Thermodynamics of Transfer Ribonucleic Acids: The Effect of Sodium on the Thermal Unfolding of Yeast tRNAPhe ERNEST0 FREIRE and RODNEY L. BILTONEN, Departments of Biochemistry and Pharmacology, University of Virginia School of Medicine, Charlottesville, Virginia 22903 Synopsis The thermal unfolding of yeast phenylalanine-specific tRNA (tRNAPhe)has been calorimetrically investigated a t several salt concentrations in the absence of magnesium. Application of the deconvolution theory of macromolecular conformational transitions allows calculation of the thermodynamic parameters of unfolding. It is demonstrated that the unfolding of tRNAPheoccurs in a sequential fashion and that four separate transitions or five macromolecular thermodynamic states exist in the temperature range 8-72OC under the experimental conditions of these studies (0.067-0.52M Na+). The enthalpy and entropy changes between states and the relative population of each state as a function of temperature and salt concentration have been obtained. Sodium stabilizes the low-temperature conformations of tRNAPhe. The increase in the melting temperatures of each transition is shown to be linearly dependent on the logarithm of sodium concentration. . These results allow calculation of the “phase” diagram for the transitions as a function of salt concentration.
INTRODUCTION Even though considerable experimental work has been directed to the study of the unfolding mechanism of several tRNA species, the thermodynamics of this process and its biological implications remain unclear. There is now considerable experimental evidence supporting the idea that the thermal unfolding of most tRNA molecules proceeds according to a multistate mechanism in which different structural regions of the molecule unfold in a sequential Unfortunately, unfolding mechanisms of this type are difficult to analyze in a direct form and therefore the thermodynamic parameters have been estimated after assuming a workable model which does not necessarily reflect the detailed characteristics of the transition. Recently, the theoretical basis for the deconvolution of a calorimetrically obtained melting profile has been developed.*& It was demonstrated that the partition function of a system can be numerically evaluated from scanning calorimetric data. Having the partition function, the deconvolution theory provides the basis for a complete dissection of a multistate melting profile without any a priori assumptions regarding the thermodynamic mechanism of the reaction. The number of discrete macroscopic energy states, the enthalpy and entropy changes between them, and the Biopolymers, Vol. 17, 1257-1272 (1978) 01978 John Wiley & Sons, Inc.
0006-3525/78/0017-1257$01.00
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FREIRE AND BILTONEN
relative population of each state as a function of temperature can be calculated in a recursive form. These results allow us to systematically investigate the thermodynamic characteristics of the thermal unfolding of yeast phenylalanine-specific tRNA (tRNAPhe)under different solvent conditions. In this article the effects of salt concentration on the melting behavior of tRNAPheare reported. In a future paper (Freire and Biltonen, in preparation) the combined effects of salt and magnesium will be reported.
EXPERIMENTAL SECTION Materials Phenylalanine-specific transfer ribonucleic acid from Brewer's yeast (tRNAPhe)was purchased from Boehringer Manheim Corp. The activity of the tRNAPhewas about lo00 pp mol phe accepted/AzM unit, representing 96-99% of the total biologically active tRNA. The tRNA solutions were prepared according to the method described by Levy et al.7 Solutions of tRNA were prepared by dissolving the tRNA in 10 mM phosphate bkfer (sodium salt) containing 5 mM NaCl and 5 m M EDTA at pH 7.2. This solution was placed in dialyzer tubing that had been boiled twice for 30 min in a solution containing 0.2M EDTA and 0.1M K&04 at pH 10 and then extensively rinsed with distilled water. The solution was then dialyzed for 2 hr at 4°C against 10'00volumes of the same buffer in order to insure complexation by EDTA of any residual Mg2+in the tRNA sample. The Mg-EDTA complex was then removed from the solution by extensive dialysis of the sample against 2000 volumes of 10mM phosphate buffer pH 7.2 containing 5 mM NaC1. The final solution was prepared in each case by extensively dialyzing the sample against the same buffer a t the desired NaCl concentration. The concentration of tRNAPhewas spectrophotometrically determined by absorbance measurements at 257 nm using an extinction coefficient of 5.40 X 105 l./mol cm.7 Typical concentrations of tRNAPhefor the calorimetric and spectrophotometric experiments were 0.3 mM and -2-3 p M , respectively.
Scanning Calorimetry A newly developed differential scanning calorimeter of the heat-conduction type based on the design of Ross and Goldberg8was used for these studies. The calorimeter was designed for measuring heat capacities and heat effects accompanying thermally induced transitions in dilute solution. The temperature range for the instrument is 0-75OC, and scanning rates from 3 to 50°C/hr can be selected. The total volume of the sample compartment is approximately 0.7 ml. The precision in terms of baseline "noise" is better than f 2 5 pcal/"C. Absolute temperature determination is better than f0.05"C.
THERMODYNAMICS OF tRNA UNFOLDING
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All experiments were begun by placing the tRNAPhesample in the calorimeter and cooling it to about 0°C. The heat capacity was then measured during heating a t a rate of 15"C/hr. For the purpose of the analysis, digitized &Cp data were recorded and stored at constant temperature-intervals of 0.1"C. All calculations were performed in a CDC Cyber 172 computer. A brief description of the calorimeter and calculation of the apparent molar heat capacity of the sample, $Cp, are given in Ref. 9.
Spectrophotometric Experiments The thermal unfolding of tRNA was also investigated by optical methods. These experiments were performed with a Perkin-Elmer 356 spectrophotometer by monitoring absorbance changes at 257 nm as a function of temperature. The temperature was continuously increased at an approximate rate of l"C/min by circulating water through a thermostated block containing both sample and reference cells. The temperature was measured with a Digitec 1501 digital thermometer whose probe was permanently immersed in the reference cell. Absorbance and temperature values were simultaneously recorded at 05°C intervals.
THEORY Consider a general multistate unfolding mechanism of the type
in which the transition from an initial folded state, Io, to a final unfolded state, I,, proceeds through (n - 1) partially folded intermediate states. The partition function, Q, of such a system can be written as Q=1
+ K 1 + KlKz + KIK2K3.. .
(24
n
=1
+ i=C1 exp(-AGi/RT)
where the initial state, Io, has been chosen as reference state, i.e., AGi = Gi - Go. T is the absolute temperature and R is the universal gas constant. Q can be obtained from the average excess enthalpy function, (AH), by means of the integral equation InQ= s T d T T~ mRT2
(3)
where To is a temperature at which all molecules exist in the initial state.4 Here, (AH) is experimentally obtained by direct integration of the apparent molar heat capacity function 4Cp
where 6Cp0 is the apparent molar heat capacity of the initial state.
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FREIRE AND BILTONEN
Population Analysis From the partition function, Q, the number of discrete macroscopic energy states, the enthalpy and entropy changes between them, and the relative population of each state as a function of temperature can be calculated in a recursive form.4 The fraction of molecules populating the initial state, Fo, is equal to Q-', and is directly evaluated from Eq. (3). The quantity ( M ) / ( l Fo) defines a new average enthalpy averaged over states 1 to n,
If the transition is of the two-state type, (AH)/( 1 - Fo) is identically equal to the total enthalpy change for the transition. For a multistate transition, however, (AH)/(l - Fo) is an S-shaped curve whose lower limit is equal to the enthalpy difference, Ahl, between the first intermediate and the is equal to initial state. The new average excess enthalpy, (AH,),
where the reference state is now the first intermediate, 11. As a partition function, Q1 is the summation over all the energy states except the initial state 10. In a way similar to that used for calculating Q, Q1 can be evaluated from the equation
If the above procedure is successively repeated, the followingset of recursion relations is obtained:
from which all the thermodynamic parameters describing the unfolding process can be determined. Each of the equilibrium constants Ki defined in Eq. (1) can be calculated in a recursive form by AS. Qi-1 - 1 -Ahi Ki Eexp = R Qi The fraction of molecules populating each particular state i , Fi, can be expressed in a recursive form as
(F+-)
Fi = Fi-i (Qi-1-
1)/Qi
(11)
from which the relative population of each state as a continuous function of the temperature can be obtained. The above formalism implies no a priori assumptions on the particular mechanism of the transition and no
THERMODYNAMICS OF tRNA UNFOLDING
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a priori estimation of the number of intermediate states; all thermodynamic quantities are calculated in a recursive, form from the experimental data.
