The molecular mechanism of thermal unfolding of Escherichia coli formylmethionine transfer RNA

J. Mol. Biol. (1974) 87, 63-88

The Molecular Mechanism of Thermal Unfolding of Escherichia coli Formylmethionine Transfer RNA D. M. CROTHERS

Depurtment of Chemistry Yule University New Haven, Corm., U.S.A. P. E. COLE

Department qf Chemistry Columbia University New York, N.Y., U.S.A. C. IV. HILBERS~

AND R. G. SHULMAN

Bell Laboratories Murray Hill, N.J., U.S.A. (Received 23 October 1973, and in revised form 26 April 1974) The molecular mechanism of thermal unfolding of Eacherichia coli tRNAfMet (in 0.17 M-NaCI without Mg*+ ) has been elucidated by a combination of relaxation kinetics and proton nuclear magnetic resonance spectroscopy. We measured the n.m.r.1 spectrum of the hydrogen-bonded ring NH protons at different temperatures and found that the resonances assigned to each arm of the cloverleaf broaden and disappear together, yielding four distinct n.m.r. “melting” transitions. Temperature-jump measurements in the same solvent showed five co-operative melting transitions, varying in relaxation time from a few microseconds to ten milliseconds. The relaxation and n.m.r. measurements were correlated by the following model. When the lifetime of a hydrogen-bonded proton in a helix is five milbseconds, its n.m.r. line will be broadened to approximately twice its intrinsic low-temperature width and appear to “melt “. The helix dissociation time constants of the relaxation effects were extrapolated by the Arrhenius equation to lower temperatures where their values were five milliseconds. The correlation of extrapolated dissociation time constants with n.m.r. melting of specific helices allowed assignments of the structural basis for each relaxation effect. The results show that the principal path for the reversible thermal unfolding of tRNAiMet under these solution conditions is first, transient opening of the dihydrouridine helix, followed by simultaneous melting of the dihydrouridine helix and a “tertiary” interaction, which does not correspond to a cloverleaf helix. The tertiary interaction is much less stable in tRNAjMet, with T, lowered by 16’C from tRNAi”“‘. The sequence of melting steps at higher temperatures is the same in the two isoacceptors: first the TYC helix melts, followed by the anticodon helix and f?naIly the acceptor stem helix. Thermodynamic and kinetic parameters are reported for these steps. t On leave from the University of Nijmegen, Nijmegen, The Netherlands. $ Abbreviations used: n.m.r., nuclear magnetic resonance; hUra, dihydronracil. 63

64

D. M. CROTHERS

ET AL.

The method of sequential melting, combining n.m.r. and relaxation kinetic techniques, is a powerful procedure for elucidating RNA secondary structure. In addition, this method allows assignment of many hydrogen-bonded ring NH proton resonances that are unresolved in the low-temperature spectrum.

1. Introduction Determination of macromolecular structure has been a major factor contributing to progress in molecular biology. However, knowledge of static structure does not necessarily lead to an explanation of macromolecular function, as evidenced by the frequency with which “conformational change” is invoked to explain particular properties of a protein or nucleic acid. In spite of the popularity of this concept, very little is known about the details of such transformations, The purpose of this paper is to outline the molecular mechanism of a particular macromolecular conformations1 change, namely the thermal unfolding of formylmethionine-specific transfer RNA from Escherichia cd. Three sources of information were essential to our investigation. First is the wealth of chemical and structural information available on tRNAfM*t from E. coli including its primary sequence and the probable cloverleaf structure, which is strongly supported by homologies with other tRNA sequences (Zachau, 1969; Arnott, 1971). This has been extended by the three-dimensional structure of yeast tRNAP harecently reported by Kim et al. (1973)) which we assume as a first approximation to apply to tRNA IMet. Second is the resolution of particular steps in the unfolding process by the technique of temperature-jump relaxation kinetics. The major problem with such studies has been identification of the structural basis for each kinetically resolved step, a tortuous and indirect assignment in previous experiments (Cole $ Crothers, 1972; Romer et al., 1970a,b; Riesner et al., 1973). It is here that the third information source played a crucial role. Recent proton magnetic resonance experiments on tRNA in H,O solutions have resolved low field resonances that can be assigned to the ring NH protons involved in base pairing in double helical regions of the molecule (Wong et al., 1972a,b; Shulman et al., 1973a,b; Lightfoot et al., 1973). Measurements of the temperature dependences of these hydrogen-bonded proton resonances showed that for E. coli tRNAfMst in the presence of Mg2+ all the resonances broadened abruptly in the vicinity of 75°C which was close to the optical melting temperature (Kearns et al., 1971b). On the other hand optical measurements of both the equilibrium melting and the relaxation kinetics of this same tRNA in the absence of Mg 2+ showed multiple relaxation processes in the millisecond region, with melting extending over a broad temperature range well below 76°C (Cole & Crothers, 1972; Cole et al., 1972). The present study is a combined n.m.r.t and temperature-jump relaxation kinetic study of E. co.5 tRNAfMet in the absence of Mg2+. We find that under these conditions, groups of resonances of tRNAfMet broaden and disappear together as the temperature is increased. Each such group can be shown to correspond to a particular arm of the cloverleaf structure of tRNAfMet. Finally, the individual relaxation kinetic signals, which correspond to melting of separate helix regions, are correlated or “mapped” with the melting steps observed by n.m.r. The important point to recognize in this mapping procedure is that n.m.r. and optical melting reflect different phenomena. As we showed in a recent study on a t See footnote on p. 63.

THERMAL

UNFOLDING

OF E. COLI

tRNAfMat

65

simple model pentanucleotide double helix (Crothers et al., 1973) the apparent melting observed as n.m.r. line broadening may be many degrees below the T, value determined in a standard U.V. melting curve. This is because the n.m.r. lines broaden when the proton lifetime in the helix becomes shorter than a particular value. Thus the n.m.r. broadening comes from a kinetic process, related to transient opening of the helix in contrast to the optical melting which reflects the equilibrium distribution. As the temperature is raised and the helix becomes sufficiently labile, the proton is transferred from the hydrogen bond in the helix to the non-hydrogenbonded coil, from which state it may exchange with water. In principle either process may determine the line broadening. The optical changes that accompany melting, on the other hand, reflect breakage and unstacking of the base pairs in the helix. When the n.m.r. line broadening is determined by the lifetime of the helix, there is a clear correspondence via this lifetime between the temperature-jump relaxation kinetics and n.m.r. melting. In the present study we find that there are five discrete relaxation signals in the Beginning at low temperature, the first melting process is melting of tRNA:y,. Our n.m.r. results, found only for tRNAiMet, and the second only for tRNA:““t. measured for tRNAiMet, indicate that the first melting step included unfolding of “tertiary” structure, probably mainly the disruption of the association between the hUra and T#C loops observed in the crystal structure (Kim et al., 1973). The hUrn helix is able to open transiently for proton exchange while the tertiary structure is still intact, and seems to melt together with the tertiary structure in tRNAiMet. There follow three approximately sequential melting steps, corresponding first to opening of the T$C helix, then the anticodon helix and finally the acceptor st,em. The melting temperature, transition enthalpy and kinetic properties of these last three helix arms are close t,o those predicted from parameters for model compounds (Gralla & Crothers, 1973n), when allowance is made for the observed average electrostatic effects in tRNAfMet. The melting of the hUra helix, however, is coupled t,o melting of the tertiary structure. A detailed comparison of the very different early melting behavior of tRNAiMet and tRNAtMet, measured on purified, uncrosslinked samples, will be reported in subsequent papers. Perhaps the most surprising feature of our results is the large difference in stability of’ t,he tertiary structure of tRNAiMst and tRNAiMet. These species differ by a single base change, replacement at position 47 of m7G in fMet 1 by A in fMet 3 (Dube et al., 1968). Since that residue is not involved in a cloverleaf helix, it is plausible that it contributes to tertiary interactions. Our results show that m7G stabilizes the tert,iary structure in tRNAiMSt. The functional role of this base change remains obscure, howcvrr.

