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* Work performed under Contract No. W-7405-eng-26 for the Atomic Energy Com-mission.

1Goodwin, Richard H., and Stepka, William, Am. J. Botany, 32, 36-46 (1945).2 Loofbourow, John R., Growth, 8 (Suppl.), 77-149 (1948).' Brumfield, R. T., Am. J. Botany, 29, 533-543 (1942).4Sinnott, E. W., and Bloch, Robert, Ibid., 26, 625-634 (1939).

ENZYMES, SPECIFIC SUBSTRA TES AND COMPETITIVEINHIBITORS AS MULTIFUNCTIONAL ENTITIES

By ROBERT J. FOSTER AND CARL NIEMANN

GATES AND CRELLIN LABORATORIES OF CHEMISTRY,* CALIFORNIA INSTITUTE OF

TECHNOLOGY

Communicated March 26, 1953

In the development of the Michaelis-Menten theory of enzyme-catalyzedreactionsl'2 it has been repeatedly recognized that under certain conditionsthe catalytically active site of the enzyme may be capable of simultaneousinteraction with two or more molecules of a particular specific substrate orcompetitive inhibitor and thus form a variety of ternary and possiblyhigher complexes.3-9 This implication of the possible multifunctionalityof a catalytically active site has led us to consider the more general situ-ation wherein not only the catalytically active site is considered to bemultifunctional but also the specific substrate or competitive inhibitor.9-'

TABLE 1

BINARY AND TERNARY COMPLEXES DERIVABLE FROM THE COMPLEMENTARY INTERAC-TION OF A BIFUNCTIONAL SPECIFIC SUBSTRATE WITH A BIFUNCTIONAL ACTIVE SITECOMPLEX INTERACTION REACTANTS CONSTANTS

ES1 (R1- pl) Ef, SJ KS1ES2 (R2 - P2) Ef, Sf Ks,ES12 (R1- pi, R2 - P2) ES,; ES2; Ef, Sf Ks,,; K85; KESES1S2 (R, - P1) (R2 - P2) ES1, Sf; ES2, Sf; Ef, 2Sf Ks1S2; Ks2s,; KESSE1S2E (R1 - P1) (R2 - P2) ES1, Ef; ES2, Ef; 2Ef, Sf KS1E2; KS2.g; KESs

For simplicity let us first consider the case where both the active site ofthe enzyme and the specific substrate are bifunctional, i.e., where the spe-cific substrate can be considered to possess two distinguishable structuralcharacteristics R, and R2 and the active site of the enzyme two structuralfeatures P1 and p2 with which R, and R2 can interact in a complementarymanner. It will be assumed that all other types of interaction, i.e., R, -P2, R2- P1, P - P1, P2- P2. P1- P2 R1 - R,, etc., can be ignored.

In contrast to the classical presentation depicted in equation (1)

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ki ksEf + Sf 'ES - Ef+P1J +P2,...* (1)

one can anticipate in the bi-bifunctional system in addition to Ef, the freeenzyme, and Sf, the free specific substrate, the possible presence of all ofthe species listed in table 1. The equilibria involved may be conveniently

Ks,2 Ks2,classified as: unimolecular, i.e., ES1 ES12 ES2; bimolecular,

Ks1 KS2 KBKSi.e., Ef + Sfr~ ES,, Ef + Sf ES2, Ef + Sf ES12, ES1 +

Ksis2 Kss,s KSIE2Sf ES1S2, ES2 + Sf ES1S2, ES1 + Ef E1S2E, ES2 +

KS2E KgssEf EiS2E; and termolecular, i.e., Ef + 2Sf ES1S2, and

KsEB2EJ + S E1S2E.Again for simplicity it will be assumed that of all of the intermediate

complexes only ES12 can be subsequently transformed into free enzyme andreaction products and that this reaction can be represented by equation(2). It is conceivable that under some circumstances the two ternary com-

kES12 ) Ef + PIr + P2r ..*(2)

plexes ES1S2 and E1S2E could also serve as reactive intermediates and it isnot implied that the transformation of ES12 into free enzyme and reactionproducts is necessarily an intramolecular process but rather that under theexperimental conditions ordinarily encountered the specific rate constantk may be that of an apparent zero order reaction with respect to [5].For the condition that [S] [5], i.e., where [S] > ([ES1] + [ES2] +

