Advancesin
`
`ENZYME REGULATION
`
`Volume 22
`
`Proceedings of the Twenty-Second Symposium on Regulation of Enzyme
`Activity and Synthesis in Normal and Neoplastic Tissues
`held at Indiana University School of Medicine
`Indianapolis, Indiana
`October 3 and 4, 1983
`
`Edited by
`GEORGE WEBER
`
`Indiana University School of Medicine
`Indianapolis, Indiana
`
`Technical editor
`Catherine E. Forrest Weber
`
`
`
`PERGAMONPRESS
`OXFORD - NEW YORK - TORONTO
`SYDNEY - PARIS : FRANKFURT
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`UK.
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`Copyright © 1984 Pergamon Press Ltd.
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`First edition 1984
`
`Library of Congress Catalog Card No. 63-19609
`
`ISBN 0 08 031498 &
`ISSN 0065-2571
`
`Printed in Great Britain by A. Wheaton & Co. Lid., Exeter
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`Advances in
`
`ENZYME REGULATION
`
`Volume 22
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`

`QUANTITATIVE ANALYSIS OF
`DOSE-EFFECT RELATIONSHIPS: THE
`COMBINED EFFECTS OF MULTIPLE
`DRUGS OR ENZYME INHIBITORS
`
`TING-CHAO CHOU* and PAUL TALALAYT
`
`*Laboratory of Pharmacology, Memorial Sloan-Kettering Cancer Center, New York, NY
`10021, and {Department of 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 andits 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 ofthe 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. K,,, Kj, Vinay)
`(5-8).
`Our understanding of dose-effect relationships in pharmacological systems
`has not advanced to the samelevel as those of enzyme systems. Manytypes of
`mathematical transformations have been proposedto linearize dose-effect
`plots, based on statistical or empirical assumptions,e.g. probit (9, 10), logit
`(11) or power-law functions (12). Although these methods often provide
`adequatelinearizations ofplots, the slopes and intercepts of such graphsare
`usually devoid of any fundamental meaning.
`
`THE MEDIAN EFFECT PRINCIPLE
`We demonstrate here the application ofa single and generalized method for
`analyzing dose-effect relationships in enzymatic, cellular and whole animal
`systems. Wealso examine the problem of quantitating the effects of multiple
`inhibitors on such systems and provide definitions of summationofeffects,
`and consequently of synergism and antagonism.
`Since the proposed method ofanalysis is derived from generalized mass
`action considerations, we caution the readerthat the analysis of dose-effect
`2
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`28
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`TING-CHAO CHOU and PAUL TALALAY
`
`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-response results by a
`uniform method which is based on sound fundamental considerations that
`have physicochemical and biochemical validity in simpler systems. Our
`analysis is based on the median effect principle of the mass action law (5-8),
`and has already been showntobesimple to apply and useful in the analysis of
`complex biological systems (13).
`
`The Median Effect Equation
`The median effect equation (6, 8) states that:
`
`f/f, = (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 morefamiliar IC), EDs), or LD, values), and
`m is a Hill-type coefficient signifying the sigmoidicity ofthe dose-effect curve,
`i.c.,m = 1 for hyperbolic (first order or Michaelis-Menten)systems. Since by
`definition, f, + f, = 1, several useful alternative forms of equation | are:
`
`f,/0 he f,) = ((f,y" a iT re [(f,y" = 1)] = (D/D,,)"
`
`f, = 1/(1 + (D,/D)"
`
`p= D,[f,/01 ~ jy"
`
`The median effect equation describes the behavior of many biological
`systems.It is, in fact, a generalized form of the enzyme kinetic relations of
`Michaelis-Menten (14) and Hill (15), the physical adsorptionisotherm of
`Langmuir (16), the pH-ionization equation of Henderson and Hasselbalch
`(17),
`the equilibrium binding equation of Scatchard (18), and the
`pharmacological drug-—receptor interaction (19). Furthermore, the median
`effect equation is directly applicable not only to primary ligands such as
`substrates, agonists, and activators, but also to secondary 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
`kinetic constants(i.e. K,,, V,,,, or K,) and irrespective of the mechanismof
`inhibition(i.e. competitive, noncompetitive or uncompetitive). Furthermore,
`itis valid for multisubstrate reactions irrespective of mechanism (sequential or
`ping-pong) (5-8).