2. Materials and Methods (a) Buffem Relaxation experiments were done on tRNA samples containing 0.001 M-phosphate, 0.01 M-sodium cacodylate, pH 7.0. Total Na+ concentration was 0.174 M. Samples dissolved in the same buffer, except that the EDTA NaGlO4 concentration wa.s 0.144 M.

dialysed against a buffer O-001 M-EDTA, O-152 M-NaCIO,, for the n.m.r. measurement were concentration was 0.006 M and

c

15 G

A

CO:IG ,,I.

c:o o-c70

-16

G

’ g:ij 0-c .‘v

4

G2~GG ”

r+

=

UAW 0, CGOCC A .,a I1 A

t c 7s

Fra. 1. The low field 300 MHz proton n.m.r. spectrum spectrwn is celoulated on the basis of t,he ring current indicated in the cloverleaf model in the insert.

5

,I?,,%

-12 -10 p.p.m. of the hydrogen-bonded ring NH protons of E. coli tRNArMst m 0.17 M-Na+ at pH 7.0. The stick contributions of the nearest neighbors (see text). The numbers refer to particular base pairs as

-14

THERMAL

UNFOLDING

OF E. COLI

tRNAf”“’

67

(b) Transfer RNA

The samples of tRNAfMet (E. coli) were obtained from Oak Ridge National

Laboratory through the generosity of Dr A. D. Kelmers. Samples were prepared for n.m.r. spectroscopy by extensive dialysis of a dilute tRNA solution against EDTA in low salt, 30-fold concentration by evaporation, and finally by extensive dialysis against buffer in a microdialysis cell. Most of the optical measurements were performed on a sample (lot no. 10-86) which contained a mixture of tRNAiMat and tRNAtMet. The n.m.r. sample (no. 15-290) contained primarily tRNAiMet. Recently available purified samples of the two isoacceptors allowed us to verify that 71 appears only for tRNAiMet and Q only for tRNAiMet (A. Stem, P. Cole & D. M. Crothers, unpublished results). (c) Relaxation

measurements

These were carried out as described previously (Cole & Crothers, 1972). In order to avoid cavitation at high temperatures, the temperature-jump size was reduced to 13 deg. C. We used a 0.05 PF capacitor and the cell resistance was 25 to 100 ohms, depending on temperature. Below 55”C, a 4.0 deg. C temperature-jump size was used. The tRNA sample used in the relaxation studies had about 15 to 20% photocrosslinking (Cole & Crothers, 1972; Favre et al., 1971). Since we found that the sample used for n.m.r. measurements was more extensively cross-linked (~40%), we checked the relaxation properties of that sample. The more extensively cross-linked sample had a reduced amplitude for the first relaxation (pi, see Results), but was otherwise similar. Relaxation amplitudes were calculated from the zero-time intercept of semi-logarithmic plots of each relaxation effect. (d) Nuclear magnetic reaonanee measurementa The n.m.r. spectra were obtained on a Varian Associates HR300 spectrometer operating near 300 MHz in the frequency sweep mode. Spectra were accumulated for 2 to 5 h in a Varian 1024 channel analyzer. Shifts are given in parts per million downfield from DSS (2,2-dimethyl-2-silapentane-5-sulfonate). The tRNA sample used for n.m.r. was 2 mM in tRNA. 3. Results

(a) Resonance assignments and nuclear magne.tic resonance melting The primary sequence of E. coli tRNAiMst is given in Figure 1, where it is shown folded into the cloverleaf form (Dube et al., 1968). This tRNA has a particularly high percentage

of G-C base pairs, with

17 G*C and only 2 A*U pairs in the cloverleaf

structure. The low field region of the 300 MHz proton n.m.r. spectra of Mg2+-free tRNAiMet at 21°C is shown in Figure 1. These resonances have been assigned to the hydrogen-bonded ring NH protons and are compared with a plot of the resonance positions

predicted

by the ring current

calculation

(Shulman

et al., 1973a) upon the

assumption that the A*U and G*C ring NH protons have intrinsic are modified

by ring current

shifts from the neighboring

positions which

bases. In general the spectra

calculated on this basis agree well enough with observations to indicate that no other mechanism needs to be considered at the present accuracy. However, while the best resolved resonances can be assigned with considerable assurance, others have ambiguous assignments because the inaccuracies in computing the spectral assignments are comparable with the observed resolution. As we will show here, the temperature dependence of the n.m.r. spectrum helps to resolve the ambiguities in the resonance assignments. The n.m.r. spectra of the tRNAiMet at different temperatures are shown in Figure 2. The numbers on the right in Figure 2 represent the integrated intensity bet,ween

II 12

13 IO

HI9

-7 I

-15

I

-14

I

- 0IIN,

-13

-12 p.p.m.

FIG. 2

I

-II

I

-10

THERMAL

UNFOLDING

OF E. COLI

tRNAfMet

Ml

-11.3 and -15 p.p.m. These intensities have been normalized so that 19 protons are assumed to have resonances in this region at the lowest temperature. This is slightly lower than the number previously measured for this region, i.e. 23 + 2 by comparison with an external standard (Kearns et al., 1971a), but is consistent with our more general findings that this region only contains resonances from the cloverleaf base pairs. Regardless of the normalization procedure adopted there is a loss of ~4 base pairs between 21 and 37°C. Furthermore, a detailed examination of the spectra shows that the four peaks designated by arrows in the 21°C spectrum broaden slightly at 27°C while at 37°C they can no longer be observed. The broadening and disappearance of these four resonances is mainly responsible for the loss of four protons in the integrated intensity between 21 and 37°C. The simultaneous broadening of the four resonances, marked by arrows in Figure 2. suggests that they are close to each other in the secondary structure and that one particular helical region is beginning to open. For several reasons it is obviously the dihydrouracil stem. This can be seen from a comparison of the ring current calculation with the 21°C spectrum in Figure 1 where the peak at -13.65 p.p.m. is assigned to A.U pair no. 11, and one proton in the peak at -11.45 p.p.m. is assigned to the G.C pair no. 10. These assignments are strongly supported by the comparison of calculated and experimental positions in Figure 1 because these particular peaks are well resolved in both the experimental and calculated spectra. This suggests that the other two peaks which broaden in this temperature range might be the remaining t,wo base pairs of the hUra helix, i.e. G*C pairs nos 12 and 13. The calculated spectrum shown in Figure 1 allows us to make with considerable confidence the assignments shown by the arrows at the top of Figure 2, because, as can be seen in Table 1, the calculated positions of these two resonances agree very well wibh the assigned positions. At t’emperatures above 37°C the melting continues. Although specific resonances are not always as well defined as below 37°C enough distinguishable resonances disappear to enable us to observe the sequential melting of the different helical arms, particularly when the spectra are superimposed. Between 37 and 43°C where the integrated intensity decreases by an additional four protons, intensity is lost in the spectral region that corresponds reasonably well to the calculated positions of the base pairs in the T#C arm. There are four G-C pairs in this arm, nos 50,52,53 and 54; we assume, as in the past, that the G-U pair does not contribute to the spectrum. From a superposition of the spectra at 43°C and 37°C it is clear that intensity is lost in two regions, i.e. in the region between -11.7 and -11.9 p.p.m. and in a narrower region near -13.1 p.p.m. Table 1 shows that assignment of the two resonances no. 52 and no. 53 to the region near -11.8 p.p.m. is in reasonable accord with the calculation. When these two peaks broaden it is expected that no. 54 will also broaden, so that this resonance is assigned to the disappearance at -13-l p.p.m. Wit)h the present accuracy we cannot tell whether or not we are losing the resonance from no. 50 in this temperature interval. If so it would have to be at -13.1 p.p,m. which is a plausible posit,ion, but which cannot be calculated accurately because of the Fra. 2. The 300 MHz proton

