[CANCER RESEARCH 43,4062-4067, September 1983]

Quantitative Neoplastic Transformation of C3H/10TV2 Fibroblasts:

Dependence upon the Size of the Initiated Cell Colony atConfluence1

Lawrence J. Mordan, John E. Mariner, and John S. Bertram2

Department of Experimental Therapeutics, Grace Cancer Drug Center, Rosewell Park Memorial Institute, Buffalo, New York 14263

ABSTRACT

The efficiency of transformation of C3H/10TV2 dbroblasts bychemical or physical carcinogens varies inversely with the seeding density of the cells. Colony size at confluence, accumulatedcell generations, and epigenetic events independent of seedingdensity have been proposed to explain this variability. By controlling the total number and colony size (i.e., cells/colony) ofinitiated cells at confluence and their accumulated cell generations, we have determined that (a) the colony size of the initiatedcells at confluence is directly related to the expression of thetransformed phenotype, (o) the probability that an initiated cellwill form a colony of transforming cells does not vary with theaccumulation of large numbers of cell generations, and (c) thetotal number of initiated cells in a confluent culture does notdetermine the number of transformed foci formed. We havedeveloped a mathematical representation which, when appliedto our results and the published results from other laboratories,clearly describes the relationship between the size of the initiatedcell colony at confluence and the expression of the transformedphenotype. These results have significant implications in thequantification of the transformation of C3H/1 OF/2 cells by chemical and physical carcinogens.

INTRODUCTION

Because the 10TV23 cell line is widely used to study mecha

nisms of carcinogen-induced neoplastic transformation in vitro

and is also used as a screening system for compounds ofcarcinogenic potential (8), the interpretation and comparison ofsuch studies requires the unambiguous quantitation of the neoplastic response. However, numerous investigators have reported that the efficiency of neoplastic transformation inducedby chemical and physical carcinogens varies inversely with theseeding density of these cells (5, 7,10,14,19).

Three hypotheses have been proposed to explain this phenomenon. Haber er al. (7) have proposed that the expression ofthe transformed phenotype is dependent on the size of a colonyof initiated cells at confluence. A similar hypothesis was independently proposed by Bertram (2), based on the effects ofserum concentration and saturation density upon transformation.Kennedy et al. (10) rejected this hypothesis in their studies on

1Supported by Grant CA21359 from the National Cancer Institute, USPHS.2To whom requests for reprints should be addressed, at Department of Exper

imental Therapeutics, Grace Cancer Drug Center, RosweH Park Memorial Institute,666 Elm Street, Buffalo, N. Y. 14263.

'The abbreviations used are: 10TW cells, C3H/10TV4 cells; INIT/1 OTV4cells,methylcholanthrene-initiated C3H/10T% cells; TPA, ^-O-tetradecanoylphorboUS-acetate.

Received February 24,1983; accepted May 27,1983.

X-ray-induced transformation and proposed a 2-stage mecha

nism in which the initiation event is frequent, while the expressionof transformation is a rare, postconfluent event dependent onlyupon the number of carcinogen-damaged (i.e., initiated) cells at

confluence. A third hypothesis has been proposed by Fernandezer al. (5), who developed a probabilistic model in which thedensity-dependent variation in transformation is due to the reversal of carcinogen-induced "activation" in a proportion of the

initiated cells with each cell generation after exposure.Resolution of these conflicting proposals would require that

the number of initiated cells, their colony size, and generationnumber be independently controlled. We have recently isolateda clone of INIT/1 OF/2 cells which exhibits properties expectedof initiated cells, including density-dependent inhibition of cell

division, latent transformation and tumor formation, and acceleration of transformation by TPA (13). Thus, by coculturing INIT/10T1/2 cells with 10"P/2 cells, we are able to reconstruct the

experiments which led to the above hypotheses by controllingthe number, colony size, and accumulated generations of thecarcinogen-initiated cells. Our results clearly demonstrate thatthe expression of transformation in initiated 1OF/? cells is directlyrelated to the size of the colony of initiated cells at confluence.Furthermore, we have developed a mathematical model whichdescribes our results, correlating transformation and colony size.This model is in excellent agreement with other published workon the transformation of 10F/2 cells.

