Stability of ribonucleic acid double-stranded helices

J. Mol. Biol. (1974) 86, 843-853

Stability of Ribonucleic acid Double-stranded Helices PHIL~N.BORER~,BARBARADENQLER,IGNACIO Department of Chemistry University

TINOCO JR

and Laboratory of Chemical Biodynamics Berkeley, Calif, 94720, U.S.A.

of California,

AND OLKE C.UHLENBECK Department of Biochemistry University of Illinois, Urbana, Ill. 61801, U.S.A. (Received 18 January 1974) The hypochromicity, as a function of temperature for 19 oligoribonucleotides capable of forming perfectly base-paired double helices, is used to extract thermodynamic parameters of helix formation. The data are analyzed by an all or none model of helix melting which permits assignment of A@, AH, and AS of formation to each of the ten possible Watson-Crick base-paired nearest-neighbor sequences. Helix stability is found to have a striking dependence on sequence, and formulae are provided to predict the T, of any RNA double helix of known sequence.

1. Introduction Oligonucleotides of known sequence and structure are excellent models for corresponding regions in nucleic acids (Gennis $ Cantor, 1970; Martin et al., 1971; Uhlenbeck et aE., 1971,1973; Craig et al., 1971; Gralla & Crothers, 1973a,b; PGrschke et al., 1973; Borer et al., 1973). Since short oligoribonucleotide helices can be melted to single-

strand coils at moderate temperatures in aqueous buffers, any property can conveniently be studied as a function of structure. Thermodynamic properties are particularly favorable because they are likely to depend on short-range interactions. Thus, a small number of model molecules may provide all the information necessary to assess the thermodynamic stability of double-stranded RNA helices. In this behavior of a set of oligoribonucleotide helices paper, we use the simple “melting” to obtain the sequence-dependent contribution of base pairs to the free energy, enthalpy and entropy of helix formation. The correlation of helix stability with G + C content has been appreciated by nucleic acid chemists for many years. What has become apparent more recently is the influence of sequence on stability. Several experimenters have accumulated evidence on synthetic high polymeric nucleic acids with regular sequences that clearly demonstrate the dependence of stability on factors other than G + C content (Chamberlin et al., 1963; Wells et al., 1965,197O; Chamberlin, 1965; Karstadt & Krakow, 1970). A calculation of the interactions between the bases in a double-stranded helix (DeVoe & Tinoco, 1962) showed that by far the largest contribution to helix stability t Present address: Department of Biochemistry and Biophysics, Division of Biophysics, of Hygiene and Public Health, Johns Hopkins University, Baltimore, Md., U.S.A.

843

School

844

ET AL.

P. N. BORER

came from vertical stacking of bases. These calculations have since been improved and extended (see Pullman, 1968 for a review). All the calculations clearly predict a large sequence-dependence of helix stability and indicate that for a given structure nearest-neighbor interactions are sufficient to understand the stability. The helices studied here provide the thermodynamic parameters which characterize the nearestneighbor contributions to RNA helix stability. The data can be used to estimate T, values for helices as a function of concentration, or to estimate T, values for helical regions of an RNA molecule.

