A Kinetic Study of the Complementation Fragments of Staphylococcal Nuclease

Abstract The complementation of fragments of staphylococcal nuclease to form an ordered structure was studied by stopped flow kinetic measurements. The increase in the intensity of tryptophan fluorescence of residue 140 on complementation was followed. The complementation of two fragments containing residues 6 to 48 and residues 49 to 149 (or 50 to 149) to form Nuclease-T' follows apparent first order kinetics, both with regard to variation of time and fragment concentration accessible to study. The first order rate constant of the formation of Nuclease-T' is in the range of 0.03 to 0.05 s-1, which is much less than that of refolding of acid-denatured intact nuclease observed by Schechter et al. (Schechter, A. N., Chen, R.F., and Anfinsen, C.B. (1970) Science 167, 886–887). The change of temperature from 5° to 45° caused only a small increase in the rate of formation of Nuclease-T'. The presence of the ligands, thymidine 3',5'-diphosphate and Ca2+, and the change of pH of the reaction mixture from 5 to 8 had no effect on the rate constant. The complementation between the fragments of residues 1 to 126 and of residues 99 to 149 and between the fragments of residues 1 to 126 and of residues 49 to 149 (or 50 to 149) also fits first order kinetics and shows rate constants equivalent to that of Nuclease-T'. Examination of the kinetic equation for the simplest model, in which specific prefolding of each fragment is required for the productive collision, and the collision is the rate-limiting step of the complementation, fails to explain these results. However, the results may be interpreted by assuming the rate-limiting step either to be the prefolding of one of the two fragments, which then combines with the other fragment, or the folding of a disordered intermediate complex formed by the two fragments.


SUMMARY
The complementation of fragments of staphylococcal nuclease to form an ordered structure was studied by stopped flow kinetic measurements.
The increase in the intensity of tryptophan fluorescence of residue 140 on complementation was followed.
The complementation of two fragments containing residues 6 to 48 and residues 49 to 149 (or 50 to 149) to form Nuclease-T' follows apparent first order kinetics, both with regard to variation of time and fragment concentration accessible to study.
The first order rate constant of the formation of Nuclease-T' is in the range of 0.03 to 0.05 s-l, which is much less than that of refolding of acid-denatured intact nuclease observed by Schechter et al. (SCHECHTER, A. N., CHEN, R. F., AND ANFINSEN, C. B. (1970) Science 167, 886-887). The change of temperature from 5" to 45" caused only a small increase in the rate of formation of Nuclease-T'. The presence of the ligands, thymidine 3',5'-diphosphate and Ca2+, and the change of pH of the reaction mixture from 5 to 8 had no effect on the rate constant.
The complementation between the fragments of residues 1 to 126 and of residues 99 to 149 and between the fragments of residues 1 to 126 and of residues 49 to 149 (or 50 to 149) also fits first order kinetics and shows rate constants equivalent to that of Nuclease-T'.
Examination of the kinetic equation for the simplest model, in which specific prefolding of each fragment is required for the productive collision, and the collision is the rate-limiting step of the complementation, fails to explain these results.
However, the results may be interpreted by assuming the rate-limiting step either to be the prefolding of one of the two fragments, which then combines with the other fragment, or the folding of a disordered intermediate complex formed by the two fragments.
Several different studies have been concerned with the rates of folding and unfolding of protein upon rapid perturbation by * On leave of absence. Present address, Department of Chemistry, Purdue University, Lafayette, Indiana 47907.
$ To whom requests for reprints should be addressed.
In the case of renaturation of acid-denat.ured staphylococcal nuclease, the over-all folding has been described by two first order processes: a rapid step (half-time, 55 ms), followed by a slower step (halftime, 350 ms) (2, 3). It has been suggested that the initial fast phase is related to a partial folding of the polypeptide chain with the formation of a number of intermediates (nucleation by helices), followed by numerous stabilizing interactions that occur as the slow step of the process (3).
