`University ol
`
`Ii
`‘(viz-:u:.<i<:siII
`
`
`
`r-I-\":r'.j-..'
`.i V.
`,,
`
`Bioche“ti1itfiI”Ph”fiirmucolouv
`
`CONTENTS
`
`/\RNo ZIMMER, AXEL PROX, HELMUT PELZER and RAINER HANKwITz: Simultaneous labelling
`with stable and radioactive isotopes in drug metabolism studies
`
`Von KER DINNENDAHL, HANS D. PETERS and PETER S. SCH<‘jNHoEER: EFFects of sodium salicy-
`late and acetylsalicylic acid on cyclic 3’,5’-AMP-dependent protein kinase
`
`KARL—HEIN7. KIESSLING and LARS PILSTROM: Cytochrome <- stimulated oxidation of ethanol
`by liver mitochondria
`
`HF-.lTAROH IWATA, ITARII YAMAvIoTo, EIICHI GOHDA, Kvon MoRITA, MITSLITAKA NAKAMURA
`and KEIKO SUM]: Potent competitive uricase inhibitors~2,8—diazahypoxanthine and related
`compounds
`YASUKO MURAKAMI and KATASHl MAKINO: On the convulsive action of castrix
`
`Z. Huszri, E, KASZTREINER, M. KURTI, M. FEKETE and J. BORSYZ 2-Hydroxy—5-carbometh—
`oxybenzyloxyamine: a new potent inhibitor of histidine decarboxylase
`
`Z. HLISZTI, E. K.ASZf1‘R[.INER, G, SZILAGYI, J. KOSARY and J. BORSYZ Decarboxylase inhibition
`and structure-activity relationship studies with some newly synthetized benzyloxyamine and
`pyridylmethoxyamine derivatives
`
`Ml('HAEL BRIGGS and MAXINE BRIGGS: Etfects of some contraceptive steroids on serum
`proteins of women
`
`C. J. PETER ERIKSSON: Ethanol and acetaldehyde metabolism in rat strains genetically
`selected for their ethanol preference
`
`SIISANNE KEIDING, PER BUCH ANDREASEN and LIS FAUI-LRHOIDTI Effect of phenobarbital
`induction on galactose elimination capacity in the rat
`
`RUSSELL J. TAYLOR, JR., FRANZ J. LFINWEBER and CIFOR(jE A. BRAUNZ 4—1midazolyl—3—
`;Imino—2-butanone (MCN-A—l293), a new specific inhibitor of histidine decarboxylase
`
`CHARLES L. HOPPEL and BERNARD TANDIER: Biochemical ellects of cuprizone on mouse
`liver and heart mitochondria
`
`KENNETH W. MILLER, EUGENE C. HEATII, KIRK H. EAsToN and JAMES V. DlN(jLLLZ Effect of
`Triton X-100 on the conjugation of tetrahydrocortisone, in rirro
`
`GERALD M. MCKENZIE and HELEN L. WHITE: Evidence for the methylation ofapomorphine
`by catechol-0—methyl-lransferase in Ixim and in l,‘I'lI‘0
`
`2213
`
`2223
`
`2229
`
`2237
`2247
`
`2253
`
`2267
`
`2277
`
`2283
`
`2293
`
`2299
`
`2311
`
`2319
`
`2329
`
`Continued on outside back caver
`
`BCPCA6 22(l8) 2213-2356 (1973)
`
`EXHIBIT
`
`Ex. 1025
`
`
`
`PB|'9Il|ll0|I PIBSS
`(cid:54)(cid:88)(cid:81)(cid:16)(cid:36)(cid:80)(cid:81)(cid:72)(cid:68)(cid:79)(cid:16)(cid:44)(cid:51)(cid:53)(cid:21)(cid:19)(cid:20)(cid:25)(cid:16)(cid:19)(cid:20)(cid:20)(cid:19)(cid:23)(cid:16)(cid:3)(cid:40)(cid:91)(cid:17)(cid:3)(cid:20)(cid:19)(cid:21)(cid:24)(cid:15)(cid:3)(cid:83)(cid:17)(cid:3)(cid:20)(cid:3)(cid:82)(cid:73)(cid:3)(cid:20)(cid:21)
`Sun-Amneal-lPR2016-01104- Ex. 1025, p. 1 of 12
`
`
`
`BIOCHEMICAL PHARMACOLOGY
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`
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`onn.