2. Materials and Methods (a) Oligonaer synthesis The syntheses of the double helices whose thermodynamic properties are considered here have been previously described (Martin et al., 1971; TJhlenbeck et al., 1971; Borer, 1972; Borer et al., 1973; Porschke et al., 1973). Briefly, they were prepared by controlled enzymic additions of nucleoside-5’-diphosphates to a primer oligomer by primer-dependent polynucleotide phosphorylase from Mkrococcus butem. (b) Measurementa Absorption at 260 nm wersus temperature was measured on an automatic recording spectrophotometer (Gilford Instruments) as described in Martin et al. (1971). Oligomers were dissolved in 1 m-NaCl, low4 M-EDTA, and buffered at pH 7-O with 0.01 M-sodium phosphate. Although standard stoppered cuvettes of 1, 2 and IO-mm path lengths were generally used, it was occasionally necessary to work at very high strand concentrations to obtain a sulilcient duplex stability. In these cases a glass-stoppered quartz cuvette with a sample chamber about 1 mm x 3 mm x 30 mm was filled with a 0.9 mm x 2.9 mm x 28 mm optical quartz spacer (Pyrocell; Westwood, N.J.). The sample chamber was covered first with a 5-mm length of 2-mm diameter silicone rubber tubing and then with a Teflon pad in such a way that when the glass stopper was inserted in the cell the tubing was pressed hard enough to seal the sample chamber. This procedure provided a 20-~1 ouvette with a very small dead volume above the sample and a path length of about 0.1 mm, thus allowing absorbances greater than 100 (in a l-cm cell) to be measured without appreciable losses due to evaporation. The exact path length was determined with a chromate solution of known absorbance. (c) Data analysis The method for obtaining the midpoint of the absorption-temperature profile (T,) has been described previously (Martin et al., 1971). We use the identical method so that our data can be compared directly with theirs. Briefly, we assume that the absorption of the double strands does not change with temperature and the absorption of the single strands in 1 M-NaCl has the same rate of change with temperature as it has in the absence of salt. Comparing the measured absorption-temperature profile with the double- and single-strand extremes leads to a measure off, the fraction of bases paired. The values of T, (f = +) could be duplicated to f2 deg. C on different samples. However, a different method of analysis of the data could change the absolute value of T, by 5 deg. C. The equilibrium constant for the formation of a duplex is:

f K = 2(1 -f)% for identical

(self-complementary)

strands and

2f K = (1 - f)% for non-identical strands, where c is the total oligonucleotide standard free energy of helix formation is given by:

strand concentration.

The

STABILITY

OF RNA

DOUBLE-STRANDED

845

HELICES

AC=‘=-RTlnK and the van’t

Hoff

relation

defines

the standard

enthalpy

of helix

formation:

AHO=-R!.k!?-, a (l/T) At a constant cularly simple

value form.

off such as T, where For self-complementary

f

= 4, the above helices

AC0 = RT,

equations

take

on a parti-

In c,

AHOcRdhC d (1/T,) and for non-identical strands c is replaced by (c/4). Thus, AH0 can be obtained from the slope of a l/Tm ver82cs log c plot, and AC0 at 25°C can be obtained from the same plot by finding the concentration corresponding to a T, of 25°C. For each helix studied in this paper, T, values were determined at six or more concentrations and fit by least squares to a l/Tm wersus log c plot; there was no apparent curvature to the plot. The values of AC0 and AH0 therefore represent the results of a number of experiments.

3. Results The thermodynamic data for 19 oligonucleotide double-stranded helices are given in Table 1. The data for the oligomers studied earlier (Martin et al., 1971; Uhlenbeck et al., 1971) were recalculated so that the numbers are in some cases slightly different from those published. As was expected, a strong chain-length and base-composition dependence of helix stability is observed. However, the far more striking fact is the very strong sequence dependence of helix stability. This can be emphasized by a variety of means. If one compares the five isomeric helices with two G*C pairs and four A-U pairs at comparable concentrations, the T, values range from -1.3”C to 28*3”C! The strong effect of sequence on stability occurs for interior sequences as well as at the ends of the helix. That is, altering a sequence at the end of the he1i.x (compare A,G, + C,U, with A.&G + CGU,) can have as large an effect as altering it in the middle (compare A,CGU, with A,GCU,). The sequence effect tends to overshadow both chain-length and base-composition effects. In order to get a similar 30 deg. C difference in T, between different chain lengths of pure AmU helices, it would be necessary to compare A,U,, a helix six residues long, and A,U,, a helix twelve residues long (Martin et al., 1971). Similarly, a composition difference of at least 25% would be needed to get a 30 deg. C shift in T, (Uhlenbeck et al., 1971). The simplest interpretation of the results is to assume that the contribution of each base pair to the stability of the helix only depends on its nearest neighbors. For example, the enthalpy of a G. C base pair will be different if it is next to an A-U base pair or if it is next to a U-A base pair. If we consider Watson-Crick base pairs and nearest neighbors only, there are 10 possible base-pair doublets. If end effects are included, two more contributions must be considered. The data in Table 1 can be used to obtain the thermodynamic contribution of each of the nearest-neighbor doublets to the stability of the model helix. The numbers obtained can then, in turn, be used to estimate the T, of any double-stranded helix. The formation of a double-stranded helix can be thought of as a concentrationdependent formation of the first base pair (initiation), followed by closing of subsequent base pairs (propagation). The first base pair involves hydrogen bonding only ;

