Biochem. J. (1966) 101, 411

Optical and Chemical Identification of Kinetic Steps inTrypsin- and Chymotrypsin-Catalysed Reactions

By T. E. BARMAN* AND H. GUTFREUNDtNational In8titute for Research in Dairying, Shinfield, nr. Reading

(Received 4 April 1966)

Previous interpretations of the mechanism of trypsin- and chymotrypsin-catalysed reactions in terms of two intermediates, the Michaelis complex and an

acyl-enzyme, were based on steady-state studies and on the observation ofindividual steps under sub-optimum conditions. In the present paper new methodsfor the rapid analysis of chemical events and for the spectrophotometric detectionof individual steps are applied to these two enzymes. These methods can be usedto study reactions with specific amino acid ester substrates. It can be shown thatthere are at least three distinct steps between the Michaelis complex and therelease of ethanol; the latter is likely to correspond to acyl-enzyme formation.The relative rates of these three steps are measured by rapid-flow techniques fromobservations of the displacement of chromophoric inhibitors and reactions withspecific substrates containing chromophores, as well as from ethanol analysesduring a single turnover ofthe enzyme reactions. It is concluded that the reactionsof trypsin and chymotrypsin with their specific substrates involve the formationof a specially reactive conformation of the enzyme-substrate complex and thatthe rate constants involved in this rearrangement are at least as important forthe overall reaction as those of the subsequent formation and decomposition ofthe acyl-enzyme.

Trypsin and chymotrypsin belong to a largegroup of enzymes that have one especially reactiveserine hydroxyl group among the 20-30 serineresidues of the protein molecules. The enzymes ofthis group all catalyse acyl or phosphoryl transferreactions, hydrolysis being a special case of transferto water as the acceptor. The first suggestion that0-serine-linked acyl or phosphoryl compounds ofthe enzymes occur as reaction intermediates camefrom Wilson, Bergmann & Nachmansohn (1950) asan interpretation of the reactions of acetyl-cholinesterase with specific inhibitors that reactwith the one reactive serine residue of the enzyme.Hartley & Kilby (1954) have shown that thereaction of chymotrypsin with nitrophenyl acetateinvolves the rapid formation of acetylchymo-trypsin and nitrophenol and the relatively slowhydrolysis of the acetyl-enzyme to form acetateand free enzyme. This discovery encouragedGutfreund & Sturtevant (1956) and Bender (forreferences see Zerner & Bender, 1964) to charac-terize the acylation and deacylation reactions of

* Present address: Department of Biochemistry, Univer-sity of California, Berkeley, Calif., U.S.A.

t Present address: Department of Biochemistry, Univer-sity of Bristol.

chymotrypsin by detailed kinetic studies withpseudo-substrates that gave signals in the form ofspectral changes during the two steps. These sub-strates are hydrolysed much more slowly bychymotrypsin than the specific substrates for thisenzyme and they also are usually good acylatingreagents. The simplest mechanism that could beformulated to describe the results obtained was asfollows:

E +AB EAB - EA+Bk-A

EA+C k+a E+AC

(1)

(2)

EAB is the Michaelis complex, EA the acyl-enzymeand C is water or some other nucleophilic acceptor.The kinetic parameters of this mechanism are:K,= k-l/k+l and Km = K,k+3/(k+2 + k+3), assumingk-1> k+2; or for the more general case Km =k+3(k-l+ k+2)/k+l(k+2+ k+3); the turnover, ko, ofthe enzyme is defined by ko= V/[E]o =k+2k+3/(k+2+k+3), where [E]o is the molar concentrationof enzyme active sites. The reversal of the secondand third steps can be neglected for low concentra-tions of products.