RESULTS Figure 1 shows the apparent heat capacity function, @Cp,of a tRNA sample containing 0.52M Na+ and no Mg2+. This scan is characterized by a melting temperature, t , (defined as the position of the maximum in & p ) , of 63.4OC and a calorimetric AH (the area under the heat capacity curve in the temperature interval 8-72°C) of 260 kcal/mol. The area under the 4Cp curve was calculated by numerical integration of the quantity (4Cp - &PO), where &PO, the heat capacity afthe initial state, was assumed to be of the form @Cpo= a bT. (PCp, was calculated by a linear leastsquares fit of the initial part of the scan (8-2OoC), and then extrapolated forward over the entire transition interval. The same procedure was applied in all the experiments. The apparent partial heat capacity of tRNA a t 20°C was insensitive to salt concentration and equal to 8 f 1kcal/K mol (0.32 f 0.04 cal/K g); the temperature dependence of +Cpo averaged 65 f 11cal/K2 mol. These numbers are in good agreement with those reported by Hinz et al.3 Table I summarizes the overall thermodynamic parameters obtained a t three different salt concentrations. , In all the experiments the thermodynamic reversibility of the transitions was checked by scanning the same sample twice. Reproducibilities better than 95%were obtained. The calorimetric t , values agreed well with the transition midpoint calculated from hyperchromicity measurements at 257
+
I
A
10
20
30
40 TEMP
50
€4
70
80
OC
Fig. 1. @ C pvs temperature profile of yeast tRNAPheat 0.52M Na+ (10-*M Na2HP04 NaHZP04,0.5M NaCl, pH 7). The solid line is the simulated @Cp profile using the deconvolution parameters. The experimental points have been plotted every 1°C; the actual number of points is 10 times greater. The dotted lines are the upper and lower baselines considered in the error analysis (see text for details).
FREIRE AND BILTONEN
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nm. The t , assigned from the hyperchromicityexperiments was calculated using the temperature at which the measured change in optical density was equal to one-half the total change in optical density measured at high temperature. Since the tRNA concentration in the calorimetric experiments was about 100 times greater than in the optical experiments, we conclude that the transition is concentration independent. The total enthalpy changes for melting are of the same magnitude, although somewhat smaller, than those reported by Hinz et aL3 The difference (seebelow) can be accounted for by the heat effects associated with transitions in the high-temperature region (72-100OC) which we are technically unable to measure with our calorimeter. This fact, however, does not affect the analysis of the transition in the temperature range of our studies. We have previously demonstrated4 that the deconvolution analysis can be performed even if the transition endpoint is unknown or experimentally inaccessible. Since the quantity of interest is the excess heat-capacity function (&p - (PCpo) [see Eq. (4)Jand its calculation is independent of the heat capacity of the final state, the analysis can always be done in the temperature range covered by the experimental data. Thus, all the results presented in this article are restricted to the temperature interval 8-72OC.
Deconvolution Analysis The average excess enthalpy function, (AH),was calculated in each case by numerical integration of (@Cp- (PCpo). The partition function, Q, was calculated with Eq. (3). The thermodynamic parameters characterizing the transition were obtained in a recursive form after successive applications of Eqs. (8) and (9). The details of the calculation procedures are given in Ref. 4. Each Ahi was set equal to the lower limit of the function (mi-1)/ (1 - Q72J [see Eqs. ( 5 ) and (8)]. In all the calculations, the various Ahi were assumed to be temperature independent. The reason for this is twofold. Privalov et a1.2 and Hinz et TABLE I Overall ThermodynamicParameters Associated with the Thermal Unfolding of tRNAPhe "a+]
tma
AHb
ASc
MVHd
m I m V H
0.067M 0.17M 0.52M
47.1 54.0 63.4
269 266 263
834 821 803
31 60 80
7.21 4.43 3.29
a Temperature of
the maximum in $Cp. Area under the heat capacity curve in the temperature interval 8-72OC; kcal/mol of tRNA. c In calm mol. Calculated from deconvolution parameters. AS = AHIT, where T , is defined by Eq. (13). d Apparent van't Hoff enthalpy in kcdmol of tRNA. Calculated with the formula: AHw = 4RT2[($Cp),dAHl. b
THERMODYNAMICS OF tRNA UNFOLDING
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al.3 have demonstrated that, in the absence of Mg2+,the overall ACp for the transition is not greater than 1 kcal/K mol, i.e., -200 cal/K mol per transition step, a figure lower than the experimental error in determining each Ahi. In addition, the magnitude of each Ahi was found to be independent of salt concentration within the limits of the experimental error. Thus, if the various Ahi are temperature dependent, this dependence is very small and for all purposes negligible. The results of the deconvolution analysis are summarized in Table 11. In all the experiments and in the temperature range covered by our studies, the unfolding reaction of tRNAPhe was characterized by four separate transitions or five enthalpically distinct states. The internal consistency of the calculated parameters with the experimental transitions was checked by comparison of the simulated $Cp function defined by the deconvolution parameters and the experimental $Cp. In all the experiments the differences between the experimental and simulated 4Cp curves were within the range of the experimental noise: This is graphically illustrated in Fig. 1. The additional high-temperature transition reported by Hinz et al.3 lies outside the temperature range of our instrument and therefore we have been unable to confirm it. According to these authors, the AH associated with this transition is equal to 58 kcal/mol and accounts for the observed differences in the overall enthalpy changes (see Table 11).
Sources of Error We have previously shown that the accuracy of the deconvolution analysis in determining the thermodynamic parameters of a multistate transition is relatively insensitive to experimental noise and errors introduced by numerical procedures employed. However, erroneous determination of the temperature dependence of $Cp,, or an erroneous determination of the concentration of macromolecule in the calorimeter cell, can influence the results of the analysis. In the first case the shape of the excess-heatTABLE I1 Deconvolution Analysis of the Thermal Unfolding of tRNAPhe Transition 1 2 3 4
“a+] = 0.067M
Aha 44 f 2 61 f 5 89f10 73 f 8
Ahb
tmC
Asd
45 60 82 68
33.4 42.1 48.5 59.0
144 194 277 220
“a+] = 0.17M t,,,= Asd 37.0 45.3 54.0 65.2
142 192 272 216
“a+] = 0.52M tmC Asd 41.4 57.1 62.1 67.9
140 185 266 214
a In kcal/mol, from deconvolution analysis at three salt concentrations (see text for details). The values quoted are averages over three salt concentrations. Ref. 3. In kcal/mol, obtained a t 5 mM sodium phosphate, 150 mM NaC1,l mM EDTA, pH 7.0. From deconvolution analysis. Here t,, is defined as the temperature at which Fi-1 = Fi. In cal/K mol, Asi = AhJT,,,,.