MATERIALS AND METHODS

Cell Culture Procedures and Cell Lines

The C3H/10TV2 mouse fibroblast cell line was cultured as describedpreviously (15). The INIT/1 OTW cell line was cloned from a culture ofmethylcholanthrene-treated 10TVÕcells and has previously been shown

to be maintained in an initiated, although morphologically non transformed, state, by culturing in media containing retinyl acetate (13).Removal of retinyl acetate from the culture medium results in transformation of INIT/1 OT1/2cells after a latent period of approximately 3 weeks,

during which they are indistinguishable from noninitiated 10TVz cells.INIT/1 OP/z cells are tumorigenic in nude mice after a latent period ofabout 6 weeks. In addition, INIT/1 OTVi cells are sensitive to the tumorpromoter TPA, which significantly shortens their latent period in vitro.Thus, the INIT/1 OT'/2 cell line exhibits the basic properties of initiated

cells and can be used to reconstruct the 10TVi transformation assaywith the significant advantage that the number and history of initiatedcells in culture can be known and controlled.

Experimental Design

Effect of Colony Size. To reproduce the effect of seeding densityupon transformation frequency, INIT/1 OTW cells were seeded at a density of 100 cells/60-mm dish followed 24 hr later by 103, 5 x 103,104, 5

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Colony Size Dependency of Transformation

x 104, or 10510TVz cells/dish. The plating efficiency of each cell line was

measured by determining the number of colonies formed in culturesreceiving 100 cells. The cocultures were fixed after 5 weeks, and thenumber of types of II and III foci (14) were determined. The efficiency oftransformation was expressed as

Transformation frequency

Number of types II and III foci

Number of clonogenic INIT/1 OP/2 cells

(A)

Colony size, equated as the number of cells/colony at confluence, wasdetermined by the equation:

Number of cells/colony =Number of cells at confluence

Number of viable cells seeded(B)

where the number of cells at confluence was approximately 6 x 10s and

the number of viable cells seeded was equal to the plating efficiency xthe seeding density.

Effect of Accumulated Cell Generations. INIT/1 OP/2 cells were keptin exponential growth over a 5-week period by weekly passaging at lowdensity (5000 cells/60-mm dish) in the absence of retinyl acetate. Ateach passage, cocultures of 100 INIT/1 OP/2 cells plus 103,104, or 105

10T/2 cells/dish were seeded, and the plating efficiency of each cell linewas determined as described above. Each set of cocultures was fixed 5weeks after seeding and scored for transformation. During this experiment, the number of cell generations accumulated within each passagewas determined from the seeding density, the plating efficiency of thecells, and the number of cells harvested at the next passage. The numberof cell generations to confluence in the cocultures was equal to

log (6 x 105/number of viable cells seeded)/log 2 (C)

Thetotalaccumulatedcell generationswas equalto the sumof thesevalues.

Total Number of Initiated Cells versus Colony Size. A cell suspension containing 4.63 x 10* 10TV2 cells/ml and 1.25 x 103 INIT/1 OP/2

cells/ml was prepared and diluted 4-, 16-, 64-, and 256-fold with medium.For each suspension, twelve 60-mm dishes were seeded with 5 ml ofcell suspension, thus producing seeding densities of from 2.5 x 10scells/dish (undiluted) down to 1 x 103 cells/dish (1:256), each containing

a constant proportion of INIT/1 OP/4:10P/2 cells. The plating efficiency ofINIT/1 OP/2 cells alone and of the cell mixture were also determined.Once the cultures at each dilution were confluent, they were treatedtwice weekly for 2 weeks with TPA (0.1 M9/ml), thus reducing the timefor expression of transformation of INIÕ/1OP/2 cells but without affectingthe efficiency of transformation (13). Cultures were fixed 4 days after thelast TPA treatment and scored for transformation. The colony size atconfluence was determined as described above.