11.5 22.1 35.1 42.3 26.0 24.3 27.7 32.6 41.9 46.8 35.4 31.5 39.3

5.3 14.6 28.3 34.7

19.1

18.2 21.9 25.8 37.0 40.7

30.6

26.4

36.2

&UI A&U, + A&U,

A&U, + A&U4

-hue

A,UAU, A,CUI + &GU, A&GUI A,GCUI

-%CUs+ &GU,

&Us

at

length = 7 -41 length = 8 -51 -52 -66 -53 length = 9 -58 length = 10 -67 -72 -63 -76 -78 length = 11 -89 length = 12 -84 length = 14 - 107

Helix Helix

Helix Helix 129 32.5 14.1 0.0977 0.0123 Helix Helix Helix 0.0219

4.79

1.17

135

4070 436 2.75 0.794

1510

13500 2040 174 347 40.7

length = 6 -26 -37 -34 -44 -46

= 25°C

T,

Total AH0 (kcal/mol)

Helix

(PM)

COnCn

- 10.4

-7.3

-8.9

-53 -6.1 - 7.4 -9.6 - 10.8

-6.1

-3.3 - 5.4 -7.6 - 8.3

-4.7

-3.4 -3.7 -5.1 -5.5 -6.0

Total dGO (kcaljmol) at 25’C

- 0.324

- 0.257

- 0.269

-0.207 -0.221 -0.187 - 0.223 - 0.225

-0.174

-0.160 -0.156 -0.196 -0.150

-0.122

- 0.0758 -0.112 - 0.0969 -0.129 -0.134

Total AS’ (kcal/mol deg.)

t None of the oligomers in this work has terminal phosphates and the phosphodiester linkage has been omitted. Thus A,U, is identical to (Ap),(Up), _ IU. helices refer to concentrat’ions of 20 PM and 200 pM for each oligomer. AH0 is obtained from $ The T, values for the non self-complementary AH0 = Ii d In c/d(l/T,). For self-complementary molecules dG“ = RX,,, In c; for non self-complementary molecules AC0 = RX, In (c/4). c = the total concentration in mol/l of the oligomers.

A,CGU, A,GCU,

A&G + CGU( U&GA2 A&GU, Ad& + CaU4 A,CGUa 16.4

100 FM

7.1

,%M

-1.3 11.3 22.1 22.8 28.3

10

T, (“C) at4

- 13.9 1.6 10.8 14.0 19.6

Moleculet

1

Thermodynamic parameters for double-stranded oligonucleotide helices

TABLE

STABILITY

OF RNA

DOUBLE-STRANDED

HELICES

84;

