[CANCER RESEARCH 49, 6615-6620. December 1, 1989]

In Vitro Pharmacodynamic Assay for Cancer Drug Development: Application toCrisnatol, a New DNA IntercalatorDavid J. Adams'

Tumor Biology Section, Division of Cell Biology, Burroughs Wellcome Company, Research Triangle Park, l^orth Carolina 27709

ABSTRACT

A ink roí¡u-rpharmacodynamic assay is described that evaluates anti-

tumor activity in vitro within a matrix of extracellular drug concentrations(C) and exposure times (7"). The results were analyzed according to the

pharmacodynamic principle: C" x T = k, where n is the concentration

coefficient and A is the drug exposure constant. This assay was used tocharacterize the antitumor activity of crisnatol (BW A770U), a memberof the new arylmethylaminopropanediol class of DNA intercalators, inMCF-7 human breast cancer cells. The assay showed that drug action

was a function of k, the extracellular drug exposure. Crisnatol had noeffect at k < 30 (n < 1); was growth inhibitory at k = 30-1000 (n = 1),cytostatic at 1500, and cytotoxic at k > 2000 MM"-h (n = 2). These effects

were directly related to increasing cellular retention of crisnatol. Thethreshold for growth inhibition was 0.02 fmol/cell, while cytoreductionrequired over 1 fmol/cell. The assay also yielded concentration-timecurves of the form C = (k/T)"" at specific surviving fractions, which were

useful in selecting exposure conditions for further studies and emphasizedthe impact of exposure time on crisnatol activity. The hyperbolic natureof these curves suggested a unique parameter for comparing antitumoragents: the minimum C x T. This parameter represents the minimumexposure conditions required for a specified level of antitumor activityand accounts for differences in concentration coefficients among agents.The pharmacodynamic assay for crisnatol illustrates the importance ofboth concentration and exposure time in drug action and suggests apharmacodynamic basis for comparing antitumor agents that conform tothe C"x T=k principle. Such agents include doxorubicin, 5-fluorouracil,

cisplatin, etoposide, and tamoxifen. Analysis of these agents in the Ml T-

7 model shows that the minimum C x T parameter gives a relativecytotoxicity profile distinct from that found with the standard K ',„>end

point. This disparity was also seen in another, less differentiated breastcancer cell line (MDA-MB-231), and in normal human skin fibroblasts.

Regardless of the end point, the in vitro cytotoxicity of crisnatol comparesfavorably with that of some clinically useful antitumor agents.

INTRODUCTION

The pharmacodynamics of antitumor activity is an importantcharacteristic of anticancer agents. Relatively few clinical studies have examined the relationship between therapeutic or toxicresponse, drug dose, and exposure time (reviewed in Refs. 1and 2). In contrast, considerable research effort has sought todefine the interdependent relationship of concentration andtime on antitumor activity. Of particular interest is whetherdrug action is strictly a function of Cx 7",since clinical response

is linearly correlated with the area under the plasma concentration-time curve for some agents (2). Several studies have foundthat antitumor activity is not related to C x T. Matsushima etal. (3) and Rupniak et al. (4) compared a number of antineo-plastic agents by in vitro clonogenic assay at l h versus 24 hand by continuous exposure, respectively. Neither group foundthat cytotoxicity was constant as a function of C x 7",but rather,

Received 1/5/89; revised 7/5/89; accepted 8/31/89.The costs of publication of this article were defrayed in part by the payment

of page charges. This article must therefore be hereby marked advertisement inaccordance with 18 U.S.C. Section 1734 solely to indicate this fact.

' To whom requests for reprints should be addressed, at Tumor Biology

Section. Division of Cell Biology, Burroughs Wellcome Co., 3030 CornwallisRoad, Research Triangle Park. NC 27709.

that exposure time was more (5-FUra2) or less (Adriamycin)

important depending on the agent. The groups therefore advised against comparing antitumor drugs at uniform times.Likewise, Pinedo and Chabner (5) concluded that methotrexatedepletion of nucleated murine bone marrow cells in vivo wasnot a simple function of C x 7".Eichholtz and Trott (6) studied

the pharmacodynamics of methotrexate in vitro and determinedthat survival was an exponential function of time and a powerfunction of concentration. Although their mathematical modeldiffered from that of Eichholtz and Trott, studies by Keefe etal. (7) confirmed the dominance of time in methotrexate cytotoxicity.