RESULTS

Effect of Seeding Density on Transformation. To examinethe effects of seeding density on transformation frequency, aconstant number of initiated cells (100) was cocultured withincreasing numbers (103 to 105) of 10P/2 cells. Since INIT/1 OP/2

cells and 10TVz cells have identical growth rates and saturationdensities (13) and since the total growth surface area is constantregardless of seeding density, the progressively increasing seeding density of the cocultured 10P/2 cells will lead to progessivelysmaller colonies of initiated cells at confluence. It was found thatthe percentage of INIT/1 OP/2 cells forming transformed foci wasdirectly dependent on the size of the initiated cell colony atconfluence (Chart 1). As the colony size at confluence increasedfrom approximately 40 cells (highest seeding density) to about

80

60

40

20

50 100 500 1000

Cells/Colony at ConfluenceChart 1. Effect of colony size at confluence on transformation of initiated 10TVz

cells. INIT/1 OTO cells (100/dish) were cultured with increasing numbers of 10T1/2cells (103 to lO'/dish), thus controlling the number of cell generations required to

attain a confluent monotayer (600,000 cells/dish). Each point represents the meanof the percentage of clonogenic INIT/1 OTO cells forming transformed foci in 10 to12 cultures 5 weeks after seeding. Bars, S.D.

3300 cells (lowest seeding density), the percentage of INIT/10P/2 cell colonies forming types II and III foci increased from0.8 to 65%. This is the maximum percentage of INIT/1 OP/2 cellsthat we have found to be able to form types II and III foci (13). Itis readily apparent that INIT/1 OP/2 cells must form a colony atconfluence in excess of approximately 40 cells in order to attainthe competence to transform. Thereafter, there is a direct relationship between colony size at confluence and the probabilityof transformation. Maximum expression of the transformed phe-

notype was reached with colonies of approximately 740 to 3300cells.

Effect of Accumulated Generations. Because an increase incolony size at confluence cannot be produced without an increase in the number of cell generations accumulated, it was notclear which of these variables influenced the expression oftransformation. An experiment was therefore performed in whichcell generations were allowed to accumulate by weekly passaging. At each passage, reconstruction experiments were set upat increasing seeding densities so that colonies of different size,total accumulated generations, and generations to confluencewere formed. The results of this experiment (Chart 2) againshowed clearly that the percentage of INIT/1 OP/2 cells formingtransformed foci was consistently dependent on the seedingdensity, which determines colony size as we have describedabove, and was not affected by the total number of cell generations accumulated over the 5-week period of the experiment.

The maximum percentage of INIT/1 OP/2 cells able to form transformed foci at each weekly interval was consistently 60 to 65%throughout the experiment, in spite of the accumulation of 40generations. Thus, no decrease in the pool of initiated cellscapable of neoplastia transformation was detected in thesestudies. Transformation of INIT/1 OP/2 cells was completely inhibited at the highest seeding density, as would be predictedfrom the results presented in Chart 1, for colonies of from 20 to50 cells.

Effects of Serial Dilution of a Mixed-Cell Suspension. The

results thus far obtained indicated clearly the requirement forlarge colonies for efficient expression of transformation. However, the results might simply reflect an increased probability oftransformation as a consequence of the increased numbers ofinitiated cells contained in these large colonies. To control forthis variable, we plated serial dilutions of a mixture of INIT/1 OP/2and 10P/2 cells. Because the final saturation density is constant,

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L. J. More/an ef al.