the subsequent ones include stacking interactions. We assume that hydrogen bonding between the bases in water involves negligible enthalpy change so that AH,O foi the initiation step is zero. Therefore, AG,D = - RT In K = - TAS,O (for initiation). We use the notation of Schefller et al. (1970) in which the equilibrium constant for initiation is written as K rather than as /3$ (see Applequist & Damle, 1965; Crothers et al., 1965). The above equation is equivalent to the assumption that K is independent of temperature. The superscript zero indicates standard conditions of one mole/liter strand concentration. This distinction is important since measurements are made at much lower concentrations, so it is necessary to extrapolate to standard conditions. The value of the initiation free energy depends on whether the helix initiates at an AU or G *C base pair ; a G* C base pair initiates more easily. We have assigned any molecule with a G *C base pair an initiation standard free energy of +5 kcal/mol oligomer at 25°C. This corresponds to an equilibrium constant uGC of 2.5 x 10T4. However, for a molecule with only AmU base pairs, AGio at 25°C is chosen as +6 kcal/mol oligomer and KAY is 4~ 10m5. These values of K are consistent with values of #I found earlier (Applequist & Damle, 1965; Crothers et al., 1965) and with a statistical mechanical analysis of the present data (M. D. Levine, unpublished work). For each subsequent base-pair addition there will be a corresponding AG and AH which depend on sequence. The superscript zero here is less important, because these steps are independent of concentration. The data in Table 1 are in principle sufficient to obtain all the ten nearest-neighbor thermodynamic contributions since each interaction is present in the oligomer in an algebraically independent fashion. However, we have found that the results are too sensitive to which particular subgroups of molecules are used in the analysis, because some contributions which occur rarely in our model molecules will have a large error associated with them. That is, if we try to obtain all ten nearest-neighbor contributions from a least-squares fit, some values obtained are unreasonable and vary greatly if an oligomer is omitted from the analysis. Instead, we prefer to obtain average values for those sequences which do not occur often in our set of molecules and, therefore, emphasize values obtained from those sequences which do occur often. We assume

A-U U-A have the same thermodynamics

v-A

and

A-U

and that all sequences of an A-U and a G*C base pair A-C U-G --

C-A G-U --

-

A-G U-C --

-A

G-A C-U

also have the same thermodynamics. These assumptions are arbitrary since they are based on the available model compounds and not on any inherent reason for the similarity in the thermodynamics of these stacking interactions. More accurate and not necessarily identical values for these stacking interactions can be assigned when more oligomers have been studied. We therefore distinguish six nearest-neighbor contributions and want to obtain their thermodynamic parameters from the thermodynamic measurements in Table 1. In order to do this, the values for initiating each

848

P. N. BORER

ET

AL.

helix (dH,O = 0, AG,O= 5 or 6 kcal/mol) were subtracted from the values from Table 1 to get propagation thermodynamic energies for each helix. For every helix, the energy of the entire helix is set equal to the sum of the energies of the relevant nearest-neighbor contributions. A set of 19 linear equations in six unknowns resulted for both the AH values and the AG values. The best least-squares values for the six unknowns were obtained by a simple computer program. The results are shown in Table 2. The AG values were obtained from all the data, but it was found that a much better fit to the AH data resulted if A,CG + CGU, was omitted. Perhaps since this helix was the least stable, the measurements were the least reliable. The large sequence and composition effects in Table 1 are mirrored in Table 2. For example, it is seen that c-c G-G c-

is more stable than

a-c C-G

which is more stable than C-G G-C Alternating A-U sequences are more stable than A’s on one strand and U’s on the other. A block of G*C base pairs followed by a block of A-U base pairs is more stable than alternating A-U and G*C pairs. Thus, within the limits of the assumptions made, the effect of sequence on the thermodynamics of the helix +- coil transitions of oligoribonucleotides has been accounted for.

4. Discussion The simplest models for understanding double helix stability were those developed for polymers in which each base pair contributes equally to AH and AC. However, these models were not suitable for the short helical regions in RNA where the composition of the helix is expected to have a large effect on its stability. Kallenbach (1968) introduced composition effects by using data from double-stranded ribopolymers to make AC dependent on the fraction of G *C pairs. The next advance was to recognize neighbor effects. Gralla & Crothers (1973a) recognized three contributions: two adjacent A-U base pairs in any order, two adjacent G*C pairs in any order, and two adjacent A-U and G*C pairs in any order. Their values for AG and AH for these three contributions were obtained by fitting the difference in measured thermodynamic values for sets of two molecules. Thus, an initiation energy did not have to be specified. If we analyze the data in Table 2 with their model (omitting A&G + CGU,) we obtain AH (kcal/mol) A-U, A*TJ G.C, G*C G-C, A*U