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`ANALYSIS OF MULTIPLE DRUG EFFECTS
`
`29
`
`The Median Effeet Plot
`The median effect equation (equation |) may be linearized by taking the
`logarithms ofboth sides, i.e.
`
`or
`or
`
`log (f,/f,) = m log (D) - m log (D,,)
`log [(f,)"' - 1]"' = m log (D) - mlog (D,,)
`log f(f," ~ 1] =m log (D) -m log (D,,)
`
`The median effect plot (Fig. 1) of y = log (£,/f,) or its equivalents with
`respect to x = log (D) is a general and simple method (13, 30) for determining
`pharmacological median doses for lethality (LD,9), toxicity (TD,,), effect of
`agonist drugs (ED,,), andeffect of antagonist drugs (IC,,). Thus, 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 f, = f,, f/f, = 1 and hence y = log
`(f,/f,) = 0] which gives log (D,,) and consequently the D,, value. Any cause-
`consequencerelationship that gives a straightline for this plot will provide the
`two basic parameters, m and D,,, and thus, an apparent equation that
`describes such a system. Thelinearity of the median-effect plot (as determined
`from linear regression coefficients) determines the applicability of the present
`method.
`
`
`
`
`
`Log[(fa)-!-1]"
`
`
`
`Log (D/Dm)
`
`FIG. 1. The median-effect plot at different slopes correspondingto m valuesof0.5, 1, 2and 3. The
`plot
`is based on the median-effect equation (equation 1)
`in which the dose (D) has been
`normalized by taking the ratio to the median-effect dose (D,). Note that the ordinatelog[(f, yi-
`iy! is identical to log [f,y' — 1] or log (f,/fy).
`
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`30
`
`TING-CHAO CHOU and PAUL TALALAY
`
`Relation of the Median-Effect Equation to Michaelis-Menten and Hill
`Equations
`In the special case, when m = 1, equation | becomes f, = [1 + (D,,/DT'
`which has the sameform as the Michaelis-Menten equation (14), v/V,,,. =[1 +
`(K,,/S)}T'. In addition, when the effector ligand is an environmental factor
`suchas an inhibitor, the equation, f, = [1 +(D,,/D)f', 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, f, in
`equation |
`is simple to obtain, whereas the determination ofV,,,, in the
`Michaelis-Menten (or Hill) equations requires approximation or extra-
`polation (6, 7). The logarithmic form of equation | describes the Hill equation.
`
`The Utility of the Median Effect Principle
`The median-effect equation has been used to obtain accurate values of ICsp,
`ED.,, LDso, or the relative potencies of drugs or inhibitors in enzyme systems
`(6-8, 21-26), in cellular systems (20, 27, 28) and in animal systems (13, 29-32).
`Analternative form of the median-effect equation (5) has been used for
`calculating the dissociation constant (K, or K,) of ligands for pharmacological
`receptors
`(33-35),
`It has
`also permitted the
`analysis of chemical
`carcinogenesis data and haspredicted especially accurately tumorincidenceat
`low dose carcinogen exposure (30, 31). By using the median-effect principle,
`the general equation for describing a standard radioimmunoassayorligand
`displacementcurve has been derived recently by Smith (36). It has also been
`used to showthat there is marked synergism among chemotherapeutic agents
`in the treatment of hormone-responsive experimental mammary carcinomas
`(32).
`In recent preliminary reports (13, 37), we have shown that,
`in
`conjunction with the multiple drug effect equations (see below), the median-
`effect plot formsthe basis for the quantitation of synergism, summationand
`antagonism of drugeffects.