regardless of seeding density, and since both cell types have thesame growth rate (13), it will be apparent that the relativeproportions of initiated and normal cells at confluence will be thesame as at the time of seeding. All cultures at confluence willcontain the same number of INIT/1OT1/2cells; they will, however,

differ in their distribution. Cultures seeded at high density (undiluted) will contain many small colonies; those seeded at lowerdensities (diluted) will contain fewer but larger colonies, with themathematical product

Colony number x cells/colony = constant (D)

These considerations also apply to the cocultured 10TV2 cells.Serial dilution of the mixed cell suspension produced no sig

nificant variation in the number of transformed foci in culturesreceiving 1:4 to 1:64 dilutions (Table 1), in spite of a 15-fold

variation in the numbers of initiated cells seeded. These resultsare similar to those reported by Kennedy et al. (10) using denovo X-ray induced transformation. When we plotted transformation frequency against colony size of the initiated cells (Chart

20 28

Total Cell Generations

36 44

Chart 2. Effect of total accumulated cell generations on the transformation ofinitiated 10T'/2cells. INIT/1OTte cells were cultured in exponential growth phasefor approximately 40 generations by weekly passaging at tow density. At eachpassage, 100 INIT/1OTVzcells were cocultured with 103 (•),10* (A), or 105 (»)10TV2cells, thus reproducing low, medium, and high seeding densities, respectively. By determiningthe plating efficiencyand the numberof cells in representativecultures, the number of cell generations accumulated during exponential growthwithin each passage and from seeding to confluence in the cocultures could becalculated. Eachpoint represents the mean transformation frequency of clonogenicINIT/1On cells in 8 to 12 cultures.

3), we again found a direct relationship between colony size andthe expression of transformation. Thus, the decrease in numberof initiated cells seeded with increasing dilution of the cell suspension appears to be offset by a closely corresponding increasein the frequency of initiated cells forming transformed foci. Thisis a consequence of the relationship between transformationfrequency, seeding density, and colony size (Chart 1).

Mathematical Representation. The data in Chart 3 clearlysuggest that the correlation between transformation frequencyand colony size (i.e. , cells/colony) at confluence could be reasonably well approximated by the logistic curve describing thegrowth of a confined population. This is not an unexpectedrelationship, since we have shown that transformation is a veryunlikely event when the colony size at confluence is small (<40cells) but becomes increasingly more probable with increasingcolony size until the maximum expression of transformation isreached, after which further increases in colony size have littleeffect on the probability of transformation. We have utilized thelogistic equation (Equation E) describing such a sigmoid relationship because its parameters are easily applied to those of thetransformation assay.

, (E)

where V(x) is transformation frequency at "x" number of cell

generations to confluence, V™*is minimum transformation frequency, V,™«is maximum transformation frequency, Xv, is thenumber of cell generations required to give 50% of the Vm»,k =V"(W(Ymax - Vmin),and Y'(xv,} is estimated slope at Y(Xy,).

We assume that transformation in the absence of carcinogenis exeedingly small; therefore, /„*,= 0. The highest experimental

value of the transformation frequency was equal to /„«x.Thesource of the analyzed data from other laboratories is listed inTable 2.

Chart 4 shows the logistic curve which best "fits" the pooled

data from Charts 1 and 3. Colony size at confluence is represented by the number of cell generations required for the viablecells seeded to reach confluence. It can be clearly seen that therelationship between colony size at confluence, expressed asthe number of cell generations from seeding to confluence, andthe expression of the transformed phenotype is quite accuratelydescribed by the logistic equation. Probit analysis of these data

