[CANCER RESEARCH 47, 1045-1051, February 15, 1987]
Growth Properties of Artificial Heterogeneous Human Colon Tumors1
John T. Leith,2 Seth Michelson,
Lynn E. Faulkner, and Sarah F. Bliven
Department of Radiation Medicine and Biology Research, Rhode Island Hospital, Providence, Rhode Island 02902 [J. T. L., S. MJ, and Division of Biology and
Medicine, Brown University, Providence, Rhode Island 02912 [J. T. L., S. M., L. E. F., S. F. B.J
include more extreme compositional states: these being AHTs
produced from initial admixtures of either 9% A:91% D or
88% A: 12% D cells. The time-dependent composition and
clonogenicity of these neoplasms were studied after disaggre
gation and compared to the original data from the 50% A:50%
D AHTs as well as to data from pure clonal tumors. We also
used the cellular sampling data from these AHTs to determine
if zonality could be observed. Further, in vivo, we investigated
7 different admixture compositions to define how this variabil
ity in the initial percentages of cell subpopulations might be
reflected in their in vivo growth kinetics using the Gompertz
equation (11). These in vivo data were then used in conjunction
with the cellular composition data to describe some overall
characteristics of this heterogeneous tumor model system.
ABSTRACT
Twoclonalcell lines(designatedas clonesA andD), originallyisolated
fromthe heterogeneousDLD-1 humancolonadenocarcinoma,
wereused
to producexenografttumorsin nude mice. Neoplasms producedfrom
eitherA or D cells alonewerecomparedto thoseproducedfroma range
of percentageadmixturesof the twosubpopulations.Then,Gompertzian
growthparameters(initial growthrates, retardationrates) were deter
mined,along with estimationof the final asymptoticvolumes.It was
foundthat the growthkinetics of the variousartificialheterogeneous
tumorscouldnot be predictedfromknowledgeof the growthparameters
of the pureclonalxenografttumors.Additionally,both pureclonaland
artificialheterogeneoustumorswere enzymaticallydisaggregatedas a
functionof timepostinjection,andit was foundthat the admixedtumors
becamemorezonalin compositionas time progressed.Further,admix
turesof extremecomposition(i.e., 9%A plus91%D or88%A plus 12%
D) remainedstablewith time,whilethoseof intermediateinitialcompo
sition(i.e., 50%A plus50%D) didnot.All of thesedata(growthkinetics, MATERIALS AND METHODS
zonality,compositionalstability)indicatethat the growthpropertiesof
heterogeneoustumorsare verycomplex.
Tumor Lines. We have previously described in detail the DLD-1
INTRODUCTION
The concept of intrinsic cellular tumor heterogeneity is well
established and well described (1). Consequently, investigations
are being made into the implications of intraneoplastic diver
sity. In particular, the concept of an "intratumor ecology"
exhibiting clonal interactions (2-8) is thought to be an impor
tant component of neoplastic growth. Also, it has been shown
that the architecture of heterogeneous tumors displays "zonal"
properties (e.g., the exhibition of melanotic and amelanotic
regions within an individual tumor) which are thought to be
important for the long-term maintenance of intratumor diver
sity (9). There are therefore two interlocking aspects of intra
tumor heterogeneity that must be studied, i.e., the potential
interactions between neoplastic subpopulations, and the local
ization and distribution of these subpopulations.
We have recently published data on appropriate experimental
conditions for the enzymatic disaggregation of xenograft solid
tumors grown from pure or admixed clonal subpopulations
from a heterogeneous human colon adenocarcinoma (10). In
this work, we also showed that the relative percentages of the
two neoplastic subpopulations used (designated as clones A and
D) in AHTs3 produced from an initial injection of 50% A:50%
D cells were not stable. Marked enrichment in one of the cell
types (clone D) occurred with increasing time postinjection
(increasing tumor age), resulting in neoplasms composed of
approximately 10% A and 90% D cells. This appeared to
indicate a preferred tumor subpopulation composition.
To further experimentally define the compositional stability
of AHTs we have extended this initial excision assay work to
Received 6/5/86; revised 10/29/86; accepted 11/12/86.
