Advances in
`
`ENZYME REGULATION
`
`Volume 22
`
`Proceedings of the Twen.'y—See0nd S'yn:po.In'nm on Regufarfan of Enzyme
`/l.:‘n'w'.=‘y and Synthesis in Norma! and Neaplaxm Trlcsues
`item’ (U Indiana University Senaof of Medicine
`Inrlfanapafis. Indiana
`October 3 and 4. 1983
`
`Edited 2';y
`G E 0 R G E WE B E R
`
`Indiana Unfvermlry Senna! of Medicine
`Indianapoffs, Indiana
`
`Technical editor
`Cainerine E. Forrest Weber
`
`
`
`PERGAMON PRESS
`
`OXFORD ~ NEW YORK - TORONTO
`SYDNEY - PARIS - FRANKFURT
`
`1 of 32
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`Alkermes, Ex. 1043
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`1 of 32
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`Alkermes, Ex. 1043
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`

`
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`AH Rfg}H.\' Re.-mrvcd. Na pm‘! :2)’ .f!n'_s‘ prn':h'<:cm'rm may bi’
`in 1
`reprorfucm’, storm‘ in :1‘ retrieval .\j1-.v.'c’n:'. or mm_\'m.t'.r.'m'.
`'
`(my form or by (my rm'an.\'. m"e'(':rarH'c'.
`:'h'('r:'r).mm'r‘. Mir-'.i.'?fl'-‘N-'
`(ape. m‘c=ctrant'c, n:'e:'hrn:fcm’. phomc‘r2py:'ng. ralrrmimg ur r:.*hw'1\':.w.
`Ivirhaur pcrm.".v.',s':'rur in xwirfngfrunr {lie pm‘J!:'_-.'!m's.
`First edition 1984
`
`Library of Congress Catalog Card No. 63—l‘}6I}‘-I
`
`ISBN 0 {)8 031498 3
`ISSN 0065-257!
`
`Primer! in Circa! Brfrairl by A. Wire-arm: 6’: Co.
`
`.’.1d.. I:'.\'erc-':‘
`
`2 of 32
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`Alkermes, Ex. 1043
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`2 of 32
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`Alkermes, Ex. 1043
`
`

`
`Advances in
`
`ENZYME REGULATION
`
`Volume 22
`
`3 of 32
`
`Alkermes, Ex. 1043
`
`3 of 32
`
`Alkermes, Ex. 1043
`
`

`
`QUANTITATIVE ANALYSIS OF
`DOSE—EFFECT RELATIONSHIPS: THE
`
`COMBINED EFFECTS OF MULTIPLE
`
`DRUGS OR ENZYME INHIBITORS
`
`TING-Cl-[A0 CHOU" and PAUL "l'AL2\LAYi‘
`
`"Laboratory of Pharmacology. Memorial Sloan—I(ettering Cancer Center, New York. NY
`IOOZI. and '1'DcpartIi1ent oi‘ Pharmacology and Experimental Therapeutics. The Johns
`Hopkins University School of Medicine. Baltimore. Maryland 21205
`
`INTRODUCTION
`
`The quantitative relationship between the dose or concentration of a given
`ligand and its effect is a characteristic and important descriptor of many
`biological systems varying in complexity from isolated enzymes (or binding
`proteins)
`to intact animals. This
`relationship has been analyzed in
`considerable detail for reversible inhibitors of enzymes. Such analyses have
`made
`assumptions
`on
`the mechanism of
`inhibition (competitive,
`noncompetitive, uncompetitive), and on the mechanism of the reaction for
`multi-substrate enzymes (sequential or ping-pong), and have required
`knowledge of kinetic constants (1-4). More recently, it has been possible to
`describe the behavior of such enzyme inhibitors by simple generalized
`equations that are independent of inhibitor or reaction mechanisms and do
`not require knowledge of conventional kinetic constants (i.e. Km, Ki, Vm)
`(5-8).
`
`Our understanding ofdose—effect relationships in pharmacological systems
`has not advanced to the same level as those ofenzyme systems. Many types of
`mathematical transformations have been proposed to linearize dose-effect
`plots, based on statistical or empirical assumptions, e.g. probit (9. I0), logit
`ill} or power-law fttnctions (12). Although these methods often provide
`adequate linearizations of plots, the slopes and intercepts of such graphs are
`usually devoid of any fundamental meaning.
`
`Tl-iii MEDIAN ['L}"l"EiC'I' l’R|N(.'lPl.E
`
`We demonstrate here the application ofa single and generalized method for
`analyzing dose—cffect relationships in enzymatic. cellular and whole animal
`systems. We also examine the problem of quantitating the effects of multiple
`inhibitors on such systems and provide definitions of summation of effects,
`and consequently of synergism and antagonism.
`Since the proposed method of analysis is derived from generalized mass
`action considerations, we caution the reader that the analysis ol'dose—effect
`.\t-Lit
`'3?-an
`27
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`Alkermes, Ex. 1043
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`4 of 32
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`Alkermes, Ex. 1043
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`

