The Mechanism of Stabilization of the Structure of Nuclease-T’ by Binding of Ligands”

The rate of unfolding of Nuclease-T’ at pH 8, 20” was determined as a function of concentration of the ligands deoxythymidine 3’,5’-diphosphate (pdTp) and Ca2+ on the basis of the rate of exchange between free fragment, Nuclease-T-(50-149) and labeled fragment, Nuclease-T-(50-149) incorporated in the structure of Nuclease-T’ (Taniuchi, H. (1973) J. Biol. Chem. 248, 5164-5174). The rate constant of unfolding of unliganded Nuclease-T’ was 4.6 x lo-’ s-l. Those of Nuclease-T’ bound with pdTp, with Ca2+, and with both pdTp and Ca2+ were 9.0 x 10m5, 1.6 x lo-‘, and 2.2 x 10m5 s-l, respectively. The association constants of pdTp and Ca2+ with Nuclease-T’ were found to be 1.0 x 10” and 2.0 x lo* M-‘, respectively. Those of pdTp with Nuclease-T’ plus Ca2+ and of Ca2+ with Nuclease-T’ plus pdTp were 4 x lo5 and 1.4 x 10’ M-l, respectively. The calculation of free energy change on the basis of the association constants shows that the magnitude of negative free energy change involved in the binding

The rate of unfolding of Nuclease-T' at pH 8, 20" was determined as a function of concentration of the ligands deoxythymidine 3', and Ca2+ on the basis of the rate of exchange between free fragment, Nuclease-T-(50-149) and labeled fragment, Nuclease-T-(50-149) incorporated in the structure of Nuclease-T' (Taniuchi, H. (1973) J. Biol. Chem. 248, 5164-5174). The rate constant of unfolding of unliganded Nuclease-T' was 4.6 x lo-' s-l. Those of Nuclease-T' bound with pdTp, with Ca2+, and with both pdTp and Ca2+ were 9.0 x 10m5, 1.6 x lo-', and 2.2 x 10m5 s-l, respectively. The association constants of pdTp and Ca2+ with Nuclease-T' were found to be 1.0 x 10" and 2.0 x lo* M-', respectively. Those of pdTp with Nuclease-T' plus Ca2+ and of Ca2+ with Nuclease-T' plus pdTp were 4 x lo5 and 1.4 x 10' M-l, respectively. The calculation of free energy change on the basis of the association constants shows that the magnitude of negative free energy change involved in the binding of either of the two ligands increases by approximately 2 kcal when the other ligand is already bound. There is a correlation between the free energy change and the suppression of the unfolding in the binding of ligands to Nuclease-T'.
The greater the magnitude of negative free energy change of the association of the ligands, the larger the increase in the stabilization energy of the structure of Nuclease-T'. The results are interpreted to suggest that the local interactions between the ligands and the binding site of Nuclease-T' may be specifically coupled with the cooperative interactions operating throughout the three-dimensional structure resulting in strengthening of the interactions throughout the structure, including those with the ligands, without a large change in conformation.
In the previous report (2) we presented a statistical mode of folding of staphylpcoccal nuclease. It is proposed that two similar native conformations of nuclease exist in higher and lower energy states, an activated and a ground state, under physiological conditions and that the folding of disordered nuclease into the activated state occurs statistically with little change in the conformational energy. The transition from the activated to the ground state would occur by development of a unique state of cooperative interactions throughout the threedimensional structure. It is assumed that the transition between the activated and ground state involves a large change of the stabilization energy maintaining the structure without a large change in conformation.