Gutfreund & Hammond (1959) and Zerner,

411

T. E. BARMAN AND H. GUTFREUND

Bond & Bender (1964) have shown that theMichaelis parameters (V and Ki) evaluated fromsteady-state rate measurements of the chymo-trypsin-catalysed hydrolysis of a range of specificsubstrates are consistent with the hypothesis thatacyl-enzymes are formed. This consistency, whichis also observed with trypsin (Baines, Baird &Elmore, 1964), is based on an argument that canbe illustrated by the following example. A seriesof widely different esters of N-acetyl-L-tryptophanare hydrolysed by chymotrypsin at the same maxi-mum velocity but with Km inversely proportionalto the rate of base-catalysed hydrolysis of the ester.From this it is argued that: (1) there must be acommon intermediate, acetyltryptophanyl-chymo-trypsin, for all the different esters; (2) k+3, thehydrolysis of this intermediate, is rate-determining;(3) k+2 varies at least qualitatively in the same wayas the base catalysis of the hydrolysis of the estersand the changing ratio k+3/(k+2 + k+3) causes thechange in K. referred to above. In addition to thiskinetic consistency with the acyl-enzyme hypo-thesis, Kezdy, Clement & Bender (1964) have givenspectral evidence for the transient formation of anacetyltryptophanyl-chymotrypsin compound inacidic (pH 2-4) solution. Further, Gutfreund &Hammond (1959), as well as Kezdy et al. (1964),have shown that during the enzymic hydrolysis ofnitrophenyl esters of specific amino acid substratesthe initial liberation of nitrophenol is faster thanthe steady-state liberation of acid.

Zerner & Bender (1964) discuss the difficulties ofobserving the individual steps in the reactions ofspecific substrates with hydrolytic enzymes. It isclearly necessary to devise methods that allow oneto follow the exceedingly fast steps in the hydrolysisof amides or alkyl esters of specific amino acids ata pH near neutrality. Bernhard & Gutfreund(1965) and Barman & Gutfreund (1965) have givena preliminary account of two new approaches tothis problem and have illustrated it with someresults obtained with the system trypsin-N-benzoyl-L-arginine ethyl ester. The competitiveinhibitor proflavine changes its spectrum when itcombines with trypsin or chymotrypsin. The ratesof enzyme-substrate reactions can be followed bymonitoring the extinction change at a fixed wave-length, as the inhibitor is displaced by the substrateand recombines with enzyme again as the productsdissociate. Barman & Gutfreund (1965) demon-strated how the rapid-quenching technique can beused to determine the rate of liberation of ethanolduring the first turnover of ester hydrolysis cata-lysed by trypsin. The conclusion reached byBarman & Gutfreund (1965) was that the rate ofliberation of ethanol, which should reflect the rateof acyl-enzyme formation, is lower than that of theformation of an intermediate indicated by dye

displacement and that another intermediate, ratherthan the acyl-enzyme, is the one described by thesteady-state kinetic argument developed above.

In the present paper this comparison of the ratesof dye displacement and recombination with therates of ethanol liberation are extended to variousconditions for the hydrolysis of specific substratescatalysed by trypsin and chymotrypsin. Further,the rates of formation and decomposition of inter-mediates in reactions of chymotrypsin are followedwith substrates containing a chromophore that isnot linked by resonance to the reactive carbonylgroup (this idea was developed by Dr S. A.Bernhard).The results presented below are intended to show

that methods are now available that should makeit possible to obtain more insight into the sequenceof events occurring during the reactions catalysedby this group of enzymes. It is shown that thearguments leading to consistency with the acyl-enzyme hypothesis are too simple. The newinformation obtained allows one to propose somedetails of the reaction pathway, but it would bepremature at this time to propose a completemechanism for reactions catalysed by trypsin andchymotrypsin.