Table1Effect of serial dilution of a mixed cell-suspensionof f 07% cells and INIT/IOFA cells on the transformationof INIT/10r/i

cells

Dilution1:0

1:41:161:641:256Total

viablecellsseeded82.5

x 10s6x10*

1.5 x 10*4x 10»1 X103Viable

INIT/10T/2 cellsseeded61205

30175195Foci/dish10.5

±1./8.3 ±1.29.1 ±1.83.0 ±0.0%

of transformation'10

3.511.0

48.060.0Generations

toconfluence3.4

5.47.49.4

11.4Cells/colony

atconfluence811

42169676

2702* Calculated from plating efficiency of 100 cells from the mixed cell suspension.6 Calculated from plating efficiency of 100 INIT/1OP/2cells.' Percentageof viable INIT/1OT12cells seeded which formed types II and III foci'' Calculated from plating efficiency of 100 cells from the undiluted suspension of INIT/1OTViplus lOTVzcells and the

saturation density of the cells.8 Calculated from the formula

Cells/cotony = 2"

where N equals the number of cell generations to confluence.' Mean ±S.D.

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Colony Size Dependency of Transformation

G 60

er

I<P

40

£ 20orr

t 10 too toooCELLS/COLONY AT CONFLUENCE

Chart 3. Transformation of A constant number of initiated cells distributed incolonies of increasing size. A mixed suspension of INIT/IOTVj and lOTVz cellswere serially 4-fold diluted and then seeded into 60-mm dishes. Since each culture

will contain the same number of cells at confluence, dilution of the cell suspensionwill cause the number of generations to confluence to increase and thus cause anincrease in colony size at confluence. Each culture was treated with TPA (0.1 -^g/ml) twice weekly after confluence. Each point represents the mean transformationfrequency of clonogenic INIT/10TW cells in 10 to 12 cultures 4 days after the lastTPA treatment.

3 6 9 12 15

GENERATIONS TO CONFLUENCE

Chart 4. Pooled data from Charts 1 (A) and 3 (•)compared to the sigmoidcurve generated by Equation E when x»= 8 and k = 1. The results of x2 analysisindicate a 97.5% "goodness of fit." Inset, probit analysis of these data, except 0%

transformation points, plotted as a percentage of maximum transformation againstcell generations to confluence.

Table 2

Source and derived data from published results of other laboratories

SourceCarcinogen (concentra

tion)

Reznikoffefa/., Chart 3-Methylcholanthrene(15 1.1 9.5

6 Mg/nH)

Haberef a/., Chart 3 Benzo(a)pyrene (20 nu) 2.5 11.5

Fernandez et al.. Table1Kennedy

et al.. Table13-Methylcholanthrene

(1

eg/ml)X-ray

(400 rads)1.9216.716.8180.51

8 Vn«.,maximum experimental percentage of seeded cells which formed trans

formed foci; x,.,, number of cell generations at which the transformation frequencywas 50% of maximum. This value was estimated from the graphed values.

For derivation of k, see "Results."

yielded a linear relationship between transformation frequencyand generations to confluence, thus indicating that the probabilityof transformation of initiated cell colonies, above the minimalcolony size, vanes in a Gaussian manner and is thus simply afunction of biological variation (6).

Obviously, the validity of this model describing the transformation of INIT/10TV2 cells requires that it be applicable to thestandard 10TV2 cell transformation assay. Therefore, we appliedthe logistic equation to published data from other laboratories inwhich the density dependence of 10TV2 cell transformation hasbeen tested (Chart 5; for sources, see Table 2). These experiments utilized methylcholanthrene [Reznikoff et al. (14) andFernandez ef al. (5)], benzo(a)pyrene [Haber ef al. (7)], and X-

rays [Kennedy ef al. (10)] as the carcinogens. In each case, therelationship between the transformation frequency and the number of cell generations to confluence (i.e., colony size) is welldefined by the logistic equation.

DISCUSSION

The primary conclusion reached from the series of reconstruction experiments described here is that the ability of a carcinogen-initiated 10"P/2 cell to express the transformed phenotype is

CELL GENERATIONS TO CONFLUENCE

Charts. Published data from other laboratories compared to sigmoid curvesgenerated by Equation E. A, Reznikoff et al. (14); B, Haber er al. (7); C, Kennedyer al. (10); D, Fernandez ef al. (5). The values of constants derived from these dataand used in the generation of each curve are listed in Table 2.

governed by the number of cells in a colony of initiated cells atthe time of confluence of the monolayer. In addition, we havedemonstrated that the accumulation of up to 40 cell generationsof exponential growth had no effect on the percentage of INIT/10T1/2 cells forming transformed foci at optimal colony size.