n.m.r. spectra of tRNAfMet (0.17 M-N&+, pH 7.0) as a function oi side of the spectra indicate the number of protons contributing as deduced from the integrated areas. The resonances assigned to the base pairs 10, 11, 12 and 13 are indicated by the arrows at the top of the Figure. The diagram at the bottom shows the line positions expeoted for baee pairs of the aoceptor stem.

tempersture. The numbers to the right-hand

70

D. M. CROTHERS

ET

AL.

TABLE 1 Comparison of assigned and dculu.ted resonance positions for t RNAfMst hydrogen-bonded ring NH protons Base pair 10 11 12 13 28 29 30 31 32 50 52 53 I 54 2 4I 3 5 6 71

Calculated

Obs. - Cela. A

-11.6 - 13.9 - 13.3 - 12.2

+0*15 +0*25 0 +0*3

- 14.6 -11.6 - 12.3 - 12.7 - 13.1

-0 +0.15 0 -0.1 0.1

-13.1

4 - 12.25 - 12.26 - 13.4

+ 0.46 + 0.46 +0*3

- 12.1

- 12.26

+0*15 +o-16

-12.65

+o-lb +0*15 +0.15 $0.16

Assigned position

- 11*4b - 13.66 - 13.3 -11.9 - 14.3 -

to - 14.8 11.46 12.3 12.8 13.2 9

-11.7

to -11.9

- 12.5

uncertain structure of the G-U pair. Finally it should be noted that not all of the intensity of the T$C base pairs is lost between 37 and 43°C. Some of this intensity was lost below 37”C, in addition to the broadenings of protons 10 to 13 noted above. The major change between 43 and 48°C is the reduction in intensity of the resonances, from base pairs in the anticodon arm. The broad resonance from A-U no. 28 at low fields between -14 and -15 p.p.m. and the well resolved resonance from G-C no. 29 near -11.4 p.p.m. both decrease between 43°C and 48°C aad have disappeared completely at 53°C. These are positive indicators of the melting of this arm. In addition to these well resolved intensity losses, one can, by subtrackg the 53°C spectrum from that at 43°C (Fig. 3), trace the disappearance of additional resonances at - 12-3, -12.8 and -13.2, which agree very well with the calculated positions of G-C pairs nos 30, 31, and 32 at -12.3, -12.7 and -13.1 p.p.m., respectively (see Table 1). Hence in this temperature range all five resonances from the anticodon helix have disappeared. Finally the remaining intensity at 53°C is rather constant up to 57”C, corresponding to approximatily seven protons, and haa approximately the same shape and intensity at both temperatures. By elimination this should correspond to the six base pairs of the amino acid acceptor stem; since the intensity discrepancy is within experimental accuracy, this is the best assignment. Once again this assignment is supported by the comparison between observed and calculated spectra as shown at the bottom of Figure 2. With the exception of G-C no. 50 all of the resonances of the base paired protons in the intact tR’NAfMBt have been assigned and are listed in Table 1. These assignments are interesting for a number of reasons. The first is that despite the fact that

72

D. M. CROTHERS

ET

AL.

the low field n.m.r. spectrum of E. wli tRNAiMet is the worst resolved of the six different tRNAs which have previously been measured (Shulman et al., 19736), it is now the most completely assigned as a result of the selective melting. Second, disregarding the uncertainties in the TI+K! helix the average deviation between calculated and observed is 0.13 p.p.m., which is only about three times the present experimental uncertainty. Of the discrepancies the largest was in the position of GG no. 13 and nearly all of its ring current shift comes from A no. 14, beyond the helix, which is assumed to be stacked as if the helix continued. Hence this discrepancy presumably reflects a real uncertainty about the structure since it has already been shown from the n.m.r. spectrum of yeast tRNAPhe (Shulman et al., 1973b) that different structures exist at just this position of the molecule. Furthermore, just as the resonance of G+C no. 13 in yeast tRNAPhe varied from sample to sample and w&h solution conditions, so too there is a difference in this region of the E. coli tRNAihPet spectrum. In the previously published 300 MHz spectrum the G*C no. 13 resonance did not appear at -11.9 p.p.m., where the spectrum was empty, but rather there was a resonance observed at -1175 p.p.m. Also, in the earlier spectrum the two resonances corresponding to G-C pairs nos 10 and 29 coincided exactly, at -11.4 p.p.m., instead of being slightly split as seen in Figure 1. Hence it is possible that the geometry of the stacking of G no. 9 and G no. 27 upon the hUra helix, which would affect the position of G*C no. 10, and the stacking in the hUra loop of A no. 14 upon G.C no. 13, may both be sensitive to salt conditions. The variability of photo-crosslinking in tRNAfMet samples may also contribute to the variability of these particular resonance positions. One reservation about the accuracy of the agreement between calculated and observed positions concerns the acceptor stem. At high temperatures where the rest of the hydrogen bonds are broken, it is reasonable to expect that the acceptor stem would be free to form a regular helix and thereby agree with the ring current shifts calculated on this basis. It is not certain that these particular resonances are at the same position in the intact molecule. Finally, it is clear that on the average the calculated positions of the resonances, which predominantly come from G-C pairs in this tRNA, are at lower fields than the observed by -0.15 p.p.m. Since the calculations assumed an intrinsic G-C position of -13.7 p.p.m. it seems that -13.6 might be a better assumption, in which case the average deviation between calculated and observed would drop to d-05 p.p.m. However, this will be discussed more quantitatively in the future. Because of the co-operative way in which sets of resonance lines broaden together there is no doubt that the present experiments reflect the opening of helical segments. In this way they resemble the pentanucleotide previously studied (Crothers et al., 1973) where the n.m.r. lines were broadened by the reduced lifetime rhc of the protons in the hydrogen-bonded helical state. If the line shape in the absence of this broadening is Lorentzian with a full width AQ, and the width actually observed is Av, then the line broadening 6v is 6v = Av - Av, (1) and l/ThC = r&J. For our purposes relation (1) will be assumed even though the unbroadened lines are not rigorously Lorentzian. From the low temperature widths we estimate that Av, w 60 Hz. With the signal to noise shown in Figure 1 it is possible to estimate

2 1. -2 ?