`
`28
`
`TINCJ-Cl-lA(J ('1 IOU anti PAUL 'l'Ai.AI.i'\Y
`
`data is concerned with basic mass-action characteristics rather than with
`
`proof of specific mechanisms. Nevertheless, it is convenient and intuitively
`attractive to analyze and normalize all types of dose—re.sponsc results by a
`uniform method which is based on sound fundamental considerations that
`
`have physieochemieal and biochemical validity in simpler systems. Our
`analysis is based on the median effect principle of the mass action law (S-8),
`and has already been shown to be simple to apply and useful in the analysis of
`complex biological systems (I3).
`
`The Median Effect Equation
`
`The median effect equation (6. 8) states that:
`
`ft/fl. = (D/D...}"‘
`
`(1)
`
`where D is the dose, f,, and f,, are the fractions of the system affected and
`unaffected, respectively, by the dose D, D", is the dose required to produce the
`median effect (analogous to the more familiar IC_.-,0. EI)_.-,,,, or 1.0-... values), and
`m is a Hill—type coefficient signifyingthe sigmoidicity ofthe dose-effect curve.
`i.e., m = 1 for hyperbolic (first order or Michaelis~Menten) systeins. Since by
`definition, f,, + f,, = 1, several useful alternative forms of equation 1 are:
`
`H
`
`= i:(fiu)“[ _ lfi : [”iI)—l _
`
`: (D/DIt|)nI
`
`£1: 1/[1 + (Du/D)]"‘
`
`D =
`
`— fiilivm
`
`The median effect equation describes the behavior of man)’ bi010giC31
`systems. It is, in fact, a generalized form of the enzyme kinetic rCl'c11i0fl5=' Of
`Michaelis~Menten (14) and Hill (IS), the physical adsorption isotherm of
`Langmuir (I6), the pH-ionization equation of Henderson and I-lasselbalclt
`(I'll).
`the equilibrium binding equation 01‘ Sc;|[t_‘,]];l['I.’.i
`[I8]. and the
`pharmacological drug-—rccept0r interaction ([9). Furthermore. the median
`effect equation is directly applicable not only to primary ligands such as
`substrates. agonists, and activators, but also to seeontlary ligands such as
`inhibitors, antagonists. or environmental factors [5, 6).
`When applied to the analysis of the inhibition of enzyme systems, the
`median effect equation can be used without knowledge of conventional
`klnctlc '30”5‘31'll5 (L6. K,,,. V,,,,,, or K,) and irrespective of the mechanism of
`inhibition fi.e. competitive, noncompetitive or uncompetitive}. Furthermore,
`it is valid for multisubstrate reactions irrespective ofmechanism (sequential or
`ping-pong) (5-8).
`
`5of32
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`Alkermes, Ex. 1043
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`5 of 32
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`Alkermes, Ex. 1043
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`

`
`!\NAl.YS|S ()1-' MUL'|‘Il-‘LE’. DRUG l:'l"l“li(.."l'.‘S
`
`29
`
`'I'lw ilrlediriit 1;)f}'ec’.' Plot
`
`The median effect equation (equation [) may be linearized by taking the
`logarithms of both sides, i.e.
`
`or
`or
`
`log (lg,/l},) = in log (D) — rn 1og{D,,.)
`log [(f_._)" — lj" = in log (D) — in log (D...)
`log [{l},)" — 1] = in log (D) — rn log (Dm)
`
`I] of y = log fl},/1],} or its equivalents with
`The median effect plot (Fig.
`respect to X = log (D) is a general and simple method (13. 30) for determining
`pharntacological median doses for lethality (_I.D5.,), toxicity {_'l"D.-,.,), effect of
`agonist drugs (Ellen), and el‘1'eet of antagonist drugs (lC5u).Tl1us. the median-
`effect principle of the mass-action law encompasses a wide range of
`applications. The plot gives the slope, m, and the intercept ofthe dose—effect
`plot with the median-effect axis [i.e. when l; = f,,, E,/in = l and hence y = log
`ti},/ii.) = 0] which gives log (D,,,) and consequently the D," value. Any cause-
`eonseqttence relationship that gives a straight line for this plot will provide the
`two basic parameters, m and Dm, and thus, an apparent equation that
`describes such a system. The linearity ofthe median—effect plot (as determined
`from linear regression coefficients) determines the applicability ofthe present
`method.
`
`Log
`
`[(fal'l—l]'l
`
`Log to/om)
`
`FIG. I. The median-elteet plot at dil'l'erent slopes corresponding to m values oI‘0.5. l. 2 and 3. The
`plot
`is based on the median-el'fect equation (equation I) in which the dose (D) has been
`normztlized by taking lltc ratio to the median—et'fcet dose(l),,.]. Note that the ordinate log[(f,)“ —
`l]" is identical to 1ug{i;,)’l - l] or log (ll./f.,).
`
`6of32
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`6 of 32
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`