By comparison, a number of studies have concluded thatantitumor drug activity is indeed a function of C x 7*.Mellett

(8) claimed that when anticancer drugs, including methotrexate,are administered on a mg/m2 basis, equal doses give equivalentarea under the plasma concentration-time curves in differentspecies, which in turn lead to equivalent toxicological or pharmacological responses. Furthermore, Eichholtz-Wirth and Ei-chhoItz-Wirth and Hietel showed that survival is directly relatedto C x T for Adriamycin (9) and cisplatin ( 10). Similarly, Lihouand Smith (11) reported that in vitro sensitivity of acute mye-locytic leukemia was C x T dependent for Adriamycin but notfor the phase-specific agents l-/3-D-arabinofuranosylcytosineand 6-thioguanine. More important, their assay was able topredict response to Adriamycin in 79% of patients when tumorswere evaluated in vitro at one-tenth the plasma Cx T, comparedto 53% predictability for 1-0-D-arabinofuranosylcytosine. Recently, Ozawa et al. (12) concluded that, in general, cell kill bycycle phase-nonspecific agents is C x T dependent if a correc

tion is made for drug stability in culture medium.Failure to observe consistent dependence of antitumor activ

ity on C x T may be explained by a long known principlegoverning bacterial disinfectant action: survival is a function ofC" x T over a broad range of log kill (13, 14). This principle

came from the empirical observation that for a specified efficacy, log transformation of concentration-time curves yields aline whose slope is defined as the concentration coefficient, n,and whose intercept is the exposure constant, k, for that levelof cell kill. While n may approach unity for some agents andthus give a simple C x T dependence, values less than 1 arecommon and, in the exceptional case of phenol, may be as highas 6(14). The relevance of this relationship to antitumor agentswas realized by Skipper (15), who suggested that new drugscould be developed based on a differential concentration coefficient for tumor cell kill versus host toxicity. While this groupdid determine the C" x T relationships for nitrogen mustardand l,3-bis(2-chloroethyl)-l-nitrosourea against various strainsof Escherichia coli (16), general application of the principle toantitumor drug development has not occurred.

The present work describes a pharmacodynamic assay basedon the C" x T = k principle and its use in the development of

crisnatol (BW A770U), a member of the new AMAP class of

2The abbreviations used are: J-FUra, 5-fluorouracil; SF, surviving fraction;MTT, 3-[4,5-dimethylthiazol-2-yl]-2,5-diphenyltetrazolium bromide; 1C«,concentration producing 1-log cell kill; AMAP, arylmethylaminopropanediol.

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PHARMACODYNAMIC ASSAY FOR CANCER DRUG DEVELOPMENT

DNA intercalators. Crisnatol is one of three AMAPs now inclinical trial. The drug was chosen for clinical developmentbased on its lipophilicity, its broad spectrum of activity inmurine and human tumor models, and its limited and nonpleio-tropic cross-resistance with established agents (17-19). Preclin-ical studies (20) show that uptake of crisnatol is concentrativeand saturable in P388 murine leukemia and MCF-7 humanbreast adenocarcinoma cells, and that the uptake and effluxkinetics are similar in sensitive and crisnatol-resistant P388cells. The drug is distributed in all major subcellular compartments, with the cytoskeleton having the highest concentrationper mg protein. While these studies give a profile of crisnatolinteraction with tumor cells, they do not relate drug uptake,efflux, and intracellular distribution to antitumor activity. Consequently, an assay was needed that would relate cell survivalto extracellular drug concentration and exposure time, and tothe resulting intracellular drug concentration. Preliminary attempts to relate crisnatol action to the extracellular C x T werepromising (21) but not optimal. Application of the C" x T = k

principle, first described in 1908, reveals that crisnatol actionis a function of C" x T and that drug retention by tumor cells

is directly related to both antiproliferative and cytotoxic effects.Recognition of the importance of the concentration coefficientto drug action lead to derivation of the minimum C x Tparameter, which accounts for n in the evaluation of antitumoractivity on a C x T basis.