METHODS AND MATERIALS

The stopped-flow technique (Gibson, 1954) was used torecord the rapid extinction changes. The particular modelused was the one described by Gutfreund (1965) with alcm. optical path and a hand barrier for moving thesyringes; a mixing chamber with eight jets was inserted inplace of the system of two jets. Interference filters (BalzersA.-G., Liechtenstein) and a 12v, 24w Mazda projectorlamp were used as a light-source at the appropriate wave-lengths. A Transtab (model H) power supply (Joyce,Loebl and Co. Ltd., Gateshead-upon-Tyne) was used forthe tungsten lamp and a type D4140 high-voltage supply(Labgear, Cambridge) for the photomultiplier (type 6256B;E.M.I. Electronics Ltd., Ruislip, Middlesex). The currentoutput of the photomultiplier was fed into a differentialamplifier (CX 1442; Solatron Ltd., Farnborough, Hants.)across a 100kQ resistance and a O0OlUF condenser. Theother channel of the differential amplifier was used to feedin a calibrated offset. The change in percentage trans-mission during experiments was recorded on a CD 1400oscilloscope (Solatron Ltd.) and photographed withl aPolaroid camera. The response of the whole system to asudden change in current was found to have a half-timeof approx. 0-7msec., as expected from the circuit. Theexperiments recorded below involved less than 20% changein transmission and the amplifier output was assumed tobe directly proportional to the concentration of the absorb-ing reaction intermediate.The experiments involving sampling of enzyme-substrate

mixtures over the time-scale of milliseconds were performedby the method described by Barman & Gutfreund (1964).Equal amounts of enzyme and substrate solutions areinjected through a mixing chamber with two jets into a

1966412

Vol. 101 TRYPSIN- AND CHYMOTRYPSIN-CATALYSED REACTIONScapillary tube (01cm. diam.) and the mixture flowedthrough this tube at a rate of 8.7m./sec. (7ml./sec.). Theend of the capillary tube dipped into a solution of suitablecomposition to stop the reaction. Different lengths oftubing were inserted into the apparatus to vary the timebetween mixing enzyme with substrate and quenching thereaction. The volume of reaction mixture delivered intothe quenching solution was determined in the way describedby Barman & Gutfreund (1964).The quenched reaction mixture (about 6-5 ml.) was

washed into a 500ml. flask with about 2ml. of HC104(3.3N) and distilled in vacuo into a U-tube immersed in amixture of solid CO2 and acetone. In this way a neutralsolution of the enzyme, which was free from ethanol andwhich would be partly reactivated when the acid is removed,was obtained without causing any acid hydrolysis of thesubstrate. The distillates were analysed for ethanolessentially by the alcohol-dehydrogenase method ofLundquist (1959). Overall alcohol blanks were obtainedby analysis of reaction mixtures with the quenching acidadded to the substrate or enzyme solution before mixing.The optical stopped-flow measurements as well as the

rapid-flow sampling experiments were carried out at roomtemperatures of 22+ 10.

Salt-free freeze-dried bovine a-chymotrypsin and trypsinwere obtained from Seravac Laboratories (Holyport,Maidenhead, Berks.) and enzyme solutions were made upin the appropriate buffers not more than lOmin. before usefor kinetic experiments. The molarities of active sites wereestimated by titration with nitrophenyl esters (see e.g.Bender, Killheffer & Roeske, 1965). This determination ofactive-site concentrations gives an operational rather thanan absolute definition since it depends on the assumptionof the simple acyl-enzyme pathway, which is not proveneven for the reaction of nitrophenyl esters.BAEE* was obtained from Seravae Laboratories,

proflavine was from British Drug Houses Ltd., Poole,Dorset, and FATEE was provided by Dr S. A. Bernhard.

RESULTS AND DISCUSSION

Reactionr between trypsin and benzoyl-L-arginineethyl e8ter. Barman & Gutfreund (1965) have shownthat at pH7-2 the rate of liberation of ethanol ina single-turnover experiment, when enzyme andsubstrate concentrations are approximately equal(about 0-1 mM), is about the same as the steady-state turnover with ko 15sec.-' at 250. In suchexperiments a small proportion of the ethanol,about 10%, is liberated much more rapidly, i.e.within 4msec., whereas the rest of the ethanol isliberated with a half-time of 50msec. The turnoverrate of the trypsin-BAEE reaction, under steady-state conditions, does not change significantly inthe range pH7.2-8-0 (Gutfreund, 1955). Fig. 1gives the results ofthe analysis of ethanol liberationduring a single turnover of the reaction of trypsinand BAEE at pH7*9 in the form of a first-orderplot. It is clear that under these conditions there

* Abbreviations: BAEE, N-benzoyl-L-arginine ethylester; FATEE, N-,B-(2-furyl)acryloyl-L-tyrosine ethyl ester.