-8.0 - 13.4 -6.4

AG (26”C, kcd/mol) -1.2 -3.6 -2.2

STABILITY

OF RNA

DOUBLE-STRANDED

HELICES

849

The unite are kcal per mol of nearest-neighbor doublet. The free energy values agree with Gralla & &others (1973a) to fO*1 kcal/mol and the AHo agree to &I koal/mol. Since the above numbers are based on much more data than were available to Gralla & Crothers, they should be more reliable within the limits of the model. In the present paper, six different neighbor contributions are recognized and evaluated. Two types of A-U, A*U interactions and three types of G-C, G-C interactions are distinguished. This extension represents a considerable advance in the evaluation of double helix stability and prepares the way for two possible further advances. First, measurements on more molecules should be made in order to evaluate accurately all ten different nearest-neighbor sequences and to determine if next nearest-neighbor interactions have important effects on helix stability. Second, enough molecules should be measured in order to allow independent evaluation of end effects. If these goals are realized, it should be possible to predict accurately the stability of a doublehelical region of RNA. Even though they are not complete, the values in Table 2 can be used to make an estimate of the melting temperature of any double-stranded RNA helix. The equations needed are derived from AGO = AH - T(AS + AS,O) = - RT In K, where AH and AS are the propagation parameters obtained from Table 2 and ASi equals the standard initiation entropy. For oligomers initiating with a G-C pair, ASi = -0.0168 kcal/mol deg. and for pure A-U oligomers AS,O = -0.0201 kcal/mol deg. For self-complementary oligomers with a strand concentration equal to c in mol/liter, TJC)

=

AH(kcal/mol) -273. OX@4576log c + AS(kcal/mol deg.) + AS,O(kcal/mol deg.)

For equal concentrations of two non self-complementary strands with a total strand concentration of c, the log c term in the equation must be replaced by log (c/4). One can also calculate the concentration necessary to obtain a desired T,. log c =

AH(kcal/mol) AS(kcal/mol deg.) + AS,O(kcal/mol deg.) 0.004576 [T,(V) + 2731 0.004576

Again for non self-complementary molecules log c is replaced by log (c/4). To illustrate the method one can consider the molecule A,U3. AH = 4 (-8.2) + (-6.5) = -39.3 kcal/mol. AS = 4 (-0.0235) + (-0.0164) = -0~1104 kcal/mol deg. ASlo = -0.0201 kcal/mol deg. At a concentration of 100 prvr, T, is calculated to be -8°C.. Martin et a2. (1971) report -13°C for the T, of A,U,. Estimated Tm values for a( variety of hexamers are shown in Table 3. It is interesting to note the 100 degree c! difference in T, estimated for G,C, and A3U,. Experiments on three additional double helices support this method for predicting oligomer stability. The equimolar mixture of A,CUG and CAGU, was found to be a very unstable helix with a T, of lo”+5 deg. C at 2000 pM strand concentration. The calculated T, at that concentration is 18°C which represents good agreement cbonsidering the low stability of the sequence in question. In another example, we predict the helix A,GC + GCU, to have a T, of 22°C at 37 p~ strand concentration. Experimental measurements of this complex are complicated by substantial selfaggregation of GCU, at low temperatures preventing accurate determination of a,

860

P. N.BORERETAL.

TABLET

Thermodynamics of adding a base pair to a double-stranded helix Reaction

-A /

(kca$eg.)

-8.2

-0~0235

1.”

.- 6.5

-0-0164

1.ci

-5.9

- 0.0127

- 2.1

- 13.0

- 0.0336

- 3.0

- 14.7

- 0.0349

-- 4.3

13.7

- 0~0298

-1.8

A0 (keel) at 26°C

/

--S--A -+

AH (kcal)

.

.

-u-u

-U

\

‘U \

Ai

U’ -A

/

.-A-U/’ + . . -U-A

-U

/

-U

-, -A \

‘A

'U.