Furthermore, we have shown that it is not the total number ofinitiated cells in a culture at confluence which determines thenumber of transformed foci formed but, rather, their distributionin colonies of appropriate size which determines their expressionof the transformed phenotype. Thus, our results strongly supportthe initial proposal by Haber ef al. (7), from experiments conducted on benzo(a)pyrene-treated 10P/2 cells, that transformation was dependent upon colony size at confluence and independent of total cell generations.

These conclusions, however, were reached with a highly selected line of cells in which neoplastia progression was arrested

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L. J. Mordan et al.

by retinyl acetate. What is the likelihood that this line is a validmodel for the events occurring in experiments utilizing chemicaland physical carcinogens in which initiated cells are produced denovo? For the following reasons, we believe our reconstructionexperiments do accurately reflect these events.

The INIT/1 OTVzcell line possesses the properties to be predicted of de novo initiated cells, with regard to growth propertiesand morphology, the ability to undergo neoplastic transformationafter a defined latent period, and sensitivity to TPA [the lack ofan absolute requirement of TPA for transformation could also bepredicted from previous studies using high concentrations of 3-methylcholanthrene (12)].

The fact that the INIT/1 OP/2 clone was distinguishable from147 other similarly treated clones on the basis of its ability togive rise to a high frequency of transformants (13) argues verystrongly against the possibility that the initiating event(s) resultingfrom carcinogen treatment occur commonly in all exposed cells,as speculated by Kennedy ef al. (10).

Data from other published experiments using 10T1/2 cells, in

which seeding density effects have been examined, fit the modelwe have proposed here with regard to the colony size dependency of transformation. This includes the data of Fernandez efal. (5) and Kennedy et al. (10), from which totally differentconclusions were reached. Of course, just because our modelfits does not make it correct; however, by the use of our initiatedline, we are in the unique position of being able to control allvariables thought to be relevant to the density of plated cells.The results that we observed in these experiments controllingfor total generation number, generations to confluence, andnumber of initiated cells at confluence lead, we believe, logicallyto the conclusions drawn.

Our results support strongly the conclusions of Haber ef al.(7), who, on the basis of sequential replating experiments conducted on benzo(a)pyrene-treated 10P/2 cells, reported that

transformation frequency was dependent upon colony size andwas independent of total cell generations.

Colony size dependency suggests a suppressive role mediated by adjacent colonies of nontransformed cells. This is notwithout precedent. We have previously shown that both de novotransformed and malignant 10T/z cells can be caused to undergoreversible growth arrest when in contact with nontransformed10T/2cells(2, 3).

Let us examine the data of Kennedy et al. (10) and Fernandezef al. (5) in more detail. After conducting experiments in whichX-irradiated cells were reseeded at progressively lower densities,

Kennedy ef al. found that, within limits, the number of transformed foci did not vary. In order to explain why variation in thenumber of irradiated cells seeded did not lead to a correspondingvariation in the yield of transformed foci per culture, they proposed that a frequent initial epigenetic event is followed by arare (mutational) event at confluence. Since confluent culturescontain identical cell numbers regardless of seeding density,identical transformation frequencies would result. They rejectedas too unlikely the possibility that the influence of colony sizeproposed by Haber ef al. (7) could be precisely balanced by theeffect of dilution. Our reconstruction experiments (Table 1) showa similar phenomenon; that is, with dilution of a mixture ofnontransformed and initiated cells, the number of transformedfoci per dish remained essentially the same, except at the extreme seeding densities. Since we are in the position to know

the number of initiated cells seeded and the number at confluence, it is clear that the effect of dilution is balancing the effectof colony size. When the transformation data of Kennedy ef al.are replotted against the colony size at confluence, the relationship between colony size and transformation frequency is apparent (Chart 5C).