FREIRE AND BILTONEN
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capacity function will be progressively distorted on the temperature scale, whereas in the second case the entire heat capacity function will be incorrect by a constant multiplicative factor, depending on the magnitude of the concentration error. Since the extrapolated baseline in these experiments was unusually long (-5O"C), we examined the possible effects of an incorrect baseline determination on the deconvolution results. This was done by systematically varying the calculated temperature dependence of &po and repeating in each case the entire deconvolution analysis. This procedure is graphically illustrated in Fig. 1,where the two dotted lines represent the maximal and the minimal slopes considered. The difference between these slopes is 30 cal/K2 mol, and exceeds the experimental error with which the slope can be determined. In addition, the difference between the absolute values of the two baselines at 70°C exceeds the magnitude of the overall ACp for the transition reported by Hinz et al.3 Thus, the results obtained in these extreme cases are upper and lower limits of the thermodynamic parameters associated with the unfolding of tRNAPhe. As shown in Table 111,the errors associated with the uncertainty in the extrapolated baseline are relatively small within the above limits. The error in the various Ahi is never greater than 10%and the melting temperatures are only slightly changed. In all cases it was concluded that four transitions occurred over the experimental temperature-interval. The influence of concentration errors on the deconvolution results was also examined. In this case the entire heat capacity function was multiplied by the constant factor (100-%E)/100, where %E is the assumed percent error in the concentration of tRNA. Concentration errors up to f10% were considered. From previous studies in this laboratory,lo we estimate that ~ WisO an upper limit for our experimental error in determining the tRNA concentration. As shown in Table 111, a 10%error in the concentration introduces larger errors in the thermodynamic parameters than those introduced by the uncertainty in the extrapolated slope. However, these errors are still small and in no way affect the deduced thermodynamic characteristics of the transition. TABLE I11 Error Analysis of the Deconvolution Parameters "a+] 0.52M
%Ea 0 0 0 0 10 -10
bb
t,:
103 95 82 70 82 82
41.9 41.6 41.4 41.2 41.0 42.1
a Assumed % error in
Ahld
tmlc
41 42 43 46 45 40
58.2 57.7 57.1 56.6 56.0 57.8
56 57 58 62 54 53
tm3c
Ah3d
tmlc
Ahdd
62.1 62.1 62.1 62.2 61.7 62.4
86 88 89 95 100 89
68.2 67.9 67.8 67.8 67.3 69
76 78 83 86 95 75
tRNA concentration. Temperature dependence of 6Cp0;in cal/K2 mol. From deconvolution analysis; tmiis the temperature at which Fj-1 = Fj In kcal/mol; from deconvolution analysis.
THERMODYNAMICS OF tRNA UNFOLDING
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We thus conclude that the unfolding transition of tRNAPhecan be accurately described in terms of five thermodynamic states over the range of experimental conditions explored. This is not meant to imply that no other intermediate states exist, but only that such states are not significantly populated during the course of the transition. Although we cannot place an exact figure upon what is significant, we estimate it to be no more than 5%. This estimate is based upon results obtained from deconvolution analysis of many experimental and computer-simulated transition curves.4
Salt Dependence of the Transition The dependence of the transition temperature on salt concentration can be studied by considering the reaction 1 0 e 14. Independently of the microscopic nature of the transition, the salt dependence of the melting temperature can be expressed a d 1 dT,ld ln[Na+] = (RTk/aH)ANa
(12)
where ANa is the number of “bound” Na+ ions released into the solution per tRNA molecule during the transition, AH is the overall enthalpy change, and T, is the temperature at which the free-energy difference, AG4, is zero. For a sequential transition mechanism, T , is given by
and can be calculated from the deconvolution parameters in Table 11. From these parameters we obtained t, of 47.1, 52.0, and 59.5”C for the experiments at 0.067,0.17, and 0.52M Na+, respectively. As shown in Fig. 2(a) these values agree reasonably well with the transition temperatures calculated from hyperchromicity measurements at 257 nm, over a wider “a+] range. This result indicates that the transition temperatures calculated from hyperchromicity measurements at 257 nm provide a good estimate for the overall T, of tRNAPhe. This is not necessarily so for a multistate transition. As typical in nucleic acids,12-14this dependence is linear over a wide salt-concentration range indicating that ANa is constant in that range. A linear least-squares fit of the data yielded dT,ld In “a+] = 5.8, from which we calculated a ANa value of 7.0 for the overall reaction. Consider now each separate step in the overall reaction. For each individual transition step, a similar relation to Eq. (12) holds, (14) dTJd ln[Na+] = (RT,$/Ahi)ANai where ANai is the differential binding term between the (i - 1)th and ith states. Thus, having Ahi and TmL at various salt concentrations [Fig. 2(b)], it is possible to estimate ANai for each transition as tabulated in Table IV. The consistency of these values is demonstrated by the good agreement
FREIRE AND BILTONEN
1266
at
*Ot
bl
Fig. 2. (a) Dependence of the melting temperature ( t , ) of tRNAPheon the logarithm of sodium concentration. Filled circles are defined as the temperature at which the O.D. change at 257 nm is one-half the total change. Triangles were calculated with Eq. (13) and the thermodynamic parameters obtained from the deconvolution analysis. (b) Dependence of the melting temperature ( t m i )of the four sequential transitions of yeast tRNAPhe on the logarithm of sodium concentration. TABLE IV Salt Dependence of the Thermodynamic Parameters Associated with the Thermal Unfolding of tRNAPhein the Absence of Mg2+104 11t 2 1 2 e3 13 e4 14 Transition
dTmi d In "a+]
ANaib a
a
1
2
3
4
3.9
7.2
6.6
4.4
0.9
1.9
2.6
1.5
From linear least-squares analysis of Tmivs ln[Na] ("C). Calculated with Eq.(14).
found between ZANai = 6.9 calculated from the deconvolution result and the overall value of 7.0 for ANa calculated from the spectroscopic results. The above results allow us to express the melting temperature of each particular transition step in terms of the natural logarithm of sodium concentration as follows: tml = 43.94 3.91 ln[Na+] tm2= 60.39 + 7.23 ln[Na+] tm3= 66.01 6.56 ln[Na+] tm4= 71.59 4.38 ln[Na+] where "a+] is the sodium concentration expressed in molh. These equations are accurate to within 1°C. For the overall melting temperature we obtain t, = 62.4 5.81 ln[Na+] (16) for the sodium concentration range of 0.001-0.5M.
+
+ +
+
THERMODYNAMICS OF tRNA UNFOLDING
1267
Relative Population of States Figure 3 shows the relative population of states, Fi, as a function of temperature for the three salt concentrations studied. As defined by Eq. (ll),the various Fi represent the average fraction of tRNA molecules populating a particular macroscopic energy state; in this sense, the population vs temperature diagrams of intermediate states are characterized by bellshaped functions which go to a maximum and then decrease to zero as the next energy state becomes populated. For a sequential transition, the relative populations of the initial and final states are the only ones characterized by S-shaped curves. Since the excess heat capacity function (6Cp - @?PO) is equal to the temperature derivative of the excess enthalpy function, ( A H ) , it follows that
Fig. 3. Relative populations vs temperature of the five thermodynamic states associated with the thermal unfolding of yeast tRNAPhea t three salt concentrations: (a) 0.067M Na+, (b) 0.17M Na+, and (c) 0.52M Na+.
FREIRE AND BILTONEN
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i.e., the contribution of each transition step to the overall 4Cp function is proportional to the derivative dFiIdT. This is illustrated in Fig, 4 for the experiment at 0.067M Na+, and should be contrasted with the usual practice of approximating the overall heat capacity function by a collection of bell-shaped curves.