`
`30
`
`'l‘lN(_'i—Cl-l.~\O Cl-{GU and PAUL 'I'AL/\l..I\Y
`
`Re!'rm'on after’ Mediari-!;]']'ecr 1'.-,‘qmrt.*'rm to Midiae!tt‘—Menren um! INN
`Equations-
`-l- (D.../D'l'
`In the special case, when rn = 1. equation 1 becomes 1;. = [l
`which has the same form as the Michaelis—Menten equation I‘ 14). v/V...“ = [1 +
`(K.../S)]". In addition, when the effector ligand is an environmental factor
`such as an inhibitor, the equation, l:, = [l + (D,,./[))]". is valid not only fora
`single substrate reaction (Michaelis-Menten equation) but also for multiple
`substrate reactions;
`the fractional effect
`is expressed with respect
`to the
`control velocity rather than to the maximal velocity (6). Furthermore. if, in
`equation I
`is simple to obtain. whereas the determination of Vnm in the
`Miehaelis-Menten (or I-lill} equations requires approximation or extra-
`polation (6. 7). The logarithmic form of equation 1 describes the Hill equation.
`
`The Utility of the Median E_/feet 1’rfncipl'e
`The median-effect equation has been used to obtain accurate values oflC5,,,
`EDS”, LDSO, or the relative potencies ofdrugs or inhibitors in enzyme systems
`{'6-—8, 21-26). in cellular systems (20. 2?. 23) and in animal systems i l 3. 29—32).
`An alternative form of the median-effect equation (5) has been used for
`calculating the dissociation constant (K, or K“) ofligands for pharmacological
`receptors
`(33-35).
`It has
`also permitted the
`analysis of chemical
`carcinogenesis data and has predicted especially accurately tumor incidence at
`low dose carcinogen exposure (30, 31). By using the median-effect principle,
`the general equation for describing a standard radioimmunoassay or ligand
`displacement curve has been derived recently by Smith (36). It has also been
`used to show that there is marked synergism among chemotherapeutic agents
`in the treatment of hormone—responsive experimental mammary carcinomas
`(32).
`In recent preliminary reports (13, 3?), we have shown that.
`in
`conjunction with the multiple drug effect equations (see below), the median-
`effect plot forms the basis for the quantitation of synergism, summation and
`antagonism of drug effects.
`
`ANALYSIS OF MUl.‘l‘lP1.lE DRUG El-‘l"EC'l‘S
`
`An Overview
`
`Over
`the past decades, numerous authors have claimed synergism,
`summation or antagonism of the effects of multiple drugs. However. there is
`still no consensus as to the meanings ofthese terms. For instance. in a review.
`Goldin and Mantel
`in 195? (38) listed seven different definitions of these
`terms. Confusion and ambiguity persist (39) despite increasing use ofmultiple
`drugs in experimentation and in therapy. This emphasizes the lack of a
`
`7of32
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`Alkermes, Ex. 1043
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`7 of 32
`
`Alkermes, Ex. 1043
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`

`
`ANALYSIS OF MUl.'['lPl.li DRUG El7l'-’l:’C'l‘S
`
`3!
`
`theoretical basis that would permit rigorous and quantitative assessment of
`the effects of drug combinations.
`Attempts to interpret the effect ofmultiple drugs have been documented for
`more than a century (39). Since the introduction of the isobol concept by
`Loewe in 1928 (40, 41) and the fractional product concept (see Appendix) by
`Webb in l963 (42), the theoretical and practical aspects of the problem have
`been the subject ofmany reviews (38, 43-5 1). Some authors have discussed the
`possible mechanisms that ntay lead to synergism, and others have emphasized
`methods of data analysis. The kinetic approach was used earlier by some
`investigators (4, 42. 52-58). but the formulations were frequently too complex
`to be of practical usefulness or were restricted to individual situations.
`Although not specifically stated, some formulations are limited to two
`inhibitors; others are valid only for first order {_Micl1aelis—Menten type)
`systems but not for higher order (Hill type) systems, and still others are valid
`only for mutually nonexclusive inhibitors but not for mutually exclusive
`inhibitors.
`
`The present authors. therefore. have undertaken a kinetic approach to
`analyze the problem. An unambiguous definition of summation is a
`prerequisite for any meaningful conclusions with respect to synergism and
`antagonism. Ironically, two prevalent concepts for calculating summation
`i.e.. the isobol and the fractional-product method. are shown to conform to
`two opposite situations. The former concept is valid for drugs whose effects
`are mutually exclusive, and the latter is valid for mutually nonexclusive drugs
`(13, 49), and thus these methods cannot be used indiscriminately (see
`Appendix). In this paper, we provide the equations for both situations and
`show that they are merely special cases of the general equations described
`recently (59). We also propose a general diagnostic plot to determine the
`applicability of experimental data, to distinguish mutually exclusive from
`nonexclusive drugs. and to obtain parameters that can be directly used for the
`analysis of summation, synergism or antagonism.
`
`Requiremcms for Analyzing Multiple Drug I-.)fects
`The following information is essential for analyzing multiple drug effects
`and for quantitating synergism, summation and antagonism of multiple
`drugs.
`1. A quantitative definition of summation is required since synergism
`implies more than summation and antagonism less than summation ofeffects.
`2. Dose—efl‘ect relationships for drug l,drug2 and their mixturelat a known
`ratio of drug I to drug 2) are required.
`a. Measurements made with single doses ofdrug 1,drug 2 and their mixture
`can never alone determine synergism since the sigmoidicity of dose—effeet
`
`8of32
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`8 of 32
`
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`
`