[ES12] + [E5152] + [E152E]) and where d[ES12]/dt - 0, i.e., where allequilibria are established rapidly relative to the rate k [ES12], and where Efdoes not interact with any of the reaction products, i.e., for initial rates, wemay, as a reasonable approximation, exclude the two termolecular processesdescribed by the constants KESS and KESE, and specify the concentrationsof the binary and ternary complexes arising from unimolecular or bimolecu-lar processes as follows:

[ES1] = [Ef] [SI/Ks1 = KS1, [ES12 ];[ES2] = [E,] [S]/KS2 = KS,. [ES12 ];[ES12] = [E,] [S]/Ks1Ks81 [E,] [S]/Ks.Ks21= [Ef] [SI/KEs;[ES152] = [ES1] [S]1KS,12 = [ES2] [S]/K3S, = KSJ2[ES12] [S]/K8SS2;[EIS2E] = [ES,] [Ef]/KSl B= [ES2] [Ef]/KsSE1 = Ks82 [ES12] [Ef]/KS1E,.For the special condition where k[ESln] is directly proportional to [E],

i.e., the one ordinarily encountered in kinetic studies of isolated enzymesystems where [S] > [E], we may ignore the contributions to the rateequation arising from the presence of E152E and arrive at equations (3)and (4).

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CHEMISTRY: FOSTER AND NIEMANN

[Ef] = [E]- {(1 + Ks12 + KS21) + (Ks12/KslS2) [IS] [ES12]. (3)[ES12] = [El [S]/(Ks8Ks8, + [S] (1 + KS12 + KS21) +

(Ks81/Ks,81) [S]2). (4)When -d[S]/dt = v, A = KslKS12, B = 1 + KS12 + KS2, and C =

Ks 2/KS,S2, the rate equation is

v = k[E] [S]/(A + B[S] + C[S]2) (5)

which may be divided by the quantity B/B to give equation (6) whereV = k[E]/B.

v = V[S]/(A' + [S] + C'[5]2). (6)

Equation (6) is of the same general character as the rate equation for theclassical treatment, i.e., equation (7), but in the latter instance V = k3 [El.

v = V[S]/(Ks + [S]). (7)

If observations are limited, by design or by chance, to the experimentalsituation where (A + B [S]) > C[S]2 it follows5 that a plot of l/vo vs. 1/ [S]owill be linear and will have an intercept of 1/V and a slope of A '/ V =Ks/ V. The fact that V = k3[E] = k[E]/B is of particular interest be-cause it generally has been assumed that k3, even though it is determined byan extrapolation procedure, is necessarily the specific rate constant for thetransformation of ES into Ef and reaction products and is therefore inde-pendent of any equilibria involved in the formation of ES. It is now clearthat the above assumption may not be valid in all cases, and that a changein V associated with a change in the molecular structure of a specific sub-strate, or of the enzyme, may not be due to only a change in k, but mayalso be due, either wholly or in part, to a change in the values of one ormore of the equilibrium constants of the various intermediate enzyme-substrate complexes.Rate equation (6) predicts inhibition by the specific substrate and the

relation existing between v and [S] for all values of [S] can be calculatedfrom this equation. V and A' are evaluated as described above and C' isevaluated from a determination of v when C' [5]2 > (A' + [S]) by a plotof vo vs. l/So based upon equation (8). It follows from equation (6) thatthe maximum velocity is attained when [S] = VA '/C'.

v = V/C'[S]. (8)

The above treatment of the interaction of a bifunctional catalyticallyactive site with a bifunctional specific substrate has already found applica-tion in an interpretation of the effect of varying concentrations of auxinsupon the growth of Avena coleoptile sections.'2

If, in a system containing an enzyme with a bifunctional catalytically

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active site and a bifunctional specific substrate, there is introduced a mono-functional competitive inhibitor I, e.g., a compound which will interactwith the active site only via a R,- P interaction we will have in additionto the complexes listed in table 1 those arising from the following equilibria:

[El1] = [Ef] [If]/KI,[ES2,1] = [ES2] [I,f/Ksri= [EI1] [S,]/Ki1s2.