In order to test whether the stabilization energy of the structure of nuclease can change substantially without a large change in conformation, we examined quantitatively the relationship between binding of ligands to Nuclease-T' and stabilization of the structure. It is known that the binding of the ligands pdTp' and Ca 2+ to nuclease (4) and Nuclease-T *The preliminary accounts of this work were presented at the Biochemistry/Biophysics 1974 Meeting (1). 'The abbreviations used are: pdTp, deoxythymidine 3',, labeled fragment, Nuclease-T-(50-149), containing on average 3 covalently bound [l-l%]-stabilizes the structure against heat denaturation (5) and suppresses the motility (6) without a large change in conformation (7-10). In the present studies we have used the rate of unfolding of Nuclease-T' as an index of the stabilization energy of the structure of Nuclease-T' (2). We have estimated the rate of unfolding of Nuclease-T' by measuring the rate of exchange between free Nuclease-T-(50-149)2 and labeled Nuclease-T-(50-149) incorporated into the structure of Nuclease-T' (2) as a function of concentration of ligands at 20". The associati6n constants of the ligands to Nuclease-T' and the rate constants of unfolding of liganded Nuclease-T' have been determined.
2Fragments of nuclease have been designated by an adaptation of the rules of the Commission on Biochemical Nomenclature (11). The prototype is "trivial name-(X-Y)," where the trivial name denotes the origin of the fragment and X and Y, the NH,-and COOH-terminal amino acids, respectively. For example, Nuclease-T is composed of two fragments,  and Nuclease-T-(50-149) (or Nuclease-T-(49-149)), of staphylococcal nuclease (5, 12). The reconstituted Nuclease-T is called Nuclease-T'.
involved in the association of the ligands and the increase in activation free energy of unfolding of Nuclease-T' by binding of the ligands are calculated. The mechanism of stabilization of the structure of Nuclease-T' by binding of the ligands is discussed in relation to the mechanism of folding of the nuclease chain.

EXPERIMENTAL PROCEDURES
The methods used for preparation of Nuclease-T' containing .
for measurement of the rate of exchange -between free Nuclease-T-(50-149) and [l-"C]acetyl-Nuclease-T-  incorporated in the structure of Nuclease-T' and for calculation of the rate of unfolding of Nuclease-T', were described previously (2) with the following exceptions.
In the exchange experiments with the ligands, a solution containing the sample of labeled Nuclease-T' in 10 to 15 ~1 of 0.1 M ammonium acetate, pH 8, was placed in a small test tube (2). Another small test tube-contained Nuclease-T-(50-149), a snecified amount (see below) of ndTo.* or Ca2+, or both and EDTA,'when necessary, in 0.9 ml of approximately 0.1 M ammonium acetate, pH 8. The two solutions were equilibrated at 20" for 10 min before they were mixed.
After incubation at 20" for a given time, the test tube containing the mixture was immediately placed in an ice bath for a few minutes.
The through the jacket with a Haake type F bath. The sample solution, in a 3-ml quartz cuvette of l-cm light path, was equilibrated at a given temperature by a separate circulation system.

Rate Constant of Unfolding of Nuclease-T' as Function of Concentration
of pdTp and Ca2+-The rate constant of unfolding of unliganded Nuclease-T' was 4.6 x lo-' s-' at 20", pH 8. The rate of unfolding of Nuclease-T' decreased with increase in concentration of pdTp in both the presence and absence of Ca2+ (Fig. 1). The apparent rate constant of unfolding approached a limiting value as the concentration of pdTp increased. The limiting value was much smaller in the presence of Ca2+ than in its absence (Fig. 1). The suppression of unfolding of Nuclease-T' was also more pronounced as the concentration of Ca2+ was increased in the presence and in the absence of pdTp (Fig. 2). Similarly, the limiting value of the apparent rate constant of unfolding was distinctly smaller in the presence of pdTp than in its absence (Fig. 2). The limiting value for the apparent rate constant of unfolding obtained when the concentration of pdTp was increased at a constant concentration (3.3 mM) of Ca'+ was equal to 2.1 x 10m5 s-l ( The rate constants of unfolding of Nuclease-T' bound with pdTp alone and bound with Ca2+ alone were 9.0 x 1O-5 and 1.6 x lo-' s, respectively, at 20", pH 8. The association constant of pdTp with Nuclease-T in the absence of Ca2+ and that of Ca2+ with Nuclease-T' in the absence of pdTp were 1.0 x 10" and 2.0 x 10' M-, respectively (20", pH 8). The association constant of Ca2+ with Nuclease-T' bound with pdTp was estimated on the basis of Equation 15 as follows. The value for the rate constant of unfolding of Nuclease-T' at zero concentration of Ca2+ in the presence of 1.6 mM pdTp (9.4 x 10m5 s-l (Fig. 2)) was assigned as the value for Y,. The value for Y, (the rate constant of unfolding of Nuclease-T' bound with both pdTp and Ca2+, in this case) was assumed to be 2.3 x lo-5 s-' (Fig. 2). The best fit of data for Equation 15 for Ca2+ in the presence of 1.6 mM pdTp ( Fig. 2) gave an association constant of Ca2+ with Nuclease-T' bound with pdTp of 1.4 x 10" Mm' (20", pH 8). The rate constant of unfolding of Nuclease-T' as a function of concentration of pdTp in the presence of 3.3 mM Ca2+ (Fig. 2) was used to calculate the association constant of pdTp with Nuclease-T' bound with Ca 2+. The calculation was carried out on the basis of Equation 24 (see "Appendix").