`
`32
`
`'I‘[N(_i-('1-IAO Cl-IOU and PAUL 'I‘A1_AI.Av
`
`curves and the exclusivity of drug effects cannot be determined from such
`measurements.
`
`relationships should follow the basic mass-action
`b. The dose—effect
`principle relatively well {e.g. niedian—el'l'ecI plots with correlation coellicients
`for the regression lines greater than 0.9).
`c. Determination of the sigmoidicity of dose—effeet curves and the
`exclusivity of effects of multiple drugs is necessary. The slope ofthe median-
`effect plot gives a quantitative estimation of sigmoitlicity. When in = l, the
`dose—effect curve is hyperbolic; when In re
`1.
`the dose-effect curve is
`sigmoidal. and the greater the m value, the greater its sigmoitlicity: !1l< l
`is a
`relatively rare case which in allosterie systems indicates negative cooperalivity
`of drug binding at the receptor sites. When the dose-—effect relationships of
`drug 1. drug 2 and their mixture are all parallel in the median-effect plot. the
`effects ofdrug I and drug 2 are mutually exclusive (59). Iflhc plots of drugs l
`and 2 are parallel but the plot of their mixture is concave upward with a
`tendency to intersect the plot ofthe more potent ofthc two drugs, their effects
`are mutually nonexclusive (59). Ifthe plots for drugs 1 and 2 and their mixture
`are not parallel to each other, exclusivity of effects cannot be established.
`Alternatively, exclusivity of effects may not be ascertained because of a
`limited number of data points or limited dose range. In these cases, the data
`may be analyzed for the “combination index“ (see below) on the basis ofboth
`mutually exclusive and mutually nonexclusive assumptions. Note that
`exclusivity may occur at a receptor site, at a point in a metabolic pathway. or
`in more complex systems, depending on the endpoint of the measurements.
`
`Equations for the Eflecrs of Multiple Drugs
`A systematic analysis in enzyme kinetic systems usingthe basic principles of
`the mass action law has led to the derivation of generalized equations for
`multiple inhibitors or drugs (8. 59}.
`
`1. For two mttruafly ext-Jusive drugs that obey flr.sl‘ order .:'o.vidiIion.s. If two
`drugs (e.g., inhibitors D, and D2) have effects that are mutually cxCltlSiV6,ll1CI1
`the summation ofcornbined effects (f;,),‘3, in first—ordcr systems (i.e., each drug
`follows a hyperbolic dose—effect curve) can be calculated from (59):
`
`(.f:|)I.2
`(fu)I.2
`
`{fi|}l
`(full
`
`: (D).
`(ED5rJ)I
`
`+
`
`+
`
`(fl! 2
`
`(D);
`{E1350}:
`
`90f 32
`
`Alkermes, Ex. 1043
`
`9 of 32
`
`Alkermes, Ex. 1043
`
`

`
`ANALYSIS Of" MULTIPLE DRUG EFFECTS
`
`33
`
`is the fraction affected and f“ is tl1e fraction unaffected, and ED“, is
`where t:,
`the concentration of the drug that is required to produce a 50% effect. Note
`thatf,+fi,=lorf3=1—f,,.
`
`2. For‘ two mutual!y J1'0f!(’JC(.‘fIJ.1'fIa’(‘ drugs that obey first order cottdfriom‘. If the
`effects of two drugs (D, and D3) are mutually non-exclusive (i.e., they have
`different modes of action or act independently) the summation of combined
`effects, (l},),_3, in a first-order system is (59):
`
`:
`
`(fa)!
`(fu)I
`
`+
`
`(fit)I.2
`
`+
`
`(fin)!
`(fin)!
`
`(D):
`(ED5U}1
`
`(Db
`+ (ED5nl2
`
`(D): {D}:
`(ED5e}i
`(ED5IJ)2
`
`(3)
`
`involving more than two
`relationships apply to situations
`Similar
`inhibitors. for which generalized equations are given in ref. 59. In enzyme
`systems, equations 2 and 3 express summation of inhibitory effects,
`irrespective of the number of substrates,
`the type or mode of reversible
`inhibition (competitive, noncompetitive or uncompetitive) or the kinetic
`mechanisms (sequential or ping-pong) of the reaction under consideration.
`The simplicity of the above equations (in which all specific kinetic constants,
`substrate concentration factors, and V,,,._,, have been cancelled out during
`derivation) suggests their general applicability [5, 6). This is in contrast to the
`mechanism-specific reactions (3, 5) for which the equations are far more
`complex.
`In more organized cellular or animal systems,
`the dose—effect
`relationships of drugs or inhibitors are frequently sigmoidal rather than
`hyperbolic.
`
`3. 199:‘ two ritttrtrrrfly e.t‘c.';'tr.s'fve drags tint! obey higher‘ t')i"(fC’." c’ondi!iom.'. The
`above concepts have been extended to higher-order {Hill-type} systems in
`which each drug has it sigmoidal dosc—effect curve (i.e., has more titan one
`binding site or exhibits positive or negative cooperativity). If the effects of
`such drugs are mutually exclusive:
`
`tt:.)..=
`fi}.)..:
`
`.‘.._
`‘
`
`tf.._h
`rm.
`
`+
`
`(ll):
`nit
`
`s
`
`_
`"
`
`{D11
`revs).
`
`+ {D}:
`(E-Dsnlz
`
`I4}
`
`where m is a Hill-type coefficient which denotes the sigmoidicity of the
`dosc—effect curve.
`
`10 of 32
`
`Alkermes, Ex. 1043
`
`10 of 32
`
`Alkermes, Ex. 1043
`
`