MATERIALS AND METHODS

Cells. The MCF-7 and MDA-MB-231 human breast tumor cell lineswere obtained from Dr. Fred Kull, Jr., Wellcome Research Laboratories, Research Triangle Park, NC, and were used within passages 150-170 and 32-53, respectively. Cells were cultured without antibiotics ina 1:1 mixture of Dulbecco's modified Eagle's medium and Ham's F12

medium; (MediaTech, Washington, DC) supplemented with glutamine,nonessential amino acids (GIBCO, Grand Island, NY), insulin (SigmaChemical Co., St. Louis, MO), and 5% calf serum (HyClone, Logan,UT, Lot 2151688). Normal human skin fibroblasts were cultured inDulbecco's modified Eagle's medium:Ham's F12 medium (1:1) con

taining glutamine and 10% heat-inactivated, iron-supplemented calfserum (which was reduced to 5% for assays). All cells were free ofMycoplasma by Micotrim assay (Hana Biologies, Inc., Alameda, CA).

Reagents. Stock solutions of crisnatol (Burroughs Wellcome Co.,Research Triangle Park, NC) and tamoxifen (Sigma Chemical Co.)were made fresh in 50% ethanol. Dilutions of doxorubicin (AdriaLaboratories. Columbus, OH), 5-fluorouracil (LymphoMed, Inc.,Rosemont, IL), cisplatin and etoposide (Bristol Laboratories, Syracuse,NY) were made from clinically formulated solutions, prepared andstored according to the manufacturer. MTT was prepared fresh inphosphate-buffered saline. Matrigel biomatrix, a urea extract from theEHS mouse sarcoma, was a gift of Dr. Hynda Kleinman, NIH. [I4C]-Crisnatol [5,11-14C]2-[(6-chrysenylmethyl)-amino]-2-methyl-1,3-pro-panediol mesylate, 48.5 mCi/mmol, was purified by thin-layer chro-matography to a radiochemical purity >98% and stored at -20°Cas a

6 mM stock in 50% ethanol. An 11 mM working stock was then madeby diluting the specific activity 1:4 with unlabeled crisnatol.

In Vitro Pharmacodynamic Assay. A schematic of the in vitro phar-macodynamic assay is shown in Fig. 1. MCF-7 cells were plated at IO4

viable cells/well in 96-well microtiter plates (Falcon, Oxnard, CA),precoated with matrigel (diluted 1:100, 0.64 ^g/well), and incubated at37°Cin a humidified atmosphere containing 5% CO2. At this plating

density, MCF-7 cells were in early log phase when drug treatmentbegan the next day. At time zero, the number of viable cells plated perwell was assessed by the MTT assay (see below). MTT is metabolizedby mitochondria! succinate dehydrogenase to the purple formazanproduct only in living cells and thus has become a standard method forquantitating viable cell number (22, 23). The coefficient of variation in

-48 -24

îÎ+Matrigel Plate Cells

24 48 72

Time (h)

Fig. I. Schematic of the in vitro pharmacodynamic assay. MCF-7 cells areplated on matrigel-coated microtiter plates 18 h before drug treatment. Cells arethen exposed to various concentrations of drug for the times shown, followed byan efflux period in drug-free medium. The assay is terminated by adding MTT tothe medium and quantitated by microscope and then by plate reader at 570 nm.The results are converted to surviving fraction, defined as the ratio of survivingcells divided by the number of viable cells plated per well. This yields a dose-response curve at each exposure time. The curves are then used to determine drugconcentrations that produce surviving fractions from 0.0005 to 4. The constantsn and k are determined by linear regression analysis of a plot of log exposuretime versus log concentration for each surviving fraction. These parameters arcthen used to compute the minimum C, T, and C' x T required for each level of

drug activity, which is summarized as a plot of minimum C X r versus survivingfraction (see Fig. 3Ä).•.drug uptake: D. drug efflux.

the plating density per well by this assay was 1-2%. Serial dilutions ofcrisnatol (1-110 MM)were added to cells in columns 2-12. At 1, 3, 4.5,9, 27, 54, 81. and 120 h, drug-containing medium was removed fromindividual rows, and the cells were washed once and refed witth 200 ß\drug-free medium. Control cells (column 1) received only drug-freemedium. A medium change was made on day 4, and the assay wasterminated on day 7 by switching to medium containing 1 mg/ml ofMTT. Following a 3-h incubation, wells were examined microscopically, and those containing less than ~100 cells were counted by hand.The MTT substrate was then removed, and the MTT-formazan wassolubilized by shaking with 100 u\ dimethyl sulfoxide for 10 min,diluted 1:4 with dimethyl sulfoxide, transferred to half-area plates(Costar, Cambridge, MA), and read at 570 nm against an air blank andreference wavelength of 750 nm in a Titertek Multiskan MCC micro-titerplate reader (Flow Laboratories, McLean, VA) interfaced with adisk storage unit (Seed 2, Mariachi; Turku, Finland). The linear rangefor the MTT assay by machine count was 400 to 40,000 MCF-7 cells/well, and the standard curve was not affected by prior exposure of cellsto nontoxic levels of crisnatol. For [l4C]crisnatol accumulation studies,