DISCUSSION Privalov et aL2and Hinz et aL3have previously analyzed the heat capacity function of tRNA by fitting the experimental data to a theoretical curve, which assumes that the sequential unfolding of tRNA can be approximated by a collection of independent noninteracting two-state processes in which each elementary process corresponds to the melting of a particular structural region of the molecule. There are several problems regarding this approximation which are circumvented by the deconvolution analysis. The first is related to the nonuniqueness of the set of thermodynamic parameters obtained by fitting the heat capacity function of tRNA to 10 or more highly correlated variables, and the arbitrariness in the determination of the number of transitions to which the experimental curve is fitted. The deconvolution analysis involves no fitting of the experimental data: the thermodynamic param-
'20
30
40
50 TEMP
60
70
OC
Fig. 4. Apparent excess heat-capacity function of yeast tRNAphe a t 0.067M Na+. The solid line is the simulated curve by the deconvolution parameters. The experimental points have been plotted every 1 O C . The dotted lines are the calculated contributions of each transition step to the overall heat capacity curve. The deviation between the calculated and experimental heat capacity curves a t high temperature is real; it most likely represents the existence of yet another transition a t higher temperature, as has been reported by Hinz et a1.3
THERMODYNAMICS OF tRNA UNFOLDING
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eters of a sequential transition are obtained in a recursive form from the actual data. The second problem is related to the range of validity of the assumption that a sequential transition can be approximated by a collection of two-state transitions. In this respect, the deconvolution analysis directly yields the thermodynamic parameters of the transition and the number of macroscopic macromolecular energy states. For this reason the deconvolution results serve as a definite test for assessing the range of validity of a model of independent transitions as an approximation to a sequential transition, and for discriminating between these two unfolding mechanisms. Under certain circumstances, the model of independent two-state transitions can provide reasonable estimates for the thermodynamic parameters of a sequential transition. This is only so, however, when a t any particular region of the independent variable, two consecutive macromolecular energy states are the only ones significantly populated and together account for -100% of the total population of molecules. This situation is experimentally realized when the individual transition steps in Eq. (1) are well separated on the temperature scale. Under those circumstances, the melting profiles of the sequential transition and the model of independent two-state transitions are identical and therefore thermodynamically indistinguishable. As shown in Fig. 3 this situation is never absolutely met in the transition region, specially at high salt concentrations, where transitions 2,3, and 4 strongly overlap. Only at intermediate salt concentrations (-0.1-0.2M), where transitions 2, 3, and 4 are separated by 7-10°C, does the model of independent transitions provide reasonably good estimates for the thermodynamic parameters. It is in this concentration range that the enthalpies and melting temperatures calculated by Hinz et al.3 qualitatively and quantitatively agree with the results of our deconvolution analysis. This is not so for their calculated melting temperatures at 20 mM NaC1. This disagreement is more a computational problem than a real difference in the experimental data. Computer simulation of their $Cp profile at 20 mM NaCl is consistent with our data for the sequential transitions of tRNAPhe. The agreement between the parameters calculated by Hinz et al.3 and the results of our analysis a t 150 mM Na+ do not imply that the various structural regions of tRNAPhemelt independently, but rather that under those particular salt conditions the melting profiles associated with the model of independent transitions and the sequential transition coincide. This coincidence can be verified by simulating the heat capacity profiles associated with the two unfolding mechanisms. There is, however, a fundamental difference between a sequential transition and a transition which is the sum of several independent twostate transitions, and this difference is primarily related to the total number of accessible macromolecular energy states. Whereas a sequential transition of n transition steps generates ( n 1)macromolecular energy states,
+
1270
FREIRE AND BILTONEN
a collection of n independent two-state transitions generates 2 n macromolecular energy states. This difference can be experimentally tested by allowing the temperature spacing between transitions to vary. For example, if the n two-state transitions of the model of independent transitions are well separated in the temperature scale, only ( n 1)macromolecular states will be populated during the unfolding reaction and the observed melting profile will be identical to that of a sequential transition. On the other hand, when the temperature spacing between transitions decreases, the Z n accessible states will progressively become populated and the melting profile will be much broader than the one expected from a sequential transition with the same parameters. At high salt concentrations or in the presence of Mg2+,where the transition steps in Eq. (1) are closely spaced (see Fig. 2), the model of independent transitions does not provide enough cooperativity to account for the observed melting profiles. This model overcounts the number of accessible macromolecular energy states and therefore overestimates the entropy of the system. Macromolecular states like, for example, the one in which the secondary structure is melted but the tertiary structure is intact are implicitly counted as accessible states even though they are not structurally allowed. For this reason this model cannot provide a consistent picture of the salt and Mg2+ dependence of the unfolding reaction. For example, the sharpest heat capacity profile attainable with this model will occur when all the Tmiare the same; under these conditions, the heat ca~ ~given , by2 pacity maximum, ( C $ C P ) ~ is
+
(C$cP)max = C (AfC/4RTi)
(18)
Z
and the unfolding transition will exhibit a maximum in the heat capacity curve of -20 kcal/K mol. With a model of independent transitions, $Cp maxima larger than 20 kcal/K mol are impossible to attain for the unfolding of tRNAPhe. The peak maximum a t 0.52M Na+ is of this order of magnitude, but the transition temperatures are dispersed over a temperature interval of about 25°C. In the presence of Mg2+,C$Cp maxima of -50 kcal/K mol have been observed3.15 (Freire and Biltonen, in preparation), indicating that the effects of salt and Mg2+cannot be interpreted by redistributing elementary two-state processes on the temperature scale. The fact that the number of macromolecular states remains unchanged after increasing the salt concentration up to 0.52Msuggests the existence of intramolecular structural constraints which prevent the independent melting of the various structural regions of the molecule. The inclusion of the additional high-temperature transition reported by Hinz et aL3 indicates that the total number of macromolecular energy states accessible to the tRNAPhe molecule in the absence of Mg2+ is six. This number is identical to the one expected from the sequential melting of the tertiary structure and the four helical regions of the molecule, but much smaller than the 32 allowed conformations expected from the independent melting
THERMODYNAMICS OF tRNA UNFOLDING
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of these structural regions. It thus appears that each branch of the tRNA molecule behaves as a single cooperative unit whose stability is determined by internal as well as intramolecular interactions. This conclusion is consistent with studies on tRNA fragments which indicate that the thermodynamic stability of isolated regions is not the same as those observed in the whole molecule.l6,17 As shown in Fig. 2, the overall melting temperature is linearily dependent on the logarithm of salt concentration over a 500-fold concentration range. This pattern is similar to that observed in DNA and synthetic polynucleotides,l2J4 suggesting a common molecular mechanism by which Na+ stabilizes the native structure of these molecules. As depicted in Fig. 2(b), the effect of Na+ on transitions 2, 3, and 4 is greater than the effect on transition 1. If the first transition is assigned to the melting of the main part of the tertiary structure, it follows that Na+ preferentially stabilizes the cloverleaf structure of the molecule. A t very high salt concentrations the high-temperature transitions are predicted to have almost identical melting temperatures, whereas the first transition is predicted to occur a t much lower temperatures. These results qualitatively agree with the salt diagrams obtained by Cole et al.18J9for other tRNA species. The above calorimetric evidence, as well as the results of the deconvolution analysis, indicate that the thermal unfolding of tRNAPhe is a sequential transition over the entire salt-concentration range of these studies. These results also indicate that the assumptions made by Hinz et al.3 for calculating the thermodynamic parameters of the transition are valid in the salt-concentration range of their studies. However, those assumptions are incorrect when the transitions are closely spaced, as occurs at high ionic strength or in the presence of Mg2+. This work was supported by a grant from the National Institutes of Health (GM20637).
References 1. Crothers, D., Cole, P., Hilbers, C. & Shulman, R. (1974) J . Mol. Biol. 87,63-88. 2. Privalov, P., Filiminov, V., Venkstern, T. & Bayev, A. (1975) J . Mol. Biol. 97, 279288. 3. Hinz, H., Filiminov, V. & Privalov, P. (1977) Eur. J. Biochem. 72.79-86. 4. Freire, E. & Biltonen, R. (1978) Biopolymers 17,463-479. 5. Freire, E. & Biltonen, R. (1978) Biopolymers 17,481-496. 6. Freire, E. & Biltonen, R. (1978) Biopolymers 17,497-510. 7. Levy, J., Rialdi, G . & Biltonen, R. (1972) Biochemistry 11,4138-4144. 8. Ross, P. & Goldberg, R. (1974) Thermochim. Acta 10,143-151. 9. Suurkuusk, J., Lentz, B., Barenholz, Y., Biltonen, R. & Thompson, T. (1976) Biochemistry 15,1393-1401. 10. Levy, J. (1972) Ph.D. dissertation, Johns Hopkins University. 11. Wyman, J. (1964) Adu. Protein Chem. 19,223-286. 12. Archer, B., Craney, C. & Krakauer, H. (1972) Biopolymers 11,781-809. 13. Manning, G. (1972) Biopolymers 11,937-949. 14. Record, T. (1975) Biopolymers 14,2137-2158. 15. Brandts, J., Jackson, W. & Yao-Chung Ting, T. (1974) Biochemistry 13,3595-3600.