The conclusion of Fernandez ef al. (5), derived from dataobtained from methylcholanthrene-treated cells seeded at differ

ent densities, was that the decrease in the number of fociobserved with decreasing seeding density was due to reductionof the fraction of initiated cells with increasing generations toconfluence. This proposal did not take into account the changein number of carcinogen-exposed cells at risk with changes in

the seeding density or the fact that cells in culture grow in aclonal manner to form colonies of cells which coalesce at confluence to form the monolayer It was also assumed that eachtransformed cell can form a scoratale focus; however, becauseof the nature of the transformation assay, it cannot be knownwhether a focus is derived from one or many cells within a colonyof initiated cells. Their model is inconsistent with the data ofHaber ef a/. (7), who showed that, with reseeding of carcinogen-exposed cells at confluence, the transformation frequency wasnot altered with the accumulation of additional cell generationsin comparison to nonpassaged cells. If inactivation had occurredwith the passage of INIT/1 OP/z cells, the model of Fernandez efal. would predict that the percentage of INIT/1 OP/a cells able totransform would decrease rapidly with the accumulation of cellgenerations. To the contrary, our results conclusively demonstrate that the percentage of INIT/1 OT/2 cells able to form typesII and III foci remains constant for at least 40 cell generations,during which time they remain sensitive to the colony sizedependence of transformation (Chart 2). As shown in Chart 5O,the results of Fernandez ef al. also demonstrate the relationshipbetween transformation frequency and colony size at confluence.

The mechanism by which the size of the initiated cell colonyat confluence may influence expression of transformation hasbeen modeled by Bell (1). In this model, a critical done size isrequired in order to escape mitotic inhibition mediated by diffusible factors, released by surrounding normal cells, which maintain tissue homeostasis. Thus, if preneoplastic cells can respondto these signals but are relatively incapable of sending or transmitting them, cells within colonies of increasing size would beincreasingly shielded from these growth-inhibitory signals. Thereis evidence that such cellular interactions occur in fibroblastsystems (2, 3, 17). What form might this communication have?Three possible mechanisms of homeostatic regulation of cells inculture seem feasible: extracellular diffusion; direct membrane-membrane interactions; and intercellular diffusion. Of the three,the first appears unlikely, as we have been unable, in otherexperiments, to demonstrate growth-inhibitory activity in conditioned medium from cultures nonpermissive for neoplasticgrowth (2, 3). This, of course, does not eliminate the possibilitythat local gradients may exist (17). Direct membrane-membraneinteractions certainly are capable of influencing the behavior ofadjacent cells, but it is difficult to see how communication couldbe transmitted throughout a colony of several hundred cells.Furthermore, while membranes or membrane extracts from non-transformed 3T3 cells have been shown to inhibit growth ofsimilar cells, no effect on neoplastic cells has been found (20,21).

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In our view, a more attractive hypothesis is that intercellularcommunication, by means of gap junctions, is the controllinginfluence in the colony size dependency of transformation. Somatic cell geneticists have demonstrated that the "metaboliccommunication" of ions and small molecules between contacting

cells creates problems in determining the frequency of variousmutant phenotypes (9). One could then imagine the existence ofa decreasing concentration gradient of growth-regulatory molecules (e.g., cyclic adenosine 3':5'-monophosphate) produced by

the normal cells surrounding a colony of initiated cells, assumingthat the initiated cells are deficient in some aspect of the generation of the regulatory substances. Transformation would occurwhen the concentration of the growth-regulatory moléculas)

drops below a threshold value, as would occur toward the centerof large colonies of initiated cells. Small colonies of initiated cellswould be inhibited from transforming by a suprathreshold levelof the regulatory molecule(s), while the transformation of intermediate-sized colonies would depend on their sensitivity to the

regulatory signals and would vary as does a normally distributedpopulation. We believe our results are consistent with this concept.