the pharmacodynamic assay was terminated by washing cells once withcalcium- and magnesium-free, phosphate-buffered saline and harvestingwith trypsin-EDTA. Samples were then transferred to scintillation vials,solubilized with 3 ml of Opti-Fluor (Packard Instruments, DownersGrove, IL), and counted in a Packard Model 1500 liquid scintillationcounter with an efficiency for I4C exceeding 95%.

Derived Parameters. Quantitation of viable cell number by MTTassay was used to compute the surviving fraction, defined as the ratioof surviving cells to the number of cells plated. Surviving fractions weregrouped into three ranges to describe increasing in vitro antitumoractivity. The antiproliferative range (1 < SF < 4), was that in whichthe tumor cell population increased during the assay, but was significantly less than the growth of untreated control cells [SF = 6.25 ±0.26(SE)]. Cytostasis occurred when there was no net change in tumor cellnumbers (SF =1). The cytotoxic range was that in which the numberof viable cells decreased during the assay (SF < I ). The drug concentration that produced a particular surviving fraction was determined bylinear interpolation (or extrapolation, if necessary) of the dose-responsecurve at each exposure time. A double log plot was then made of theresultant concentrations versus respective exposure times. This plot wasanalyzed by least squares linear regression to give the pharmacodynamicparameters n (-slope), and k (the antilog of the intercept) for that

surviving fraction. Finally, n and k were used to compute a unique endpoint, the minimum C x T (see below). This approach does not reflecttumor cell heterogeneity, either in drug sensitivity or mitochondria!

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PHARMACODYNAMIC ASSAY FOR CANCER DRUG DEVELOPMENT

metabolism. Furthermore, the expression of drug action is assumed tooccur within a limited number of cell doublings (2.6 ±0.1 doublingsfor control MCF-7 cells).

RESULTS

Relation of n and k to Crisnatol Action in MCF-7 Cells. Logtransformation of the equation C" x T = k yields the linearrelationship: log T = —nlogC + log k. Therefore, a double logplot of exposure time versus concentration at a specific survivingfraction will produce a line with slope —n and intercept log k.The results from such plots are listed in Table 1 for MCF-7cells exposed to crisnatol. Most linear regression correlationcoefficients exceeded 0.95, indicating that the C" x T = krelationship holds throughout the growth inhibitory and cyto-toxic ranges. The concentration coefficient, n, rose as the surviving fraction decreased, going from 1 in the growth inhibitoryrange to about 2 in the cytotoxic range. When the concentrationcoefficient was subsequently plotted against log surviving fraction and curve fit by polynomial regression analysis, n wasfound to be a fourth-order polynomial function of survival (datanot shown). Knowing this relationship permitted precise calculation of k for any combination of concentration and time(Table 2 and Fig. 2).

The importance of n to drug action is emphasized in Table2, which compares different combinations of C and T that givesimilar C x T. An exposure of 3 /¿Mcrisnatol for 9 h wasequitoxic to 10 ^M for 3 h, as was 26 //M for l h versus 1 pMfor 27 h. These iso-C x T pairs all had n values approaching 1

Table 1 Validity of the C" x T = k relationship as a function of survival

Crisnatol activity was assessed by pharmacodynamic assay in MCF-7 cells.Linear regression analysis was performed on plots of log T versus log C at 11surviving fractions to give n (-slope), log k (intercept), and R2 (correlation

coefficient). Values represent the intcrassay mean ±SE from 7 experiments; themean coefficient of variation in n and log k for all surviving fractions is 3%.