The rate equation for this situation is given by

v = k[E] [S]/IA(1 + [I]/K1) + (1 + Ks8 +Ks21 (1 + [I]/K8Z1)) [SI + C[S]21 (9)

which can be simplified by the substitution B1 = 1 + Ks., + Ks. (1 +[I]/KS211) to giveV = (k [E]/BI) [S]/ { (BA '/BI) (1 + [I]/KII) +

[SI + (BC'/BI) [S]21. (10)

It can be seen from equations (6) and (10) that if Vo = k[E]/B in the ab-sence of the inhibitor and VI = k[E]/BI in the presence of the inhibitor,V1 = (B/BI) VO and KR1 and the ratio B/B, can be evaluated by compari-son of the slopes and intercepts of e.g., 1/vo vs. 1/ [S]O plots with and with-out added inhibitor where the slope in the absence of the inhibitor isA '/ Voand in the presence of the inhibitor A '(1 + [Il/Ki1)/ Vo and the interceptin the absence of the inhibitor is 1/ Vo and in the presence of the inhibitor1/ Vo(B/BI). Thus in contrast to the classical treatment1-8 which pre-dicts that the addition of a competitive inhibitor to a system containingenzyme and specific substrate will cause, in the above plot, only an increasein the slope and no change in the value of V, the present treatment pre-dicts not only a change in the slope, but also a change in the value of V inthe presence of the inhibitor from that in the absence of the inhibitor by anamount equal to B/BI. There are at least three factors that may be re-sponsible for the present lack of experimental confirmation of this predic-tion: (1) the relatively low order of precision found in most enzymaticstudies; (2) the subjective nature of the methods ordinarily used in theconstruction of the plots; and (3) the fact that one of the several possibleinteractions may be so dominant that the value of B/Br is equal to unityto within the limits of experimental error. In any event it is apparentthat any perturbation of the various equilibria controlling the concentra-tion of the reactive enzyme-substrate complex or complexes, whether pro-duced by alternate modes of combination of the specific substrate with theenzyme or by an added competitive inhibitor, will influence to some degreethe value of the so-called specific rate constant when the latter value, i.e.,k8, is determined by an extrapolation procedure.For a system containing a bifunctional catalytically active site, a bi-

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VOL. 39, 1953 CHEMISTRY: FOSTER AND NIEMANN

functional specific substrate and a bifunctional competitive inhibitor, thefollowing additional equilibria must be considered:

[E12] = [E,] [If]/K1,[ES112] = [ES1] [If,/Ks1. = [EI2] [S]/KI12S1[EI12] = [EI1]/KI. = [E12]/KI, = [Ef] [I,f /KEI[EI112] = [EI1] [If]/K1r, = [EI2] [If]/KI21g.

The rate equation for this situation is given by

V = (B/Br1) V0 [S]/ I (B/B,1) A '(1 + [I]/K, + [I]2/K11K11,) +[S] + (B/Br12) C' [S]21 (11)

where BIl, = 1 + Ks12(1 + [I]/Ksj) + Ks21(1 + [Il/Ks51) and 1/K& =1/KI, + 1/K12 + 1/K11K1,2 + 1/K12K121. The character of this equationis such that an approximate graphical solution should give values for K,only at low values of [I]. However it is again seen that the specific rateconstant will be influenced by the concentration of the inhibitor and thevarious equilibrium constants.