`
`34
`
`']‘[N(J-CHAD CHOU and PAUI. TAl-.»’\Li'\Y
`
`ll‘
`4. For‘ two mtttually norte.\‘du.s't‘ve tfrttgs that obey Mt:/Jet’ order c’r)m.’£tt'0ii.s‘.
`the effects of two drugs (D, and D3) are mutually nonexclusive and if each
`drug and their combination follow a sigmoidal do.~:e—et't'ect relation.-.-hip with
`m''‘ order kinetics, then this relationship becomes (59):
`
`n;,}.‘3 %_
`(mi;
`'
`
`#+ if");
`rm»
`
`';+ l’f§.).(f}>;
`tunic»
`
`in
`
`(Rh
`
`(D).
`(EDSDJI
`
`+
`
`{D};
`
`(D): {D};
`
`(130:-n). (BUM (5)
`
`In the special case where {l.;),.3 = (l;,},.3 = 0.5. equations 2 and 4 become:
`
`(D):
`woo
`
`+ (D):
`woo
`
`_
`
`which describes the ED,;., isobologram.
`Similarly. equations 3 and 5 become:
`
`+
`
`(D).
`(EDsu}:
`
`+
`
`{D}:
`(EDsn}.»
`
`(D). (D):
`{EDs.i): (ED.su}z
`
`Z I
`
`®
`
`(7)
`
`which does not describe an isobolograrn, because oftlte additional term On the
`left.
`
`In the Appendix it is shown that equation 3 or ? can be rcadil)’ U-‘ml rm
`deriving the fractional product equation ofwebb (42), and equation 4 I-‘EH1 bi?
`used for deriving the generalized isobolograrn equation for any desired E,
`value. Thus, for the isobologram at any fractional effect E, = it per cent. the
`generalized equation is:
`
`QLi.mh_
`{Dlh
`(DJ:
`
`(3)
`
`The limitations of the fractional product concept and the isobologram
`method are detailed in the Appendix.
`
`11 of32
`
`Alkermes, Ex. 1043
`
`11 of 32
`
`Alkermes, Ex. 1043
`
`

`
`35
`
`=’\N=*\l.Y-‘its OI-' MUL'l'|PI.[£ DRUG 1-.'F1=L‘c1's
`5. Qtrrriimtitfoii of
`.s'wtc’l"
`ism
`.
`.
`cmtagortisrn. When
`»
`_
`_
`_
`l_ I
`I
`-
`‘
`3"
`Jmmtirmart mm’
`§
`experimenta tesu tsare cnteredmto equations 2-5 ifthesum ofthe two terms
`in equation 2 or 4. or the sum ofthc three terms in equation 3 or 5 is greater
`than, equal
`to, or smaller than I,
`it may be inferred [hm ama onism
`summation of synergism Of efr°"‘5- "*3SP€CilV€l}'
`has been observedgTherei
`mic‘ from equations 2'5‘ if “"3 Combined observed effect is greater than the
`calculated additive effect
`ff),
`sync,
`-
`.
`.
`.
`.
`,
`,
`.
`.
`.
`,
`‘
`--'
`-3’
`815m ts ind ‘t
`'
`'
`'
`antagonism 15 indicated.
`1&1 ed‘
`If H '5’ Smducr‘
`.
`.
`.
`.
`1
`,
`11 is‘ however‘ mnveniem to dcsignatc a “combination "rides" (CI) for
`quantifying synergism. summation. and antagonism,
`as follows:
`
`C1 = 1' + (—__Dl=
`(D.).
`to‘);
`
`for mutually exclusive drugs, and
`
`C1: (A +
`(Dal:
`
`(D):
`(DJ:
`
`
`+ (DMD).
`t_D_.), (Dr),
`
`(9)
`
`(10)
`
`for mutually nonexclusive drugs.
`For mutually exclusive or nonexclusive drugs_
`when CI < [. synergism is indicated.
`CI = 1, summation is indicated.
`Cl > 1. antagonism is indicated.
`To determine synergism, summation and antagonism at any effect level
`(i.e.. for an)’ {I Villllei. Ill“ l3l’0CC<1l1t'e involves three steps: i) Construct the
`tnediall-fiflificl Plm l.ECl1"-
`l) which determines in and D," values for drug 1,
`drug 2 and their ‘3"“‘bl“"“i0n1 ill for a given degree ot'et'l‘ect (i.e.. a given tT__
`value representing x per cent affected). calculate the corresponding doses [i.e.,
`(D31, {_[)a)_, and t_D,).__.] by using the alternative form of equation 1, D, = D,"
`[[;/(1 _ [:.]_|""'; iii) calculate the combination index (CI) by using equations 9 or
`10. where {DJ and (DJ: 31“? from 5199 (ill. and {DJL3 {also front step (ii)'] can
`be clissected into (D), and (D); by their known ratio, P/Q. Thus, (D)[ = {D,}._3
`X P/{P + Q) and (D); = l_U,.)._3 X Q/(P + Q). CI values that are smaller than.
`equal to, or greater titan I. represent synergism. summation and antagonism,
`respectively.
`To facilitate the calculation, a computer program written in BASIC for
`automatic graphing of CI with respect to E, has been developed. Samples of
`this computer simulation are shown in the examples to be given later. A
`sample calculation ot‘CI without using a computer is also given in Example 1.
`
`12 of32
`
`Alkermes, Ex. 1043
`
`12 of 32
`
`Alkermes, Ex. 1043
`
`

