Fluorescence and Kinetic Studies on the Divalent Metal Ion Induced

THEJ O U R N A L

OF BIOLOCICAI. CHEMISTRY Voi. 256, No. 11, Issue of June 10. pp. 5656-5661.1981 Printed m U . S . A.

Fluorescence and Kinetic Studies on the Divalent Metal Ion Induced Conformational Changesin DNase A* (Received for publication, July 14, 1980,and in revised form, January 12, 1981)

Richard H. TullisS, Ken. A.Dills, and Paul A. Price From the California Biomedical Research Foundation, La Jolla, California 92121 and the Department of Biology, University of California, San Diego, La Jolla, California 92093

DNase A has a broad, asymmetric fluorescence emisundergo Ca"-induced structural changes, perhaps the most M$+ sion peak centered at341 nm. Binding of Ca2+ of dramatic effects have been seen with bovine pancreatic DNase to DNase shifted the peakto 342 nm and caused a 10% X. Half of the maximum fluorescence enhancement. CaZ+binding to DNase A has been shown to induce conforchangeoccurredat 6 X lo-' M Ca2'or at 6 X M mational changes which result in complete protection from Mgf". The change in fluorescenceis most likely due to proteolytic inactivation by trypsin and chymotrypsin (7) a conformational change in DNase which occurs whenchanges in optical rotation as measured by both ORD and CD Ca2+or M 8 + is bound to the nonspecific tight Ca2+ (7), induction of ultraviolet difference spectra (8),reformation binding siteon DNase. of disulfide bonds in the fully reduced protein (9), and a slow The kinetics of the fluorescence change, followed by increase in activity (activation) of the enzyme preincubated stopped flow techniques, show a fast phase (66%) and a slow phase (35%).At 1 m~ Ca2+,the half-time for the with calcium prior to assay ( 5 ) . Preliminary studies have 3.5 min. indicated that some of these processes such as thegeneration fast phase is 17 ms, and for the slow phase, Both phases of the reaction are first order in DNase of the ultraviolet difference spectra, are fast, while others, and independent of Ca2+ at concentrations above1 m ~ .such as activation, are slow (5). In this study we have measured both equilibrium states and the rate of Ca'+-induced DNase incubated with CaZ+ undergoes a slow (tl,2 s 6 min) 1.5-fold increasein activity. This activationfol- conformation change using steady state and stopped flow lows pseudo-first order kinetics and is not due to the fluorescence. presence of additional Ca2+ in the substrate. EXPERIMENTAL PROCEDURES The simplest hypothesis which accounts for these data, and previously reported studies on the effect of Materials-DNase A was purified from Worthington DP grade Ca2+on DNase, is that DNaseexists in 3 conformational DNase according to themethod of Otsuka and Price (10).The enzyme states at 25 "C and pH 7.5. The kinetics are consistent thus prepared was stable for >24 h at 37 "C, pH 8 (IO m~ Tris buffer) in the absence of Ca*'. Three times crystallized a-chymotrypsin was with a mechanism which can be diagrammed as: slow A* - A A

-

+ Ca2+

very fast

ACa

fast

BCa

" . -

very

B

+ Cas+

where A*, A, and B represent three conformational states of DNase. ~

Metal ions play a crucial role in biological processes. Ca", for example, is involved in a myriad of cellular and organismic functions including hormone action (1, 2), nerve conduction (3),muscle contraction and cell mobility ( 4 ) ,and cell adhesion (4, 5 ) . In general such effects are specific to Ca2+in that they cannot be substituted by Mg'+ or most other common divalent metal ions ( 5 ) . On a molecular level, one of the most most general effects of Ca2+interaction appears to be the induction of conformational changes in proteins (1, 5 ) . Among the proteins which * This work was supported in part by Grants GM-16603 from the United States Public Health Service and NP-150 from the American Cancer Society. The costs of publication of this article were defrayed in part by the payment of page charges. This article must therefore be hereby marked "aduertisement" in accordance with 18 U.S.C. Section 1734 solely to indicate this fact. 4 To whom correspondence should be addressed. Current address, Department of Community Medicine ("022) University of California, San Diego, La Jolla, CA 92093. Q Current address, Department of Chemistry, University of Florida, Gainesville, FL 32611.