2OC

L----AX=260nm

2ops

i=266nm

L44ms

F‘ = 67.6”C

X=2flonm

in 0 I7*r-No+

7,=47.6OC

I X=266nm

7‘ : 7859

lOInS

X=266nm

2

mr

trace at the bottom 1. Oscilloscope traces illustrating the 5 rclasation effects observed in the melting of tRSAk’“Ct in 0,17 M-N& +. The horizontal FLATIS of the picture indicates the absorbance before the tc~mperat,rlre-jump. The temperature-jump size is 4.0 deg. C’ for the effects designated 7I and r2 anti 1.S after the tompcraturc-jlwnp. deg. C for TV, TV. and 7j. Total light intensity is 5 V. ‘I’, ie the final tcmpcraturc

Tf=60

7‘ =26.5OC

fRNAfMe’(E.co/r)

THERMAL

UNFOLDING

OF E. COLZ

tRNAc”et

?:I

when an individual line has been broadened by a factor of two ; lesser or greater broadenings however are harder to estimate. Hence the n.m.r. measurements determine the conditions under which 6v M 7r x 60 Hz Or 7hc Rs 5 x 10-3 s, w&h shorter or longer 7hc values being consistent with the n.m.r. observations but not determinable. (b) Optical melting a function

of concentration

Since the tRNA concentration used in the n.m.r. experiments is lo2 to lo3 times higher than in typical optical experiments (1200 A&ml versus 1 to 12 A,,,/ml), we determined the optical melting behavior of the tRNAfMst n.m.r. sample at 336 nm. As seen in Figure 4, the transition temperatures in 0.17 M-Na + at high and low tRN14 concentrations are basically the same, indicating that the thermal denaturation behavior is largely independent of the tRNA concentration. The n.m.r. sample shows a broader high temperature transition due to evaporation problems in the sample cell in this temperature range. For the low temperature transition, the n.m.r. sample exhibits less optical change in the 20 to 40°C region, which corresponds to the reduced amplitude of the first relaxation effect due to a smaller fraction of tRNAiMet. and t#herefore is presumably not a concentration-dependent effect.

-

IO0

Temperature PC)

FIG. sample studies 0.1 mm

profiles for the tRNA 4. Comparison of tRNAfMet (0.17 M-N&+) optical denaturetion used in the n.m.r. experiments (0) end tRNA IMet at a concentration typical of the optical (0). The wavelength of measurement was 335 nm. The n.m.r. sample was melted in a pathlength cell.

(c) Relaxaiion

measurements

We found five resolvable relaxation effects in the melting of tRNAfMet illustrated by the photographs in Plate I. The two times observed at low temperature, 71 and TV, are the effects measured earlier (Cole & Crothers, 1972) and called 71&Stand -rsLoW. respectively. Figure 5 shows the temperature variation of the amplitude of the optical change associated with each particular relaxation. We define the T, value for each transition as the t,emperature at the maximum of the corresponding differential melting curve in Figure 5. In separate experiments with purified tRNAtMet and

D. M. CROTHERS

74

tRNAfM*‘(Ecuh)m

20

QG

ET AL.

017u-No+

’ ’ 70’ I 00’ lJ

60 Tempercture (“C)

FIG. 6. Differential thermal transition profiles for the 6 tRNArMet relaxation effects as determined dirootly by temperature-jump. The total amplitude AA for eaoh effect is obtained from the zero-time intercept of the semi-logarithmic plot and divided by the temperature-jump size. The resultant AA/AZ’ is then plotted verszls the temperature corresponding to the midpoint of the temperature-jump size (either 4.0 deg. C for 71 and r2 or 1.8 deg. C for TV,r4, and TV). The amplitude for +o was measured at 280 nm while the other 4 effects were measured at 266 nm.

tRNAiMet we found that the large signal 7s arises from tRNAtMat and the smaller signal 71 arises from tRNAiMet. No other sharply peaked differential melting transitions were observed, although measurements at 266 nm revealed contributions from fast relaxations characteristic of unstacking in single strand regions. These relaxations appea,red mainly in the temperature range between 50 and 9O”C, where the tRNA is partly melted, and were of two kinds. One was the sub-microsecond effect previously reported for single stranded oligomers (Porschke t Eigen, 1971; Craig et al., 1971), and the other had a time constant of about five microseconds. This second effect is analogous to that seen as a minor component in the unstacking kinetics of poly(A) (Cole, 1972) and as an important component in the unstacking of single stranded oligo[d(A-T)] (D. C. Liebe & D. M. Crothers, unpublished observations). These relaxation effects are distinguished from those shown in Figure 5 because they cover a wide temperature range and therefore have small enthalpy changes and do not reflect co-operative loss of structure. Because the fastest co-operative relaxation 7s is slower by only a factor of two to three than one of the non-specific unstacking effects, we found it more convenient

to measure

r3 at 280 nm where its amplitude

dominates

over the non-

specific relaxation. Figure 6 shows the time constants for each of the five relaxations seen in Plate I and Figure 5. With the single exception of 7s the relaxation times are virtually independent

of temperature

at the lowest temperatures

at which they can be detected;

the time constant decreases sharply as the T, value is passed for each transition. Since the relaxation times are well separated on the time axis, and moderately well separated on the temperature scale, it is permissible and convenient to think of each relaxation as approximately corresponding to a transition between two states. (The effects of coupling between relaxations are considered in the Discussion.) Within this approximation we can use a simple equation (Gralla & Crothers, 1973b ; see Table 2) to estimate the enthalpy change of each effect. The values calculated from the width at half height of the differential peaks in Figure 5 are shown in Table 2, along with T, values for each transition.

THERMAL

IrNFOLDING

OF

E. COLT

tRX’A’“‘e’

’ ’ 29’ ’ 26’ ’ 2’ 10-G 1’ ’ 33’ ’ 32’ ’ 31’ ’ 3.0 34 I/Tf x 103PK-‘1

FIG. 6. Variation of the 6 tRNAfMet relaxation times with reciprocal temperature. Where appropriate, a line representing l/kbl hae been drawn through the high temperature 7 values and 2r at T = T,, and extrapolated back to the k3mp0r8tUE at which the dissociation time constant is 6 ms. The temperature where 8 twofold broadening is observed for the n.m.r. lines of 8 particular helix is indicated by 8 bar, giving experimental uncertainties, on the 6 msec line The temperature uncertainties were estimated so as to include the effects of uncertainties in the time. r3 was measured at 280 nm; all other relaxation times were measured at 266 nm. Tr is the final temperature after the temperature-jump. The cross enclosed by a circle represents 27= l/kmlat T= T,.