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 in
accordance with 18 U.S.C. Section 1734 solely to indicate this fact.
' Supported by American Cancer Society Grants PDT 243A and IN-45Z.
2 To whom requests for reprints should be addressed, at Department of
Radiation Medicine and Biology Research, Rhode Island Hospital, 593 Eddy St.,
Providence, RI 02902.
3 The abbreviations used are: AHT, artificial heterogeneous tumor; CFE,
colony-forming efficiency; CC, carrying capacity; CY, cell yield.
tumor system from which the clone A and clone D subpopulations were
obtained (12-16). Briefly, the original tumor specimen obtained at
biopsy was histologically heterogeneous, and the cell line established
from it was designated as DLD-1. The A and D subpopulations were
obtained by soft agar cloning of the DLD-1 parent line. These lines are
distinct in morphology, in chromosome number, and in their responses
to a number of chemical and physical agents (12-14, 16, 17). In vivo,
clone A cells produce poorly differentiated tumors, while the D cells
produce moderately differentiated colon cancers. Our results to date
indicate that the clone A and D subpopulations are responsible for the
morphological heterogeneity observed in the parent neoplasm (13, 15,
18). The clone A and D tumor lines are maintained in tissue culture in
our laboratory according to previously published procedures (13, 16,
17), and they are replenished from frozen stock every 3 to 4 mo.
Tumor Disaggregation Procedures. We have previously published in
detail the procedures for disaggregation of AHTs (10). In the studies
reported here, we disaggregated solid tumors at approximately 3-day
intervals throughout the growth period. The neoplasms were excised,
and 6 (tumor weight, <700 mg) or 12 samples (tumor weight, >700
mg) were taken based on previously published sampling procedures
(10). Samples were minced by scalpel, enzymatically dissociated (0.5%
trypsin-EDTA, 40 min, 37"C; Grand Island Biological Co., Grand
Island, NY), and counted by hemacytometer; and single cells were
seeded into 60-mm plastic dishes (Becton-Dickenson Labware, Ruth
erford, NJ). Colonies developed at 37°Cwhile in a humidified incubator
(NAPCO, Portland, OR) with a 95% air-5% CO2 environment for
about 14 days. Colonies were then fixed and stained using 0.5% crystal
violet in absolute methanol, and colonies containing more than 50 cells
were counted by eye for estimation of the overall CFE from each
sample.
Each colony was visually inspected using phase-contrast microscopy
during the course of development and characterized as being of either
clone A or clone D morphology, as each colony type has a unique
appearance. Photomicrographs of these clone A and D colonies have
appeared in several publications (12, 13). To ensure the validity of this
procedure, we selected colonies of each morphological type on a random
basis from a number of different dishes and from different tumors
disaggregated on different days. Individual colonies were trypsinized
after isolation using sterile microwells, and the cells were transferred
to a 25-cm2 flask (Becton-Dickenson Labware, Rutherford, NJ) and
allowed to proliferate until a sufficient number were available for
karyotyping. The cultures were treated with colchicine to collect mitotic
cells, which were treated with hypotonie salt solution, vitally stained,
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GROWTH
PROPERTIES
OF HETEROGENEOUS
and spread on glass slides. The chromosome content of the cells was
determined using a x 100 dry objective. Because clone D cells contain
45 to 46 chromosomes while clone A cells contain 70 to 90 chromo
somes (13), it was possible to absolutely determine the ancestry of each
colony and to correlate this with the morphological assessment. In no
case was a colony of mixed chromosomal content noted, and in no case
was there any discrepancy between the morphological and the karyotypic assessment of colony identity. We were therefore confident that
not only could the overall CFE from each tumor be measured, but that
we could also determine the relative proportions of clone A and D cells
as a function of time postinjection for each admixture condition.
Sampling Procedures and Mathematical Techniques. The sampling
procedures have been previously described (10) and were based on the
design of Wallen et al. ( 19). Briefly, 6 to 12 (generally 12) samples were
taken from each tumor for cell yield, compositional, and clonogenic
studies. We endeavored to distribute these samples throughout the
tumor volume so as to measure, as "randomly" as possible, the geo
metrical distribution of cell types in the tumor. It is important to note
that we could determine the actual proportions of A and D cells in
these samples.