The combination of two fragments, covering the amino acid sequence of staphylococcal nuclease, but lacking enzymic activity and ordered structure, form enzymically active complexes by noncovalent bondings (7-10) (Fig. 1). So far, two types of complexes have been observed. One active complex, called Nuclease-T' r (or type I complex), is formed by complementation of fragments of residues 6 to 48 and of residues 49 to 149 (or 50 to 149) (8). Another (type II complex), containing overlapping sequences, is formed from fragments of residues 1 to 126 and of residues 99 to 149 (9). The physical properties of the complexes resemble those of intact nuclease, although the level of biological activity is less. In particular, recent x-ray diffraction studies, comparing the crystals of Nuclease-T and Nuclease-T' with those of intact nuclease, have shown that these crystals are isomorphous (14).
The formation of Nuclease-T' from Nuclease-T-(6-48) and Nuclease-T-(49,50-149) may be described by the reaction shown in Equation 1 Nuclease-T-(648) Nuclease-T' k, 1 Fragments of nuclease have been designated by an adaptation of the rules of the Commission on Biochemical Nomenclature (13). The prototype is "trivial name-(X-Y)," where the trivial name denotes the origin of the fragment and X and Y the NHe-and COOH-terminal amino acids, respectively. For example, Nuclease-T- (49, is the mixture of Nuclease-T-(49-149) and Nuclease-T-(50-149) isolated from Nuclease-T (8). Nuclease-T, obtained from nuclease by limited digestion with trypsin, is composed of Nuclease-T-  and Nuclease-T-(49,56-149) (8). The reconstituted Nuclease-T from its component fragments is called Nuclease-T'. and is devoid of sulfhydryl groups and disulfide bonds (11,12). A single tryptophan residue is at position 140 in nuclease and, therefore, it is located in Nuclease-T-(49-149).
See Footnote i for the designation of fragments.
where kf and k, are the rate constants in the forward and reverse directions, respectively. The dynamic equilibrium state of the reaction (Equation 1) involving the unfolding and refolding of the three-dimensional structure of Nuclease-T, has been demonstrated by measurement of exchange of free Nuclease-T-(50-149) with labeled Nuclease-T-(50-149) incorporated in Nuclease-T' (15). It has been shown that the rate constant in the reverse direction of Equation 1 is highly temperature-dependent (halftime, 148 min at 10"; 19 min at 20") (15). Since the rate-limiting step of the exchange between free Nuclease-T-(50-149) and the incorporated Nuclease-T-(50-149) is the dissociation of Nuclease-T (15), the exchange experiment does not give quantitative information concerning the rate of association of the two fragments. In the present studies we have directly measured the rate constant in the forward direction for the complementation of nuclease fragments under various conditions.
The nuclease molecule contains a single tryptophan at residue 140 (11). The fluorescence emission spectra of Trp-140 of the fragments in solution is the same as that of free tryptophan (9,16). On the other hand, the tryptophan fluorescence of intact nuclease and of the ordered complexes shows an emission maximum with a much higher intensity and at a shorter wavelength than that of the disordered fragments (16)) being consistent with the fact that in the three-dimensional structure of nuclease the side chain of Trp-140 resides in a nonpolar environment (17,18). The progressive change of the intensity of tryptophan fluorescence was followed after mixing of two solutions each containing one of the two complementing fragments. Insofar as the in crease in intensity of tryptophan fluorescence reflects the formation of the ordered structure, these studies give information that is useful to an understanding of the mechanism of folding of nuclease. where ZO and I,,, are the relative fluorescence intensitv at zero and infinite time, respectively. X is the sum of the rateconstants of forward (folding, k,) and backward (unfolding, k,) reactions, that is x = kl + k, (see Equation  1). At and below 25" the value for k, is small compared with k, (15) and the value for X is, then, approximately equal to that for k,.