20

-- 'Burst' = 86-5 aM-ethanol (48%)*8

1-6 a,4-40

tD j.4_

1-2

0 8 16 24 32Time (msee.)

Fig. 1. First-order plot of the rate of liberation of ethanolduring the reaction of trypsin (0-2mM) with BAEE(0-18mM) in 0-08M-sodium phosphate buffer, pH7.9. Thereaction was quenched by injecting enzyme-substratemixture of the age indicated into an approximately equalvolume of 0-36N-H2SO4.

occurs a much larger 'burst' of very rapid ethanolrelease, whereas about 50% of the ethanol isreleased with a half-time of 16msec., giving a first-order rate constant 43-5sec.-1, nearly three timesthe steady-state liberation of ethanol. Identicalresults were obtained in sodium phosphate and intris buffers (0.1M, pH 7-9).As pointed out by Bernhard & Gutfreund (1965),

if the rate of ethanol liberation during the firstturnover of the reaction of trypsin with BAEEwere characterized by k+2 (eqn. 1) the apparentrate k+2 at a given substrate concentration shouldbe k+2{[S]/([S] + K,)}. They also estimated from theKJIKm ratio that the k+2/ko ratio should be about1000, i.e. k+2 should be 1.5 x 104sec.-1 and k+2 at[5] 0-2mM should be about 700sec.-1. Clearly thiscalculation is only correct for the case [S]> [E]o,which does not hold for the single-turnover experi-ments reported here. It is, however, evident thatthe rate of ethanol liberation is not rapid enoughto correspond to the rate of enzyme acylationrequired for the simple scheme. The point that thefirst-order kinetics for the second half of theethanol liberation is also not consistent with sucha simple model is discussed again below.Bernhard & Gutfreund's (1965) studies of the

rate of displacement, on addition of BAEE, ofproflavine bound by trypsin, as well as the rate ofrecombination of the dye with enzyme at the endof the enzyme-substrate reaction, were extendedover the range pH4-8-7-9. The rate of recombina-tion of proflavine and trypsin is easier to interpretthan the displacement of dye, especially over therange pH4-8-7-2, when the rate of recombination

413

T. E. BARMAN AND H. GUTFREUND

.2 UI._

c cL.r

I1- I in~EG 5

1-

200Start msCc.

Fig. 2. Record of the change in transmission at 470mgduring the reaction of trypsin (02 mM), proflavine (0.2mm)and BAEE (0 2mM) in OlM-acetate buffer, pH5-3.

20Start msec.

Fig. 3. Record of the change in transmission at 470m/Aduring the reaction of trypsin (0 1 mM), proflavine (0 2mm)and BAEE (04 mM) in 0-1M-tris buffer. pH7.9.

is identical with that observed by Gutfreund (1955)for the overall turnover rate for the trypsin-catalysed hydrolysis of BAEE. However, whenthe pH is raised from 7 2 to 7 9, though there is nosignificant change in turnover number, the rate ofdye recombination is increased nearly threefold andcorresponds to the rate (k 43.5sec.-1) of the first-order phase of ethanol liberation. Fig. 2 gives therecord of dye displacement and recombination atpH5-3. There are several difficulties about theinterpretation of the kinetics and pH-dependenceof the dye-displacement reaction, which is morecomplex than that interpreted by Bernhard &Gutfreund (1965). It is, however, clear that thedisplacement of dye is characteristic of a step thatprecedes the labilization of ethanol (Bernhard &Gutfreund, 1965; Bernhard, Lee & Tashjian, 1966).It has also been shown (S. A. Bernhard, personalcommunication) that, during the single-turnoverreaction of trypsin with the p-nitrophenyl ester ofa-N-benzyloxycarbonyl-L-lysine in the presence ofproflavine, the liberation of p-nitrophenol isaccurately first-order and slower than the dis-placement of proflavine from the enzyme. Aspointed out by Bernhard & Gutfreund (1965) therate of displacement of proflavine from enzyme, atenzyme and substrate concentrations about 0 1 mm,does not reflect the formation of the smal amountof initial enzyme-substrate complex, but it iscaused by the subsequent formation of some otherintermediate.