`
`ANALYSIS OF MULTIPLE DRUG EFFECTS
`
`An Overview
`
`the past decades, numerous authors have claimed synergism,
`Over
`summation or antagonism oftheeffects of multiple drugs. However,thereis
`still no consensusas to the meanings ofthese terms. For instance, in a review,
`Goldin and Mantel
`in 1957 (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 ofa
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`ANALYSIS OF MULTIPLE DRUG EFFECTS
`
`31
`
`theoretical basis that would permit rigorous and quantitative assessment of
`the effects of drug combinations.
`Attemptsto interpret the effect of multiple 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
`Webbin 1963 (42), the theoretical and practical aspects of the problem have
`been the subject of many reviews (38, 43-51). Some authors have discussed the
`possible mechanisms that may 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 (Michaelis-Menten type)
`systems but not for higher order (Hill type) systems, andstill 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 conceptis valid for drugs whose effects
`are mutually exclusive, and thelatter 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 parametersthat can bedirectly used for the
`analysis of summation, synergism or antagonism.
`
`Requirements for Analyzing Multiple Drug Effects
`The following informationis 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 antagonismless than summationofeffects.
`2, Dose-effect relationships for drug 1, drug 2 and their mixture (at a known
`ratio of drug 1 to drug 2) are required.
`a. Measurements madewith single doses of drug |, drug 2 and their mixture
`can never alone determine synergism since the sigmoidicity of dose-effect
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`32
`
`TING-CHAO CHOU and PAUL TALALAY
`
`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. median-effect plots with correlation coefficients
`for the regression lines greater than 0.9).
`c. Determination of the sigmoidicity of dose-effect curves and the
`exclusivity ofeffects of multiple drugs is necessary. The slope of the median-
`effect plot gives a quantitative estimation of sigmoidicity. When m= 1, the
`dose-effect curve is hyperbolic, when m # 1,
`the dose-effect curve is
`sigmoidal, and the greater the m value, the greater its sigmoidicity; m< lisa
`relatively rare case whichin allosteric systems indicates negative cooperativity
`of drug binding at the receptor sites. When the dose-effect relationships of
`drug 1, drug 2 and their mixture areall parallel in the median-effect plot, the
`effects of drug | and drug 2 are mutually exclusive (59). If the plots of drugs |
`and 2 are parallel but the plot of their mixture is concave upward with a
`tendencytointersect the plot of the more potent ofthe twodrugs, their effects
`are mutually nonexclusive (59). If the plots for drugs | 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 ofa
`limited numberof data points or limited dose range. In these cases, the data
`may be analyzed for the ‘combination index”(see below) on the basis of both
`mutually exclusive and mutually nonexclusive assumptions. Note that
`exclusivity may occur at a receptorsite, at a point in a metabolic pathway, or
`in more complex systems, depending on the endpoint of the measurements.
`
`Equations for the Effects of Multiple Drugs
`A systematic analysis in enzymekinetic systemsusing the 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 mutually exclusive drugs that obey first order conditions. If two
`drugs(e.g., inhibitors D, and D,) haveeffects that are mutually exclusive, then
`the summation of combinedeffects(f,), 9, in first-order systems(i.c., each drug
`follows a hyperbolic dose-effect curve) can be calculated from (59):
`
`(f.)i.2 say
`(fwi.2
`
`(fi
`(fur
`
`
`4 (fi
`(fue
`
`
`(D),
`(EDs),
`
`mn
`
`(D),
`(EDs)
`
`(2)
`
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`

`ANALYSIS OF MULTIPLE DRUG EFFECTS
`
`33
`
`wheref, is the fraction affected and f, is the fraction unaffected, and EDsois
`the concentration of the drug that is required to produce a 50% effect. Note
`that f, +f, = l orf, =1-f,.