The value for X is obtained as the value which gives the best fit of Equation 2 to the observed data of relative fluorescence intensities and time values covering three or four half-lives of the reaction. The value for X is presented below as the first order rate constant where R is the molar ratio of Nuclease-T-  to Nuclease-T-(49,50-149), C is the initial concentration of Nuclease-T-(49,50-149), and a is the fraction of Nuclease-T' produced.
The latter is the value corresponding to t,hat of the ordinate of Fig. 2. The data of a versus R were fitted to an equilibrium expression (Equation 3), and the corresponding value of the equilibrium constant at 25" for the format,ion of Nuclea.se-T' was 6.3 x lo5 M-l (Fig. 2).
Kinefics of Complementation-The kinetic curve of the increase in tryptophan fluorescence intensity after stopped flow mixing of Nuclease-T-  and Nuclease-T-(49,50-149) is shown in Fig.  3. The fluorescence intensity at the end of the reaction was equivalent to the amount of Nuclease-T' expected for the reactants present. The kinetic data invariably showed a good fit to first order kinetics (Fig. 4). The value for the rate constant calculated on the basis of first order kinetics had little depend-   (Table I). On the other hand, an attempt to fit the rate data to second order kinetics resulted in a large varlation of the value for the rate constant (Table II), refiecting a poor fit of an individual set of kinetic data to second order kinetics. Therefore, the apparent kinetic behavior of the formation of Nuclease-T' from the two fragments is best described as a first order process, even though the reaction requires both components. All rate constants described below are calculated on the basis of first order kinetics.
When the increase in the tryptophan fluorescence intensity in the early time period was followed as an oscilloscope trace (Fig. 5), the value calculated for the first order rate constant was 0.09 s-1 and the half-time was 7.7 s. The reaction appears to be more rapid in the early phase, although the difference may be within the experimental error of The data is from the experiment given in Fig. 3 and that of Nuclease-T' at a given time is the value for c at that time. these early measurements.
Here the precision is poor when looking at only a small per cent of the total change during the early part of a relatively slow process.
EJ'ect of &gun&--It is known that the binding of calcium ions and pdTp* to nuclease and Nuclease-T stabilizes the structures against heat denaturation (7), presumably not by acceleration of the folding but by suppression of the unfolding reaction (15). Table III shows the kinetic analysis of the effect of the ligands on the rate of formation of Nuclease-T'.
The apparent first order rate constant for the reaction does not change by the addition of one or both ligands, being consistent with the idea that ligands do not influence folding.
Ejj'ect of ph'-Previous studies indicated that the equilibrium constant for the formation of Nuclease-T' from the two fragments is dependent on pH such that the formation of Nuclease-T' is essentially absent at pH 4.0 and reaches a maximum at pH 6, as the pH of the mixture increases (9). However, the rate of forma-  II   TABLE  IV Trial Jit for second order kinetics The observed data (see Fig. 3 and Table  I Nuclease-T' was determined over the temperature range of 5 to 45" in the absence and in the presence of pdTp and Ca*+ ( Table  V). The values for the rate constant are at the same level at all temperatures, whether the ligands were present or not, although the rate constant may be decreasing slowly as temperature decreases (Table V) . Above 40" the rate of unfolding of Nuclease-T apparently exceeded that of the forward reaction (Equation l), since no increase in the intensity of the fluorescence was observed after mixing the two fragments in the absence of the ligands. However, when both ligands were present, the forward reaction could be examined at 45" and still be detected at 52" (Table V), presumably as a result of the suppression of the unfolding (15).
Complementation of Nuclease-(l-126) and Nuclease-(99-149) The combination of Nuclease-(l-126) and Nuclease-(B-149) forms the ordered complex of type II having an enzymic activity of approximately 15% that of intact nuclease (9). The ordered complex presumably excludes the segments of overlapping amino acid sequence, which may occur somewhere between residues 114 and 124, with the redundant portion protruding from the ordered structure (9).