\ /

-U

'/

/

--A\--C + . -U-G

+ -U \

‘\G

\

‘\

G/

c/ -A

/

-U-A . --A-u

/

--B-G . . -u-c

\

“C

\

\

A/

A/

--c’

/

--C---A + . . -G -U

-G

--G/ +

\

‘U ‘\

---c ‘,

-G-A . -c-u

/ . \

‘U \

G/ -C

/ -f

-G

/ . \

‘c

-G

-C-G . -6-c

\\

/ --f

-C

/

--Gc ” -C-G

\

‘G \ c’ -C

/ +

-G

--cc/ . -G-G

. \

‘G \

11 value for the standard (strand concn equals 1 M) free energy of initiation kcal for an A,U base pair and + 5.0 kcal for a G.C’ base pair is assumeci.

at 26Y

of -4 6.0

STABILITY

OF RNA

DOUBLE-STRANDED

851

HELICES

3

TABLE

Calculated values of melting temperatures for double-stranded oligonucleotide helices

Molecule

Calculated at 100

&Us A&+ CUs &GUs+&Ws A&UC + CAGU, A&G + CGU, A,CGU2 A,GCU2 &GdJ~ + AaGUz ACGUCG + CGACGU ACGCGU GCGCGC G&s Gs+Cs The T, values for the non self-complementary each oligomer.

T, /AM

Experimental at

100

(“C)

(“C)

-8

-13

0 5 11 14 19 28 32 39 60 66 94 99

T,

PM

22 28

helices refer to concentrations

of 200 PM for

helix absorbance. However, the observed absorbance-temperature profile at 37 PM has an inflection point at 18°C. Since the inflection point of a transition is usually within 5 deg. C of the T, satisfactory agreement between experiment and model is achieved. Finally, Gennis & Cantor (1970) reported the T, of A& + GU, at 1250 PM strand concentration to be 30.5”C. The calculated T, for this complex is 27°C. The parameters in Table 3 can also be used to estimate the T, of very long polymers of known sequence where the concentration term and ASiD become negligible. For a very long polymer T, = AH/AS. These calculated values will be less accurate than for oligomers because of the long extrapolation and the possible temperature dependence of AH and AS. Furthermore, long-range interactions can become more important in polymers of simple repeating sequence. Nevertheless, the free energy values in Table 2 do predict the correct order of stability for some synthetic ribopolymers. Poly(A-U) *poly(A-U) is more stable than poly(A) *poly(U) (Chamberlin, 1965) and poly(G)*poly(C) is more stable than poly(G-C)*poly(G-C) (Karstadt & Krakow, 1970). The limitations in the parameters given in Table 2 should be kept well in mind when they are used. First, only six distinct nearest-neighbor parameters are used and end effects are assumed not to exist. Thus the stability of special sequences and short helices may not be predicted as accurately. Second, the parameters are derived from a series of similar molecules in the sense that all contain considerable blocks of A-U base pairs. Perhaps more varied sequences will alter the parameters somewhat. Third, the values of AH and AS are assumed independent of temperature. Thus, predictions of T, are probably most accurate in the same temperature range (0 to 40°C) in which the model compounds were measured. Finally, all predictions are for perfect helices without extra unpaired bases at the end. This last limitation is

852

P.N.BORER

ETAL.