obtained from Sigma. Solutions of chymotrypsin were made up to 100 mg/ml in 1mM HC1 and used fresh. Chymotrypsin and DNase activity were measured as described by Otsuka and Price (10). Reagent grade CaC12 and MgCL were obtained from Mallinckrodt. All other reagents used were reagent grade or ultrapure. Fluorescence Spectra-Corrected fluorescence emission and excitation spectra were obtained on a Turner model 100 spectrofluorometer. Metalion titrations were performed by adding 5- to 20-pl aliquots of standard solutions ofCaC1, or MgCL to 3.0 ml of 2 X M DNase in 50 mM Tris buffer, pH 7.5. The solution was gently mixed by inversion and allowed to equilibrate. Emission spectra were then recorded in the expanded scale mode at various time intervals. Equilibrium was achieved in 20 to 30 min after the addition of metal. The data were corrected for dilution. Free CaZ' concentration was calculated from the data of Price (11). Stopped Flow Fluorescence-Stopped flow measurements were made in a Durrum Gibson stopped flow spectrophotometer operated in the fluorescence mode with a 315 nm blue cutoff filter. Temperature was maintained at 25 "C with a Lauda circulating water bath. All solutions were degassed 2 to 4 h under vacuum just prior to use. The trigger to stop time was 6 ms and the dead time was estimated to be 2 ms. RESULTS

Effect of Ca2+ on the Intrinsic Fluorescence of DNaseThe fluorescence emission spectrum of DNase A with and without Ca2' is shown in Fig. 1. The excitation spectrum showed a maximum at 282 nm, which shifted to 283 nm on the addition of Ca2'. The emission spectrum was a single, broad asymmetric peak centered at 341 nm. Addition of Ca2+ shifted the center of the peak to about 342 nm and caused a marked enhancement of fluorescence. The maximum fluores-

5656

Conformational St!Utes of DNase A

A (nm) FIG. 1. The effect of calcium on the fluorescence of DNase A. DNase = 0.04 m g / d in p = 10 mM Tris, pH = 7.5. No added Ca2', -; 10 mM CaC12,- - -. Excitation and emission bandwidth, 10 nm.

/-7

loot

/

L 801

-log

i

[C2+]

FIG.2. Spectrofluorometric titration of the calcium-induced fluorescence enhancement in DNase. Conditions were as in Fig. 1.

5657

form with those shown in Fig. 1. However, the fluorescence enhancement was approximately 5% lower for Mg2+than for Ca2+. The addition of 1 mM Ca'+ to a solution containing Mg" did not significantly increase the DNase in 7 2 mM fluorescence. Fluorescence Titration of DNase with Ca2+-Fig. 2 shows the results of the fluorescence spectral titration of DNase with Ca2+at pH 7.5 in 10 mM Tris buffer. The results are plotted as the percent maximum fluorescence enhancement against the negative log of the free Ca". The titration curve has a midpoint a t about 6 X M. This value is close tothe average dissociation constant of the two high affinity Ca" binding sitesonDNase, 1.4 X M as determined by gel filtration using 45Ca( 11). The difference may reflect an additional contribution from Ca2+binding to the weaker metal ion binding sites at high Ca2+ concentrations. Since both the UV difference spectral and fluorescence changes occur in the same range of Ca'+ concentrations, and since both changes are the result of the alterations in the environment of the protein chromophores, we conclude that theconformational change which gives rise to the UV spectral changes also accounts for the observed changes in fluorescence. Fluorescence Spectral Titration of DNase with Magnesium-Fig. 3 displays the results of the fluorescence spectral titration of DNase with MgCL at pH 7.5. The midpoint of the curve occurred a t 6 X M which is close tothe average dissociation constant (2 X M) for Mg2+binding to the two Mg binding sites on the enzyme (11). Mg2+cannot bind to the Ca'+ specific high affinity binding site (11). Thus, Mg'+ or Ca2+binding to thenonspecific tight binding site is responsible for the fluorescence spectral change. Control reactions in which DNase was mixed with buffer showed no significant change in fluorescence. The total fluorescence change was the same in both rapid reaction and equilibrium measurements of any given Ca" concentration. Stopped Flow Kinetics of the Ca2+-inducedFluorescence Change inDNase-When DNase was mixed with Ca2+at pH 7.5, a biphasic reaction was observed. The reaction consisted of a fast change (complete in 1 s) followed by a much slower reaction (complete in about 30 min). Since the reaction rate was so different in the 2 phases, they will be discussed separately. Representative oscilloscope tracings for the fast reaction are shown in Fig. 4. This phase of the reaction represented about 65% of the total fluorescence enhancement. A plot of the logarithm of per cent reaction (fast phase only) against time (Fig. 5 ) indicated a single fiist order process which was essentially independent ofCa" concentration above 1 mM Ca". The reaction half-times and the calculated fist order