Alterations in the communicating ability of cells may be part ofthe transforming process, since neoplastic cells have beenshown to couple poorly with other such cells, while coupling toan intermediate degree with nontransformed cells (4, 11). Bydemonstrating in our laboratory rescue from ouabain cytotoxicityas a criterion for gap junctional communication, we have shownthat 10TV2 cells and their transformed counterparts are in communication.4 This model calls for the transfer of small informa

tional molecules from cell to cell to effect rescue.We have demonstrated with our data and that of other labo

ratories that the effect of seeding density on 10T% cell transformation can be accurately represented by the logistic equation.This representation offers an improved "fit" over that proposed

by Haber ef a/. (7), even though the concept is very similar. Webelieve that the parameters of this model, including /„„,„,Y(x,.,),KM,,and k, may be useful in describing the relative effectivenessof various carcinogens, promoters, or anti-promoters. For ex

ample, the variations seen in the number of cell generations toconfluence resulting in one-half maximum transformation (x«,)for

the different experiments listed in Table 2 may reflect differencesin the serum or the carcinogen and/or its dose and deservesfurther experimentation.

These studies have presented a basic explanation for theextreme variability in the efficiency of transformation observedwith variation in the seeding density of C3H/10T% cells andstrongly suggests that true transformation frequencies shouldbe based upon the number of cells surviving carcinogen treatment as originally proposed by Reznikoff ef al. (14) and not uponthe number of foci per dish as in more recent studies (5,10). Itis clear that if the modulating effect of colony size is not considered and controlled for, then quantitation of the response tocarcinogens will be uninterpretable and comparisons betweendifferent carcinogens or the results of different laboratories willbe impossible.

One problem not completely answered by this analysis is the

4 P. J. McCormick and J. S. Bertram, unpublished results.

apparently very high transformation frequency seen in the X-ray

experiments, with low seeding density, of Kennedy ef al. (10).Such high frequencies certainly suggest very frequent initiatingevents, which were not suggested in previous data from thatlaboratory (19), from our selection of the INIT/10P/2 clone (13),or in the studies of Fernandez ef a/. (5) using 3-methylcholan-

threne.

ACKNOWLEDGMENTS

We are grateful to Dr. Raymond Baker for his thoughtful and constructivecriticisms of this manuscript. We thank Dona Alleyne for her excellent technicalassistance and Jo Ellen Budnick for careful editing of this manuscript.

REFERENCES

1. Bell, G. I. Models of carcinogenesis as an escape from mitotic inhibitors.Science (Wash. D. C.), 792: 569-572,1976.

2. Bertram, J. S. Effects of serum concentration on the expression of carcinogen-induced transformation in the C3H/10T% CL8 cell line. Cancer Res., 37: 514-523,1977.

3. Bertram, J. S. Modulation of cellular interactions between C3H/10TV4 cells andtheir transformed counterparts by phosphodiesterase inhibitors. Cancer Res.,39: 3502-3508.1979.

4. Corsaro, C. M., and Migeon, B. R. Comparison of contact-mediated communication in normal and transformed human cells in culture. Proc. Nati. Acad.Sei. U. S. A., 74: 4476-4480,1977.

5. Fernandez. A., Mondai, S., and Heidelberger, C. Probabilistic view of thetransformation of cultured C3H/10T% mouse embryo fibrobiasts by 3-meth-ylchdanthrene. Proc. Nati. Acad. Sei. U. S. A., 77: 7272-7276,1980.

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SEPTEMBER 1983 4067

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1983;43:4062-4067. Cancer Res   Lawrence J. Mordan, John E. Martner and John S. Bertram  Colony at ConfluenceFibroblasts: Dependence upon the Size of the Initiated Cell Quantitative Neoplastic Transformation of C3H/10T½

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