`
`2. For two mutually nonexclusive drugs that obeyfirst order conditions. If the
`effects of two drugs (D, and D,) are mutually non-exclusive(i.e., they have
`different modes ofaction or act independently) the summation of combined
`effects, (f,),2, in a first-order system is (59):
`
`(io _ Gy, Ge, ah
`(fy).
`(f.)
`(f)
`(fs (Gu)
`
`
`_ (D),
`(Dy, Di )
`
`
`
`(EDy) (ED~(ED) (ED 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 ofreversible
`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 whichall 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. For two mutually exclusive drugs that obey higher order conditions. The
`above concepts have been extended to higher-order (Hill-type) systems in
`which each drug has a sigmoidal dose-effect curve (i.e., has more than one
`binding site or exhibits positive or negative cooperativity). If the effects of
`such drugs are mutually exclusive:
`
`(fi
`i =
`(fia
`(of Lh
`
`‘i
`
`+
`
`a
`
`(fide
`(fi)
`
`(D),
`a
`i (D),
`
`(EDs)
`(EDso
`
`(gy
`
`where m is a Hill-type coefficient which denotes the sigmoidicity of the
`dose-effect curve.
`
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`

`34
`
`TING-CHAO CHOU and PAUL TALALAY
`
`4. For two mutually nonexclusive drugs that obey higher order conditions. \f
`the effects of two drugs (D, and D,) are mutually nonexclusive andif each
`drug and their combination follow a sigmoidal dose-effect relationship with
`m" order kinetics, then this relationship becomes (59):
`
`®ialz. Texls,ee] =,fewery=
`
`
`
`a Beane +|a Fe en
`(fia
`(f,);
`(f.,)p
`(fi), (f,)
`
`
`(D);
`‘.
`(D);
`(EDs),
`(EDs),
`
`(D), (D),
`(EDs); (EDso),
`
`(5)
`
`In the special case where (f,),» = (f,),2 = 0.5, equations 2 and 4 become:
`
`(Dy, Db
`(ED.),
`(EDs)
`
`-
`
`(6)
`
`which describes the ED.) isobologram.
`Similarly, equations 3 and 5 become:
`
` (Dy, @h
`-
`(D) (D):
`
`(ED),~~(ED) (EDs), (ED); (7
`
`
`
`which doesnot describe an isobologram,because ofthe additional term on the
`left.
`is shown that equation 3 or 7 can be readily used for
`In the Appendix it
`deriving the fractional product equation of Webb (42), and equation4 can be
`used for deriving the generalized isobologram equation for any desiredf,
`value. Thus, for the isobologram at anyfractional effect f, = x per cent, the
`generalized equation is:
`
`
`Dy , Ox _
`(D,);
`(D,)
`
`(8)
`
`The limitations of the fractional product concept and the isobologram
`methodare detailed in the Appendix.
`
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`35
`ANALYSIS OF MULTIPLE DRUG EFFECTS
`5. Quantitation of
`synergism,
`summation and antagonism. When
`experimentalresultsare entered into equations 2-5, ifthesu bef two terms
`in equation 2 or4, or the sum ofthe three terms a equation 3 or 5 is greater
`than, equal
`to, or smaller than 1,
`jt may be inferred that qntsaoniin
`summation or synergism ofeffects, respectively, has been observed. There-
`fore, from equations 2-5, if the combined obse
`‘ect
`is
`r
`calculated additive effect, (f.),,
`tved effect is greater than the
`2» Synergism is indicated;
`if
`it
`is
`smé
`eres
`d;
`is smaller,
`if it
`antagonism is indicated.
`It
`is, however, convenient to designate a
`combination index” (CI) for
`Bere
`:
`‘
`quantifying synergism, summation » and antagonism, as follows:
`
`cr= @h , Oy
`(D,);
`(D,);
`
`0)
`
`for mutually exclusive drugs, and
`
`= © , © , OM
`
`
`(D.),=(Dy)~~(D,), (D),); (10)
`
`for mutually nonexclusive drugs,
`For mutually exclusive or nonexclusive drugs,
`when CI<I, synergism is indicated.