Survivingfraction43210.50.10.050.010.0050.0010.0005n.02

0.05.010.04.220.07.560.06.580.05.590.04.580.04.720.04.730.06.840.07.88

0.04Log

A1.33

±0.061.64±0.072.25

±0.093.00±0.083.19+0.073.38±0.063.43±0.073.82±0.083.89+0.114.25

±0.134.46+ 0.06A20.94

0.020.950.010.960.010.980.000.980.000.970.010.980.000.980.010.980.010.96

±0.010.92±0.02

Table 2 Effect of concentration coefficient on surviving fraction at iso-C x 7"

A pharmacodynamic assay was performed as described in "Materials andMethods." using radiolabeled crisnatol on MCF-7 cells. The concentration coef

ficient and exposure constant were determined from plots of log T versus log Cat 11 different surviving fractions. A plot of concentration coefficient versus logSF was made and polynomial regression performed with SigmaPlot software(Jandel Scientific, Corte Madera, CA). These data were fit by the fourth-orderpolynomial function: n = 1.47 - 0.468 x log SF - 0.537 x (log SF)! - 0.249 x(log SF)3 - 0.0357 x (log SF)4 (R2 = 0.969), which was then used to compute k(= C" X 7")for each combination of input concentration and exposure time.

ExposureABA

BA

BABC(fiM)2.8

10.126.21.21

292.22.857.6T

(h)9

32783.554

3Cx

T25.2

30.326.2

32.4100.2

92.2151.2

172.8n0.78

0.890.81

0.671.17

1.681.27

1.78C"xT(MM-*)20.2

23.714.1

30.8104.8

2014.7201.5

4119.5SF4.3

3.74.1

4.92.5

O.g2.1

0.01

10 102 103 10* 105 106 107 108

0.0001-

Fig. 2. Correlation of cellular crisnatol retention to antitumor activity inMCF-7 cells. A pharmacodynamic assay was performed with [l4C]crisnatol asdescribed in "Materials and Methods" with the concentration coefficient, n,

determined as a continuous function of survival as described for Table 2. Cellsurvival (O) and drug retention by whole cells (A) were then plotted as a functionof the external drug exposure, k. The retention of crisnatol is linear with respectto k and follows the regression line: log fmol/cell = 0.981 ±0.027 x log A -2.937 ±0.079; /V= 75, R2 = 0.946. Dotted lines are the 95ri confidence bands.

and produced the same degree of growth inhibition (SF = 4).From this limited analysis, one might have concluded thatcrisnatol was a simple C x /"-dependent agent. However, further

examination revealed that l JJMfor 83 h was not equivalent to92 MMfor 1 h nor was 3 I¿Mfor 54 h equivalent to 58 n\t for 3h. While each pair was iso-C x 7",there was a 20-fold differencein C" x T. This difference in exposure was reflected in marked

degrees of action. While 3 ^M for 54 h produced significantgrowth inhibition, 58 jtM for 3 h effected a 2-log cell kill. Theseresults indicated that a small number of C x T combinationswere inadequate to establish a pharmacodynamic profile forcrisnatol.

Correlation of Survival to Crisnatol Retention by MCF-7 Cells.While it is important to know the relation of antitumor activityto extracellular drug exposure, it is biologically more relevantto determine how that activity is related to cellular retention ofdrug, defined as the residual cellular concentration of crisnatol,both parent drug and metabolites, after uptake and efflux. Fig.2 relates various levels of crisnatol activity to drug retention byMCF-7 cells as a function of increasing extracellular drugexposure, or k. Crisnatol had no effect at k values less than 30,despite retention of up to 0.01 fmol drug/viable cell. Exposuresfrom 30-1500 nM"-h had an antiproliferative effect, corresponding to a 2-log increase in cellular drug until cytostasis wasreached at 1 fmol/cell. Cytotoxicity ensued at higher retentionsas k exceeded 2500 I¿M"-\I.Since these results represent total

residual radioactivity in harvested cells divided by the viablecell number, the results may have overestimated the active drugconcentration per surviving cell, but are within the range observed for lethal agents (0.2-20 fmol/cell; Ref. 14, p. 119).

Concentration-Time Relationships for Crisnatol and Derivation of the Minimum C x T. Fig. 2 reveals the thresholdexposures and drug retentions that are required for crisnatolaction and thereby provides a useful pharmacodynamic framework for further in vitro studies. However, this format is not asuseful for comparing antitumor agents, which ideally should bedone on a C x T rather than C" x T basis. To make such

comparisons, pharmacodynamic assay results are expressed asconcentration-time curves. Fig. 3A shows the C x T requiredfor a 1-log kill of MCF-7 cells by crisnatol. This is the linearform of the double log plot that was used to determine n and kat a surviving fraction of 0.1. The data fit the curve C =