cence enhancement was 10% measured at 340 nm. Changing the excitation wavelength to 276 nm caused a reduction in fluorescence intensity and a slight broadening on the short wavelength side of the emission peak (data not shown). This typeof fluorescence spectrum is typical of tryptophan containing proteins such as the serum albumins (12-14). It is possible that tyrosine residues contribute to a small extent to the fluorescence of DNase, as evidenced by the slight, short wavelength broadening of the emission band when fluorescence is excited at 276 nm (13). The Ca"-induced fluorescence enhancement is most likely due to a conformational change in DNase which alters the exposure of tyrosine and/or tryptophan to solvent. Tullis and Price ( 5 , 8 ) have shown that the ultraviolet difference spectrum which arises on thebinding of Ca2+to DNase, is due to a conformational alteration in DNase which results in the loss of exposure of DNase chromophoresto solvent. Such changes alter the polar character of the medium in the vicinity of the affected residues, resulting in a red shift of the absorption spectrum and an enhancement of fluorescence. Effect of Mg2+on the Fluorescence Spectrum of DNaseAddition of Mg2+ to the enzyme at pH 7.5 also caused an FIG. 3. Spectrofluorometric titration of DNase with magneenhancement of fluorescence. The spectra were identical in sium. Conditions were as in Fig. 1.

Conformational States

5658

of DNase A

FIG. 4. Representativeoscilloscope tracing of the calcium-induced fluorescence enhancement of DNAse at pH 7.45. DNase = 1.3 X 10." M in 10 mM Tris, pH 7.5. Each horizontal diuision represents 10 ms and each vertical dioision represents 0.1 V.

0

1

I

I

1

'

I I

o

o

-

0.4

.

-. a6 -

y

I

+

,donuCo2+

-

I ~ Y G I ~

A 0.1 mu cp2+

\

-

'\\

-

\A

0

LE

a\x

--

g o'8: I 1.0

O

Pi

1.2 1.4 1.6

0

I

30

2 Y

-

\\ €0

I

BO

I

I

I

1

1

120

I50

180

210

240

TIME

a TIME ( s e d

FIG. 6. Kinetics of the slow phase of fluorescence enhancement of DNase induced by calcium. DNase = 1.3 X M in 10 mM Tris buffer, pH 7.5, 1 mM CaCI?; 0.1 mM CaCl?. Each point represents the average of at least 3 determinations.

Ims-~

FIG. 5. First order plot of DNase fluorescence enhancement. Fast phase. DNase = 1.3 X M in 10 mM Tris, pH 7.5; X, 0.1 M CaCI?;0, 1 mM CaCI?; A, 0.1 mM CaC12. Each point represents the average of at least 3 determinations.

TABLEI Rate constants and half-reaction times for the fastphase of the Caz+-inducedfluorescence enhancement in DNase at pH 7.5 and 25 "C Kt,, tl,z (Ca") free" rnM

P"

rns

100

58 44 38

12

10

1

0.05 "

16 17 90

Free Ca2+was calculated from the data of Price ( 1 1).

TIME beel FIG. 7. First order plot of the slow phase of DNase fluorescence enhancement conditions as in Fig. 7.

constants are displayed in Table I. T h e half-time for the rapid T h e kinetics of the slow phase of the fluorescence enhancement due to Ca" binding to DNase is shown in Fig. 6. This reaction was 12 ms a t 100 mM Ca" and 17 ms at 1 mMCa". phase of the reaction took several minutes to complete and When Ca2' was reduced to 0.1 mM, the reaction half-time increased to 90 ms while the reaction course itself remained represented about35%of the totalfluorescence enhancement. fist order up toat least 90% completion. The overall increase A logarithmic plotof the extentof reaction against time(Fig. in fluorescence in the fast phase under these conditions was 7) showed the reaction tobe fmt order. At a Ca" concentration of 1 mM, the half-reaction time was 3.5 min ( k = 3.3 X reduced by about 35%.