The value for the rate constant of unfolding of unliganded Nuclease-T' and those of Nuclease-T' bound with Ca2+ alone and of Nuclease-T' bound with both pdTp and Ca'+, (4.6 x lo-', 1.6 x 10m4, and 2.1 x 10m5 s-l, respectively) were assigned as the values for Y,,, Y, and YPc, respectively. The value for K, was assumed to be 2.0 x lo2 M-'.

Relationship
between Free Energy Change Involved in Binding of Ligands to Nuclease-T' and Degree of Suppression of Unfolding Nuclease-T'- Table  I lists the values obtained above for the association constant of the ligands with Nuclease-T' and for the rate constants of unfolding of liganded Nuclease-T'.
The free energy change involved in the binding of the ligands and the activation free energy of unfolding of Nuclease-T' bound with the ligands are also shown in Table I. If the binding of the ligands with Nuclease-T' follows the equilibrium reaction expressed in Equations 5 to 8 (under "Appendix") and K,, KS, KS, and K, represent the corresponding association constants (Table I), the product of K, and K, should be equal to that of K, and K, (Equation 9). The calculated values for K,K, and for K,K, are 1.4 x iO* and 0.8 x 10' (M-'), respectively ( Table I). The two values may be regarded as fairly close, considering the experimental errors involved in the estimation of each value of the association constants (2). The values for R = K,/K, and for R = K,/K, (Equation 10, under "Appendix") are much greater than unity indicating the existence of strong cooperativity in the binding 20 40 60 50 of pdTp and Ca*+ with Nuclease-T' (see "Appendix"). The 0 strong enhancement of the binding of one ligand in the presence of the other is consistent with the earlier observations of Cuatrecasas et al. (4) showing that pdTp binds to nuclease only in the presence of calcium ion.
There is an intimate relationship between the strength of binding of the ligands to Nuclease-T' and the stabilization of -the structure of Nuclease-T'.
The greater the magnitude of negative free energy change involved in the binding of the I0.r _ ligands to Nuclease-T', the smaller the rate constant of unfolding of Nuclease-T' bound with the ligands (   of nuclease and Nuclease-T' was determined by amino acid analysis. removed without any effect on the enzymic activity of the The Drocedure to set the Drotected Pockels cell-cuvette holder unit in complex. Therefore, tyrosine residue 113 located near pdTp the Eel1 compartment of-the polarimeter sometimes caused a slight misalignment of the Pockels cell due to a mechanical situation involved in the attachment of the jacketed block (see "Experimental Procedures"). This resulted in a shift of the base-line of the measurement which could not be accurately corrected in the calculation of ellipticity (18). The apparent difference of the magnitude of change of ellipticity by thermal transition in the two experiments of Nuclease-T' (Curues I and 2) is probably caused by the mechanical situation of the instrument. However, the mode of change of circular dichroism of each sample should be independent of this disadvantage since the unit placed in the cell compartment was not moved during the series of the measurements as a function of temperature.