particularly important if one is attempting to estimate the equilibrium const.ant and melting temperatures for the interaction of an oligomer with a polymer. A statistical analysis of the melting behavior of the oligomers in this paper which accounts for the large breadth of the transition indicates that the equilibrium constant of formation for an end base pair may be as much as 90% lower than for an identical internal pair (M. D. Levine, unpublished data). Thus, the unpaired bases in the polymer at either end of the complementary oligomers will have a marked effect on the T, of the complex. Experiments with pure A-U helices indicated that, an extra residue at either end may contribute nearly half as much as an additional base pair (Martin et al., 1971). Needless to say, any special conformation of the polymer as found in tRNA will also influence the stability of the helix (Uhlenbeck, 1972). One of the main reasons for obtaining the thermodynamic data in Table 2 is that it can be combined with data for loops, mismatches and G*U pairs, as compiled by Tinoco et al. (1973). Although based on the same molecules, the AG (25°C) data for helical regions in that publication are obtained from a statistical mechanical analysis of shapes of melting curves and, therefore, have values slightly different (-&lo%) from those presented here. If AH values for loop initiation, G*U pairs and mismatches w?ereknown, the T, of any proposed RNA structure could be calculated using the data in Table 2. Unfortunately, very little data is available on this point,. Gralla & Crothers (1973) have proposed values for G *U base pairs and have assumed that the AH of initiation for all loops and bulges is zero. We find a large AH for initiation of hairpin loops containing C residues and closed by an A*U base pair (Uhlenbeck et al., 1973). It may be that AH of loop formation depends strongly on the number and type of bases in the loop. Furthermore, AH may depend markedly on temperature. Until these problems are settled, we will refrain from trying to predict RNA secondary structure at temperatures far from room temperature. This work was supported by grants from the National Institutes of Health; GM10840 to one of us (I. T.), GM41393 to another author (P. N. B.) and GM19059 to a third author (0. C. U.). We thank Mr Cemal Kemal and Mr David Koh for their excellent technical assistance. One of us (0. C. U.) is a recipient of a Career Development Award from the National Institutes of Health. REFERENCES Applequist, J. & Damle, V. (1965). J. Amer. Chem. Sot. 87, 1450-1458. Borer, P. N. (1972). Ph.D. Thesis, University of California, Berkeley. Borer, P. N., Uhlenbeck, 0. C., Dengler, B. & Tinoco, I., Jr (1973). J. Mol. BioZ. 80, 759771. Chamberlin, M. J. (1965). Fed. Proc. Fed. Amer. Sot. Exp. Biol. 24, 1446. Chamberlin, M., Baldwin, R. L. & Berg, P. (1963). J. Mol. BioZ. 7, 334-349. Craig, M. E., Crothers, D. M. & Doty, P. (1971). J. Mol. Bid. 62, 383-401. Crothers, D. M., Kallenbach, N. R. & Zimm, B. H. (1965). J. Mol. BioZ. 11, 802420. DeVoe, H. & Tinoco, I., Jr (1962). J. Mol. BioZ. 4, 500-517. Gennis, R. B. & Cantor, C. R. (1970). Biochemistry, 9, 4714-4723. Gralla, J. & Crothers, D. M. (1973a). J. Mol. Biol. 73, 497-511. Gralla, J. & Crothers, D. M. (1973b). J. Mol. BioZ. 78, 301-319. Kallenbech, N. R. (1968). J. Mol. BioZ. 37, 445-466. Karstadt, M. & Krakow, J. S. (1970). J. BioZ. Chem. 245, 752-758. Martin, F. H., Uhlenbeck, 0. C. & Doty, P. (1971). J. Mol. BioZ. 57, 201-215. PGrschke, D., Uhlenbeck, 0. C. & Martin, F. H. (1973). Biopolymers, 12, 1313-1335.

STABILITY

OF RNA

DOUBLE-STRANDED

HELICES

8.53

Pullman, B. (ed.) (1968). &foZecuZar Associations iu Biology, Academic Press, New York. Scheffler, I. E., Elson, E. L. & Baldwin, R. L. (1970). J. Mol. Biol. 48, 145-171. Tinoco, I., Jr, Borer, P. N., Dengler, B., Levine, M. D., Uhlenbeck, 0. C., Crothers, D. M. & Grslla, J. (1973). Nature New Bid. 246, 40-41. Uhlenbeck, 0. C. (1972). J. Mol. BioZ. 65, 25-42. Uhlenbeck, 0. C., Martin, F. H. & Doty, P. (197 1). J. Mol. BioZ. 57, 217-229. Uhlenbeck, 0. C., Borer, P. N., Dengler, B. & Tinoco, I., Jr (1973). J. &ZoZ. BioZ. 73, 483496.

Wells, R. D., Ohtsuka, E. & Khorana, H. G. (1966). J. Mol. BioZ. 14, 221-240. Wells, R. D., Larson, J. E., Grant, R. C., Shortle, B. E. 85 Cantor, C. R. (1970). J. Mol. BioZ. 54, 465-497.