Conformational States TABLEI1 The effectof Ca2+incubation on DNase I activity DNase (1 mg/ml) was incubated with either I mM EDTA or the indicated [Ca"] in 5 mM Tris, pH 7.5, at 37 "C for 10 to 15 min prior to assay. All assays weredone at 25 "CandpH7.5using the hyperchromicityassay of Kunitz as modified by Price (9) under optimal ionicconditions (2.5 mM MgC12 and 0.5 mM CaC12). The contributions of Ca" from the enzyme to the assay solutions were negligible.

'

Sample

Specific activitym::$am

-'a

unitslmg

EDTA-treated DNase DNase + 0.5 mM Ca2+ DNase + 50 mM Ca2'

736 1120

1180

64

95 102

I

I

,6

I 500 I

0

20

40 lime

of DNase A

5659

all the Ca"+ binding proteins which have thus far been studied,

the Ca*+-induced changes in DNase I are perhaps the most striking. Tullis and Price(5,8) Poulos and Price (7), and Price et al. (9, 15) have shown that Ca2+binding to one or another of the tightestCa2+ bindingsites on DNase causes the enzyme toassume a highlyfoldedconformationwhich results in characteristicalterations in thespectralproperties of the molecule and protection from proteolyticinactivation. The results of thisstudy show that in addition to the previously described spectroscopic alterations, Ca2+ induces an enhancement of DNase fluorescencewhich appears to correlate with the appearance of activity. The fluorescence change is consistent with the observation that Ca'+ binding to DNase causes a conformational change which reduces the exposure of aromatic aminoacid residues to solvent water(5, 8). Since DNase is inactive in the absence of Ca" (15) it is reasonable to suppose that highly folded Ca":DNase is the active form. The stop-flowfluorescencekinetic patterns we obtained have shown the presence of two pseudo-fist orderconformational changes, one of which is slow (ti,* = 3.5 min) and another which is fast (tlI2= 17 ms). In order to simplify the analysis, we consider the fast and slow phases of the reaction separately. There are 3 model systems which give the required linear fist order plot seen in the fast phase of the reaction. These mechanisms may be diagrammedas follows:

I

60

(min)

FIG. 8. The kinetics of the slow Ca2+-induced activity increase. DNase (10pg/ml) was incubated in 1 mM CaC12, 10 mM Tris, pH 7.5, at 25 "C. Activity was measured as described under Experimental Procedures. Measurements of initial activity required 15 to 30 S.

lo-" s"). Reducing the Ca2+ concentration to0.1 mM did not These models have been analyzed by Strickland et al. (16), significantly affect either the rate or the extent of the slow Grimaldi and Sykes(17), and by us ( 5 ) .Model I would apply phase of reaction. A slow fluorescence change might occur if the protein were only under the condition that Ca2+>> Kd. Under this condidenatured and formed aggregates due to the rapidmixing in tion, the reaction would be pseudo-fist order. Thus, a 100the reaction chambers.T o check this possibility, the activity fold decrease in Ca2+should cause a 100-fold decrease in the of the enzyme was measuredbefore mixing and at the end of apparent rate of the reaction. Table I shows that this model the slow phase of the reaction(Le. about 30 min). Surprisingly, is not correct since a 100-fold decrease in Ca2' causes only a of conformawe found that the specific activity of the enzyme had increased slight reduction in the rate. The maximum rate from 740 to 1132 units/mg. This was confirmed in a separate tion change is approximately lo6 times slower than the rate series of control experiments (Table11). Thus theslow phase expected for a reaction controlled by CaZ+binding (18-20). In the remaining twomodels, the rate-limiting step in the of fluorescence enhancement could not be caused by aggregation of inactive enzyme. Furthermore, since Ca2+ is present reaction is presumed to be the unimolecularconformation in the assay mix, the Ca"-induced activity increase must be change between thespecies designated A and B which results in the characteristic spectral alterations. The basic difference much slower thantheassaytime (-30 s arerequiredto between these models is that in 11 the metal binds DNase only perform an assay). Slow Activation of DNase I by Ca2+-The rate of activity in theB conformation while in I11 the metalbinds to both the increase observed after rapidmixing wit,h Cazf was measured A and B forms. In the latter case, the driving force for the in order to see if the rate corresponded to the slow phase of conformation change must come from the difference in the conformers. reaction. The results, shown in Fig. 8 depict a slow ideal. free energy of Ca2+ binding to the two Considering model 11, it can be shown that this mechanism (pseudo) fist order increasein DNase activityin the presence of the of 1 mM Ca2+ at pH 7.5 and 25 "C. The half-time for the isinconsistentwiththeobservationthattherate reaction was tlIP= 6 min. The rateof reaction was independent reaction decreases as the [Ca"] decreases, The argument is of enzyme concentration, again indicating that aggregation as follows: the observed rate constant for mechanism I1 is given by the expression (5, 16, 17) was not involved. The rate was also independent of[Ca"] M Ca". Thus,the increasein activityappears to above correspond to theslow phase of fluorescence enhancement. DISCUSSION

