. spectroscopy and calorimetry provide equivalent means for determining the melting temperature of a thermally induced transition in a ribo-oligonucleotide. Comparison with polymer data reveals that an A . U base-pair in an oligomer is energetically equivalent to an A . U base-pair in the corresponding polymer. In ~ddition, there appears to be no salt dependence for the enthalpy change. An important and logical extension of this work will involve transition calorimetry on ribo-oligonucleotides under a variety of solution conditions. These studies allow the determination of the temperature dependence of the enthalpy change. Such heat-capacity data are essential if a complete understandlng of conformational transitions in nucleic acid systems is to be achieved.

T H E H E L I X - T O - C O I L T R A N S I T I O N OF rA~U~

563

APPENDIX The results of the previous sections clearly indioate that evaluation of the helixto-coil transition of AvU~ b y means of the all-or-none approximation results in a calculated van't Hoff enthalpy change that is too low. The calculations that follow are an attempt to correct the calculated van't Hoff enthalpy change for any error introduced by the assumption of an all-or-none model for the transition. The success of these calculations will be judged b y how close they bring the values of AHv.m to the calorimetrically determined enthalpy change. Gralla & Crothers (1973) have developed equations that attempt to correct the van't Hoff enthalpy for contributions resulting from intermediate states. Their approach will be used here. A refinement of the treatment of Grana & Crothers would involve assigning a reduced equih'brium constant to the two terminal base-pairs. This is the frayed-end model of Levine (1974). Equations have been developed for such an approach and are presented below. Corredion for the ~resence of i ~ ¢ r ~ d ~ e 8~e~ For a molecule of the form AnU,, Applequist & Damle (1965) have shown that the equilibrium constant K for forming all bonded dlmeric states is 2n $-1

where ~8 is the equilibrium constant for forming the first base-pair. Following the treatment of Gralla & Crothers (1973), equation (A1) can be written as

K = KoB,

(A2)

Ko = ~s 2",

(A3)

K =

~s2-B,

(A4)

B ---- (I + 2s -x + 3s -~ + 48 -8 + ...).

(AS)

One should note that for the all-or-none approximation B = I and K = Ko. Thus in order to correct for the contribution of intermediate states, the first few terms in the series B should be taken into account. The desired corresponding expression for the enthalpy change can be derived by substituting equation (A4) into the van't Hoff equation and solving for AHTota~ (note: AHTota1 ---- 2~ ~JHB.p., where AHB.p. refers to the enthalpy change for forming one A - U base-pair and can be taken from the calorimetric results). Thus the total enthalpy cbange (~HT) for forming the intact dlmer can be calculated from the equation: (2~HB.p.s -~ ~- 6AH~.p.a -2 ~- 12AHs.p.s -8 -[- . . . ) ~JH~ = AHv... + B (A6) In the more general notation this expression can he written as: 2n

Z~HT

AHv.H. _~ iffil 2n--1

(A7)

(i + 1)s-'

~64

K.J.

BRESLAUER

ET

AL.

Application of this equation to the data presented here results in a correction of approximately 8 kcal tool -~ to be added to the van't Hoff enthalpy of 78.3 kcal mo l- L This calculation indicates that the inclusion of intermediate states can account for just under 4 0 ~ of the observed difference between the calorimetric and the van't Hoff enthalpy changes.

Oontrib~ion fro~ i~ermed~e atate~ and frayed enda The treatment that follows not only takes into account the intermediate states, but also considers the two terminal base-pairs to be destabilized by a factor 8 relative to the internal base-pairs. For this case it can be shown that the equilibrium constant K for forming all bonded dlmeric states can be written as: 2n--2

K = ,Sa~'-2 (,~8)~ +/3 ~ [2(,~8)82"-"+~)+ i82n-"+i)].

(AS)

i=0

In addition it can be shown that B, where B ---- K/Ko, can be written as: 2.--2

B = 1+

~

[8((~a)-;L8- i + i((~8)-28-"-I)].