Fig. 3 shows the record ofproflavine displacementand recombination during the reaction of trypsinwith BAEE at pH7-9. The displacement at thispH is so fast that the time-scale of this experimentonly resolves its final portion. There is, however,a distinct lag phase between the rapid dye dis-placement and the relatively slower first-orderrecombination. This indicates yet another kineti-cally distinct step between those responsible fordye displacement and dye recombination. Thecorrelation between those steps and the chemical

=

0a-oIcL. I

t10

Start msCc.

Fig. 4. Record of the change in transmission at 340m,uduring the reaction of chymotrypsin (0.27mm) withFATEE (0 22mM) in 0*08M-phosphate buffer, pH6.6.

events of alcohol and acid liberation are discussedbelow together with the results obtained fromstudies with chymotrypsin.

Reaction between chymotryp8in and N-fl-(2-furyl)-acryloyl-L-tyrosine ethyl e8ter. Preliminary studiesin Dr S. A. Bernhard's Laboratory showed that inacidic solutions a single turnover of chymotrypsinwith FATEE could be followed in a conventionalspectrophotometer. The extinction changes duringthe reaction, which are maximal at 325mu, involvefirst a rapid increase and then a somewhat slowerdecrease. Even in the stopped-flow apparatus thehighest pH at which both phases of the reactioncould be followed was 6-6. Fig. 4 shows a recordof such an observation at 340m,u, which is a moreconvenient wavelength to use in our equipment.From such records one can calculate a number ofimportant parameters of the reaction. The rapidincrease in extinction has already started beforethe reaction mixture has reached the observationchamber of the stopped-flow apparatus. A reason-able estimate of the rate of this reaction can bemade from the half-time of 2msec. of the rest ofthe rise. This would give a rate constant of350sec.r', which must be corrected for the response

414 1966

Vol. 101 TRYPSIN- AND CHYMOTRYPSIN-CATALYSED REACTIONS20O

1-6

b \

0

0-8

0-4

0 l0 20 30

Time (msec.)

Fig. 5. First-order plot of the rate of liberation of ethanolduring the reaction of chymotrypsin (0.27mM) withFATEE (0.22mM) in 0 08M-phosphate buffer, pH6 6. Thereaction was quenched by injecting enzyme-ubstratemixture of the age indicated into an approximately equalvolume of 0*36N-H2SO4.

time of 1 msec. for the circuit of the instrument.Such a correction gives k 540sec.'l as an approxi-mate value for the reaction. The subsequentdecrease in extinction has a half-time of 25msec.,which corresponds to a rate constant of 28sec.'1,which is within experimental error the same as thesteady-state turnover of chymotrypsin withFATEE at pH 6.6.

Exactly the same reaction mixture of chymo-trypsin and FATEE was studied in the rapid-flowquenching apparatus and a first-order plot of therate of ethanol liberation is given in Fig. 5. It isespecially noteworthy that the reaction followsfirst-order kinetics (k 147sec.-l) over at least 95%of its course. This point has already been raised inconnexion with the reactions of trypsin. If therate of liberation of ethanol or nitrophenol (withnitrophenyl esters) characterizes the rate of forma-tion of the acyl-enzyme as described by eqn. (1),under conditions of the present experiments, when[E]o! [S]o<K,, the formation of EA would haveto deviate from first-order kinetics. However, inthe chymotrypsin-FATEE reaction it has beenshown that some other intermediate is formedabout four times as fast as the liberation of ethanol.The rate of liberation of ethanol corresponds to thefirst-order transformation of one intermediate intoanother. The complexity of the situation isincreased even further by the finding that displace-ment of proflavine from chymotrypsin by FATEEoccurs somewhat faster than the increase in

extinction at 340m,u. In summary, we have thefollowing steps during the chymotrypsin-FATEEreaction: (1) formation of Michaelis complex; (2)displacement of proflavine; (3) increase in extinc-tion at 340m,u; (4) liberation of ethanol; (5)decrease in extinction at 340m,.