The values for the midpoints of thermal transition of nuclease and Nuclease-T' in the absence of the ligands are approximately 50 and 33", respectively (2). In the presence of 21 FM on pdTp and 5 mM of CaCl,, the values for the midpoints of the transition of nuclease and Nuclease-T' were approximately 65 and 45", respectively, and in the presence of 158 pM of pdTp and the same concentration of CaCl, they were approximately 68 and 48", respectively (Fig. 3). The values for the apparent rate constant of unfolding of Nuclease-T' (20") at 21 and 158 pM of pdTp, calculated on the basis of Equation 24 (see "Appendix") under the conditions used in the experiments in Fig. 3 (Curues 1 and 2, respectively), are 9.5 x 10m5 and 3.1 x 1O-5 s-', respectively.
The difference between these two values is qualitatively consistent with the shift toward higher temperature of thermal transition of Nuclease-T' at the higher concentration of pdTp' (Fig. 3).

DISCUSSION
Although pdTp and Ca2+ may interact with Nuclease-T' in a nonspecific way, it is assumed that the ligands bind only in the specific binding sites, elucidated by x-ray crystallographic studies of the three-dimensional structure of liganded nuclease (19) and that the binding of the ligands results in the observed suppression of unfolding of Nuclease-T'. The atomic coordi-'Preliminary experiments show that the rate constant of unfolding of Nuclease-T' in the presence of both pdTp and Cal+ is highly dependent on temperature similarly to unliganded Nuclease-T' (2). However, further studies, including determination of change of enthalpy, involved in the association of ligands to Nuclease-T' are necessary before the kinetic parameters of the unfolding and refolding of Nuclease-T' can be quantitatively correlated with the thermodynamic parameters of the thermal transition. may be assumed to belong to Nuclease-(l-126).
Hence, there may be no direct contact between pdTp and Nuclease-(99-149) in the ordered structure of type II complex.s Nonetheless, the interactions between Nuclease-( 1-126) and Nuclease-(99-149) in type II complex are strengthened by the binding of ligands. These observations indicate that the suppression of unfolding of Nuclease-T' by the binding of ligands is due not to prevention of an orderly unfolding but rather to strengthening of the cooperative interactions throughout the three-dimensional structure.
The free energy of binding of either pdTp or calcium ion to Nuclease-T' decreases by approximately 2 kcal when the other ligand is already bound. Arnone et al. (19) have pointed out that the minimum possible distance between the calcium ion and an oxygen atom of the 5'-phosphate group of pdTp in the structure of liganded nuclease (3 A) is too great for any strong interaction.
Therefore, the cooperativity between the binding of pdTp and calcium ion to Nuclease-T' is probably due not to a direct interaction between the two bound ligands but rather to the coupling of the interactions in the ligand-binding sites with the interactions in the three-dimensional structure of Nuclease-T'. This hypothesis is supported by the observations that the increase in the activation free energy of the unfolding of Nuclease-T' by binding of both pdTp and Ca'+ is greater than the sum of the increase in the activation free energy of the unfolding caused by binding of each ligand (Table I).
Unlike unfolding, the rate of folding of Nuclease-T' is independent of temperature and the presence of ligands (17). These observations imply that the energy barrier of folding of Nuclease-T' is entropic, and the magnitude of the energy barrier is unchanged in the presence of pdTp and calcium ion. That is, the rate of formation of Nuclease-T' from the two fragments is determined by the probability of two polypeptide chains folding to a specific spatial arrangement, and the rate of the statistical search of the specific folding does not increase in the presence of the ligands. In contrast, we assume that the energy barrier of unfolding of Nuclease-T' is increased by binding of the ligands and that the increase of the energy barrier is equal to the increase in the stabilization energy maintaining the structure of Nuclease-T'. For example, the "Residues 114 to 149 can be removed from an atomic model of nuclease without disturbing any other residues.