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PHARMACODYNAMIC ASSAY FOR CANCER DRUG DEVELOPMENT

xo°\00\00\0o-

1u•

1-0.1LiÉr

0.01•C-0.001n

nnm20 « 60 80 100 120

Exposure Time (h)

10 100 1000Minimum CxT (¿iM—h)

Fig. 3. Determination of the minimum CxT" required for crisnutol action

against MCF-7 cells. A pharmacodynamic assay forcrisnatol was performed withMCF-7 cells as described in "Materials and Methods." The concentration coef

ficient, n, and exposure constant, k. were determined by linear regression analysisof log C versus log T plots at 11 different surviving fractions. A, one suchconcentration versus time plot (for SF = 0.1). but expressed on linear rather thanlog scales to reveal the hyperbolic relationship of concentration and time asdefined by the curve: C = (k/T)"" or (2399/7")062'. To illustrate the utility of thiscurve, the time required for a I -log kill of MCF-7 cells by a clinically relevantconcentration of crisnatol can be computed, i.e., 9 ^M drug, the peak plasmaconcentration in man, requires a 72-h exposure in vitro (A). The minimum C x/"(•)is found at the intersection of the curve, C = (k/T)t/a. with the dotted line.

C = nT or 1.59 x T. This corresponds to a minimum C of 24 pM and minimumT of 15 h. B, complete minimum CxT" survival curve for crisnatol action inMCF-7 cells. •.minimum C x T"computed from coordinates shown in A. Points,

¡nterassaymean from seven experiments. The standard error is not shown sinceit is less than the symbol size.

(k/T)l/n, which permits computation of C x T for any combi

nation of C and T within the ranges tested. The hyperbolicnature of the concentration-time curve reveals the impact thatexposure time has on the IC90 concentration of crisnatol. TheIC90 rises sharply at exposure times less than 10 h, while thereis little change after 20 h. In between these extremes lies aunique point at which concentration and time are both at aminimum. This point, defined as the minimum CxT, servesas a common reference point for such curves and is derived asfollows:

or

at the minimum.

or

C"T= k«logC + log 7"= log k

n/C(dC/dT) +1/7=0

dC/dT = -C/nT

dC/dT= -1,

C= nT

(A)

(B)

Thus, the minimum Cx T will occur at the intersection of theline C = nT with the curve C = (k/T)Un (see Fig. 3A). Rear

ranging Equation B and substituting it into Equation A givesthe following relationships:

or

and

= nk

minimum C = (nk)1

minimum 7"= minimum C/n

Table 3 gives the computed minimum C, T. and C x r basedon Equations C and D for crisnatol in the MCF-7 in vitromodel. This analysis reveals the differential effects of concentration and exposure time on the minimum CxT product.Drug concentration and exposure time contributed equally tothe minimum C x 7" in the antiproliferative range (n = 1),

whereas concentration had more impact than time in the cyto-toxic range (n = 2). Furthermore, the level of crisnatol exposurewas not linearly related to drug action. A 10-fold increase inminimum CxT, from 20 to 200 /JM-//, gave only a half-logincrease in growth inhibition (SF = 4 to SF = 1), while another4-fold increase in exposure produced a dramatic 3-log cell kill.This result is reflected in the sigmoid minimum CxT curveshown in Fig. 3Ä.This plot, which represents the end point ofthe pharmacodynamic assay, summarizes the minimum exposure conditions required for the entire range of crisnatol actionagainst MCF-7 cells.

Application of the Pharmacodynamic Assay to Other Agentsand Cell Models. To demonstrate that the utility of the in vitropharmacodynamic assay is not restricted to crisnatol, DNAintercalators, or to the MCF-7 cell line, the activity of severalclasses of established agents was evaluated in MCF-7 cells,MDA-MB-231 cells, and in primary cultures derived fromnormal human skin fibroblasts. The MDA-MB-231 cell line isa poorly differentiated breast carcinoma, which unlike MCF-7,lacks most steroid hormone receptors (24) and was derivedfrom a patient who had failed prior combination chemotherapywith 5-fluorouracil/prednisone, and cyclophosphamide/doxo-rubicin/methotrexate (25). Thus, these models represent a morerapidly growing (4.1 doublings/assay), steroid hormone-insensitive, possibly drug-resistant breast tumor, and a slow growing