General dicuw8ion. The formation of acyl-enzymes during the reaction of chymotrypsin ortrypsin with nitrophenyl esters is demonstratedreadily by observing the relative rate of liberationof nitrophenol and acid during the first turnover ofthe enzyme. The same type of experiment cannotbe carried out to investigate the reactions of alkylesters. The liberation of ethanol cannot be followeddirectly in the stopped-flow apparatus. The directobservation of the reduction of NAD+ in thepresence of alcohol dehydrogenase is not a practicalproposition for monitoring the rate of appearanceof ethanol under the conditions used for the studyof the first turnover of proteolytic enzymes. Therapid-sampling method employed here to obtainthe rate of liberation of ethanol on a millisecondtime-scale has one fundamental weakness. To stopthe reaction at the chosen time-interval aftermixing enzyme with substrate, the enzyme has tobe reversibly or irreversibly inactivated. Thisinactivation could itself produce some reactionintermediate that is not on the normal pathway.Fig. 5 indicates that the rate of liberation ofethanol was first-order, but this may be the resultof two distinct causes. An acyl intermediate ofchymotrypsin may be formed with concomitantliberation ofethanol at pH 6-6 at the rate indicated,or some other intermediate may be formed at thisrate but this intermediate is converted into theacyl-enzyme when the reaction is quenched withacid. This uncertainty of interpretation of thequenching experiments is not resolved at presentand it is only possible to say that some intermediateis formed at the rate indicated. This intermediatemight be an acyl-enzyme, but in any case the acyl-enzyme is not formed more rapidly than the rateconstant ofethanol liberation. It is possible that thediphasic rate of liberation of ethanol during thereaction between trypsin and BAEE (Fig. 1) is dueto two intermediates' being responsible for theamounts of free ethanol found after quenching.The first of these intermediates is formed veryrapidly and is converted into the acyl-enzyme onquenching, whereas the second intermediate, theacyl-enzyme, is formed more slowly from the first.The first intermediate would have to be in equili-brium with the Michaelis complex. There is someevidence for this from experiments at pH7-2. Ithas been stated by Barman & Gutfreund (1965)that a small amount of ethanol is liberated morerapidly than the rest. When the size of this 'burst'of ethanol was determined over a range of BAEE

415

416 T. E. BARMAN AND H. GUTFREUND 1966concentrations, the following results were obtained.The molar ratio of 'burst' to trypsin concentration(constant at 0-2mM) at 0-2nmi-, 1-0mM- and 10mM-BAEE was 0-1, 0-2 and 0.5 respectively.The methods described in the present paper were

developed to attempt the examination of individualsteps ofsome enzyme reactions, at or near optimumpH, with specific substrates that have reactivitiessimilar to the natural ones. The study of thereaction mechanisms of enzymes at sub-optimumpH or with pseudo-substrates has yielded muchuseful information but obviously has its pitfalls.The changing balance of different steps, as well asthe appearance of side reactions and conformationchanges in the protein because of change in pH,can give a wrong picture of the relative importanceof intermediates of the reaction. The conformationof the active site of an enzyme is likely to becritically dependent on the composition of thesolution and on the structure of the substrate com-bined with it. The use of pseudo-substrates, likethe study of the reactivities of essential groups onthe active site with inhibitors and reagents, is notlikely to give information about the true reactivityof such groups within the enzyme-substratecompound.The conclusion to be drawn from the experiments

described in the present paper is that there are otherimportant intermediates in reactions catalysed bytrypsin and chymotrypsin besides the Michaeliscomplex and the acyl-enzyme. Detailed kineticstudies of the dependence of the individual stepson reagent concentrations andpH should eventuallyallow one to improve any proposed model of thereaction mechanism. The existence of a numberof steps contributing to the overall rate during thesteady state account for superficial agreement withthe simple acyl-enzyme model, which fails in detail.