The obsrrvctl first o&r kiut+c: hcl~avior for tlw rom$rnwnt~~tion of disordcrrtl fragments untlcr a variety of cspcrimrntal conditious limits the iiumbrr of plausiblr mec~hanisms that should bc consitlcrctl to explain the folding process. The first mechanism to bc rousidered is that Nuclcase-T-  and Kucleasc-T-(49-149) i1ltlependrntly fold into the "native"   (Table VI). If the ligands were omitted, the total increase in the int,eusity of the fluorescence at, the completion of the reaction was less than that i11 the prcscncc of the ligands.
The observations indicate that the rate of the unfolding of the complex is appreciable at 25", causing a smaller equilibrium concentration of type II complrs. The \.31uL' fo1 the rate constn11t appeared to bc higher in the absclncr of ligantls than in the prescncc of ligantls (Table VI). When Nuclease-(l-126) and Nuclease-T-(49,50-149) :W mixed, two types of ordered compleses are formctl simultaiicously, that is, 011e form (type I) is the binding of Xucleasc-'l'-(49,50-149) to that part of Nucleasc-(l-126) co11taiuing r&duos 6 to 48, and the other (type II) is the binding of Nuclcasc-(l-126) to the COOKtcrmi11al part (say, residues 114 to 149, SEC above) of Nuclease-T-(49,50-149) (9). The rate process for the formation of fhe ordered complcses from the two fragments in the presence of ptl'l'p aud <'a2+ was again fitted to first order kinetics as shown in Table VII. In t,he absence of ligands, however, the rate constant, appeared to irlcrease slightly, as noted before for the complementation of NW clease-(l-126) and Nuclease-(99-149).
The observations might suggest that tl1e ligands bind weakly to Nuclease-(l-126), intcrfering with the formation of the ordered complex by comple- The solution of these differential equations is complicated by the number of parameters involved.
However, if only thr initial rate of formatioii of Nuclease-T' is considered, the following npproximate trcattnent may be allowed.
The solution of the quadrat,ic equation for dT/dt leads to Equation 19 dT +k A k2k4 dt=2 1 + k3C + yy c > k2k4 2 (klA + k3C + -k5 where the negative sign is chosen by considering that the observed value for the initial rate of formation of Nuclease-T' is not greater than that for the rate of formation of prefolded Intermediates B and D from A and C, respectively, that is, dT/dt 5 klA and dT/dt 5 k3C.4 As seen in Equation 19, the init'ial rate 4 If the populations of B and D existing in the equilibrium state in the solutions of Nuclease-T-  and Nuclease-T-(49-149), respectively, are appreciable, the value for dl'/dl may not be necessarily smaller than those for lc,A and k,C at the time when the two solutions are mixed. In this case, the kinetic equation describing the initial phase of formation of Nuclease-T' is simply Equation 7. Therefore, the initial rate of formation of Nuclease-T' should follow second order kinetics with regard to change of the concentration of fragments. dr dt -+ k3C (lase 1 may describe the situation where the equilibriutn relationships between A and B and between C and D occur very rapidly, as compared to the collision between H and D to form Nuclease-T', that is, Step 5 is the rate-limiting process (k2 >> h, kq >> kg, x-1 >> ks, ka >> ks). In this case, the initial rate of formation of Nuclease-T' should be proportional to the product of the tions would not be sufficient to contribute to the observed increase in the intensity of tryptophan fluorescence upon mixing the two solutions.
of Nuclease-T' depends (Equation 32).7 On the other hand, if the value for Ks is larger than lop4 M, the initial rate of formation of Nucleasc-T' would respond to the increase in the initial con-,$entration of Nuclease-T-(49-149) in a manlier approaching a secoucl order reaction (Table VIII).
In summary, the kinetic studies reported above consistently followed apparent first order kinetics with each complementing system. It is clear, however, that further studies are required before one of these suggested mechanisms of fragment complementation may be proved.