(A9)

As before, the desired expression for the enthalpy change can be derived by substituting equation (A8) into the van't Hoif equation and solving for AHTota~. This leads to an expression for the total enthalpy change for forming the intact dlmer when contributions are included for intermediate states and terminal base-pair fraying: 2n--2

2(S8)-lAHB.p. ÷ ~ i[i(88)-28 - " - ~ + 2(Bs)-la-q~HB.p. AHr = AHv.H. +

~=o

B (A10)

Using the values for AHB.p. and s reported here as well as a value of 0-1 for 8, equation (A10) yields a correction term of approximately 14 kcal m ol -L This represents approximately 6 7 ~ of the value needed in order to bring the van't ~ o f f and the calorimetric enthalpies into agreement. These calculations would appear to indicate that the difference between the van't Hotf and the calorimetric enthaipy data cannot be entirely explained in terms of contributions from intermediate states or base-pair fraying. We wish to thank Dr Minou Bina-Stein for her expert assistance with the temperaturejump experiments and Ms Barbara Dengler and Mr David Koh for their excellent technical assistance with the oligonucleotide synthesis. We are also grateful to Professor D. M. Crothers for helpful discussions. We acknowledge the support of National Institutes of Health grant GM10840, the U.S. Atomic Energy Commission and the Rutgers Research Council. REFERENCES Appleby, D. & Kallenbach, N. (1973). Bio'poZymera, 12, 2093-2120. Applequlst, J. & Damle, V. (1965). J. Amer. Chem. Soc. 87, 1450-1458. Bloomfield, V. A., Crothers, I). M. & Tinoco, I. (1974). PhysicuJ Uhem~trry of Nucleic _4c/ds, p. 313, Harper & Row, New York. Borer, P. N. (1972). Ph.D. Thesis, University of California, Berkeley. Borer, P. N.p I)engler, B., Tinoco, I. & Uhlenbeck, O. C. (1974). J. 3~oL J~io~. 86, 843-853.

T H E H E L I X - T O - C O I L T R A N S I T I O N OF rATU7

5{~i

Craig, M. E., Crothers, D. M. & Dory, P. (1971). J. MoL Biol. 62, 383-401. Danforth, R., Krakauer, H. & Stur~evant, J. M. (1967). z~ev. ~ci. Inatr. $8, 484-487. Eigen, iYI. & de Maeyer, L. C. (1963). Te~hnique~ in Organic Ghemistry (Friess, S. L., Lewis, E. S. & Weissberger, A., eds), vol. 8, part II, pp. 895-1054, Interscience Publishers, New York. Gralla, J. & Crothers, D. M. (1973). J. MoL Biol. 78, 497-511. Krakauer, H. & Sturtevant, J. M. (1968). Biopolymera, 6, 491-512. Levine, M. (1974). Ph.D. Thesis, University of California, Berkeley. Martin, F. H., Uhlenbeck, O. C. & Dory, P. (1971). J. MoL Biol. 57, 201-215. Neumann, E. & Ackermann, T. (1967). J. Phya. Chem. 71, 2877-2379. Rawitscher, M. S., Ross, P. D. & Sturtevant, J. M. (1963). J. Amer. Chem. ~o¢. 85, 19151918. Ross, P. & Scruggs, R. (1965). Biopolymers, 3, 491-496. Scheflter, I. E., Elson, E. L. & Baldwin, R. L. (1970). J. Mol. Biol. 48, 145-171. Sturtevant, J. M. (1969). Proc. 1st Int. Conf. Calorimet/ty and ~Thermody~amics, Warsaw. Thach, R. E. (1966). I n Proeedurez in 17ucleio Acid Re~eazch (Cantoni, G. L. & Davies, D. R., eds), pp. 520-534, Harper & Row, New York. Tinoco, I., Uhlenbeck, O. C. & Levine, M. D. (1971). Nature (London), 230, 362-367. Tinoco, I., Borer, P. N., Dengler, B., Levine, M. D., Uhlenbeck, O. C., Crothers, D. M. & Gralla, J. (1973). Nature Nsw Biol. 246, 40-41. Tornllnson, R. V. & Tener, G. M. (1963). Biochemistry, 2, 697-702. Tsong, T. Y., Hearn, R. P., Wrathall, D. P. & Sturtevant, J. M. (1970). Biochemist/ry, 9, 2666-2677. Zimm, B. H. & Bragg, J. K. (1959). J. Chem. Phys. 31, 526-535.