`
`36
`
`‘l‘lN(i-CIIM) cHou nnd I’.»’\UL T.='\l.Al.AY
`
`l-‘.QUA'l‘l(JN
`APPLICATIONS OF THE MEDIAN iil’l"l£C'I'
`AND l’[.OTS "I'D 'I'l-ll-I ANALYSIS 0|-' MUl.'l'll’l.l:
`l)R[.lGS OR |Nl'llBl'['()RS
`
`Emmple L Inhibitiori of Al'cak0t' Dehydrogennw by Two Mirrtirrlfv I:'.\'cft:3i've
`lnhib:'roi's
`
`Yonetani and Theorell (55) have reported the inhibition of horse livcr
`alcohol dehydrogenase by two inhibitors (1, = ADP-ribose and I3 = ADP)
`both of which are competitive with respect to NAD. Velocity measurements in
`the presence ofa range of concentrations of the two inhibitors (alone and in
`combination) and control velocities were retrieved from the original plot. and
`tabulated in ref. 59. The results are most conveniently expressed as fractional
`velocities (L) which are the ratios of the inhibited velocities to the control
`
`velocities, and therefore correspond to the fraction ofthe process unaffected
`(L). The fractional velocities in the presence ofADP-ribosc (95-1375 pm). ADP
`(05-25 pm), and a combination OFADP-ribose and ADP at a constant molar
`
`ratio of 190 : I , have been plotted as log [(f,,)" — 1] with respect to log(I){Fig. 2}.
`For ADP-ribose, m = 0.968, I5" = 156.] pm with a regression coefficient ofr =
`0.9988. For ADP, m = 1.043, [50 = 1.65? pm and r = 0.9996. For ADP-ribose
`and ADP in combination (molar ratio 190:1). mm = 1.004, {l5,U),_3 = |07.0 pm
`and r = 0.9997. It is clear that both inhibitors follow first-order kinetics {i.e.. m
`E I} and that A DP-ribosc and ADP are mutually exclusive inhibitors (i.e., the
`
`20
`
`I5
`
`';' L0
`J_-:3
`a»
`._.
`2
`
`0.5
`
`0
`
`-06
`
`n
`°
`-1
`
`I‘: DDPR
`I2: ADP
`I,+ I}; |9D:I
`
`2
`
`I
`
`I,¢-I,
`
`II
`
`-D5
`
`I
`0
`
`.J..
`0.5
`
`1
`0 5
`
`l
`2 O
`
`|
`2.5
`
`1
`10
`
`J
`1 D
`tag 111
`
`FIG. 2. Median-effect plots of the experimental data of Yonelani and Tlieorell {S5} |'”|' HR‘
`inhibition of horse liver alcohol tlehydrogenase by two inutually exclusive inhibitors. II
`is ADP-
`ribose {ADPR}. l: is ADP. and 1, + [3 is :1 mixture ofAI)P—rihose and AD!’ in a molar ratio of
`|9ll:i. The abscissa represertlsiogllh (O). Iug[l}_u (0).or1og|(l}. -I- tl}_.}I‘ I90: I :A}. ln this case it is
`convenient to Lise the terms |'r:iction:1| velocity Iii.) which is the ratio ofthe inhibited to the control
`velocity and therefore corresponds to the fraction that is ttnal'|'eetcd ( |}.).| from Chou and '[‘n|a1a_v
`{59)].
`
`13 of 32
`
`Alkermes, Ex. 1043
`
`13 of 32
`
`Alkermes, Ex. 1043
`
`

`
`i'\NAL.YS]S or MUl.'I'IP[.I£ l)RU(j tit-‘I~‘l£t_"['S
`
`37
`
`Pk“ {"7 ‘ll’: _‘30mb5l1i1li0n til" inhibitors parallels the plots for each of the
`component
`inhibitors). These conclusions are in agreement with the
`interpretations obtained by Yonetani and Theorell (55) and Chou and Tztlalay
`{59) using different methods. For the present analysis, knowledge of kinetic
`constants and type of inhibition is not required. The plots show excellent
`agreement between theory and t:xpt:rimem_
`with this knowledge of the V” 3“d Isu values for each inhibitor and the
`combination tit at constant molar ratio. it is possible to calculate the inhibitor
`combination Index (CI) for it series ofvalnes off“ (Fig. 3), The CI values are
`‘—‘1"3° W 1 ‘wcr the “nu” “‘-"8‘3 Or 1:. values. suggesting strongly that the
`inhibitory effects of ADP-ribose and ADP are addi1jw,_
`:I
`
`2
`
`1
`
`“""‘----u-.-u—._
`-
`
`"'""-.':-‘-:-"':--:---.--..........................,,.....
`
`Antagonistic
`
`_' Addxtxve
`
`synerp,-is: in:
`
`
`
`F a
`
`FIG. 3. Computer-generated g1':tpl'Ilt:11l presentation of the Ctlmbiliulitilt index {Cl} with respect to
`l‘r:tt.'tion nffectetl (fa) l’~"|' lllL' iidditiveinhibitionbyA1Jl’~riboseancl ADi’(molttr t'attiool'l9l}:l]of
`horse liver ill¢0l10] d|=l'|Yd"0L'.t-‘llétse. The plot is based on eqttation 9 [mutually exclusive] as
`described in the section etttitletl“Qttztnlitatioit (‘.|fS)"nt:l'gl5lI‘I,Slll!‘Ill‘l:!lit)I'I:l!1{lA11lllgClI1iSm."Cl is
`the combination index wltielt is equal ‘” [ml -4 D. it + (Di;/(DJ: [see text for sample calculation}.
`Cl /.
`l. = l etntl 2 I
`represent synergistic. additive and ttnlagotiislie effects, respectively.
`A1l|1m.g|1 plots oi’ Cl .wi1|t respect to F, ezt It be obtained by step—hy-step ettleulatlions. it is much
`nt_r_)|‘t: eonveliient to use computer SlI‘|'I1I1¢'I.[it)n. The pttrnmetcrs were obtained (IS described in Fig.
`2. by the use of linear regression analysis or computer simuhttion.
`
`We now give a sample calculation of the combination index (CI) for an
`arbitrarily selected value of £4 = 0.9:
`From equation 1, D,‘ = D“, [ffl/{_l — £J)]"'“.
`Since I]
`is ADP~ribose and I2 is ADP,
`then (D99), = 156.1 pm [0.9/(1 — 0.9)]""-"“‘ = 1511 ,t.tM
`(Din); = 1.65? pm [0.9/fl — 0.9)]"""'” = 13.62 ptM
`(D.,.,)L3 = l07.0 pm [(1.9/(1 — 0.9)]“'”"" = 954.6 ,t.tM
`
`14 of32
`
`Alkermes, Ex. 1043
`
`14 of 32
`
`Alkermes, Ex. 1043
`
`