Present circumstances do not justify the presentation of a general treat-ment of the case of the trifunctional catalytically active site interactingwith a tri- or bifunctional specific substrate since in the former instance thesimplest treatment involves a minimum of 14 intermediate complexes andthe possibility of 4 reactive complexes. It may be noted that restrictedcases involving the interaction of a trifunction catalytically active site withtri- and bifunctional specific substrates have been considered previously.'-,-

It is believed that the most important conclusion that has been developedfrom the treatment given in this communication is that the so-called spe-cific rate constants as ordinarily determined, i.e., the k3 values, may bedependent upon the various equilibria involved in the formation of thereactive intermediates and that changes in the values of kg that are asso-ciated with changes in the molecular structure of specific substrates are notnecessarily a reflection of changes in the susceptibility of ES to subsequentreaction but may be caused either wholly or in part by changes in theequilibrium concentrations of ES.

* Contribution No. 1790.1 Michaelis, L., and Menten, M. L., Biochem. Z., 49, 333 (1913).2 Michaelis, L., Advances in Enzymology, 9, 1 (1949).3 Haldane, J. B. S., Enzymes, Longmans, Green and Co., London (1930).4 Murray, D. R. P., Biochem. J., 24,1890 (1930).c Lineweaver, H., and Burk, D., J. Am. Chem. Soc., 56, 658 (1934).6 Straus, 0. H., and Goldstein, A., J. Gen. Physiol., 26, 559 (1943).7 Goldstein, A., Ibid., 27, 529 (1944).8 Segal, H. L., Kachmar, J. F., and Boyer, P. D., Enzymologia, 15, 187 (1952).9 Huang, H. T., and Niemann, C., J. Am. Chem. Soc., 75, 1395 (1953).

20 Huang, H. T., and Niemann, C., Ibid., 74, 5963 (1952).

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GENETICS: A. A. B UZZA TI-TRA VERSO

1' Huang, H. T., and Niemann, C., Ibid., 74, 4634 (1952).12 Foster, R. J., McRae, 1). H., and Bonner, J., PROC. NATL. ACAD. Sci., 38, 1014

(195i2).

PAPER CHROMATOGRAPHIC PATTERNS OF GENETICALLYDIFFERENT TISSUES: A CONTRIBUTION TO THEBIOCHEMICAL STUDY OF INDIVIDUALITY*

By ADRIANO A. BUZZATI-TRAVERSOtDEPARTMENT OF ZOOLOGY, UNIVERSITY OF CALIFORNIA, BERKELEY, CALIFORNIA

Communicated by Curt Stern, January 16, 1953

The discovery of differences related to descent, and the description inchemical terms of how a known genotypic condition present in the zygotemay determine, or be related to, a definite morphology of the adult organ-ism, are two of the aims of genetics. Paper partition chromatography offresh tissues or body fluids in animal and plants provides a simple tool forthe pursuit of these aims. In this report data will be presented showing howthis technique, an outgrowth of the work initiated by Hadorn and Mitchell,1makes it possible to recognize genotypic differences hidden under identicalmorphological features; indications will be given, too, as to the range ofapplicability of the procedure used. Much remains to be studied yet,especially at the biochemical level, on the very material here presented.It seems worth while, however, at the present stage of these investigations,to summarize some of the results obtained. It is hoped that this mightstimulate similar work on the same or other organisms and especially at-tract the interest and the cooperation of the biochemists.

Chromatographic Techlnique.-Both general proceduresof chromatographicseparation, by descending flow and by capillary ascent of the solvent,have been used in most cases. As the former allows a better separation ofthe spots than the latter, if not otherwise stated all the data and photo-graphs reported have been obtained from chromatograms developed bydescending flow, following standard techniques (see, e.g., Balston and Tal-bot2). For ascending chromatograms the technique of Williams and Kirby,3as modified by Hadorn and Mitchell,' has been used.

Sheets of Whatman No. 1 filter paper of various sizes were prepared asfollows. In case of the descending chromatograms a light pencil line wasdrawn 3 in. from the edge to be dipped into the solvent, and samples forchromatography were placed at 1 in. or 4-cm. intervals along this line. Incase of the ascending chromatograms the pencil line was drawn 1.5 cm.from the edge and samples applied at 1-cm. intervals. Details aboutthe treatment of animal and plant tissues and fluids will be given below.

376 PROC. N. A. S