Dixon and Massey (20) have described techniques for sampling
dichotomous populations and fitting observed proportions to normally
distributed curves. In the fitting procedure, the two members of the
sample populations are assigned values of either 0 or 1 (i.e., either clone
A or clone D), and an estimate of the proportion of either type in the
total population is made. In this approach, it is possible to derive a
normal distribution (with the parameters, ¡t,a2) for the distribution of
sample proportions. Estimates for the sample distribution parameters
I//, <r2)are based upon the population proportion, variance, and sample
size. The specific question that can then be addressed is whether the
clonal tumor subpopulations (A and D) which are initially injected in
a homogeneous mixture remain homogeneously distributed throughout
the tumor volume with increasing tumor age. If not, one would predict
the appearance of "zonality" as shown by Fidler and Hart (9). If this
hypothesis is correct, the distribution of standard normal deviates
derived from the tumor samples should itself be standard normal.
Goodness-of-fit criteria for fitting observed data to the normal distri
bution are given by Dixon and Massey (20) using the x2 statistic.
TUMORS
plated into 60-mm2 plastic tissue culture dishes (Becton-Dickenson
Labware, Rutherford, NJ), with 5 ml of complete RPMI-1640 medium,
and colonies were allowed to develop. As clone A and clone D colonies
have distinctly different morphologies as described previously, it was
possible to scan the developing colonies (x 10 magnification, phasecontrast microscopy) to identify them as being either clone A or clone
D colonies, and to determine the relative percentage of each. As the
colony-forming efficiencies of these cells as determined from exponen
tially growing cultures are essentially the same (about 60%), these
visual scans yielded the above quoted values of the actual percentage of
A:D cells injected. Control experiments involving plating of various
percentages of A and D cells in vitro yielded clonogenic results always
consistent with the independent CFEs of the two cell lines.
Measurement of Tumor Size. The solid tumors were measured by
calipers in two orthogonal diameters, and the volumes were calculated
using the formula for a prolate ellipsoid
V (mm3) = L x
where L and W are the major and minor diameters (in mm), respec
tively. We have used this technique in previous work (21). The average
volumes along with standard errors for each tumor group were then
plotted as a function of time to obtain the tumor growth curves. Volume
measurements began at about Day 7 postinjection and extended over
the next 30 to 35 days. All measurements for all tumor groups were
made by a single individual. The experiments done on the 7 different
admixture conditions constitute a more complete verification experi
ment of preliminary data on compositionally dependent tumor growth
that has been previously reported (22). These previous data were
performed on admixtures that were identical in composition to the
work done on tumor disaggregation (i.e., 9% A:91% D; 50% A:50% D;
and 88% A: 12% D).
Analysis of Tumor Growth Curves. We used the classical Gompertz
equation (11) to describe the tumor growth kinetics, which in closed
form is
Nft)
Therefore, we can test the null hypothesis by fitting the derived standard
normal variâtesto the normal distribution with a mean of zero and a
variance of one. If the x2 statistic is greater than the critical value (95%
confidence limits), we may accept the alternate hypothesis, i.e., that the
distribution of proportions observed from the AHTs does not fit a
normal distribution, and, from that, infer the subpopulations were not
mixed homogeneously and that the tumor was indeed "zonal."
Production of Xenograft Tumors. Mice bearing the nu/nu gene on an
outbred Swiss background were obtained from the Charles River Breed
ing Laboratories, Wilmington, MA, and were maintained in the Animal
Resource Facilities of Brown University, Providence, RI. Mice were
kept in a laminar flow hood under specific-pathogen-free conditions,
with sterilized food, bedding, and water. Mice of both sexes, approxi
mately 5 to 7 wk of age, were used in the studies.
At the time of injection, exponentially growing tumor cells were
enzymatically removed (0.03% trypsin-EDTA; GIBCO) from plastic
flasks and resuspended in Hanks' basic salt solution (GIBCO). A total
of 1 x IO7 cells was then injected into the upper hip region in a total
volume of 0.25 ml. Mice were ear tagged for individual monitoring and
were separated into various groups on a random basis.