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`J.
`CoO1=ER—Yale University School ofMedicine, New Haven,
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`M.
`J. MICHELsoN——Sechenov
`Institute of Evolutionary
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`Physiology & Biochemistry, Leningrad
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`JACK MONGAR—University College, London
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`
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`(cid:54)(cid:88)(cid:81)(cid:16)(cid:36)(cid:80)(cid:81)(cid:72)(cid:68)(cid:79)(cid:16)(cid:44)(cid:51)(cid:53)(cid:21)(cid:19)(cid:20)(cid:25)(cid:16)(cid:19)(cid:20)(cid:20)(cid:19)(cid:23)(cid:16)(cid:3)(cid:40)(cid:91)(cid:17)(cid:3)(cid:20)(cid:19)(cid:21)(cid:24)(cid:15)(cid:3)(cid:83)(cid:17)(cid:3)(cid:21)(cid:3)(cid:82)(cid:73)(cid:3)(cid:20)(cid:21)
`Sun-Amneal-lPR2016-01104- Ex. 1025, p. 2 of 12
`
`Copyright © 1973
`
`
`
`Biochemical Pharmacology, Vol. 22, pp. 3099-3108. Pergamon Press, 1973. Printed in Great Britain.
`
`RELATIONSHIP BETWEEN THE INHIBITION CONSTANT
`(K1) AND THE CONCENTRATION OF INHIBITOR WHICH
`CAUSES 50 PER CENT INHIBITION (150) OF AN ENZYMATIC
`REACTION*
`
`YUNG-CH1 CHENG and WILLIAM H. PRUSOFF
`
`Department of Pharmacology, Yale University School of Medicine, New Haven, Conn. 06510, U.S.A.
`
`(Received 15 March 1973; accepted 27 April 1973)
`
`Abstract—A theoretical analysis has been made of the relationship between the inhibi-
`tion constant (K,) of a substance and the (I50) value which expresses the concentration
`of inhibitor required to produce 50 per cent inhibition of an enzymic reaction at a
`specific substrate concentration. A comparison has been made of the relationships
`between K; and 150 for monosubstrate reactions when noncompetitive or uncompetitive
`inhibition kinetics apply, as well as for bisubstrate reactions under conditions of com-
`petitive, noncompetitive and uncompetitive inhibition kinetics. Precautions have been
`indicated against the indiscriminate use of [50 values in agreement with the admonitions
`previously described in the literature. The analysis described shows K, does not equal
`150 when competitive inhibition kinetics apply; however, K, is equal to 150 under condi-
`tions of either noncompetitive or uncompetitive kinetics.
`
`MANY DRUGS are believed to exert their biological effect as a consequence of enzyme
`inhibition. One approach to the understanding of the mechanism of action of such
`drugs has been to study the effect of drug concentration on the rate of reaction of an
`isolated enzyme. Several approaches have been used to describe the extent of in-
`hibition such as 150 (concentration of inhibitor producing 50 per cent inhibition),
`(I/S)5o (concentration of inhibitor relative to substrate concentration producing 50
`per cent inhibition), and K, (the dissociation constant of the enzyme—inhibitor complex,
`or the reciprocal of the binding affinity of the inhibitor to the enzyme).
`‘
`Although the relationship between the inhibition constant (K,) and [50 of a com-
`petitive inhibitor of a monosubstrate reaction has been discussed,“ a detailed
`comparison of such a relationship for either bisubstrate reactions when competitive,
`noncompetitive or uncompetitive inhibition kinetics exist, or for monosubstrate
`reactions when the latter two types of inhibition kinetics apply has not been presented.
`An understanding of the relationship between [50 and K, under these conditions and
`the theoretical basis for their determination is critical to appropriate interpretation of
`the experimental data, as well as for comparison of the literature values of I50 or
`(I/S)5o. Blakley3 has indicated the limitations in the use of (I/S)50 relative to the K1.
`Although what is presented is no doubt readily apparent to the enzyme kineticist,
`those who are less familiar with enzyme kinetics and yet concerned with studying the
`effect of drugs on enzymes may find this communication useful.
`
`* This research was supported by United States Public Health Research Grant CA-05262.