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FREIRE AND BILTONEN
16. Riesner, D., Maass, G., Thiebe, R., Philippsen, P. & Zachau, H. (1973) Eur. J . Biochem. 36.76-88. 17. Kallenbach, N., Ma, R., Ofengand, J. & Siddiqui, M. (1973) Biopolymers 12, 12471257. 18. Cole, P., Yang, S. & Crothers, D. (1972) Biochemistry 11,4358-4367. 19. Cole, P. & Crothers, D. (1972) Biochemistry 11,4368-4381.
Received August 10,1977 Accepted September 16,1977
INTRODUCTION Even though considerable experimental work has been directed to the study of the unfolding mechanism of several tRNA species, the thermodynamics of this process and its biological implications remain unclear. There is now considerable experimental evidence supporting the idea that the thermal unfolding of most tRNA molecules proceeds according to a multistate mechanism in which different structural regions of the molecule unfold in a sequential Unfortunately, unfolding mechanisms of this type are difficult to analyze in a direct form and therefore the thermodynamic parameters have been estimated after assuming a workable model which does not necessarily reflect the detailed characteristics of the transition. Recently, the theoretical basis for the deconvolution of a calorimetrically obtained melting profile has been developed.*& It was demonstrated that the partition function of a system can be numerically evaluated from scanning calorimetric data. Having the partition function, the deconvolution theory provides the basis for a complete dissection of a multistate melting profile without any a priori assumptions regarding the thermodynamic mechanism of the reaction. The number of discrete macroscopic energy states, the enthalpy and entropy changes between them, and the Biopolymers, Vol. 17, 1257-1272 (1978) 01978 John Wiley & Sons, Inc.
0006-3525/78/0017-1257$01.00
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FREIRE AND BILTONEN
relative population of each state as a function of temperature can be calculated in a recursive form. These results allow us to systematically investigate the thermodynamic characteristics of the thermal unfolding of yeast phenylalanine-specific tRNA (tRNAPhe)under different solvent conditions. In this article the effects of salt concentration on the melting behavior of tRNAPheare reported. In a future paper (Freire and Biltonen, in preparation) the combined effects of salt and magnesium will be reported.
EXPERIMENTAL SECTION Materials Phenylalanine-specific transfer ribonucleic acid from Brewer's yeast (tRNAPhe)was purchased from Boehringer Manheim Corp. The activity of the tRNAPhewas about lo00 pp mol phe accepted/AzM unit, representing 96-99% of the total biologically active tRNA. The tRNA solutions were prepared according to the method described by Levy et al.7 Solutions of tRNA were prepared by dissolving the tRNA in 10 mM phosphate bkfer (sodium salt) containing 5 mM NaCl and 5 m M EDTA at pH 7.2. This solution was placed in dialyzer tubing that had been boiled twice for 30 min in a solution containing 0.2M EDTA and 0.1M K&04 at pH 10 and then extensively rinsed with distilled water. The solution was then dialyzed for 2 hr at 4°C against 10'00volumes of the same buffer in order to insure complexation by EDTA of any residual Mg2+in the tRNA sample. The Mg-EDTA complex was then removed from the solution by extensive dialysis of the sample against 2000 volumes of 10mM phosphate buffer pH 7.2 containing 5 mM NaC1. The final solution was prepared in each case by extensively dialyzing the sample against the same buffer a t the desired NaCl concentration. The concentration of tRNAPhewas spectrophotometrically determined by absorbance measurements at 257 nm using an extinction coefficient of 5.40 X 105 l./mol cm.7 Typical concentrations of tRNAPhefor the calorimetric and spectrophotometric experiments were 0.3 mM and -2-3 p M , respectively.
Scanning Calorimetry A newly developed differential scanning calorimeter of the heat-conduction type based on the design of Ross and Goldberg8was used for these studies. The calorimeter was designed for measuring heat capacities and heat effects accompanying thermally induced transitions in dilute solution. The temperature range for the instrument is 0-75OC, and scanning rates from 3 to 50°C/hr can be selected. The total volume of the sample compartment is approximately 0.7 ml. The precision in terms of baseline "noise" is better than f 2 5 pcal/"C. Absolute temperature determination is better than f0.05"C.
THERMODYNAMICS OF tRNA UNFOLDING
1259
All experiments were begun by placing the tRNAPhesample in the calorimeter and cooling it to about 0°C. The heat capacity was then measured during heating a t a rate of 15"C/hr. For the purpose of the analysis, digitized &Cp data were recorded and stored at constant temperature-intervals of 0.1"C. All calculations were performed in a CDC Cyber 172 computer. A brief description of the calorimeter and calculation of the apparent molar heat capacity of the sample, $Cp, are given in Ref. 9.
Spectrophotometric Experiments The thermal unfolding of tRNA was also investigated by optical methods. These experiments were performed with a Perkin-Elmer 356 spectrophotometer by monitoring absorbance changes at 257 nm as a function of temperature. The temperature was continuously increased at an approximate rate of l"C/min by circulating water through a thermostated block containing both sample and reference cells. The temperature was measured with a Digitec 1501 digital thermometer whose probe was permanently immersed in the reference cell. Absorbance and temperature values were simultaneously recorded at 05°C intervals.
THEORY Consider a general multistate unfolding mechanism of the type
in which the transition from an initial folded state, Io, to a final unfolded state, I,, proceeds through (n - 1) partially folded intermediate states. The partition function, Q, of such a system can be written as Q=1
+ K 1 + KlKz + KIK2K3.. .
(24
n
=1
+ i=C1 exp(-AGi/RT)
where the initial state, Io, has been chosen as reference state, i.e., AGi = Gi - Go. T is the absolute temperature and R is the universal gas constant. Q can be obtained from the average excess enthalpy function, (AH), by means of the integral equation InQ= s T d T T~ mRT2
(3)
where To is a temperature at which all molecules exist in the initial state.4 Here, (AH) is experimentally obtained by direct integration of the apparent molar heat capacity function 4Cp
where 6Cp0 is the apparent molar heat capacity of the initial state.
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FREIRE AND BILTONEN
Population Analysis From the partition function, Q, the number of discrete macroscopic energy states, the enthalpy and entropy changes between them, and the relative population of each state as a function of temperature can be calculated in a recursive form.4 The fraction of molecules populating the initial state, Fo, is equal to Q-', and is directly evaluated from Eq. (3). The quantity ( M ) / ( l Fo) defines a new average enthalpy averaged over states 1 to n,
If the transition is of the two-state type, (AH)/( 1 - Fo) is identically equal to the total enthalpy change for the transition. For a multistate transition, however, (AH)/(l - Fo) is an S-shaped curve whose lower limit is equal to the enthalpy difference, Ahl, between the first intermediate and the is equal to initial state. The new average excess enthalpy, (AH,),
where the reference state is now the first intermediate, 11. As a partition function, Q1 is the summation over all the energy states except the initial state 10. In a way similar to that used for calculating Q, Q1 can be evaluated from the equation
If the above procedure is successively repeated, the followingset of recursion relations is obtained:
from which all the thermodynamic parameters describing the unfolding process can be determined. Each of the equilibrium constants Ki defined in Eq. (1) can be calculated in a recursive form by AS. Qi-1 - 1 -Ahi Ki Eexp = R Qi The fraction of molecules populating each particular state i , Fi, can be expressed in a recursive form as
(F+-)
Fi = Fi-i (Qi-1-
1)/Qi
(11)
from which the relative population of each state as a continuous function of the temperature can be obtained. The above formalism implies no a priori assumptions on the particular mechanism of the transition and no
THERMODYNAMICS OF tRNA UNFOLDING
1261
a priori estimation of the number of intermediate states; all thermodynamic quantities are calculated in a recursive, form from the experimental data.