`
`38
`
`‘1'lN(i~(‘|!A() CHOU and PAUL 1'.:\1.A1.Av
`
`therefore, {_CI).,(, =
`
`Since in the mixture l,:I3 = 190:],
`then. {D.,,,),‘3 can be dissected into:
`(D). = 954.6 X [I90/{I90 + 1)] = 949.6 ,uM
`(D); = 954.6 X [I/(190 + |}] = 4.998 _ttM
`93ifll‘.“’_' + = 0.9955.
`1511 ;.cM
`13.62 ;.tM
`Since value of (CI).,u is close to 1, an additive effect of ADP—ribose and
`ADP at f, = 0.9 is indicated.
`A computer program for automated calculation ofm. D,,,, [),.r. and CI at
`different f_, values has been developed.
`
`Example 2. Inhibition ofA.-‘coho! Deiiydragenase by Two Mumaliy Non-
`Exclusive Inhibitors
`
`Yonetani and Theorell (55) also studied the inhibition ofhorse liver alcohol
`dehydrogenase by the two competitive, mutually nonexclusive inhibitors: 0-
`phenanthroline (1,) and ADP (13). The fractional velocity {f,,) values retrieved
`from the original plot are given in ref. 59, and are presented in the form ofa
`median-effect plot,
`i.e., log [l'fl.)“' — 1] with respect
`to log 1'!) (Fig. 4).
`r;—
`Phcnanthroline gives m = L303, I5” = 36.81 pm and r= 0.9982, and ADP gives
`in = I.l8?, 150 = 1.656 p.M and r = 0.9842. These data again show that both
`inhibitors follow first order kinetics (i.e., rn W 1}. However, when the data for
`
`20
`
`I‘ :0-pmznonihroline
`-
`w I, :AfJP
`:9 11+I2:
`|?.4:l
`
`log[if,i"-Li
`
`-0.5
`
`0
`
`0.5
`
`I.0
`
`L5
`
`2.0
`
`2.5
`
`log I I 1
`
`FIG. 4. The median-effect plot 0|‘ experimental data of Yonetani and 'I'l1eore1| (55) for the
`inhibiiion of horse liver alcohol dehydrogenase by two mutually nenexeltisivc inhibitors. 1.
`is u-
`phenantltroline, 1;
`is ADP. and E, + [2 is a mixture ofo-phcnantltrolim: and AIJP {molar ratio
`114:1). The abscissa represents log (I). (I), log {I}; (O), or log [(1]. + {l}_»_| (:3) [from Chou and
`Talalay (59]].
`
`15 of 32
`
`Alkermes, Ex. 1043
`
`15 of 32
`
`Alkermes, Ex. 1043
`
`