`3099
`
`(cid:54)(cid:88)(cid:81)(cid:16)(cid:36)(cid:80)(cid:81)(cid:72)(cid:68)(cid:79)(cid:16)(cid:44)(cid:51)(cid:53)(cid:21)(cid:19)(cid:20)(cid:25)(cid:16)(cid:19)(cid:20)(cid:20)(cid:19)(cid:23)(cid:16)(cid:3)(cid:40)(cid:91)(cid:17)(cid:3)(cid:20)(cid:19)(cid:21)(cid:24)(cid:15)(cid:3)(cid:83)(cid:17)(cid:3)(cid:22)(cid:3)(cid:82)(cid:73)(cid:3)(cid:20)(cid:21)
`Sun-Amneal-|PR2016-O1104- Ex. 1025, p. 3 of 12
`
`
`
`3100
`
`YUNG-CHI CHENG and W. H. PRUSOFF
`
`THEORETICAL ANALYSIS
`
`Several kinetic situations are described below that have the following limitations;
`(1) the reaction in the absence of the inhibitor follows a simple Michaelis—Menten
`equation; (2) the rate of the reaction depends on the amount of the enzyn1e—substrate
`complex; (3) a rapid equilibrium steady state method is used;4 and (4) only reversible
`inhibitors are discussed.
`
`Reactions involving one substrate
`
`V T‘
`0
`
`V
`S
`max
`Km + S
`
`(1)
`
`Vmax = maximum velocity; V0 = velocity in the absence of the inhibitor; Km =
`Michaelis constant of the substrate (S); S = substrate concentration.
`Case I. When a competitive inhibitor (1) is present.
`
`E;,ES—>E+P
`tr
`E]
`
`V, =
`
`Km (1 -I-
`
`+ S
`
`I
`
`(2)
`
`V, = velocity in the presence of inhibitor; I = inhibitor concentration; K, = dis-
`sociation constant of E1.
`
`When I = I50, V0 Z 2 V1, then
`
`By rearrangement:
`
`21/max S
`
`Vmax S
`
`I
`
`I50 = K, (1 +
`
`m
`
`Equation (3) is identical to that described by Webb:2
`
`(3)50 — Km + S.
`I
`__ K,
`K,
`
`(3)
`
`4)
`
`(
`
`The equation derived by Baker‘ makes the assumption that V0 = V,,,,,, in the
`beginning of the derivation:
`
`(Z) = E _ IS
`
`S so
`
`Km
`
`S
`
`(5)
`
`(cid:54)(cid:88)(cid:81)(cid:16)(cid:36)(cid:80)(cid:81)(cid:72)(cid:68)(cid:79)(cid:16)(cid:44)(cid:51)(cid:53)(cid:21)(cid:19)(cid:20)(cid:25)(cid:16)(cid:19)(cid:20)(cid:20)(cid:19)(cid:23)(cid:16)(cid:3)(cid:40)(cid:91)(cid:17)(cid:3)(cid:20)(cid:19)(cid:21)(cid:24)(cid:15)(cid:3)(cid:83)(cid:17)(cid:3)(cid:23)(cid:3)(cid:82)(cid:73)(cid:3)(cid:20)(cid:21)
`Sun-Amneal-lPR2016-01104- Ex. 1025, p. 4 of 12
`
`
`
`Relationship between K, and 150
`
`3101
`
`which is diflerent from equation (4). However, since most investigators have S > Km
`in their assay condition, there would be no significant difference between equations
`(4) and (5), and hence these equations may be transformed into equation (6).
`
`(‘l
`
`S 50
`
`Km
`
`(6)
`
`Since I50 will depend on the substrate concentration used in the assay (equation 3),
`it is impossible to compare [50 values from one laboratory with those from another
`unless identical assay conditions are used. Bakerl has indeed considered the substrate
`concentration by his use of (I/S)50. Appropriate comparison of the effect of one
`compound relative to another may be made, provided that S > Km, and both com-
`pounds are competive inhibitors. Without prior determination of the type of
`inhibition such compounds exert, the relativevalues of (I/S)5o have questionable mean-
`jng, Thus, for example, one might have assumed that 3-N-methy1—5-iodo-2'-deoxy-
`uridine would be like 5-iodo-2’-deoxyuridine, a competitive inhibitor of thymidine
`kinase when thymidine is the variable substrate. However, uncompetitive inhibition is
`observed with N-methyl-5-iodo-2’-deoxyuridine when thymidine is the variable sub-
`strate, and competitive inhibition kinetics when ATP-Mg“ is the variable substrate.5
`Having determined that the two compounds being compared are indeed com-
`petitiveinhibitors, one can effectively use (I/S)50 values for the purpose of comparison.