RESULTS Figure 1 shows the apparent heat capacity function, @Cp,of a tRNA sample containing 0.52M Na+ and no Mg2+. This scan is characterized by a melting temperature, t , (defined as the position of the maximum in & p ) , of 63.4OC and a calorimetric AH (the area under the heat capacity curve in the temperature interval 8-72°C) of 260 kcal/mol. The area under the 4Cp curve was calculated by numerical integration of the quantity (4Cp - &PO), where &PO, the heat capacity afthe initial state, was assumed to be of the form @Cpo= a bT. (PCp, was calculated by a linear leastsquares fit of the initial part of the scan (8-2OoC), and then extrapolated forward over the entire transition interval. The same procedure was applied in all the experiments. The apparent partial heat capacity of tRNA a t 20°C was insensitive to salt concentration and equal to 8 f 1kcal/K mol (0.32 f 0.04 cal/K g); the temperature dependence of +Cpo averaged 65 f 11cal/K2 mol. These numbers are in good agreement with those reported by Hinz et al.3 Table I summarizes the overall thermodynamic parameters obtained a t three different salt concentrations. , In all the experiments the thermodynamic reversibility of the transitions was checked by scanning the same sample twice. Reproducibilities better than 95%were obtained. The calorimetric t , values agreed well with the transition midpoint calculated from hyperchromicity measurements at 257
+
I
A
10
20
30
40 TEMP
50
€4
70
80
OC
Fig. 1. @ C pvs temperature profile of yeast tRNAPheat 0.52M Na+ (10-*M Na2HP04 NaHZP04,0.5M NaCl, pH 7). The solid line is the simulated @Cp profile using the deconvolution parameters. The experimental points have been plotted every 1°C; the actual number of points is 10 times greater. The dotted lines are the upper and lower baselines considered in the error analysis (see text for details).
FREIRE AND BILTONEN
1262
nm. The t , assigned from the hyperchromicityexperiments was calculated using the temperature at which the measured change in optical density was equal to one-half the total change in optical density measured at high temperature. Since the tRNA concentration in the calorimetric experiments was about 100 times greater than in the optical experiments, we conclude that the transition is concentration independent. The total enthalpy changes for melting are of the same magnitude, although somewhat smaller, than those reported by Hinz et aL3 The difference (seebelow) can be accounted for by the heat effects associated with transitions in the high-temperature region (72-100OC) which we are technically unable to measure with our calorimeter. This fact, however, does not affect the analysis of the transition in the temperature range of our studies. We have previously demonstrated4 that the deconvolution analysis can be performed even if the transition endpoint is unknown or experimentally inaccessible. Since the quantity of interest is the excess heat-capacity function (&p - (PCpo) [see Eq. (4)Jand its calculation is independent of the heat capacity of the final state, the analysis can always be done in the temperature range covered by the experimental data. Thus, all the results presented in this article are restricted to the temperature interval 8-72OC.
Deconvolution Analysis The average excess enthalpy function, (AH),was calculated in each case by numerical integration of (@Cp- (PCpo). The partition function, Q, was calculated with Eq. (3). The thermodynamic parameters characterizing the transition were obtained in a recursive form after successive applications of Eqs. (8) and (9). The details of the calculation procedures are given in Ref. 4. Each Ahi was set equal to the lower limit of the function (mi-1)/ (1 - Q72J [see Eqs. ( 5 ) and (8)]. In all the calculations, the various Ahi were assumed to be temperature independent. The reason for this is twofold. Privalov et a1.2 and Hinz et TABLE I Overall ThermodynamicParameters Associated with the Thermal Unfolding of tRNAPhe "a+]
tma
AHb
ASc
MVHd
m I m V H
0.067M 0.17M 0.52M
47.1 54.0 63.4
269 266 263
834 821 803
31 60 80
7.21 4.43 3.29
a Temperature of
the maximum in $Cp. Area under the heat capacity curve in the temperature interval 8-72OC; kcal/mol of tRNA. c In calm mol. Calculated from deconvolution parameters. AS = AHIT, where T , is defined by Eq. (13). d Apparent van't Hoff enthalpy in kcdmol of tRNA. Calculated with the formula: AHw = 4RT2[($Cp),dAHl. b
THERMODYNAMICS OF tRNA UNFOLDING
1263
al.3 have demonstrated that, in the absence of Mg2+,the overall ACp for the transition is not greater than 1 kcal/K mol, i.e., -200 cal/K mol per transition step, a figure lower than the experimental error in determining each Ahi. In addition, the magnitude of each Ahi was found to be independent of salt concentration within the limits of the experimental error. Thus, if the various Ahi are temperature dependent, this dependence is very small and for all purposes negligible. The results of the deconvolution analysis are summarized in Table 11. In all the experiments and in the temperature range covered by our studies, the unfolding reaction of tRNAPhe was characterized by four separate transitions or five enthalpically distinct states. The internal consistency of the calculated parameters with the experimental transitions was checked by comparison of the simulated $Cp function defined by the deconvolution parameters and the experimental $Cp. In all the experiments the differences between the experimental and simulated 4Cp curves were within the range of the experimental noise: This is graphically illustrated in Fig. 1. The additional high-temperature transition reported by Hinz et al.3 lies outside the temperature range of our instrument and therefore we have been unable to confirm it. According to these authors, the AH associated with this transition is equal to 58 kcal/mol and accounts for the observed differences in the overall enthalpy changes (see Table 11).
Sources of Error We have previously shown that the accuracy of the deconvolution analysis in determining the thermodynamic parameters of a multistate transition is relatively insensitive to experimental noise and errors introduced by numerical procedures employed. However, erroneous determination of the temperature dependence of $Cp,, or an erroneous determination of the concentration of macromolecule in the calorimeter cell, can influence the results of the analysis. In the first case the shape of the excess-heatTABLE I1 Deconvolution Analysis of the Thermal Unfolding of tRNAPhe Transition 1 2 3 4
“a+] = 0.067M
Aha 44 f 2 61 f 5 89f10 73 f 8
Ahb
tmC
Asd
45 60 82 68
33.4 42.1 48.5 59.0
144 194 277 220
“a+] = 0.17M t,,,= Asd 37.0 45.3 54.0 65.2
142 192 272 216
“a+] = 0.52M tmC Asd 41.4 57.1 62.1 67.9
140 185 266 214
a In kcal/mol, from deconvolution analysis at three salt concentrations (see text for details). The values quoted are averages over three salt concentrations. Ref. 3. In kcal/mol, obtained a t 5 mM sodium phosphate, 150 mM NaC1,l mM EDTA, pH 7.0. From deconvolution analysis. Here t,, is defined as the temperature at which Fi-1 = Fi. In cal/K mol, Asi = AhJT,,,,.
FREIRE AND BILTONEN
1264
capacity function will be progressively distorted on the temperature scale, whereas in the second case the entire heat capacity function will be incorrect by a constant multiplicative factor, depending on the magnitude of the concentration error. Since the extrapolated baseline in these experiments was unusually long (-5O"C), we examined the possible effects of an incorrect baseline determination on the deconvolution results. This was done by systematically varying the calculated temperature dependence of &po and repeating in each case the entire deconvolution analysis. This procedure is graphically illustrated in Fig. 1,where the two dotted lines represent the maximal and the minimal slopes considered. The difference between these slopes is 30 cal/K2 mol, and exceeds the experimental error with which the slope can be determined. In addition, the difference between the absolute values of the two baselines at 70°C exceeds the magnitude of the overall ACp for the transition reported by Hinz et al.3 Thus, the results obtained in these extreme cases are upper and lower limits of the thermodynamic parameters associated with the unfolding of tRNAPhe. As shown in Table 111,the errors associated with the uncertainty in the extrapolated baseline are relatively small within the above limits. The error in the various Ahi is never greater than 10%and the melting temperatures are only slightly changed. In all cases it was concluded that four transitions occurred over the experimental temperature-interval. The influence of concentration errors on the deconvolution results was also examined. In this case the entire heat capacity function was multiplied by the constant factor (100-%E)/100, where %E is the assumed percent error in the concentration of tRNA. Concentration errors up to f10% were considered. From previous studies in this laboratory,lo we estimate that ~ WisO an upper limit for our experimental error in determining the tRNA concentration. As shown in Table 111, a 10%error in the concentration introduces larger errors in the thermodynamic parameters than those introduced by the uncertainty in the extrapolated slope. However, these errors are still small and in no way affect the deduced thermodynamic characteristics of the transition. TABLE I11 Error Analysis of the Deconvolution Parameters "a+] 0.52M
%Ea 0 0 0 0 10 -10
bb
t,:
103 95 82 70 82 82
41.9 41.6 41.4 41.2 41.0 42.1
a Assumed % error in
Ahld
tmlc
41 42 43 46 45 40
58.2 57.7 57.1 56.6 56.0 57.8
56 57 58 62 54 53
tm3c
Ah3d
tmlc
Ahdd
62.1 62.1 62.1 62.2 61.7 62.4
86 88 89 95 100 89
68.2 67.9 67.8 67.8 67.3 69
76 78 83 86 95 75
tRNA concentration. Temperature dependence of 6Cp0;in cal/K2 mol. From deconvolution analysis; tmiis the temperature at which Fj-1 = Fj In kcal/mol; from deconvolution analysis.