`
`ANAIXSIS O!"-' M|_JLTlPl.l.E DRUG El-‘ITIECTS
`
`39
`
`the mixture ofo-phenztnthroline and ADP (constant molar ratio l?.4:l) are
`plotted in the same manner. a very different result is obtained: mm = 1.742
`(apparent). ([,¢,),‘3 = 9.1 I6 pm and r = 0.9999. The dramatic increase in the
`slope of the plot for the mixture (in comparison to each of its components},
`clearly indicates that o-pltenanthroiine and ADP are mutually nonexclusive
`inhibitors.
`
`levels are given in Figure 5. The
`The combination indices at various C,
`results indicate that there is a moderate antagonism at low 1:, values and a
`marked synergism at high 1:, values.
`
`-
`
`.____W"“
`
`--o,,
`
`Antagonism
`
`1
`5 ynerg 1 sn
`
`
`
`I-'10. 5. (Totnputer-generated graphical presentation oI'thc combina1ioI1 index (Cl 1 with respect to
`fraction alfecled IE.) for the inhibition of horse liver alcohol dehytlrogenase by ;| nuimu-c 91‘ .9-
`phenilrttltrolilie and ADP {molar ratio l7.4:ll. The method of analysis is the same as that
`described in the legend to Fig. 3. except that equation [0 (mutually non-exclusive) is used.
`
`lnftfiiirion ofrhe Incorporation oj'Deoxyt:r:‘dr‘ne into the DNA of
`Exrmtp.-‘e 3.
`L[2i'I.’) Leukemia C't'i'!.r by Meritorrexare {MTX) and I-,B-D-
`Arabfrtofitranosyfcylosine (arr:-C)
`
`Murine 1.1210 leukemia cells were incubated in the presence ofa range of
`concentrations of MTX (0. l—6.4 ,ttM), of ara-C (0.0?32—5.0 pm), or a constant
`molar ratio mixture of MTX and ara~C {_I:0.7‘82), and the incorporation of
`dcoxyuridine into DNA was then determined. The fractional inhibitions (f.,)
`of dUrd incorporation are shown in Table 1. Analysis of the results by the
`median effect plot (Fig. 6) gave the following parameters: for MTX. m =
`1.09 I, D", = 2.554 ,uM. r = 0.9842; for are-C, m = 1.0850, D,,, = 0.06245 pm. and
`
`16 of32
`
`Alkermes, Ex. 1043
`
`16 of 32
`
`Alkermes, Ex. 1043
`
`

`
`40
`
`TlN(i—(_‘HAO CHOU and PAUI. 'I'Al.Al.AY
`
`TA BLE I. IN]-lIB['l'l()N OF [(i-'1-l|Dl£0XYURlI)lNE I‘dUt‘L|} lN(‘(JRI‘(J]\‘.:'\'l‘I{)N INTO
`DNA IN LIZIU IJJUKEMIA Cl"-LLLS BY M|;'I'I|()'['I?.]_-"X.-’\‘|'li IMTX) .-’\N]) 1-H-0-
`ARABIND]’URAN(JSY[.(‘Y’]'OSINli I.-’\R:'\-C). AIIJNEE AND IN C()M|§|NA‘I‘l{)N
`
`5'-Tuctitmul inhibition Hi.) :11 [urn-('[ of
`
`M'I'X
`;.t.\-“I
`
`(1
`
`0.782
`JJM
`
`[).l5t':-
`p.\I
`
`U.3|3
`pm
`
`(1.625
`;.c.\I
`
`L25
`pm
`
`2.5
`pm
`
`5.0
`;..tM
`
`H.582
`U.4U5
`
`(L715
`
`0.58?
`
`U.H(:[l
`
`U.92{I
`
`0,955
`
`U.98U
`
`[L993
`
`U
`O
`0.0348
`0.1
`NL)*
`11.2
`ND
`0.4
`0.140
`0.3
`0.415
`1.6
`U.9'I'U
`0.573
`3.2
`
`
`LLTSS6.4 N1)
`
`U.?7"S
`
`0.31%
`
`(1.943
`
`‘Result :10! used because of Iilrgl: variation between duplicates.
`Ll2]0 murinc Ictlkcmiu cells (3 >‘'. ID" cells) were incubutctl in l;'agIt:‘.~s btmal|11cdium{2D]iItlIIc
`presence and tihscncc of various coaiccntraltiolts of MTX ntld 2l|‘i1-C and I.l1u.-ir mixlurc (molar
`ratio. 110.782} at .1?°C for 20 min and then incubated with [}.5 mt: fl ;..:C‘i) ol‘{(>—‘]-litllird. :11 3T’C'
`for 30 min. I"'rat:1ion:t| inhibition (|', or ll.) ul‘ [6—’HJt.lUIti incorporation into pcrchloriu acid-
`insolublc DNA |'rttclion was then I‘J:'lclIs11l‘C(l as previously described (20). All nicasurcntcnlx were
`made in duplicate.
`
` 1.\ra—C + MT><
`
`i0.7B2'.1J
`
`
`
`logWe)"-114
`
`-2
`
`—|
`
`0
`
`I
`
`2
`
`3
`
`log
`
`[Concemral':on, ;.tM]
`
`FIG. (2. Median-cI'{L-ct plol showing lht: inhibition of[6—’H}t|Urd incorporation into DNA of
`L 12 ll) Jnurinc leukemia cells by mcthou't:xz1lc(MTX), (O): arabinofttrnltosylcytosinc [_:1r;1-C}. (X):
`or their mixture (l:0.'?82). {+). Dat;1l'ron1Tab|c 1 ltavc been used.
`
`I = 0.9995. For the combination of MTX and ara-C (120,732). the paratneters
`were: m = 1.1296, D,“ = 0.2496 pm, and r = 0.9995. The combination index
`
`(Fig. 7') shows a moderate antagonism between the two drugs at all values of
`fractional inhibition.
`
`17 of 32
`
`Alkermes, Ex. 1043
`
`17 of 32
`
`Alkermes, Ex. 1043
`
`

`
`AN.r\1_YSlS or MU1-'['lPLl_-I DRUG Er«'r~'r-:C'rs
`
`41
`
`CI
`
`1
`
`Antagonism
`
`J
`synergism
`
`
`
`‘I. Computer-generated gr