`CI = 1, summation is indicated.
`CI > 1, antagonism is indicated,
`To determine synergism, summation and antagonism at any effect level
`(i.e., for any {, value), the procedure involves three steps: i) Construct the
`median-effect plot (Eqn. 1) which determines m and D,, values for drug 1,
`drug 2 and their combination; ii) for a given degreeofeffect(i-e., a givenf,
`value representing x per cent affected), calculate the corresponding doses[i.e.,
`(D,),, (D,) and (D,),2] by using the alternative form of equation 1, D, = D,,
`[£,/(1 - £,)}'"; tii) calculate the combinationindex (CI) by using equations 9 or
`10, where (D,), and (D,), are fromstep(ii), and (D,), 5 [also fromstep(ii)] can
`be dissected into (D), and (D), by their knownratio, P/Q. Thus, (D), =(D,)}»
`« P/(P + Q) and (D), = (D2 X Q/(P + Q), CI values that are smaller than,
`equalto, or greaterthan 1, represent synergism, summation and antagonism,
`respectively.
`To facilitate the calculation, a computer program written in BASIC for
`automatic graphing of CI with respect to f, has been developed. Samples of
`this computer simulation are shown in the examples to be given later. A
`sample calculation of CI without using a computeris also given in Example 1.
`
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`36
`
`TING-CHAO CHOU and PAUL TALALAY
`
`APPLICATIONS OF THE MEDIAN EFFECT EQUATION
`AND PLOTS TO THE ANALYSIS OF MULTIPLE
`DRUGS OR INHIBITORS
`
`Example 1. Inhibition of Alcohol Dehydrogenase by Two Mutually Exclusive
`Inhibitors
`Yonetani and Theorell (55) have reported the inhibition of horse liver
`alcohol dehydrogenase by twoinhibitors (I, = ADP-ribose and I], = ADP)
`both of which are competitive with respect to NAD. Velocity measurementsin
`the presence of a 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 (f,) which are the ratios of the inhibited velocities to the control
`velocities, and therefore correspondto the fraction of the process unaffected
`(f,). The fractional velocities in the presence of ADP-ribose (95-375 um), ADP
`(0.5-2.5 um), and a combination of ADP-ribose and ADP ata constant molar
`ratio of 190:1, havebeen plotted as log [(f,)' - 1] with respectto log (I) (Fig.2).
`For ADP-ribose, m = 0.968, I) = 156.1 uM with a regression coefficient of r=
`0.9988. For ADP, m = 1.043, Ij) = 1.657 wm and r = 0.9996, For ADP-ribose
`and ADPin combination (molarratio 190:1), m,= 1.004, (Ix);» = 107.0 um
`and r=0,9997.It is clear that both inhibitorsfollow first-order kinetics(i.e., m
`= 1) and that ADP-ribose and ADP are mutually exclusive inhibitors (i.e., the
`
`1,: ADPR
`«
`T,: AOP
`o
`@ 1,41): 190:
`
`2
`
`i
`
`Itl,
`
`I,
`
`20
`
`i)
`
`= 10
`
`o5
`
`°o
`
`-05
`
`a=
`
`a
`2
`
`
`J
`l
`ar.
`_L
`1
`i
`!
`-0.5
`0
`0.5
`lo
`0.5
`2.0
`2.5
`30
`log (1)
`
`FIG. 2, Median-effect plots of the experimental data of Yonetani and Theorell (55) for the
`inhibition of horseliver alcohol dehydrogenase by two mutually exclusive inhibitors. 1,
`is ADP-
`ribose (ADPR), I, is ADP, and 1, + I, is a mixture of ADP-ribose and ADPin a molar ratioof
`190:1. The abscissa represents log (1); (@), log (Lp (0), or log [(1)) + (Dp (19051; A). In this case itis
`convenient to use the terms fractional velocity (f,) whichis the ratio ofthe inhibited to the control
`velocity and therefore corresponds tothefraction that is unaffected ({,,). [from Chou andTalalay
`(59)].