(d) Combination of nuclear magnetic resonance melting and relaxation The present n.m.r. melting experiments indicate that each arm of the cloverleaf acts as a unit in exchange of the hydrogen-bonding protons. Furthermore, experiments on model oligonucleotides have shown a single resolvable relaxation effect for melting of each helix section (Gralla & Crothers, 1973a,b; Gralla et al., 1974). We expect that there should be a relaxation effect corresponding to the melting of each helix arm and assign three of the five observed effects to cloverleaf helices. (Coupling between the transitions could produce more than one relaxation per helix section; these complications are considered in the Discussion.) Figure 6 shows the n.m.r. “melting” temperature, drawn as a bar at the five-millisecond level covering the temperature, with estimated uncertainty, at which one observes broadening of the resonance lines from each particular helix. The problem is then to associate each relaxation effect with an n.m.r. melting temperature. In our earlier experiments on n.m.r. melting of a model oligonucleotide (Crothers et al., 1973), we found that the temperature of n.m.r. line broadening could be predicted by estimating the temperature at which the helix dissociation lifetime is five milliseconds. This same model is consistent with our present experiments, and allows us to interpret them simply. We have previously discussed the possibility that under certain conditions factors other than the helix dissociation rate could determine the lifetime of the proton in the double helix (Crothers et al., 1973). Experiments on this general problem are in progress, and preliminary results showing selective

30*1

(fMet

70&2

Anticodon arm 77&2

6112

T#C arm

Acceptor arm

46+1

“ Tertiary ” interaotion in fMet 1 + hUra

3)

T&a (“C)

Structural region

76

76

69

47 (hUra)

-

Predicted (“C)

Tkb

10’

70*10=

5s+ 16’

54f

52&Y,

30fLY.K

AH” (kcal/mol)

63

45

43

-

Predicted AHb (kcal/mol)

of the melting transitions

77

52

55

50

25

Eta (kcal/mol)

of tRNAfMet

1.3 x 10’

1.2 x 10’

1.8 x 10’

1.1 x 104

A~266~ (x-l cm-l)

B De&red as the temperature at the maximum of the differential melting curve (Fig. 5). b Estimated from the data of Gralla & Crothers (1973a) ; the Jacobson-Stockmayer (1950) expression is used for loops larger than 9. T, correoted to 0.17 MNa+. c Determined from the left or right half-width of the differentral melting curves (Fig. 5) using the equation given by Gralla & Crothers (19736). AH = 3.2/(1/Tr,, - l/T,), where T, is the temperature at the right or left half-height. The choice of left or right half-height was made to minimize effects of coupling between relaxations, or to minimize experimental error. * Dissociation activation energies Et were determined from the slope of the mapping lines in Fig. 6. B Extinction coefficient changes (expressed in terms of molar tRNA concentration) at 266 nm for melting of each region. The values were calculated from an analog for hairpin helices of the equation given by Gralla & Crothers (19736) and refer to the T, for each transition. * AH determined from left half-width. 8 AH determined from right half-width.

5

Transition

Some thermodynamic, kinetic and optical properties

TABLE 2

THERMAL

UNFOLDING

OF E. COLZ

tRNAfMet

7;

melting of single base pairs in tRNAEf& have been presented elsewhere (Hilbers et a.1.. 1973); an analysis of the applicable n.m.r. conditions is given in the Appendix. Given the simple assumption that, n.m.r. line broadening is determined by the helix lifetime, it is straightforward to assign a structural meaning to several of the observed relaxation effects. Consider the two-state transition between helix (h) and coil (c) k-1 hC. ---cThe relaxation time 7 is related to the rate constants by the relations : l/~ = k, + k _ 1. On the high temperature side of T, for a particular transition, 7 is dominated by the helix dissociation rate constant k-, (Cole & Crothers, 1972). Furthermore, at T,, 27 = l/k-,. Hence a line through the high temperature T values and the point 2r at T, represents l/k- 1 and should intersect the five millisecond line in the n.m.r. melting range for the helix that corresponds to that relaxation. The construction of the set of lines that connect T values with n.m.r. melting points is the procedure we call “mapping”. In favorable cases there is little or no ambiguity in the mapping process, because the following constraints apply: (a) the mapping line must pass through 27 at T, and the high temperature T values, and its slope must yield an activation energy in reasonable agreement with the enthalpy of helix melting. (Since 7 is usually nearly constant well below T,, k, is virtually temperature independent, and in this event the activation energy for k- 1 would equal the reaction enthalpy.) (b) Each n.m.r. melting range must be associated with one optical relaxation effect. (Note that coupling of relaxations can complicate this constraint; see the Discussion.) With the constraints (a) and (b) we can associate r3 with melting of the T$C helix and 75 with melting of the stem, as shown diagrammatically in Figure 6. Since 72 is absent for tRNAiMet, it cannot arise from melting of the anticodon helix. Hence even though either r2 or 74 could formally be mapped into melting of the anticodon helix (Fig. 6) we draw the actual mapping line to connect r4 with exchange of the anticodon helix hydrogen-bonded protons. This leaves no alternative for 72 but melting of tertiary structure, which is consistent with our previous arguments (Cole & Crothers, 1972) based on the optical properties of the transition. The mapping lines resulting from these considerations are drawn in Figure 6. Activation energies Ef for k-, calculated from the slope of the lines are included in Table 2. In all cases these agree within experimental error with the enthalpy change for the transition measured from the width of the differential melting curves, as is expected if k, is temperature independent. There is no reliably measured optical transition that maps into the observed exchange of the hUra helix protons. A reasonable mapping line could be drawn for TV, but since that transition is absent in tRNAtMet, it cannot be melting of the hUra helix. It is most probable that, hUra helix melting occurs mainly when the tjertiaq structure melts, which would be expected if loss of tertiary structure destabilizes the hUra helix. However, the exchange of the hUra protons at 25°C indicates clearly that the hUra helix can open transiently when the tertiary structure is intact. We are pursuing attempts to observe optically this transient opening, using purified samples of the two tRNA fMet isoaccepting species. These studies will also provide further details on the melting of tertiary structure and the unexpected difference between the two molecules in tertiary structure stability.

78

D. M. CROTHERS

ET

.4 1,. pi

~*“i)tl Acceptor end /

‘-------CCAcH . .

.

.

.

.

.

l

.

.

.

\-,-Anticodon

loop

Aon C P F:

’\ .*’ CAnttcodon

loop

FIQ. 7. Schematic of the molecular mechanism of thermal unfolding of tRNAfMec. The hUra helix can open transiently at low temperature, followed by the simultaneous disruption of “tertiary interactions” and the hUra helix, and then, in succession, T$C helix, anticodon helix, and finally the acceptor stem.

Figure 7 shows a diagrammatic outline of the molecular mechanism of thermal unfolding of tRNA fMet. The mechanism shown is the major path followed; since the individual thermal transitions do overlap somewhat, there will be minor contributions from states in which the order of melting is inverted. An example would be a state with the acceptor stem melted but the anticodon helix intact.

4. Discdon (a) Comparison of equilibrium helix melting paramters with model compound e&mates The transition temperature and enthelpy of each of the four cloverleaf arms can be estimeted from empirical free energy parameters collected by Gralla & Crothers (1973a). The stabilities of the T#C, hUra and anticodon helices are calculated as if they were independent hairpin helices. Since the acceptor stem melts last, we assumed it to be a hairpin helix closing a loop of 69 nucleotides. The free energy of this large loop was estimated by assuming that the loop closure probability for loops between 9 and 59 nucleotides is described by the Jacobson & Stockmeyer (1950) formula. This procedure is supported by the observed rates of loop closure, as described below. All other free energy parameters are those given by Gralla & Crothers (1973a). The theoretical free energy parameters refer to 1 M-S&h concentration. It was therefore necessary to adjust the estimates to O-17 M-N&+ , the condition of the present