THERMODYNAMICS OF tRNA UNFOLDING
1265
We thus conclude that the unfolding transition of tRNAPhecan be accurately described in terms of five thermodynamic states over the range of experimental conditions explored. This is not meant to imply that no other intermediate states exist, but only that such states are not significantly populated during the course of the transition. Although we cannot place an exact figure upon what is significant, we estimate it to be no more than 5%. This estimate is based upon results obtained from deconvolution analysis of many experimental and computer-simulated transition curves.4
Salt Dependence of the Transition The dependence of the transition temperature on salt concentration can be studied by considering the reaction 1 0 e 14. Independently of the microscopic nature of the transition, the salt dependence of the melting temperature can be expressed a d 1 dT,ld ln[Na+] = (RTk/aH)ANa
(12)
where ANa is the number of “bound” Na+ ions released into the solution per tRNA molecule during the transition, AH is the overall enthalpy change, and T, is the temperature at which the free-energy difference, AG4, is zero. For a sequential transition mechanism, T , is given by
and can be calculated from the deconvolution parameters in Table 11. From these parameters we obtained t, of 47.1, 52.0, and 59.5”C for the experiments at 0.067,0.17, and 0.52M Na+, respectively. As shown in Fig. 2(a) these values agree reasonably well with the transition temperatures calculated from hyperchromicity measurements at 257 nm, over a wider “a+] range. This result indicates that the transition temperatures calculated from hyperchromicity measurements at 257 nm provide a good estimate for the overall T, of tRNAPhe. This is not necessarily so for a multistate transition. As typical in nucleic acids,12-14this dependence is linear over a wide salt-concentration range indicating that ANa is constant in that range. A linear least-squares fit of the data yielded dT,ld In “a+] = 5.8, from which we calculated a ANa value of 7.0 for the overall reaction. Consider now each separate step in the overall reaction. For each individual transition step, a similar relation to Eq. (12) holds, (14) dTJd ln[Na+] = (RT,$/Ahi)ANai where ANai is the differential binding term between the (i - 1)th and ith states. Thus, having Ahi and TmL at various salt concentrations [Fig. 2(b)], it is possible to estimate ANai for each transition as tabulated in Table IV. The consistency of these values is demonstrated by the good agreement
FREIRE AND BILTONEN
1266
at
*Ot
bl
Fig. 2. (a) Dependence of the melting temperature ( t , ) of tRNAPheon the logarithm of sodium concentration. Filled circles are defined as the temperature at which the O.D. change at 257 nm is one-half the total change. Triangles were calculated with Eq. (13) and the thermodynamic parameters obtained from the deconvolution analysis. (b) Dependence of the melting temperature ( t m i )of the four sequential transitions of yeast tRNAPhe on the logarithm of sodium concentration. TABLE IV Salt Dependence of the Thermodynamic Parameters Associated with the Thermal Unfolding of tRNAPhein the Absence of Mg2+104 11t 2 1 2 e3 13 e4 14 Transition
dTmi d In "a+]
ANaib a
a
1
2
3
4
3.9
7.2
6.6
4.4
0.9
1.9
2.6
1.5
From linear least-squares analysis of Tmivs ln[Na] ("C). Calculated with Eq.(14).
found between ZANai = 6.9 calculated from the deconvolution result and the overall value of 7.0 for ANa calculated from the spectroscopic results. The above results allow us to express the melting temperature of each particular transition step in terms of the natural logarithm of sodium concentration as follows: tml = 43.94 3.91 ln[Na+] tm2= 60.39 + 7.23 ln[Na+] tm3= 66.01 6.56 ln[Na+] tm4= 71.59 4.38 ln[Na+] where "a+] is the sodium concentration expressed in molh. These equations are accurate to within 1°C. For the overall melting temperature we obtain t, = 62.4 5.81 ln[Na+] (16) for the sodium concentration range of 0.001-0.5M.
+
+ +
+
THERMODYNAMICS OF tRNA UNFOLDING
1267
Relative Population of States Figure 3 shows the relative population of states, Fi, as a function of temperature for the three salt concentrations studied. As defined by Eq. (ll),the various Fi represent the average fraction of tRNA molecules populating a particular macroscopic energy state; in this sense, the population vs temperature diagrams of intermediate states are characterized by bellshaped functions which go to a maximum and then decrease to zero as the next energy state becomes populated. For a sequential transition, the relative populations of the initial and final states are the only ones characterized by S-shaped curves. Since the excess heat capacity function (6Cp - @?PO) is equal to the temperature derivative of the excess enthalpy function, ( A H ) , it follows that
Fig. 3. Relative populations vs temperature of the five thermodynamic states associated with the thermal unfolding of yeast tRNAPhea t three salt concentrations: (a) 0.067M Na+, (b) 0.17M Na+, and (c) 0.52M Na+.
FREIRE AND BILTONEN
1268
i.e., the contribution of each transition step to the overall 4Cp function is proportional to the derivative dFiIdT. This is illustrated in Fig, 4 for the experiment at 0.067M Na+, and should be contrasted with the usual practice of approximating the overall heat capacity function by a collection of bell-shaped curves.