`If the concentrations of inhibitors A and B required to produce 50 per cent inhibition
`at a particular substrate concentration are significantly difl"erent yet close, one may
`amplify the difierence by augmenting the substrate concentration.
`Case II. When a noncompetitive inhibitor is present.
`
`E 3+. ES —> E + P
`IJFKIS IJFKH
`Elfi ESI
`
`Vmax S
`V1 1- o
`K,,,(1+--)+S(1—l——>
`
`KIS
`
`Kli
`
`When I 2 150, V0 = 2 V, and:
`
`2Vmax S
`
`Vmax S __
`
`Km + S n
`
`<
`
`150)
`
`Km 1 —l— — + S 1 + —
`KIS
`K11
`
`(
`
`150).
`
`By rearrangement of the above equation:
`
`I = K
`
`so
`
`S
`K
`S 4' — .
`
`(,..+ )/(KIS+K“)
`
`(8)
`
`When K” = K”, that is when the affinity of inhibitor to the free enzyme (E) and the
`enzyme—substrate complex (ES) is the same, then equation (8) may be transformed into:
`
`150 = K” or K”, or more simply, K1.
`
`(9)
`
`(cid:54)(cid:88)(cid:81)(cid:16)(cid:36)(cid:80)(cid:81)(cid:72)(cid:68)(cid:79)(cid:16)(cid:44)(cid:51)(cid:53)(cid:21)(cid:19)(cid:20)(cid:25)(cid:16)(cid:19)(cid:20)(cid:20)(cid:19)(cid:23)(cid:16)(cid:3)(cid:40)(cid:91)(cid:17)(cid:3)(cid:20)(cid:19)(cid:21)(cid:24)(cid:15)(cid:3)(cid:83)(cid:17)(cid:3)(cid:24)(cid:3)(cid:82)(cid:73)(cid:3)(cid:20)(cid:21)
`Sun-Amneal-|PR2016-01104- Ex. 1025, p. 5 of 12
`
`i;
`
`
`
`3102
`
`YUNG-CHI CHENG and W. H. PRUSOFF
`
`Since S > K,,, in most assays performed, then equation (8) may be transformed into;
`
`I50 —
`
`1)
`Km 1
`K15 + Kli
`
`and hence,
`
`150 = KIS[<? +
`
`Km
`
`K
`
`(10)
`
`Provided that Km/S < K15/Kn (since Km/S may be adjusted) apply, equation 10 may
`then be transformed into either:
`
`150 = KM
`
`(11)
`
`O1‘
`
`(§)5o=1/l%:+1f,,.)~
`
`Thus it is quite apparent that there is no value in comparing the effect of inhibitors on
`the basis of (I/S)”, because I50 equals K, (equation 11).
`It should be emphasized that the dependence of I50 on S is different from that
`observed above with the competitive inhibitor.
`Case III. When an uncompetitive inhibitor is present.
`
`E#ES——>E+P
`K1’H/I
`ESI
`
`V, =
`
`Km + (1 —1— E) S
`
`(13)
`
`When I= 150, V0 = 2 VI, then
`
`Vmax S
`
`2Vma,, S
`
`1<,,,+s=Km+(1+£9)S'
`
`KI
`
`Rearrangement of the above equation results in:
`
`K
`:n+S
`
`150
`= —,
`SKI
`
`(cid:54)(cid:88)(cid:81)(cid:16)(cid:36)(cid:80)(cid:81)(cid:72)(cid:68)(cid:79)(cid:16)(cid:44)(cid:51)(cid:53)(cid:21)(cid:19)(cid:20)(cid:25)(cid:16)(cid:19)(cid:20)(cid:20)(cid:19)(cid:23)(cid:16)(cid:3)(cid:40)(cid:91)(cid:17)(cid:3)(cid:20)(cid:19)(cid:21)(cid:24)(cid:15)(cid:3)(cid:83)(cid:17)(cid:3)(cid:25)(cid:3)(cid:82)(cid:73)(cid:3)(cid:20)(cid:21)
`Sun-Amneal-|PR2016-O1104- Ex. 1025, p. 6 of 12
`
`
`
`Relationship between K, and 150
`
`3103
`
`150 1 KI
`
`K
`
`+ J).S
`
`When S > K,,,, equation (14) may be simplified into
`
`[so = Kb
`
`(15)
`
`In this situation, 150 is independent of S provided that S > Km. Thus there is no
`value to express the data in terms of (I/S)50.