Ca2+ is important to the structure and activity of many The kinetic expression for this model which is exactly analoproteins includingconcanavalin A, trypsin, Staphylococcal gous to a simple first order rateof approach toequilibrium (9) nuclease, a-amylase, thermolysin, and calmodulin (1-60). Of predicts that as the concentrationof Ca2+ decreases the rate

Conformational States

5660

of the reaction will either increase or stay thesame depending on the relative values of k-l and k l (16). This is inconsistent with the observation that the rate of the observed reaction decreased at [Ca”] below 1mM. Thus, mechanism I1 can also be qualitatively ruled out. Mechanism 111’ can be shown to be both qualitatively and quantitatively consistent with the rate and equilibrium data. The observed rate constantK for the interconversion of A and B in the presence of Ca‘+ is given by the expression derived in Appendix I, namely k1

k= 1+-

Kd

[Ca”] [Ca”]

k- I

+

1+-

K’d

In this mechanism the observed rate constant again depends on the [Ca2’]. This expression predicts that as [Ca’+] decreases the rate of the reaction will decrease asvery [Ca”] approaches K d in accord with the experimental observations (Table 1). In addition, the values of K d , K ’ d , k l , and k - ] can be uniquely determined from the equilibrium fluorescence measurements and the rate datausing onlythe assumption that thereaction goes to completion in the presence of high concentrations of Gal'. This is reasonable since at high [Ca”’] the enzyme is completely protected from proteolytic inactivation by chymotrypsin, trypsin, and proteinase K (7).2 If any fraction of the enzyme remained in the more unfolded form, any one of these proteases should be capable of inactivating the DNase. The pertinent expression in this case is

where %F is the per cent of the maximum fluorescence enhancement observed at any particular [Ca“]. M, K ‘ d = 4 The values thus obtained were Kd = 6.9 X x M, kl = 58 s-l, and k-1 = 0.4 s”. Using these values, the expected rate of reaction and the %BCa atequilibrium have been computed and arecompared with the observed values in Table 111. The predicted values showexcellent agreement with the experimental results, with th exception of the rate constant at M Ca2+.The reason for this one discrepancy is unclear. From these arguments it seems reasonable to conclude that the fast phase of the Ca2+-inducedfluorescence enhancement proceeds primarily via a Ca2+-boundintermediate and not by the binding of Ca2+to a rareform of DNase as in mechanism 11. The slow phase of the fluorescence enhancement is again a pseudo-first order process which does not depend on [Ca”] M. The two simplest modelswhich might account above for the overall reaction can be diagrammed as follows: verv

of

DNase A

TABLE 111 Comparison of observed and expected values for rate constants and equilibrium values of fluorescence (Ca”) free 70 F,,., IF d &,ha Kq“1,. s-l

100 mM

10 mM 1 mM 100 pM 50 pM 20 pM 10 pM 10 1 PM

100 100 90 58 41 24 11 0.0

99 99 93 58 50 21

58 44 38 7.7

58 56 41 6.6

0.1

slow A * “--.A very fast fast fast A+Ca2’”---ACa-BCa~B+Ca2’

(V)