DISCUSSION Privalov et aL2and Hinz et aL3have previously analyzed the heat capacity function of tRNA by fitting the experimental data to a theoretical curve, which assumes that the sequential unfolding of tRNA can be approximated by a collection of independent noninteracting two-state processes in which each elementary process corresponds to the melting of a particular structural region of the molecule. There are several problems regarding this approximation which are circumvented by the deconvolution analysis. The first is related to the nonuniqueness of the set of thermodynamic parameters obtained by fitting the heat capacity function of tRNA to 10 or more highly correlated variables, and the arbitrariness in the determination of the number of transitions to which the experimental curve is fitted. The deconvolution analysis involves no fitting of the experimental data: the thermodynamic param-
'20
30
40
50 TEMP
60
70
OC
Fig. 4. Apparent excess heat-capacity function of yeast tRNAphe a t 0.067M Na+. The solid line is the simulated curve by the deconvolution parameters. The experimental points have been plotted every 1 O C . The dotted lines are the calculated contributions of each transition step to the overall heat capacity curve. The deviation between the calculated and experimental heat capacity curves a t high temperature is real; it most likely represents the existence of yet another transition a t higher temperature, as has been reported by Hinz et a1.3
THERMODYNAMICS OF tRNA UNFOLDING
1269
eters of a sequential transition are obtained in a recursive form from the actual data. The second problem is related to the range of validity of the assumption that a sequential transition can be approximated by a collection of two-state transitions. In this respect, the deconvolution analysis directly yields the thermodynamic parameters of the transition and the number of macroscopic macromolecular energy states. For this reason the deconvolution results serve as a definite test for assessing the range of validity of a model of independent transitions as an approximation to a sequential transition, and for discriminating between these two unfolding mechanisms. Under certain circumstances, the model of independent two-state transitions can provide reasonable estimates for the thermodynamic parameters of a sequential transition. This is only so, however, when a t any particular region of the independent variable, two consecutive macromolecular energy states are the only ones significantly populated and together account for -100% of the total population of molecules. This situation is experimentally realized when the individual transition steps in Eq. (1) are well separated on the temperature scale. Under those circumstances, the melting profiles of the sequential transition and the model of independent two-state transitions are identical and therefore thermodynamically indistinguishable. As shown in Fig. 3 this situation is never absolutely met in the transition region, specially at high salt concentrations, where transitions 2,3, and 4 strongly overlap. Only at intermediate salt concentrations (-0.1-0.2M), where transitions 2, 3, and 4 are separated by 7-10°C, does the model of independent transitions provide reasonably good estimates for the thermodynamic parameters. It is in this concentration range that the enthalpies and melting temperatures calculated by Hinz et al.3 qualitatively and quantitatively agree with the results of our deconvolution analysis. This is not so for their calculated melting temperatures at 20 mM NaC1. This disagreement is more a computational problem than a real difference in the experimental data. Computer simulation of their $Cp profile at 20 mM NaCl is consistent with our data for the sequential transitions of tRNAPhe. The agreement between the parameters calculated by Hinz et al.3 and the results of our analysis a t 150 mM Na+ do not imply that the various structural regions of tRNAPhemelt independently, but rather that under those particular salt conditions the melting profiles associated with the model of independent transitions and the sequential transition coincide. This coincidence can be verified by simulating the heat capacity profiles associated with the two unfolding mechanisms. There is, however, a fundamental difference between a sequential transition and a transition which is the sum of several independent twostate transitions, and this difference is primarily related to the total number of accessible macromolecular energy states. Whereas a sequential transition of n transition steps generates ( n 1)macromolecular energy states,
+
1270
FREIRE AND BILTONEN
a collection of n independent two-state transitions generates 2 n macromolecular energy states. This difference can be experimentally tested by allowing the temperature spacing between transitions to vary. For example, if the n two-state transitions of the model of independent transitions are well separated in the temperature scale, only ( n 1)macromolecular states will be populated during the unfolding reaction and the observed melting profile will be identical to that of a sequential transition. On the other hand, when the temperature spacing between transitions decreases, the Z n accessible states will progressively become populated and the melting profile will be much broader than the one expected from a sequential transition with the same parameters. At high salt concentrations or in the presence of Mg2+,where the transition steps in Eq. (1) are closely spaced (see Fig. 2), the model of independent transitions does not provide enough cooperativity to account for the observed melting profiles. This model overcounts the number of accessible macromolecular energy states and therefore overestimates the entropy of the system. Macromolecular states like, for example, the one in which the secondary structure is melted but the tertiary structure is intact are implicitly counted as accessible states even though they are not structurally allowed. For this reason this model cannot provide a consistent picture of the salt and Mg2+ dependence of the unfolding reaction. For example, the sharpest heat capacity profile attainable with this model will occur when all the Tmiare the same; under these conditions, the heat ca~ ~given , by2 pacity maximum, ( C $ C P ) ~ is
+
(C$cP)max = C (AfC/4RTi)
(18)
Z
and the unfolding transition will exhibit a maximum in the heat capacity curve of -20 kcal/K mol. With a model of independent transitions, $Cp maxima larger than 20 kcal/K mol are impossible to attain for the unfolding of tRNAPhe. The peak maximum a t 0.52M Na+ is of this order of magnitude, but the transition temperatures are dispersed over a temperature interval of about 25°C. In the presence of Mg2+,C$Cp maxima of -50 kcal/K mol have been observed3.15 (Freire and Biltonen, in preparation), indicating that the effects of salt and Mg2+cannot be interpreted by redistributing elementary two-state processes on the temperature scale. The fact that the number of macromolecular states remains unchanged after increasing the salt concentration up to 0.52Msuggests the existence of intramolecular structural constraints which prevent the independent melting of the various structural regions of the molecule. The inclusion of the additional high-temperature transition reported by Hinz et aL3 indicates that the total number of macromolecular energy states accessible to the tRNAPhe molecule in the absence of Mg2+ is six. This number is identical to the one expected from the sequential melting of the tertiary structure and the four helical regions of the molecule, but much smaller than the 32 allowed conformations expected from the independent melting
THERMODYNAMICS OF tRNA UNFOLDING
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of these structural regions. It thus appears that each branch of the tRNA molecule behaves as a single cooperative unit whose stability is determined by internal as well as intramolecular interactions. This conclusion is consistent with studies on tRNA fragments which indicate that the thermodynamic stability of isolated regions is not the same as those observed in the whole molecule.l6,17 As shown in Fig. 2, the overall melting temperature is linearily dependent on the logarithm of salt concentration over a 500-fold concentration range. This pattern is similar to that observed in DNA and synthetic polynucleotides,l2J4 suggesting a common molecular mechanism by which Na+ stabilizes the native structure of these molecules. As depicted in Fig. 2(b), the effect of Na+ on transitions 2, 3, and 4 is greater than the effect on transition 1. If the first transition is assigned to the melting of the main part of the tertiary structure, it follows that Na+ preferentially stabilizes the cloverleaf structure of the molecule. A t very high salt concentrations the high-temperature transitions are predicted to have almost identical melting temperatures, whereas the first transition is predicted to occur a t much lower temperatures. These results qualitatively agree with the salt diagrams obtained by Cole et al.18J9for other tRNA species. The above calorimetric evidence, as well as the results of the deconvolution analysis, indicate that the thermal unfolding of tRNAPhe is a sequential transition over the entire salt-concentration range of these studies. These results also indicate that the assumptions made by Hinz et al.3 for calculating the thermodynamic parameters of the transition are valid in the salt-concentration range of their studies. However, those assumptions are incorrect when the transitions are closely spaced, as occurs at high ionic strength or in the presence of Mg2+. This work was supported by a grant from the National Institutes of Health (GM20637).
References 1. Crothers, D., Cole, P., Hilbers, C. & Shulman, R. (1974) J . Mol. Biol. 87,63-88. 2. Privalov, P., Filiminov, V., Venkstern, T. & Bayev, A. (1975) J . Mol. Biol. 97, 279288. 3. Hinz, H., Filiminov, V. & Privalov, P. (1977) Eur. J. Biochem. 72.79-86. 4. Freire, E. & Biltonen, R. (1978) Biopolymers 17,463-479. 5. Freire, E. & Biltonen, R. (1978) Biopolymers 17,481-496. 6. Freire, E. & Biltonen, R. (1978) Biopolymers 17,497-510. 7. Levy, J., Rialdi, G . & Biltonen, R. (1972) Biochemistry 11,4138-4144. 8. Ross, P. & Goldberg, R. (1974) Thermochim. Acta 10,143-151. 9. Suurkuusk, J., Lentz, B., Barenholz, Y., Biltonen, R. & Thompson, T. (1976) Biochemistry 15,1393-1401. 10. Levy, J. (1972) Ph.D. dissertation, Johns Hopkins University. 11. Wyman, J. (1964) Adu. Protein Chem. 19,223-286. 12. Archer, B., Craney, C. & Krakauer, H. (1972) Biopolymers 11,781-809. 13. Manning, G. (1972) Biopolymers 11,937-949. 14. Record, T. (1975) Biopolymers 14,2137-2158. 15. Brandts, J., Jackson, W. & Yao-Chung Ting, T. (1974) Biochemistry 13,3595-3600.
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16. Riesner, D., Maass, G., Thiebe, R., Philippsen, P. & Zachau, H. (1973) Eur. J . Biochem. 36.76-88. 17. Kallenbach, N., Ma, R., Ofengand, J. & Siddiqui, M. (1973) Biopolymers 12, 12471257. 18. Cole, P., Yang, S. & Crothers, D. (1972) Biochemistry 11,4358-4367. 19. Cole, P. & Crothers, D. (1972) Biochemistry 11,4368-4381.
Received August 10,1977 Accepted September 16,1977