`
`Reactions involving two substrates
`
`When both substrates are added sequentially to the enzyme, the reaction follows
`either a rapid equilibrium random or ordered mechanism. The rate equation""3 is:
`
`Vmax AB
`V =———-.~———j
`°
`K,.,,K,, + K,,B + K,,A + AB
`
`1
`( 6)
`
`Ki, = dissociation constant of substrate A.
`Case IV. If the inhibitor competes for the free enzyme (E) with either substrate A
`or B in a random mechanism reaction, or with the first substrate in an ordered sequen-
`tial mechanism, then
`
`51 .17 E
`
`EAB —> Products
`
`x //
`
`EB
`
`01'
`
`E1 é E é EA ; EAB —> Products, and the rate equation will be:
`
`Vmax A3
`V, = —~I——~—.
`Kia-Kb
`+
`+ KaB + KbA +
`I
`
`(17)
`
`By mathematical treatment similar to that performed in the previous cases, and
`V0 i 2 VI, I 1 I50,
`
`2 V,,,,,, AB
`
`_
`
`Vm, AB
`
`KMK,
`
`(1 +
`
`+ K,,B + K,,A + AB
`
`I
`
`K"“K” + K“B + K’’‘4 ‘L AB
`
`(cid:54)(cid:88)(cid:81)(cid:16)(cid:36)(cid:80)(cid:81)(cid:72)(cid:68)(cid:79)(cid:16)(cid:44)(cid:51)(cid:53)(cid:21)(cid:19)(cid:20)(cid:25)(cid:16)(cid:19)(cid:20)(cid:20)(cid:19)(cid:23)(cid:16)(cid:3)(cid:40)(cid:91)(cid:17)(cid:3)(cid:20)(cid:19)(cid:21)(cid:24)(cid:15)(cid:3)(cid:83)(cid:17)(cid:3)(cid:26)(cid:3)(cid:82)(cid:73)(cid:3)(cid:20)(cid:21)
`Sun-Amneal-lPR2016-01104- Ex. 1025, p. 7 of 12
`
`
`
`3104
`
`YUNG-CHI CHENG and W. H. PRUSOFF
`
`This equation may be rearranged into:
`
`I _K(1+ K,, 3+/1+ AB)
`5° _ ’
`Km,
`K.-.
`K. Kb '
`
`When K“ = K,-,,, equation (18) may be simplified to:
`
`B
`A
`I =K(1+—)(1+—),
`50
`I
`K“
`Kb
`
`(13)
`
`19
`
`)
`
`(
`
`which basically is similar to equation (3); however, equation (19) takes into account an
`additional substrate.
`Equations (18) and (16) may also be transformed into:
`
`I50 =
`
`A B
`V
`max? __ KI.
`V0 Km Kb
`
`(20)
`
`Since most assays are performed under optimal conditions in which either V0 =
`Vmx, or A > K,, and B > K0, then both equations (19 and 20) may be transformed into:
`
`AB
`I =——K.
`so
`KMKI,
`1
`
`21
`
`Thus the 150 value will depend on the concentration of both substrates A and B.
`Case V. When the reaction follows either an ordered sequential or a rapid equili-
`brium random mechanism, the inhibitor acts as a noncompetitive inhibitor and can
`bind to all of the enzyme species in the reaction with the same affinity:
`
`E1
`
`E
`
`'EAB —+ Products.