(1.6 doublings/assay) normal cell control. Table 4 lists thepharmacodynamic parameters for a 1-log cell kill by the agents:doxorubicin (anthracycline), etoposide (epipodophyllotoxin),cisplatin (alkylator). 5-fluorouracil (antimetabolite), and ta-moxifen (antiestrogen). These agents act through a variety ofmechanisms that, with the exception of doxorubicin, do notinvolve DNA intercalation. The results indicate that cytotoxicactivity of a diversity of established agents conformed to theC" x T principle in two distinctly different breast cancer cell

lines as well as in normal skin fibroblasts. with correlationcoefficients that generally exceeded 0.95. Furthermore, theseagents exhibited a range of concentration coefficients that differwith each cell model. The importance of accounting for variation in concentration coefficient with the minimum C x T endpoint was evident when comparison was made to the standard1C»end point (evaluated at a 3-h drug exposure). By eithermeasure, doxorubicin was the most cytotoxic agent in each cell

Table 3 Pharmacodynamic parameters for crisnatol versus MCF-7 cells

Pharmacodynamic parameters for crisnatol were computed from the n and kvalues listed in Table 1 by the following formulae: minimum C = (n x A)""*";minimum T= minimum C/n. The mean coefficient of variation for the minimumCxT" over all survival fractions is lc/o.

ives(C)(D)Survivalfraction43210.50.10.050.010.0050.001

0.0005Minimum

C<fM)4.76.611.317.720.524.125.330.932.539.044.70.30.50.60.50.50.40.61.01.21.4

2.5Minimum

TW4.7

±0.56.6±0.49.3±0.211.413.015.216.0IS.O18.921.3

23.90.30.40.40.40.40.70.51.6Minimum

CxT"(nM-h)23

±445105202268366407556617833

109166101311172835401426618

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PHARMACODYNAMIC ASSAY FOR CANCER DRUG DEVELOPMENT

Table 4 Application of the pharmacodynamic assay to other agents and cell models at I-log cell killPharmacodynamic assays were performed with established agents in the MCF-7 and MDA-MB-231 breast cancer cell lines as described in "Materials and

Methods." Assays done on primary cultures derived from normal skin fibroblasts were modified by plating 8000 cells/well (confluency equivalent to tumor cells), and

by incubating with MTT substrate for 6 h. Results represent the average of at least three assays.

AgentMCF-7DoxorubicinC

risnatolC'isplatinTamoxifenIjoposidc5-FluorouracilMDA-MD-231DoxorubicinC'risnatolTamoxifen5-FluorouracilNormal

Human SkinFibroblastsDoxorubicinC'risnatolTamoxifen5-Fluorouraciln1.191.591.382.

.124.210.761.581.742.961.222.021.736.68NA"Log

k1.743.383.635.3211.693.701.863.566.495.181.873.593.23K20.990.970.970.970.970.980.980.980.970.980.950.970.93MinimumC X T

(xM-A)393661.1081.16012.78115.897253401.14044.5692l375788Normalizedminimum C xT"192830328408114461.783118381C«,*(flM)1268232108442C15,37

T960988.536°76188Normalized

ICV16149371.28117119481913

°Value divided by that for most active agent.* Cytotoxicity from 3-h drug exposure.c Extrapolated value.d NA. agent did not achieve 1 log cell kill under assay conditions.

model. Crisnatol, which ranked second, was slightly less activeby minimum C x T than by ICgo. However, results for the otheragents were significantly different when assessed by the minimum C x T parameter. For example, in MCF-7 cells, etoposideand 5-FUra had similar activity by minimum C x T, whereasby 1C«)etoposide was over 30 times more active. Likewise, theminimum C x T for cisplatin and tamoxifen were equivalent,but the ICgo for cisplatin was about twice that of tamoxifen.The reason for this difference lies in the range of concentrationcoefficients for these agents, from less than 1 (5-FUra) to over4 (etoposide), together with differences in the exposure constant, k.