`
`13 of 32
`
`Alkermes, Ex. 1043
`
`13 of 32
`
`Alkermes, Ex. 1043
`
`

`

`ANALYSIS OF MULTIPLE DRUG EFFECTS
`37
`plot for the combination of inhibitors parallels the plots for each of the
`component
`inhibitors). These conclusions are in agreement with the
`interpretations obtained by Yonetaniand Theorell (55) and Chou and Talalay
`(59) using different methods. For the present analysis, knowledge ofkinetic
`constants and type of inhibition is not required. The plots show excellent
`agreement between theory and experiment.
`‘with this knowledge of the m and Is) values for each inhibitor and the
`combination at a constant molar ratio, it is possible to calculate the inhibitor
`combination index (Cl) for a series of values of f, (Fig. 3). The Cl values are
`close to | over the entire range of f, values, suggesting strongly that the
`inhibitory effects of ADP-ribose and ADPare additive.
`3
`
`2
`
`1
`
`etrecemeerriees,
`
`spergmengteeepeeeeneweset*apecengeeneyteerysempeeenpeees
`
`Antagonistic
`
`4* Additive
`
`
`
`Synergistic
`
`FIG. 3. Computer-generated graphical presentation of the combination index (C1) with respect to
`fraction affected(f,) for the additive inhibition by ADP-ribose and ADP (molarratioof 190:1) of
`horse liver alcohol dehydrogenase. The plot is based on equation 9 (mutually exclusive) as
`described in the section entitled “Quantitation of Synergism, SummationandAntagonism.” Cl is
`the combinationindex whichis equal to (D)(D,); +(D) (Dp (see text for sample calculation).
`Cl < 1, = 1 and > |
`represent synergistic, additive and antagonistic effects, respectively.
`Althoughplots of Cliwith respect to f, can be obtained by step-by-step calculations,it is much
`more convenient to use computer simulation. The parameters were obtained as described in Fig.
`2, by the use of linear regression analysis or computer simulation.
`
`Wenow give a samplecalculation of the combination index (CI) for an
`arbitrarily selected value off, = 0.9:
`From equation 1, D, = D,, [f,/(1 - £,)]”.
`Since 1,
`is ADP-ribose and I,
`is ADP,
`then (Dy); = 156.1 um [0.9/1 - 0.9)]°* = 1511 um
`(Dy), = 1.657 xm [0.9/(1 - 0.9)77°" = 13.62
`(Dy)2 = 107.0 um [0.9/1 - 0.9)]'" = 954.6 uM
`
`14 of 32
`
`Alkermes, Ex. 1043
`
`14 of 32
`
`Alkermes, Ex. 1043
`
`

`

`38
`
`TING-CHAO CHOU and PAUL TALALAY
`
`therefore, (CD y° =
`
`Since in the mixture I, :1, = 190:1,
`then, (Dp), can be dissected into:
`(D), = 954.6 X [190/(190 + 1)] = 949.6 um
`(D), = 954.6 * [1/(190 + 1)] = 4.998 um
`949.6 uM ¥ 4.998 uM
`1511 um
`13.62 jum
`is close to 1, an additive effect of ADP-ribose and
`Since value of (CI)s,
`ADP at f, = 0.9 is indicated.
`A computer program for automated calculation of m, D,,, D,, r, and CI at
`different f, values has been developed.
`
`= 0.9955.