Solid tumors were obtained after injection of (a) either pure clone A
or clone D cells alone, (*) a 90% A: 10% D admixture, (c) a 75% A:25%
D admixture, (d) a 50% A:50% D admixture, (e) a 25% A:75% D
admixture, or (/) a 10% A:90% D admixture. The composition of
these injection admixtures was verified in two ways. First, an aliquot
of cells from the initial admixtures was counted, and cell volume was
determined using a Model ZM Coulter Counter (Coulter Electronics,
Hialeah, FL). As clones A and D differ significantly in size when
growing exponentially, plots of the cell volume distribution indicated
that approximately the correct number of cells of each type has been
injected as indicated by integration of appropriate regions under the
cell volume curve. Second, cells from the initial admixtures were also
- exp(-At)]
Intuitively, this equation states that a population of cells, represented
by the number \ (r) at time i. will grow exponentially at the instanta
neous rate of g(t). However, in the Gompertz formulation of growth,
this initial growth rate (&,) is itself decreasing exponentially at a
constant rate ut I (the so-called retardation factor). A standard deriv
ative-free nonlinear regression package (BMDPAR) (23) was used to
fît
the observed data to the Gompertz equation using a weighted leastsquares estimate with the weighting factor being equal to the variance
of the observations at each step. The program generates a set of
estimates for each of the 3 parameters which minimizes the weighted
residual sum of squares from the fitted data. Other obtained results
include the asymptotic standard deviations of each parameter estimate.
Standard statistical techniques were used to test for significant differ
ences among these kinetic parameters for the various admixed and
homogeneous tumor xenograft conditions.
We also calculated a value designated as the asymptotic final volume
or CC of the various tumor conditions. The value is determined by
letting V(r) approach infinity and is calculated as
CC = JV„exp(g„//0
RESULTS
Tumor Disaggregation Studies. In Fig. 1,1.we show data for
the CYs obtained from either pure clone A or clone D tumors
as a function of time postinjection. There is an increase in CY
for both which reaches a maximum of 0.8 to 1.0 x 10s cells/
mg at about 30 to 35 days. After this time CY decreases, but
clone A neoplasms show a more rapid drop in CY between 30
and 40 days postinjection with a more or less constant value of
CY thereafter. At 60 days, the CY values are approximately
equal (about 2 x IO4cells/mg). Using the data from Fig. I,i. it
1046
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GROWTH
PROPERTIES
OF HETEROGENEOUS
TUMORS
CLONE A + CLONE D (9:91)
5
10
o
m 10
10
(predicted yield)
ui
O
O
5
i
I
I
10
15
20
I
I
25
30
35
40
45
DAYS POSTINJECTION
L-
50
1-
55
1
60
65
101
o
5
10
15
18
CLONE A + CLONE D (50:50)
20
I
I
I
25
30
35
40
45
DAYS POSTINJECTION
50
55
60
65
CLONE A + CLONE D (88:12)
m 10
/
ni
U
10
10
(predicted
15
20
yield)
25
30
35
40
DAYS POSTINJECTION
45
50
60
70
80
3
10
10
15
25 25 55 35 40 45
DAYS POSTINJECTION
50
55
60
65
Fig. 1. Cell yield (cells/mg) for either pure clonal tumors (A) or artificial heterogeneous tumors (B to D) enzymatically disaggregated, as a function of time after
initial tumor cell injection. In B to D, a predicted cell yield is indicated (dashed lines) based on the data from the pure clonal tumors (A). Bars, SE.
is then possible to predict what the cell yields should have been
from the various AHTs, and these data are shown in Fig. l, B
to D. Generally, the CY data from the AHTs are consistent
with predicted values (indicated by the dotted lines), although
the CY value in the early sampling period is always higher than
the predicted values. A particularly good correspondence be
tween predicted and actual values is illustrated by the 88%
A: 12% D tumor data in Fig. ID.