Bernhard et al. (1966) have proposed that thesubstrates and competitive inhibitors of trypsinand chymotrypsin are bound in a hydrophobiccrevasse of the enzyme molecule. One or more ofthe steps observed may be controlled by the forma-tion or unfolding of the proper conformation of theenzyme-substrate complex to give it optimumreactivity with specific substrates. The reactiveconformation would be induced (Koshland, 1958)after the formation of the Michaelis complex andits stability would depend on the reactivity of thebond to be hydrolysed. Such a phenomenon wouldmake it possible that the transfer of the substrateand the groups on the catalytic site of the enzyme,from an aqueous into a non-polar medium, mighthave a considerable effect on the reactivity of theresulting enzyme-substrate intermediate. It wouldbe unwise to make too close a comparison of thetrypsin-BAEE and chymotrypsin-FATEE re-actions. Although there are considerable similarities

in the qualitative behaviour of the two systems,the quantitative relation between the individualsteps is sufficiently different for the two enzymesfor alternative steps to be rate-determining. It willbe of importance to determine the rate of acidliberation during single-turnover experiments.This could probably be best resolved in a rapid-flow calorimeter. The resulting information wouldenable one to build up a more complete picture ofthe relative rates of different chemical events andof the conformation changes during the overallreactions of these two enzymes with their specificsubstrates. The pH-dependence of conformationchanges of chymotrypsin has been studied byOppenheimer, Labouesse & Hess (1966).

We are indebted to Dr S. A. Bernhard for a free exchangeof unpublished data and for discussion and advice, whichmade a considerable contribution to the present paper.This work was supported by grants from the U.S. PublicHealth Service and the U.S. Department of Agriculture(PL480).

REFERENCES

Baines, N. J., Baird, J. B. & Elmore, D. T. (1964). Biochem.J. 90,470.

Barman, T. E. & Gutfreund, H. (1964). In Rapid Mixingand Sampling Techniques, p. 339. Ed. by Chance, B.,Eisenhardt, R. H. & Lonberg-Holm, K. K. New York:Academic Press Inc.

Barman, T. E. & Gutfreund, H. (1965). Proc. nat. Acad.Sci., Wash., 53, 1243.

Bender, M. L., Killheffer, J. V. & Roeske, R. W. (1965).Biochem. biophys. Res. Commun. 19, 161.

Bernhard, S. A. & Gutfreund, H. (1965). Proc. nat. Acad.Sci., Wash., 53, 1238.

Bernhard, S. A., Lee, B. F. & Tashjian, Z. H. (1966). J.molec. Biol. 18, 405.

Gibson, Q. H. (1954). Disc. Faraday Soc. 17, 137.Gutfreund, H. (1955). Trans. Faraday Soc. 51, 441.Gutfreund, H. (1965). An Introduction to the Study ofEnzymes, p. 124. Oxford: Blackwell Scientific Publica-tions.

Gutfreund, H. & Hammond, B. R. (1959). Biochem. J.73, 526.

Gutfreund, H. & Sturtevant, J. M. (1956). Proc. nat. Acad.Sci., Wash., 42, 719.

Hartley, B. S. & Kilby, B. A. (1954). Biochem. J. 56, 288.Kezdy, F. J., Clement, G. E. & Bender, M. L. (1964).

J. Amer. chem. Soc. 86, 3690.Koshland, D. E. (1958). Proc. nat. Acad. Sci., Wash., 44,

98.Lundquist, F. (1959). Meth. biochem. Anal. 7, 246.Oppenheimer, H. L., Labouesse, B. & Hess, G. P. (1966).

J. biol. Chem. 241, 2720.Wilson, I. B., Bergmann, F. & Nachmansohn, D. (1950).

J. biol. Chem. 186, 781.Zerner, B. & Bender, M. L. (1964). J. Amer. chem. Soc.

86, 3669.Zerner, B., Bond, R. P. M. & Bender, M. L. (1964). J.Amer. chem. Soc. 86, 3674.