`
`Example 2. Inhibition of Alcohol Dehydrogenase by Two Mutually Non-
`Exclusive Inhibitors
`Yonetani and Theorell (55) also studied the inhibitionofhorse liver alcohol
`dehydrogenase by the two competitive, mutually nonexclusive inhibitors: o-
`phenanthroline (I,) and ADP (I,). 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, ie., log [(f,y' — 1] with respect
`to log (1) (Fig. 4). 0-
`Phenanthroline gives m = 1.303, Is) = 36.81 uM and r=0.9982, and ADP gives
`m = 1,187, Is) = 1.656 wm and r = 0.9842. These data again show that both
`inhibitors follow first order kinetics (i.e., m ~ 1). However, when the data for
`
`20
`
`: O- phenanthroline
`* I,
`* I, : ADP
`4 I,+1,: 17.4:1
`
`log[(fy)"'=1]
`
`-0.5
`
`oO
`
`0.5
`
`Lo
`
`1.5
`
`2.0
`
`2.5
`
`log (1)
`
`FIG. 4. The median-effect plot of experimental data of Yonetani and Theorell (55) for the
`inhibition ofhorse liver alcohol dehydrogenase by two mutually nonexclusive inhibitors, |; is o-
`phenanthroline, h is ADP, and }, + 1; isa mixture of o-phenanthroline and ADP (molar ratio
`17.4:1). The abscissa represents log (1), (@), log (Ip (©), or log [(1), + (Dp J (A) [from Chou and
`Talalay (59)].
`
`15 of 32
`
`Alkermes, Ex. 1043
`
`15 of 32
`
`Alkermes, Ex. 1043
`
`

`

`ANALYSIS OF MULTIPLE DRUG EFFECTS
`
`39
`
`the mixture of o-phenanthroline and ADP (constant molarratio 17.4:1) are
`plotted in the same manner, a very different result is obtained: m,, = 1.742
`(apparent), (sy), = 9.116 wm and r = 0.9999. The dramatic increase in the
`slope ofthe plot for the mixture (in comparison to each of its components),
`clearly indicates that o-phenanthroline and ADP are mutually nonexclusive
`inhibitors.
`levels are given in Figure 5. The
`The combination indices at various f,
`results indicate that there is a moderate antagonism at low f, values and a
`marked synergism at high f, values,
`
`3
`
`2
`
`cI
`
`fh
`
`‘
`*.
`Antagonisa
`s Sensis Roe teh nmenmel
`retry.
`
`Synergism
`
`FIG. 5, Computer-generated graphical presentation ofthe combinationindex (CI) with respect to
`fraction affected (f,) for the inhibition ofhorse liver alcohol dehydrogenase by a mixture ofo-
`phenanthroline and ADP (molar ratio 17.4:1). The method of analysis is the same as that
`described in the legend to Fig, 3, except that equation 10 (mutually non-exclusive) is used.
`
`Example 3. Inhibition ofthe Incorporation of Deoxyuridine into the DNA of
`L1210 Leukemia Cells by Methotrexate (MTX) and 1-B-p-
`Arabinofuranosyleytosine (ara-C)
`Murine L1210 leukemiacells were incubated in the presence of a range of
`concentrations of MTX (0.1-6.4 4), of ara-C (0.0782-5.0 uM), or a constant
`molar ratio mixture of MTX and ara-C (1:0.782), and the incorporation of
`deoxyuridine into DNA was then determined. Thefractional 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 =
`1.091, Dj, = 2.554 um, r= 0.9842; for ara-C, m= 1.0850, D,, = 0.06245 um, and
`
`16 of 32
`
`Alkermes, Ex. 1043
`
`16 of 32
`
`Alkermes, Ex. 1043
`
`

`

`40
`
`TING-CHAO CHOU and PAUL TALALAY
`
`TABLE 1. INHIBITION OF[6H]DEOXYURIDINE(dUrd) INCORPORATION INTO
`DNAIN L1210 LEUKEMIA CELLS BY METHOTREXATE (MTX) AND 1-B-p-
`ARABINOFURANOSYLCYTOSINE (ARA-C), ALONE AND IN COMBINATION
`
`Fractional inhibition (f,) at [ara-C| of
`0
`0.782
`0.156
`0.313
`0.625
`£25
`25
`5.0
`MTX
`
` MM uM BM uM eM BM EM
`
`
`
`
`
`BM
`
`0.582
`0.405
`
`O.715
`
`0.587
`
`0.860
`
`0.926
`
`0.955
`
`0.980
`
`0,993
`
`0
`0
`0.0348
`0.1
`ND*
`0.2
`ND
`0.4
`0.140
`0.8
`0.415
`1.6
`0.970
`0.573
`3.2
`
`
`0.7556.4 ND
`
`0.775
`
`O.878
`
`0,943
`
`*Result not used because of large variation between duplicates.