binding of pdTp to Nuclease-T' results in a free energy change On the basis of Equation 10, the following three cases can be of -5.4 kcal. Part of this free energy change (-1 kcal) is considered. contributed by the stabilization of the structure (Table I). In other words, if the local interactions with pdTp at the binding Case 1 R = 1, that is K, = K,, K, = K, Case 2 R > 1, that is K, > K,, K, > K, site do not specifically couple with the interactions operating Case 3 R < 1, that is K, < K,, K, < K, throughout the three-dimensional structure of Nuclease-T', the free energy change involved in the binding of pdTp would be -4.4 kcal instead of -5.4 kcal and no ligand-induced stabilization of Nuclease-T' would occur. On the basis of these considerations we interpret the stabilization of the structure of Nuclease-T' by binding of ligands as follows. The local interactions between the ligands and their binding sites are coupled with the cooperative interactions operating in the three-dimensional structure to strengthen both the interaction maintaining the three-dimensional structure and the interactions between the ligands and their binding sites.
The coupling of the two interaction systems provides a stabilization energy of approximately 2 kcal (Table I) without a gross change in the conformation of Nuclease-T' (21). By analogy we speculate that the lowering of the energy of the native structure of nuclease occurs without a large change in conformation by specific coupling of the local interactions throughout the three-dimensional structure after the disordered polypeptide chain is folded into the native conformation On making the substitutions and eliminations we have Accordingly, X FIG. 4. Diagram of the relationship between the apparent rate constant (Y) of unfolding of partially liganded Nuclease-T and those of (10) unliganded (Y,) and liganded (YJ Nuclease-T'. X, concentration of a ligand; k, rate constant of unfolding.
In Case 1 the binding of pdTp and Ca2+ to Nuclease-T' is independent of the presence of the other ligand. In Case 2, the binding of either of the two ligands is enhanced when the other ligand is bound. In Case 3, the binding of either of the two ligands is weakened when the other ligand is bound. The three cases of relationship between the association constants described above are not restricted to the reactions of the system composed of 2 small molecules and 1 large molecule. As far as a system containing three elements satisfies the equilibrium Equations 1 to 4, one of the three cases will be observed in the relationship between the association constants in the system (see, for example, Let the values for the rate constants of unfolding of Nuclease-T in the absence of and at saturation with the ligand be Y, and Y,, respectively, and let Y be the value for the apparent rate constant of unfolding of Nuclease-T at ligand concentration X (Fig. 4). Since the rate of unfolding of Nuclease-T is dependent only on the concentration of Nuclease-T in the first order (2), the apparent rate of the unfolding at ligand concentration X may be expressed as Y. T. This should be the sum of the rates of unfolding of unliganded and liganded Nuclease-T as shown in Equation 13. The substitution for a in Equation 12 using Equation 14 gives Since the values for T and Y, are known, the values for Y, and K can be obtained as the values to give the best fit of Equation  15 to the set of data of X and Y. The association constant is calculated as the reciprocal of K.
Estimation of Association Constant of a Ligand with Nuclease-T Bound by a Second Ligand-In the experiments determining the rate of unfolding of Nuclease-T as a function of concentration of pdTp at 3.3 mM of Ca2+ (see Fig. l), the concentration of Ca2+ was not sufficient to saturate Nuclease-T in the absence of pdTp. However, since the association constant of Ca2+ to Nuclease-T is much greater in the presence of pdTp than in the absence (Table I), it may be assumed that all Nuclease-T bound with pdTp is also bound with Ca2+. Since the molar quantity of Ca2+ is in large excess to that of Nuclease-T it may also be assumed that the concentration of free Ca2+ was the same, 3.3 mM, even if all Nuclease-T was bound with Ca2+. Therefore, [ , Y can be expressed in terms of [Cl, P, and T as variables as K2, K,, Y,, Y,, and Ypc as constants. If the values for [Cl, T, K, Y,, Y,, and Y,,c are known, Y can be calculated as a function of P for a given value for K,. Then, the value for K, may be estimated as the value to give a best fit curve of Equation 24 to the data of P and Y by visual inspection.