`XEB/X W’
`
`EABI
`
`JP Kr
`EBI
`
`Then, the velocity is described by:
`
`V, : _ (22)
`I
`(KiaKb + KaB ‘l’ KBA 'l‘ AB) (1 + I
`
`When V0 = 2 V,, I = I50, and upon substitution of equation 16 for V0 and equation
`(22) for V1, one obtains:
`
`I50
`KiaKb + K413 ‘l’ KbA ‘l’ AB = I? (KiaKb + KaB + K1114 "l" AB)
`I
`
`(cid:54)(cid:88)(cid:81)(cid:16)(cid:36)(cid:80)(cid:81)(cid:72)(cid:68)(cid:79)(cid:16)(cid:44)(cid:51)(cid:53)(cid:21)(cid:19)(cid:20)(cid:25)(cid:16)(cid:19)(cid:20)(cid:20)(cid:19)(cid:23)(cid:16)(cid:3)(cid:40)(cid:91)(cid:17)(cid:3)(cid:20)(cid:19)(cid:21)(cid:24)(cid:15)(cid:3)(cid:83)(cid:17)(cid:3)(cid:27)(cid:3)(cid:82)(cid:73)(cid:3)(cid:20)(cid:21)
`Sun-Amneal-|PR2016-O1104- Ex. 1025, p. 8 of 12
`
`
`
`Relationship between K, and I50
`
`and hence,
`
`150 = Kb
`
`3105
`
`(23)
`
`Thus the Value of 150 does not depend on the substrate concentration and will be
`equal to K,. The 150 Value obtained under these conditions can be compared between
`1aboratories without concern with the substrate concentration.
`Case VI. When the reaction follows an ordered sequential mechanism, the inhibitor
`can compete with either the first substrate A for the free enzyme, or with the second
`substrate for the EA complex, or both:
`
`E :2 EA 3% EAB —> Products.
`it
`A it
`E] :EAI
`
`Then
`
`VmaxAB
`V, = ———I——:—~—;~———.
`K,.,,K,, (1+ —) + K,,B + K,,A(1+ —) + AB
`
`K15
`
`K11‘
`
`(24)
`
`When V0 = 2 V,, I = I50, and by combining equations (23) and (16), one obtains:
`
`KiaKb + KaB ‘i"‘ KIJA +
`
`K,-“Kb
`1 [50 K
`IS
`
`Kb/1
`+ ‘F .
`Ii
`
`This equation may be transformed into:
`
`=
`
`I50
`
`)[(KiaKb
`Vmax
`< V0 A -
`K13 + Kli
`
`——
`
`B
`
`L)
`_ Vmax
`‘(I/0)/B K,sA+Kn'
`
`(25)
`
`Under the rare condition when K” = K” and V0 = Vnm, equation (25) can be
`simplified to:
`
`and
`
`B
`I = K .—
`so
`, Kb
`
`I
`_
`
`(3)50
`
`K,
`= __
`
`K,,
`
`26
`
`>
`
`<
`
`2
`
`W
`
`(cid:54)(cid:88)(cid:81)(cid:16)(cid:36)(cid:80)(cid:81)(cid:72)(cid:68)(cid:79)(cid:16)(cid:44)(cid:51)(cid:53)(cid:21)(cid:19)(cid:20)(cid:25)(cid:16)(cid:19)(cid:20)(cid:20)(cid:19)(cid:23)(cid:16)(cid:3)(cid:40)(cid:91)(cid:17)(cid:3)(cid:20)(cid:19)(cid:21)(cid:24)(cid:15)(cid:3)(cid:83)(cid:17)(cid:3)(cid:28)(cid:3)(cid:82)(cid:73)(cid:3)(cid:20)(cid:21)
`Sun-Amneal-|PR2016-O1104- Ex. 1025, p. 9 of 12
`
`
`
`3106
`
`YUNG-CHI CHENG and W. H. PRUSOFF
`
`Case VII. When the reaction follows an ordered sequential or rapid random mech-
`anism, and the inhibitor can only bind to the EAB complex:
`
`A EN/E { /EAB —> Products.
`
`“\EB K 1L K:
`EABI
`
`Then,
`
`Vmax A3
`V, = ————-——-————7——.
`K,-,,K,, + K,,B + K,,A + (1 + F) AB
`I
`
`(28)
`
`When V0 = 2 V,, I = 150, and by combining equations (28) and (16), one obtains:
`
`I
`K,.,,K,, + K,,B + K,,A + AB = -133 AB,
`I
`
`which may be transformed into:
`
`150 =
`
`Vmax
`
`V0
`
`K1.