Where A, A *, and B + represent conformational states of DNase. Both models predict an initial reaction burst (ie.fast phase) followed by a slower phase. However, in mechanism IV the enzyme must be rapdily converted to BCa prior to undergoing the rate-limiting slow conversion to B *Ca. Thus, any [Ca”] which slowsthe rateof the fast reaction (i.e.[Ca”] K d ) must also affect the rate of the slow reaction. This is inconsistent with the observation that at M Ca2+the fast phase of the reaction is markedly slowed (Fig. 5) while both the rate and extent of the slow phase remain unaffected (Fig. 6). Thus, mechanism V is the simplest modelwhich can account for the data. This conclusion is consistent with the observation of a slow 50% activity increase in the specific activity accompanying the slow fluorescence enhancement and indicates that in the absence of Ca”, a fraction of the enzyme may be in an inactive, unfolded conformation. Slow conformational changes ( i e . reactions with half-times of more than 1 min) have been reported for several proteins. Concanavalin A undergoes a slow metal ion-induced conformational change when Mn2+is added to theCa2’:concanavalin A complex (21). Substrate binding to acetylcholine receptors causes a slow alteration which is presumed to be due to a conformational change (22). The importance of such changes is not known but it is possible that they may be involved in adaptation to continuous stimuli or the generation of metabolic oscillations. The 3-state Ca“-involved conformational model suggested by our data is remarkably similar to current models for the Ca”-calmodulin interaction (1).Given the widespread nature of Ca2+effects and the observation that in nearly all cases, Ca2+interaction with proteins results in major conformational alterations (5, 6), it is possible that similar 3-state models will be applicable to other Ca2+binding proteins. REFERENCES

-

1. Cheung, W. Y. (1980) Science 20’7.9-27 2. Rasmussen, H., et al. (1974) CRC Crit. Rzu. Biochem. 1,95-148 B*Ca B * + Ca2’ 3. Williams, D. R. (1971) The Metals of Life, Van Nostrand-RheinBCa hold Co., New York 4. Winegrad, S. (1969) in Mineral Metabolism (Comar, C. L., and Bronner, F., eds) Vol. 3, p. 191, Academic Press, New York ’ The derivation of the rate expression for Mechanism 111 is pre- 5. Tullis, R. H. (1975) Ph.D. thesis, UniversityofCalifornia, San Diego sented in miniprint at the end of this paper. Miniprint is easily read 6. Roche, R. S., and Voordouw, G . (1978) CRC Crit. Rev. Biochem. with the aid of a standard magnifying glass. Full size photocopies are 5, 1-23 available from the Journal of Biological Chemistry, 9650 Rockville 7. Poulos, T. L., and Price, P. A. (1972) J. Biol. Chem. 247, 2900Pike, Bethesda, MD 20014. Request Document No. 80M-1430, cite 2904 author(s), and include a check or moneyorder for $1.60 per set of 8. Tullis, R., and Price, P. A. (1974) J . Biol. Chem. 249,5033-5037 photocopies. Full size photocopies are also included in the microfiim 9. Price, P. A,, Stein, W. H., and Moore, S. (1969) J. B i d . Chem. edition of the Journal that is available from Waverly Press. 244,929-932 R H Tullis. K. A. Dill. and P. A. Price, unaublished observations.

slow

’

fasl

Conformational States 10. Otsuka, A. S., and Price, P. A. (1974)Anal. Biochem. 62,180-187 11. Price, P. A. (1972) J. Biol. Chem. 247,2895-2899 12. Chen, R. F. (1963) in Fluorescence Theory, Instrumentation and Practice (Guilbaut, G. G., ed) p. 138, Marcel-Dekker, New York 13. Steiner, R. F., and Weinryb, I. (1970) Excited States of Proteins

and Nucleic Acids, Plenum Press, New York 14. Udenfriend, S. (1969) Fluorescence Assay in Biology and Medicine Academic Press, New York 15. Price, P. A. (1975) J. Biol. Chem. 250, 1981-1986 16. Strickland, S., Palmer, G., and Massey, V. (1975) J. Biol. Chem. 250,4048-4052

Richard

of DNase A

17. Grimaldi, J. J., and Sykes, B. D. (1975) J . Biol. Chem. 250, 16181624 18. Jensen, A., and Williams, R. G. (1968) in Progress in Coordination Chemistry (Casi, M., ed) p. 162, Academic Press, New York 19. Gurd, F. R. N. (1970) in Physical Princ@Zes and Techniques of Protein Chemistry (Leach, S. J., ed) Part B, p. 365, Academic Press, New York 20. Eigen, M., and Hammes, G. G. (1963)Adu. Enzymol. 25, 1-38 21. Koenig, S. H., Brewer, C. F., and Brown, R. D. (1978) Biochemistry 17,4251-4260 22. Quast, U., et al. (1978) Biochemistry 17,2405-2414

8. Tullis. Kul A. D i l l and Paul A. Price

I n v e r t i n g both s i d e s and s u b r t l t u t m g i n for the value of X y i e l d s

[i+s]I+*]

vhlch can be f a c t o r e d t o qiw

K'

ACa

=D0-BCa

5661