`L1210 murine leukemia cells (8 * 10° cells) were incubated in Eagle’s basal medium (20) in the
`presence and absence of various concentrations of MTX and ara-Candtheir mixture (molar
`ratio, 1:0.782) at 37°C for 20 min and then incubated with 0.5 wm (1 pCi) of [6-H ]JdUrd, at 37°C
`for 30 min. Fractional inhibition (f, or f,) of [6H ]dUrd incorporation into perchloric acid-
`insoluble DNA fraction was then measuredas previously described (20). All measurements were
`made in duplicate.
`
` Ara-C + MTX
`
`(0.782:1)
`
`eae mm
`
`wes miter
`
`nie ert
`
`nce
`
`-1
`
`o
`
`|
`
`2
`
`log
`
`(Concentration, 7M]
`
`_|
`3
`
`4
`
`9
`
`-l
`
`-2
`-2
`
`as
`y
`
`2=
`
`o2
`
`FIG. 6. Median-effect plot showing the inhibition of [(6~H]dUrd incorporation into DNA of
`L1210 murine leukemia cells by methotrexate (MTX), (©); arabinofuranosylcytosine (ara-C), (*);
`or their mixture (1:0.782), (+). Data from Table | have been used.
`
`r= 0.9995. For the combination of MTX and ara-C (1:0.782), the parameters
`were: m = 1.1296, D,, = 0.2496 wo, and r = 0.9995. The combination index
`(Fig. 7) shows a moderate antagonism between the two drugsatall values of
`fractional inhibition.
`
`17 of 32
`
`Alkermes, Ex. 1043
`
`17 of 32
`
`Alkermes, Ex. 1043
`
`

`

`ANALYSIS OF MULTIPLE DRUG EFFECTS
`
`41
`
`a
`
`be
`
`sg——
`
`cI
`
`-
`
`Neeeeeteesccecevetteteseg,
`
`Antagonism
`ol
`Synergism
`
`
`
`FIG, 7. Computer-generated graphical presentation ofthe drug combination index (CI) with
`respect to fraction affected(f{,) for the inhibitoryeffect of a mixture of methotrexate (MTX) and
`arabinofuranosyleytosine (ara-C) (molar ratio, 1:0.782) on the incorporation of[6-H]dUrd into
`DNA of L1210 murine leukemia cells. The data from Table | andthe parameters obtained from
`Fig. 6 have been used for this plot on the assumption that the drugs act in a mutually exclusive
`manner (equation 9).
`
`Example 4. Inhibition of the Incorporation of Deoxyuridine into the DNA of
`1.1210 Leukemia Cells by Hydroxyurea (HU) and 5-Fluorouracil (5-FU)
`Murine L1210 leukemia cells were incubated in the presenceof a range of
`concentrations of hydroxyurea (50-3,200 uM), or 5-fluorouracil (4.0-256 ym),
`and of a constant molar ratio mixture of hydroxyurea and 5-fluorouracil
`(12.5:1), and the incorporation of deoxyuridine (dUrd) into DNA was then
`determined. Thefractional inhibitions (f,) of dUrd incorporation are shown
`in Table 2. Analysis of the results by the median effect plot (Fig. 8) gave the
`following parameters: for hydroxyurea, m = 1.196, D,, = 34.09 um, and r=
`0.9908; for 5-fluorouracil, m= 1.187, D,, = 8.039 uM, and r= 0.9978; and for
`the mixture of hydroxyureaand5-fluorouracil (12.5:1), m= 1.407, D,, = 225.8
`po