In Fig. 2A, the CFEs of cells from disaggregated pure clone
A and D tumors are shown. The CFE of these neoplasms is not
equivalent over the sampling period. Clone D tumors at all
times show a higher CFE than do clone A tumors, with maxi
mum values of about 20% and 15%, respectively, being reached
at about 20 days postinjection. Also, the CFE of clone D tumors
remains at about this level for the entire sampling period, while
the CFE of clone A tumors begins to steadily decrease at about
30 to 35 days, reaching a value of about 3% by 60 days
postinjection. The data shown in Fig. \A can then be used (as
with the CY data) to predict the CFE values that should have
been attained from the various AHTs, depending on the initial
composition. The data on the overall CFE (i.e., without discrim
ination as to colony ancestry) from the AHTs are shown in Fig.
2, B to D. Generally, as with the CY data, the relationship
between predicted and observed CFE is good.
In Fig. 3, we show the specific tumor composition (i.e., the
actual clonogenic survival of A and D cells) of each type of
admixture as a function of time postinjection. Again, a set of
predicted values can be made, based on the CFE values from
each pure tumor type (Fig. 2A), and on the initial starting
percentages of A and D cells in the various AHTs. In Fig. 3A,
data for the 9% A:91% D tumors are shown, and the predicted
percentages of A and D colonies agree well with the observed
values. The percentages remain fairly constant over the duration
of the sampling period, although there is some enrichment of
clone D cells at long times postinjection, consistent with the
decrease in the CFE of clone A cells (Fig. 2/4). This does not
mean that the actual number of clone A cells is decreasing: only
that the relative percentage of A:D cells is changing. The data
from the 50% A:50% D tumors are shown in Fig. 3B. Here,
deviation from the expected result is seen, as the relative per
centage of clone A colonies decreases more rapidly than pre
dicted and approaches a constant value of about 10% by about
Day 40 postinjection as we have previously pointed out (10).
The data from the obverse mixture (88% A: 12% D) are shown
in Fig. 3C, and again significant deviation from expected re
sponses is seen. Instead of a rapid reassortment to an intratumor situation where clone D cells predominate (cf. Fig. 2A)
there is the establishment of a constant, stable percentage of
clone A and D cells which is not different from the composition
of the initial injection admixture.
Tumor Zonality Studies. In testing the spatial zonality of the
tumors, we established a statistical hypothesis about the distri
butions of the normalized variâtes.Our assumption was that
these were distributed in accordance with a standard normal
distribution, and we tested that hypothesis by using a standard
goodness-of-fit criteria (20). The results of this analysis are
plotted in Fig. 4. Fig. 4A is a theoretical expected distribution.
The plot represents the number of expected proportions ob
served on each day as a function of standard deviation (a = 1
by definition). We segmented the standard deviation range
(-2.2, 2.2) into intervals of length 0.2. Fig. 4B plots the
accumulated normalized variâtesobserved in the "natural" tu-
1047
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GROWTH PROPERTIES OF HETEROGENEOUS
TUMORS
100
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DAYS POSTINJECTION
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10
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DAYS POSTINJECTION
Fig. 2. Colony-forming efficiencies (percentage) for either pure clonal tumors (A) or artificial heterogeneous tumors (B to />} after enzymatic disaggregation, as a
function of time after initial tumor cell injection. In B to D, a predicted overall CFE is indicated (dashed lines) based on the data from the pure clonal tumors (A).
Bars, SE.
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Fig. 3. Cellular composition of artificial heterogeneous tumors originally injected with 9% A:91% D, 50% A:50% D, or 88% A: 12% D admixtures (A to Q as a
function of time. The open and closed circles indicate the average composition of A and D cells, respectively, found in disaggregated tumors, while the dashed line
indicates the predicted composition based on cell yield and overall clonogenic data (Figs. 1 and 2). (B is based on previously published data: published with permission
from Invasion & Metastasis).
mor mix (i.e., 9% A:91% D). At Day 35 postinjection, we can
reject the null hypothesis (i.e., the distribution is standard
normal) at a 95% confidence level. Fig. 4C shows the results
obtained from the 50:50 admixture. This condition is highly
unstable with respect to composition, and the goodness-of-fit
criteria reject the null hypothesis at Day 18. Fig. 41) shows the
results obtained from tumors grown from an obverse mixture
(88% A: 12% D). Using the goodness-of-fit criteria, we again
reject the null hypothesis, this time at Day 21.