`
`Thus, when
`
`V0 = Vrnaxa I50 = Kb
`
`(29)
`
`When the reaction follows a “ping-pong” mechanism6'8 and involves two substrates,
`the rate equation will be:
`
`yo = ._ln:><_-’11’__
`K,,A —l- KaB + AB
`
`(30)
`
`Case VIII. An inhibitor, 1, aflects both forms of the enzyme, E and E ~ X I
`
`A
`l
`
`Product,
`T
`
`E
`
`lLKu
`E1
`
`E ~ X
`
`lLKz~2
`E1 ~ X
`
`B
`l
`
`Product,
`T
`
`E
`
`The rate equation9 is:
`
`VI =
`
`I
`K 1
`—— A
`b( + K”)
`
`+
`
`V
`
`AB
`
`I
`max
`K, (1 —) B
`+ K“
`
`.
`
`-1-
`
`AB
`
`(cid:54)(cid:88)(cid:81)(cid:16)(cid:36)(cid:80)(cid:81)(cid:72)(cid:68)(cid:79)(cid:16)(cid:44)(cid:51)(cid:53)(cid:21)(cid:19)(cid:20)(cid:25)(cid:16)(cid:19)(cid:20)(cid:20)(cid:19)(cid:23)(cid:16)(cid:3)(cid:40)(cid:91)(cid:17)(cid:3)(cid:20)(cid:19)(cid:21)(cid:24)(cid:15)(cid:3)(cid:83)(cid:17)(cid:3)(cid:20)(cid:19)(cid:3)(cid:82)(cid:73)(cid:3)(cid:20)(cid:21)
`Sun-Amneal-lPR2016-01104- Ex. 1025, p. 10 of 12
`
`A
`
`
`
`Relationship between K, and [50
`
`3107
`
`When I = 150, V0 = 2 V,, and by combining equations (30) and (31), one obtains:
`
`KA K,,B AB: —
`
`" +
`
`+
`
`(B K” + A K“
`K“ 1)
`1
`Kb
`
`—
`
`and
`
`1 =
`
`5°
`
`V0 /(B K” “L A K“
`K,, 1)
`1
`VW Kb
`
`———.
`
`—
`
`I
`
`5°
`
`(32)
`
`(33)
`
`Although K” is generally not equal to Kl-2, in the specific situation when K,-1 does
`equal K,-2, equation (31) can be transformed into:
`
`’s° = (1 t 17:59) Kw
`
`AB
`
`<34)
`
`Case IX. When the reaction follows a ping-pong mechanism, an inhibitor affects
`only one form of the enzyme——E or E ~ X. The rate equation will be:
`
`O1‘
`
`OI‘
`
`Vmax AB
`V, = ——————I————
`KbA+K,,(1+
`>B+AB
`
`Kil
`
`Vmax
`V, = —-—————————-——
`I
`
`.
`
`K,,(1—l—-—)A—l—K,,B—|—AB
`
`Ki2-
`
`(35)
`
`(36)
`
`When I = 150, V0 = 2 V1, and by combining equations (35) and (30), one obtains:
`
`I
`K,,A + K43 + AB = K,,A 1%
`
`I —K (1+K"B+B)
`50 * i1
`Kb '
`
`Similarly, equation (36) can be transformed into:
`
`I "
`
`so ~ :2
`
`<1+ KaB -l- A)
`
`KbA
`
`K“ -
`
`37
`
`)
`
`(
`
`(38)
`
`The effect of an enzyme inhibitor in a Variety of situations has been analyzed.
`Before the equations described above may be used, one must determine the type of
`
`DISCUSSION
`
`(cid:54)(cid:88)(cid:81)(cid:16)(cid:36)(cid:80)(cid:81)(cid:72)(cid:68)(cid:79)(cid:16)(cid:44)(cid:51)(cid:53)(cid:21)(cid:19)(cid:20)(cid:25)(cid:16)(cid:19)(cid:20)(cid:20)(cid:19)(cid:23)(cid:16)(cid:3)(cid:40)(cid:91)(cid:17)(cid:3)(cid:20)(cid:19)(cid:21)(cid:24)(cid:15)(cid:3)(cid:83)(cid:17)(cid:3)(cid:20)(cid:20)(cid:3)(cid:82)(cid:73)(cid:3)(cid:20)(cid:21)
`Sun-Amneal-lPR2016-01104- Ex. 1025, p. 11 of 12
`
`
`
`3108
`
`YUNG-CHI CHENG and W. H. PRUSOFF
`
`inhibition involved. This is readily established by applying the rules discussed by
`Cleland.5"3 The relationship between K, and 150 varies. For instance, when a non.