THERMAL

UNFOLDING

OF

E. COLZ tRNArMet

79

experiment. This we did by using the observed salt dependence of the first and second transition steps in equilibrium melting curves for tRNAfMet (Cole et d., 1972). (This is only an approximation, since the individual transitions that make up these steps may differ slightly in their salt dependencies.) The resultg of these calculations are shown in Table 2. The predicted enthalpy and T, values agree reasonably well with experiment, although the parameters seem to underestimate LIH consistently. The predicted T, of the hUra helix happens to agree closely with T, for the relaxation effect r2. This must be coincidental since the results show that TV cannot consist solely of melting the hUra helix. However, the calculation is consistent with the idea that the hUra helix melts when the tertiary structure unfolds. (b) Comparison of kinetic values with model compounds At temperatures substantially below a particular T, value, the relaxation time is approximately the reciprocal of the rate of helix formation. For hairpin helices closing moderate sized loops, this time has been found to be 10 to 100 microseconds (Coutts, 1971; Dourlent et al., 1970; Gralla & Crothers, unpublished observations) in rough accord with the time constants of about 15 and 80 microseconds found for T#C! and anticodon helices, respectively. The faster closure of the TI,@ helix may result from nucleation by stacking on the acceptor stem helix. The anticodon helix, in contrast, must grow from a newly formed helix nucleus (Pijrschke & Eigen, 1971; Craig et al., 1971). The rate of closure of the acceptor stem helix is decidedly slower, however, as would be expected for such a large loop. The entropy loss on ring closure should enter the rate constant for that process ; if the Jacobson & Stockmayer (1960) expression is valid for loops between 7 and 59 bases long, then the rate of loop closure for the stem helix should be slower than closure of the anticodon helix by the ratio of (59/7)“j2. This predicts a ratio of 25, in agreement with the observed ratio of (2 ma/80 p) = 25. This justifies the assumption that a Gaussian chain model may be used to calculate loop closure probabilities for rings larger than nine unbonded bases. The unusual temperature dependence of 76 (acceptor stem) below its T, value may be explained by recognizing that its melting transition overlaps that of the anticodon helix (see below). (c) The “typical”

hairpin he&xx

T#C, antiwdon and acceptor stem

Once the tRNA tertiary structure is disrupted, three helices remain whose equilibrium and kinetic melting properties are in reasonable accord with expectation based on the properties of model oligomers, when allowance is made for the average electrostatic effects in tRNAfMet. Because of its slowness and unusual temperature dependence, the last effect, r6, could be assigned to melting of the acceptor stem without further information, while from the n.m.r. melting behavior and optical properties we associate r3 and 74 with TI,IX and anticodon helices, respectively. (d) “Atypical” melting processes: tertiary interaction and the dihydrouracil helix The relaxation effect with the largest amplitude at 266 nm is r2, which by correlation with the n.m.r. results does not arise solely from melting of a cloverleaf helix se&on, although it probably includes melting of the hUra helix. The only realistic additional source we see for this effect in the crystal structure of tRNAPhe (Kim et al.,

80

D. M. CROTHERS

ET

AL.

1973) is the interaction between the hUra and T$C loops. The total enthalpy of the melting process 72 is about 50 kcal/mol, of which the calculation predicts 28 kcal could come from melting the hUra helix. The slow formation time (“7 ms) is consistent with joining regions of the molecule that are widely separated in the melted form. A possible indicator of the process 7s in the n.m.r. spectra is loss of the resonance at -10 to -11 p.p.m. in the temperature range corresponding to TV. It has been suggested that these resonances are from non-hydrogen-bonded ring NH protons whose exchange rates with H,O are decreased by the tertiary structure (Wong et al., 1972aJ). (e) Comparison

with earlier work

In our previous work on the thermal denaturation of tRNA (Cole et al., 1972; Cole & Crothers, 1972; Yang & Crothers, 1972) we divided the process into “early” and “late” transitions, as dictated by the biphasic character of the melting profile. Our general interpretation was that the “early” transition involved loss of tertiary structure, and probably also melting of the hUra helix. That analysis agrees with the present results, since ~~ and rz constitute the early melting transition. However, our present results show that 71 comes from tRNAiMet and 7s from tRNAiMet. The only other tRNA whose thermal unfolding has been studied in detail comparable to E. coli tRNAfMet is yeast tRNAPhe (Romer et al., 1970a,b; Riesner et al., 1973). According to the most recent interpretation (Riesner et al., 1973), the first of five observed relaxations is melting of tertiary structure. The general order of double helix melting appears to be different in the two tRNAs, which is not surprising in view of the different G + C contents and t,heoretical stabilities of the cloverleaf helices. However, there is one clear anomaly in the comparison of the properties of the two tRNAs. According t’o the results of Riesner et al. (1973), the hUra helix in tRNAPhe is one of the last to melt, and is stable to temperatures far above the range where hUra melts in tRNAfMet. Yet the base sequence of the hUra helix is identical in the two instances, except for reversed polarity relative to the loop. Hence if the assignment of hUra melting is correct in both cases, the stability of the hUra helix is significantly affected by factors other than the double helix itself. One possibility to consider is interactions within the hUra loop, whose sequence differs in the two tRNAs. Finally, we note that Riesner et al. (1973) reported differences in stabilities of particular tRNA Phehelices depending on whether these were measured in fragments or in the whole tRNA. They ascribed these differences to electrostatic interactions. This same finding is true for the anticodon, T$C and acceptor stem helices of tRNAfMet, since we get agreement between predicted and observed transition temperatures only when we adjust T, values by using the measured average dependence of transition temperatures on salt concentration. Since this dependence is considerably larger for tRNA (Cole et al., 1972) than for isolated hairpins (Scheffler et al., 1968), the tRNA helices in 0.2 M-Nat are substantially destabilized by elect,rostatic interactions in the whole tRNA. (f) Possible di$kulties

in the mapping

procedure

We mentioned above that the mapping procedure uses the assumption that the n.m.r. lifetime of the proton in the double helix is limited by the dissociation lifetime of the double helix. Circumstances may arise in which this is not the case, for example

THERMAL

UNFOLDING

OF

E. COLI tRNA’Met

81

when the coil -+ helix conversion is very fast as in the T$C arm ; these are discussed in the Appendix. In addition, some other difficulties could arise. Specifically, we have been assumiug (a) that the rate of double helix dissociation can be linearly extrapolated to lower temperatures (as in Fig, 6), and (b) that the mechanism of exchange occurs by the path which governs the thermal unfolding. Two possible difficulties from the breakdown of these assumptions can be simply illustrated by examples. Referring to Figure 6 and the mapping line for the T$C helix, we note that this passes through the temperature region where the “tertiary” structure melts. If the formation of tertiary structure greatly altered the rate of dissociation of the TtjC helix, then the mapping line would not be linearly extrapolated. It is for this reason that we cannot draw a mapping line for the hUra helix: melting of tertiary structure greatly alters t,he equilibrium and kinetic properties of the hUra helix. The difficulty arising from assumption (b) can be illustrated by the failure to predict correctly the tritium exchange kinetics from the thermal unfolding kinetics. If the mapping line for the acceptor stem is extrapolated to 0°C the lifetime of the helix would be about IO8 seconds. Since tritium exchange is much fast,er t,han this (Goldstein et al., 1972) we conclude that some mechanism other than complete dissociation of the acceptor stem helix determines the rate of tritium exchange of t(he protons in that helix. Our reason for pointing out these possible difficulties is that the mapping procedure is new and therefore should be used with caution. However, the self consistency of the method as applied to tRNAfMst is a strong argument for its validity in that case. (g) InJEuence of cozlpling on relaxadm properties For clarity in the presentation and interpretation of our relaxation kinetic results, we have suppressed the possible complications arising from coupling between relaxation processes. In Figure 7 a single path for thermal unfolding of tRNAfMet is presented. This is strictly correct only if the differential melting curves in Figure 5 do not) significantly overlap, so that each transition is complete before the subsequent effect hegias. If this is not true, then intermediates with inverted orders of melting will result, leading, in principle, to additional relaxation effects. This complication is potentially serious only for r4, which overlaps significantly with rs and TV. Within the accuracy of our measurements we were able t’o find only one relaxation effect corresponding to melting of the anticodon helix (r4). This is what one would expect if the rate of opening and closing that helix is independent of whether the acceptor stem helix is intact or not. In this case, which is physically reasonable to it first approximation, only one relaxation should appear. The time constants and amplitude should characterize melting of the anticodon helix taken as a simple independent unit. In a similar manner, melting of the T#C helix appears to be independent of the state of the anticodon helix. In both these cases, however, the margin of experimental error is fairly large: if two relaxation times differ by less than a factor of 2, we would not be able to resolve them. Hence, for example, the kinetic constants for forming the anticodon helix could differ by a factor of 2 depending on t,he state of the acceptor stem, and we would still express the effect as a single relaxation. The error margin is smaller for slower relaxations where our signal-to-noise ratio is better. 6

82

D. M. CROTHERS

ET

AL.