In Vivo Growth Kinetic Studies. In Table 1 we have summa
rized the best fit Gompertzian parameters from the volumetric
growth curves for the various tumor conditions studied along
with their respective asymptotic standard deviations. From
these results, we can then infer that the initial size, initial
growth rates, and retardation rates for the various tumor pop
ulations vary significantly with composition. Using the Gompertz data listed in Table 1, it is possible to derive the carrying
capacity of these various tumor conditions. These values are
plotted in Fig. 5 and are, respectively, 8,870, 10,200, 18,720,
12,020, 12,440, 5,360, and 6,720 mm3, respectively, for the
pure A, pure D, 10% clone A:90% clone D, 25% clone A:75%
clone D, 50% clone A:50% clone D, 75% clone A:25% clone
D, and 90% clone A: 10% clone D tumors. These data clearly
show a statistically significant dependence of the final predicted
1048
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GROWTH PROPERTIES OF HETEROGENEOUS TUMORS
2
10
1
15
1
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o
f
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O
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o.
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K
O
10
20
40
60
80
100
PERCENTAGE OF CLONE A
Fig. 5. Plot of the carryingcapacity(asymptoticfinal volume)for each of the
xenograftsolidtumors as a function of the original percentageof cloneA cells in
the tumor.
stroma (the so-called tumor bed effect) on the expression of
tumor heterogeneity.4
Sigma unit«
Fig. 4. Plots of the distributions of percentages of A and D cells found in
artificial heterogeneous tumors as a function of time postinjection. In .-(, a
theoretical distribution which is applicable to all experimental admixtures is
shown,illustratingthat if the subpopulationsof cellswithin artificialadmixtures
were homogeneouslymixed, a Gaussian distribution in time would be expected
from disaggregationstudies (,/). In B to /'. the observed distributions for 9%
A:91% D (B), 50% A:50% D (Q, and 88% A:\2% D disaggregatedtumors are
shown. Note that the distributions are not Gaussianlydistributed,indicatingthe
presenceof zonal heterogeneity.
Table 1 Gompertzianparameters of growthfor artificial heterogeneoustumors
producedfrom varyingproportionsof twohuman colonadenocarcinoma
subpopulationsCellular
parameterJV„
compositionof
(days'1)0.409 (days'1)0.081
(mm3)56.9
tumorClone
xenograft
3.94"26.5
±
0.0140.465
±
0.0020.084
±
A cells only
(25)»
±0.001
±0.009
90% A + 10%D (31)
±1.33
0.307 ±0.022 0.070 ±0.004
75% A + 25% D (32)
66.8 ±8.66
181.9±11.0 0.300 ±0.013 0.071 ±0.003
50% A + 50% D (28)
232.4 ±18.6 0.292 ±0.019 0.074 ±0.005
25% A + 75% D (29)
243.2 ±12.5 0.291 ±0.011 0.067 ±0.003
10%A + 90% D (30)
93.2 ±9.63Go 0.432 ±0.024A 0.092 ±0.004
Clone D cells only
(25)Gompertz
" Mean ±SD (asymptotic) derived from a nonlinear parameter estimation
package(BMDPAR)(23),representingthe SD of eachestimator givenan infinite
samplesize.
bNumbers in parentheses,number of samples from which the Gompertzian
parameterswere derived.