`competitive or an uncornpetitiveinhibitor is studied in a monosubstrate enzymatic
`reaction, 15,, will be equal to K,, provided certain conditions are met (equations 11 and
`15). I-Iowever,‘if the inhibitor is a competitive inhibitor, I50 will be equal to K, (1 .5.
`S/Km) (equation 3). The equations (3, 8, 14, 18, 23, 25, 29, 33, 37) have described the
`relationship of I50 to K, when both the type of inhibitor and the reaction mechanism
`vary. It is readily apparent that the relationship of [50 to K, is dependent upon the
`type of inhibition and the mechanism of the reaction. It has been established that
`(I/S)5,, may not be used in the absence of such knowledge without producing great
`uncertainties as to its meaning. K, does not equal I50 when competitive inhibition
`kinetics apply; however, K,
`is equal to 15,, under the conditions of either non-
`competitive or uncompetitive kinetics.
`When a group of inhibitory compounds have an identical mechanism of action, a
`direct comparison of the 15,, values among them will suflice to determine the relative
`efiicacy, provided the assays are performed under the same conditions. However, in
`certain cases, when the K, value of each compound is required, it may be impractical
`to perform the kinetic studies required to determine the K, for each. In this situation,
`it is still possible to calculate the K, values, provided one knows the K, of one com-
`pound, by using the relationship:
`
`(15,). _(K1)1
`(I50)2 — (K02.
`
`This may be done without knowing the reaction mechanism or type of inhibitor in
`detail, except for Cases II, VI and IX, in which a certain assumption must be made
`beforethis general rule applies. In Cases II and VI, the assumption is that K,S = K“,
`and in Case IX, that K” = K,,.
`When comparing the 15,, values of compounds that inhibit a specific enzyme derived
`from the same source, but reported from different laboratories, a few important
`factors must be considered: (1) Are the assay conditions the same? (2) Do the com-
`pounds have the same reaction mechanism for their inhibitory effect?
`
`REFERENCES
`
`1. B. R. BAKER, Design ofActive-site-directed Irreversible Enzyme Inhibitor p. 202. Wiley, New York
`(1967).
`2. J. L. WEBB, Enzyme and Metabolic Inhibitors p. 106. Academic Press, New York (1963).
`3. R. L. BLAKLEY, The Biochemistry of Folic Acid and Related Pteridines (Eds. A. Neuberger and
`E. L. Tatum), p. 162. North Holland, Amsterdam (1969).
`. S. CHA, J. biol. Chem. 243, 820 (1968).
`. P. VOYTEK, P. K. CHANG and W. H. PRUSOFF, J. bial. Chem. 247, 367 (1972).
`. W. W. CLELAND, Biochim. biophys. Acta 67, 104 (1963).
`. W. W. CLELAND, Biochim. biophys. Acta 67, 173 (1963).
`. W. W. CLELAND, Biochim. biophys. Acta 67, 188 (1963).
`. N. MOURAD and R. E. PARKS, JR., J. biol. Chem. 241, 271 (1963).
`
`©OO\lO\U1-B
`
`(cid:54)(cid:88)(cid:81)(cid:16)(cid:36)(cid:80)(cid:81)(cid:72)(cid:68)(cid:79)(cid:16)(cid:44)(cid:51)(cid:53)(cid:21)(cid:19)(cid:20)(cid:25)(cid:16)(cid:19)(cid:20)(cid:20)(cid:19)(cid:23)(cid:16)(cid:3)(cid:40)(cid:91)(cid:17)(cid:3)(cid:20)(cid:19)(cid:21)(cid:24)(cid:15)(cid:3)(cid:83)(cid:17)(cid:3)(cid:20)(cid:21)(cid:3)(cid:82)(cid:73)(cid:3)(cid:20)(cid:21)
`Sun-Amneal-lPR2016-01104- Ex. 1025, p. 12 of 12