DISCUSSION

In a definitive monograph, Clark (14) discussed the interdependence of concentration and time on drug action and, inparticular, the application of the C" x T= k principle to cellular

cytotoxicity. He recognized that the kinetics of heterogeneoussystems involve complex chain processes that are not adequately described by simple mathematical relationships, a factborne out by subsequent, more sophisticated mathematicalmodels of pharmacodynamics. Nevertheless, the C" x T = k

concept is a useful pharmacodynamic model that may explainthe apparent lack of C x T dependence observed by others. Forexample, application of this principle to the data of Matsushimaet al. (3) for 5-FUra toxicity against PC-7 lung adenocarcinomacells reveals a concentration coefficient significantly less than1 (0.46). Likewise, analysis of the data of Pinedo and Chabner(5) for methotrexate yields an n of 0.33 (R2 = 0.992). Thus,

agents whose action reportedly was not a function of C x T, doconform to the C" x T principle in both in vitro and in vivo

models. Clearly, the concentration coefficient is an importantproperty and must be taken into account when comparingantitumor agents. Clark stressed that drug activities could becompared at concentrations that produce equal action in equaltime only if their n values were similar. This fact has gonelargely unrecognized, with the exception of Pittillo et al. (16).who determined /; values of 0.858 for l,3-bis(2-chloroethyl)-l-nitrosourea and 0.573 for nitrogen mustard against E. coli (16).

These authors used the C" x T = k relationship to extrapolatethe concentration and time required for a 1-log kill, as well asthe time needed for various levels of cell kill.

The direct dependence of survival upon cellular retention ofcrisnatol as a function of k, rather than exposure dose alone,may also explain why other investigators have not found aconsistent relationship between extracellular and intracellulardrug levels and survival. For example, Eichholtz-Wirth (9)examined doxorubicin activity on Chinese hamster lung fibroblasts and found that survival was a simple exponential functionof extracellular drug concentration, but was neither an exponential nor a simple power function of intracellular drug concentration. On the other hand, Eichholtz-Wirth and Hietel (10)found a linear relationship between survival of CH, HaK, andHeLa cells and the intracellular concentration of cisplatin,which was due directly to the level of extracellular drug. Theseauthors concluded that sensitivity to cisplatin was due mainlyto differences in drug uptake through the membrane. Interestingly, Clark proposed that the concentration coefficient reflectsthe dominance of membrane adsorption and diffusion processeson the rate of drug action. For n = 0.3-0.5, the rate of actiondepends on cell surface adsorption, while for n = 1-2, inwarddiffusion is more important. An n > 3 indicates action by anall or none process, such as protein denaturation by phenol(14). The actual relation of n to mechanism is unknown butcould reflect different affinities for drug targets, differentthreshold concentrations for drug-target interaction, or multiple targets with different locations within the cell. Multipletargets could reflect multiple mechanisms of drug action. Sincecrisnatol exhibits two distinct concentration coefficients thatseparate its antiproliferative and cytotoxic ranges, the drug mayhave at least two different mechanisms.

The pharmacodynamic assay clearly has limitations, beingan empirical approach based on a simple mathematical modelfor a very complex process. The assay evaluates agents underideal conditions of drug-tumor interaction and does not accountfor factors like metabolism, which are not modeled in vitro[crisnatol is extensively metabolized in vivo (26, 27)]. Moreover,the assay may not apply to certain classes of antitumor agents(12), which were not represented in Table 4. Despite these

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PHARMACODYNAMIC ASSAY FOR CANCER DRUG DEVELOPMENT

limitations, the pharmacodynamic assay provides a useful profile for new antitumor drugs. The assay correlates differentdegrees of action with specific thresholds of cellular drug,providing a framework for mechanism studies. Concentration-time curves can be used to estimate any combination of C x 7",

including the minimum C x T, that are required for a specifiedefficacy. By accounting for differences in concentration coefficients, the minimum C x T can provide accurate comparisonof new drugs like crisnatol to other antitumor agents. Accordingly, the cytotoxic activity of crisnatol against MCF-7 andMDA-MB-231 cells compares favorably with that of someestablished agents. Finally, this approach can distinguish theactivity of AM AP isomers in vitro consistent with their antitu-mor activity in vivo.3 Thus, the pharmacodynamic assay couldhelp to define structure-activity relationships in large analogueseries like the AMAPs and should prove useful in antitumordrug development.

ACKNOWLEDGMENTS

The author thanks Pamela Watkins for expert cell culture supportand scientific collaboration. Dr. Gerald Hajian for help with statisticalanalyses and derivation of the minimum C x 7", and Drs. Richard

Tuttle, Kenneth Bair, and Fred Kull, Jr., and Allen Jones for theircritical reviews of the manuscript.

REFERENCES

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1989;49:6615-6620. Cancer Res   David J. Adams  Application to Crisnatol, a New DNA Intercalator

Pharmacodynamic Assay for Cancer Drug Development:In Vitro

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