A more easily detected effect of coupling between relaxations is to be seen in the increase of 7s with temperature below its T, value. Since 7s is much slower than r4, one can think of it as a relaxation between ststes in which the acceptor helix is open or closed, with fast equilibration of the anticodon helix in both of these states. As the anticodon helix melts, the average loop that must be closed to form the acceptor helix becomes larger. Hence the closure time and TV increase perceptibly with temperature. In general, we expect that relaxations corresponding to melting of simple hairpin helices will be relatively little affected by the state of the rest of the molecule, and to a first approximation will not be coupled kinetically together. The rate of closing large loops that contain hairpin helices may, however, depend strongly on whether those helices are intact or not, and it may not be possible to consider such a loop as a single, independent unit. (h) Is the native state the form of minimum free energy? One of the important questions concerning macromolecular folding is whether the native state is the conformation of minimum free energy, or whether kinetic factors determine the path of folding, possibly producing a final state which is not the thermodynamically preferred conformation. Our results permit some progress to be made in answering this question for tRNA IMet. For example, 60°C is below the melting temperatures of the T#C, anticodon and acceptor stem helices, so that those parts of the secondary structure are predominantly intact at that temperature. However, according to Figure 6, only about 206 milliseconds would be required for dissociation of the most stable helix, the acceptor stem, under these conditions. Thus, if an alternate secondary structure were preferred at 6O”C, there should be adequate time for dissociation of the native secondary structure and formation of the alternate form. Therefore the thermodynamically preferred secondary structure at 60°C must almost certainly be that which we observe. The same argument is reasonably convincing at 46”C, where the last step in the thermal refolding of tRNAiMet occurs. Under these conditions about 10 seconds would be required for complete dissociation of the acceptor stem. If the thermodynamically preferred form had a totally different secondary structure, whose formation required dissociation of the acceptor stem, with stabilization by a tertiary structural interaction formed at 46”C, then the time scale to seek out this conformation would still be reasonable. Hence from these considerations we suggest that it is extremely likely that tRNAfMet under our salt conditions is in its lowest free energy state, reached by an understandable kinetic pathway. (i) Possible junctional signi$cunce These experiments show that in the absence of Mga+ the hUra helix and tertiary interactions are a weak link in the tRNA lMet three-dimensional structure. Since the hUra helix is located near the junction of the two paths of the “L” structure (Rim et al., 1973), its disruption would allow flexibility of motion between the two major functional sites, namely the anticodon and amino acid acceptor sites. Independent movement of the anticodon and acceptor arms could simplify the mechanistic problems of protein synthesis. For example, if tRNA can become transiently flexible, it could be moved in two steps from one site to another on the ribosome, either the

THERMAL

OF E. COLZ

UNFOLDING

tRNAfMet

83

acceptor stem and amino acid first, followed by the anticodon and messenger RNA, or the other way around. Our results imply that this flexibility could be contributed by unbonding of the hUra helix and/or the tertiary structure. However, the apparent stability of the hUra helix in tRNAPhe indicates that other tRNAs should be examined before generalizations can be made. The view that tRNA structure is reversibly altered during the course of protein synthesis is greatly strengthened by the recent demonstration by Schwarz et al. (1974) that the T#CG sequence in tRNAPhe becomes accessible for oligomer binding when the tRNA is attached to the 30 S ribosomnl subunit.

5. Conclusion The experiments described here provide a view of the molecular mechanism of thermal unfolding of a macromolecule. Since there is such extensive knowledge of tRNA structure, we have not emphasized the conclusions about the intact secondary and tertiary structure that could be drawn from our measurements. However, our observation of four n.m.r. melting zones, with chemical shift values for virtually all the hydrogen-bonded ring NH protons, and the temperature-jump relaxation effects, when combined with the nucleotide sequence of tRNAfMet, would have allowed us to conclude that the molecule has the cloverleaf secondary structure and one major region of tertiary interaction with appreciable hypochromism. It is evident that these same methods can be applied to other tRNAs whose structures are unknown.

APPENDIX

The mapping procedure used to correlate the optical and n.m.r. melting is based on the assumption that the n.m.r. linewidth is determined by the dissociation rate of the helix. This interpretation of the line broadening should be applied with care especially when the coil to helix conversion is very fast. When exchange between two different states A and B occurs, the lifetime r that determines the broadening of the n.m.r. line may vary from the lifetime of one particular state, rA say, to *A

rB

7=-, rA

+

TB

a combination of the lifetimes of both states. In the latter case the lifetime is equivalent to that obtained from the temperature-jump method for a monomolecular reaction, i.e. 7-l = k, + km,, where the transition between the two states is followed optically. As shown below, in some instances the exchange of the ring NH proton between three sites, namely helix, coil and water, has to be invoked in order to explain the line broadening in n.m.r. According to the temperature-jump kinetics the rate of conversion from coil to helix of the T&! stem (7;‘) is 3 x IO5 s-l at 37°C. The dissociation rate 7~~’of the T$! helix at this temperature is about 2 x lOa s-l and for the following reasons this means that on an n.m.r. time scale the interchange between helix and coil is close to or in the fast exchange limit. In this limit (which neglects exchange with water)

84

D. M. CROTHERS

ET

AL.

the line broadening is not determined by the helix lifetime, lifetime

but by the average

which for the TI,GCstem is equal to 2 x 10d6 s. On an n.m.r. time scale a system is in fast exchange between two states when rAw << 1, where Aw = 277(vb--~J, and IQ, and vc are the resonance frequencies of the ring NH proton in the helix and coil states, respectively. Since in our experiment Y,, - vg z 900 Hz, TAW M 10-l, which is indeed smaller than one. Thus if we only take into account the interchange between helix and coil the line broadening of the T#C arm is not simply determined by the helix lifetime. This is also true for the melting of the anticodon stem, although there is close to unity. However, the exchange of the ring NH protons in the coil form with water may modify this picture completely and we therefore investigate below how the exchange with water influences the linewidths of the low field resonances. To that end we adopt the following reaction schemes:

TAW

hHZcH cH + H*OH = cH* + HOH. Thus the ring NH protons are able to exchange between three different environments, h, c and w. The Bloch equations for this case are obtained by extending McConnell’s derivation (McConnell, 1958; Pople et al., 1959) for exchange between two states to the three states of interest. The equations relevant to the description of the lineforms of this system are readily shown to be:

where Q is the complex magnetic moment, aA = l/(T,,) -i(w*--w), and ~ii is the probability per unit time of a nucleus in state A jumping to state B. As usual y is the nuclear gyromagnetic ratio, M ,,* the z component of the magnetization in state A, and H, the amplitude of the r.f. field at frequency w/27r. Note that the direct exchange of helix with water has been omitted in these equations. For some boundary conditions the equations can easily be solved and simple relationships between the line broadening and the lifetimes of the species can be obtained. We give examples for the most important situations that occur for the system under consideration. (a) Slow exchange 6etuteen helix and coil and between co4 and water

In this situation where 7&r and rch’ << (+,-- w,) ; T,;’ and 7;: << (We--w*), there is no overlap between the resonances so that for example at UJ~the contribution of

THERMAL

UNFOLDING

OF E. COLI

tRNAfMe’

8.5

T in GOcan be neglected. Hence the Bloch equations can be written as follows :

dG, -g + c&$ + 76’Gh = -iyHIM,,

dGC

Solution of these equations leads to the well known result that the lines can be observed separately and the linewidths are given by 7f8v = 7-l with r-1 r ~g’,

(7;’ + T,-,‘), or T;:

for the three resolved resonances, and in this case broadenings of the low field resonances are determined by the lifetime of the helix. (b) Slow exchange between helix and coil and fast exchange between coil and water The conditions are T&’ and 7;’ equations for this situation are:

< (a&-~+);

(T,-k

+

T,-,‘)

>> IwW--wcl. The Bloch

dG, x + ah4 + T&'G, = -iyH,Mo,

dGc+

dt

cc,G, +

2 + a,G,

(T&'

+ T,-,‘)G~ - 7&‘Gw = -iyH,M,,,

+ T,-,‘G, - ~,-,‘a~ = -iyH,M,,.

In this case the line broadening of the ring NH protons in the hydrogen bond is determined by the lifetime of the double helix, and the mapping procedure is valid. The coil and water resonances will have merged into one signal and because of the low concentration of nucleic acid one would expect the combined resonance to have a resonance frequency approximately equal to that of water. (c) Fo,.stexchunge between helix and coil and slow exchange between coil and water This situation might be of interest in the melting of the T$C and anticodon arms and will be worked out in some detail. Since we are only interested in the broadening of the low field resonances it is sufficient to consider the following two equations: d6.i T + cc,G, + T~~‘G~- TZ’G, = -iyH,M,h dGc x + u,G, + T~‘G~ + T,-,‘G, - TG’G~ = -iyH,M,,. In the usual steady state approximation dG/dt is assumed to be zero and for the total magnetization G = Gi, -j- G, we obtain G, + G, = -iyH,M,

Tnc+ Toh+ WcnfhT~ + %Tohbcfh + %fc) (TnoQn+ 1) (T,,% + W; + 1) -1 *

86

D. M. CROTHERS

ET

AL.

When exchange between helix and coil is very fast all terms containing the average lifetime, ThCTCh 7= The + Tch ’ can be neglected except for the product r~~;lf,,. Note that in the event that rhc and rCh are grossly unequal T approximately equals the smaller. We consider two extreme situations.

This means that helix and coil interchange many times before exchange with water occurs. In this case the linewidth is given by 1 -=Ta and the line position by G = &w,, + and f. is consequently small so that

J-h Ta, few,.

Under our experimental

conditions f,, m 1

The observed line broadening is determined not by the lifetime of the helix but by “leakage” of the ring NH protons from the coil to water and one is not allowed to apply the simple mapping procedure of Figure 6 to relate the temperature-jump kinetics to the n.m.r. line broadening. In this case the lines can be narrow and shifted to 73,which should be a function of temperature. This would be expected for “frayed” ends of helical oligonucleotides.

In this situation exchange with water occurs virtually The linewidth can be shown to be

every time the helix is open.

and the lifetime of the helix determines the line broadening, so that the mapping is valid. The line position is given by w=. The exchange between coil and water can occur via proton transfer to OH-, phosphate ions or buffer. Because of the concentration of phosphate ions and buffer one would expect them to dominate the proton transfer reaction. From the pK difference between uracil and cacodylate we estimate that 72 g lo6 to IO6 s-l. For the TI,& arm near the n.m.r. “melting” temperature 70h w 2 x 10e6 s < -rhc. Hence~M2x10-5sand~~~1~ 1s comparable to unity. This indicates that widths of the Tt,E resonances might not be completely determined by the lifetime of the helix, but might also be functions of 70h and rcw, and makes the mapping in this particular case somewhat uncertain. On the other hand one can calculate from these relations that the line broadenings of the anticodon resonances are determined by the lifetime of its stem, since 7.;: > 1.

THERMAL

The direction that rcw would take can T,, fc < 1, and one procedure is invalid,

UNFOLDING

OF E. COLZ

tRNAfM”‘

87

the correction of the mapping lines for the influence of 7ch and readily be determined from these considerations. Well below can set fc = r,,Jrhc. In the limiting case (i), where the mapping rch/rcw < 1, and one can write the inequality

Hence in this limit, broadening, which occurs when fc/rcw m 2 x lo2 s-l, implies that 7hcis less than five milliseconds. Therefore, the line representing the true extrapolation of the 7hc values for the T#C helix in Figure 6 could have a slightly smaller slope than the mapping line actually drawn. We conGder it very unlikely that this modification would be sufficient to invalidate the identification of the T#C relaxation. The work at Yale was supported by a grant (GM12589) from the National Institutes of Health. One of us (D. M. C.) holds a Career Development Award (GM19978) from the same source. Another author (P. E. C.) was supported by a Damon Runyon postdoctoral fellowship, and one of us (C. W. H.) gratefully acknowledges partial support by the Niels Stensen Stichting.

REFERENCES Arnott, S. (1971). Prog. Biophys. Mol. Biol. 22, 181-213. Cole, P. E. (1972). Ph.D. Thesis, Yale University. Cole, P. E. & Crothers, D. M. (1972). Biochemistry, 11, 4368-4374. Cole, P. E., Yang, S. K. & Crothers, D. M. (1972). Biochemistry, 11, 4368-4368. Coutts, S. (1971). B&him. Biophys. Acta, 232, 94-106. Craig, M. E., Crothers, D. M. & Doty, P. (1971). J. Mol. Biol. 62, 383-401. Crothers, D. M., Hilbers, C. W. & Shulman, R. G. (1973). Proc. Nut. Acud Sci., U.S.A. 70, 2899-2901. Dourlent, M., Thrierr, J. C., Brun, F. & Leng, M. (1970). Biochem. Biophys. Res. Commun. 41, 1590-1596. Dube, S. K., Marcker, K. A., Clark, B. F. C. & Cory, S. (1968). Nature (London), 218,

232-233. Favre, A., Michelson, A. M. & Yaniv, M. (1971). J. Mol. Biol. 58, 367-379. Goldstein, R. N., Stefanovic, S. & Kallenbach, N. R. (1972). J. Mol. Bid. 69, 217-236. Gralla, J. & Crothers, D. M. (1973a). J. Mol. Btil. 72, 497-511. Gralla, J. & Crothers, D. M. (1973b). J. Mol. BioZ. 78, 301-319. Gralla, J., Steitz, J. & Crothers, D. M. (1974). Nature New BioZ. 248, 204-208. Hilbers, C. W., Shulman, R. G. & Kim, S. H. (1973). Biochem. Biophye. Res. Commun.

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