tumor volume on the relative percentage of A or D cells in
these neoplasms which cannot be explained as simple algebraic
averages of the percentage of compositions. A linear leastsquares regression analysis of the dependence of (log) CC upon
the percentage of line A cells in the tumor (excluding the pure
A or D tumors) yields the equation, CC (mm3) = 4.2300 0.0060 x (% of A cells), with a correlation coefficient of-0.907
(P < 0.05) (20). All of these observations on volumetric growth
and compositional stability in the AHTs have been replicated
in studies of the influence of X-ray damage to normal tissue
DISCUSSION
The primary finding of this study is that there are differences
in the kinetic parameters of growth among art ¡fidaiheteroge
neous tumors that (a) are dependent on the relative initial
percentages of clone A and D cells used to produce the solid
neoplasms, and (b) cannot be predicted on the basis of growth
kinetic data from the tumors produced by either clone A or D
cells growing independently (22). These results are well exem
plified in Fig. 5, where the calculated asymptotic final volumes
are shown as a function of the composition of the initial
injection mixture, and the dependence of volume on the per
centage of clone A cells is clear. It should be noted that the
original histology of the parental 1)1,1)1 adenocarcinoma was
predominantly of the well-differentiated D donai type with a
morphological minority of the poorly differentiated A donni
type (13). It was estimated that "the clone A subpopulation,
(comprised) not more than 10 percent of the parent DLD-1
line" (13) (i.e., a 10% A:90% D admixture). While the relation
ship of this observation to our in vivo experimental findings
may be fortuitous, it is worthy of special notice that the 10%
A:90% D artificial heterogeneous tumors seem to have a growth
advantage in terms of final attained volume (Fig. 5), as com
pared to any other condition (22). Also, the relationship of the
asymptotic final volume to intratumor compositional stability
is of interest. The two extreme compositional admixtures (i.e.,
90% A plus 10% D or 10% A plus 90% D) have significantly
different calculated final volumes as compared to the volumes
of the pure A and D tumors, but are compositionally stable
(Fig. 3, A and C). In contrast, the tumors comprised of 50% A
plus 50% D cells have final volumes which are not different
than either the pure A or D tumors, but are compositionally
unstable (Fig. 3B).
4J. T. Leith, S. F. Bliven, L. E. Faulkner, and S. Michelson, manuscript in
preparation.
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GROWTH
PROPERTIES
OF HETEROGENEOUS
Our data may therefore indicate that some type of "donai
interactions" exists. However, as Heppner (7) and Heppner and
coworkers (24-26) have pointed out, if clonal interactions do
exist, multiple mechanisms are likely involved. While some of
these mechanisms may require cell-cell contact, others may not,
although an appropriate environment (e.g., solid tumor, sphe
roid, artificial capillary culture) appears needed for their opti
mum expression. In this regard, in a study relevant to our work
(27), based on the analysis of diploid and tetraploid subpopu
lations from an Ehrlich ascites tumor line, Janssen and Revesz
showed that a balance was maintained between subpopulations
which appeared to be related to the combined volume of the
diploid and tetraploid cells. Makino (28) also showed that two
different ascites tumor lines could apparently control each
other's growth rates. Miller et al. (29) have shown potentiation
of growth of a mouse mammary line (('I-SI) isolated from a
hyperplastic nodule by a tumor subpopulation (68H) isolated
from a different heterogeneous mouse mammary adenocarcinoma. Miller et al. (3) have also demonstrated that some mouse
mammary adenocarcinoma subpopulations can alter the take
rate, latency period, or actual growth kinetics of other subpopulations in vivo. A similar effect has been shown by Tofilon et
al. (30) who cocultured a fast-growing line of rat brain tumor
cells (9L) with a slower-growing variant (9LR3) using spheroids
and found that the slow-growing line would attain the growth
rate of the 9L line. In general, growth rate effects in admixed
situations have previously indicated that one typically notes
that either "slow-growing" subpopulations will speed up, or
"fast-growing" subpopulations will slow down (7, 26, 31), al
though the direction of such changes is not a priori predictable.
Our quantitative results do not agree with these quantal re
sponses.
While we do not know the mechanism(s) by which the com
position-dependent changes in growth rates or carrying capacity
(Fig. 5; Table 1) are produced, there are a number of nonexclu
sive possibilities. As stated by Heppner et al. (31), "the hetero
geneity of the tumor cell populations is mirrored by the heter
ogeneity in the infiltrating populations." In this regard, Rios
TUMORS
of in vivo coculturing (i.e., AHT) affected the transition between
the quiescent and proliferative states, differences in solid tumor
growth kinetics could be envisaged. Concomitantly, differences
in other parameters, such as the potential doubling time or cell
loss factor, may be involved, particularly as Watson (36) has
shown that these factors are strongly dependent on tumor
volume.
As tumor cells can promote formation of new blood vessels
via endogenously produced angiogenesis factors (37), potential
differences in this ability between clone A and D cells may
impact on vascular structure and function. Related to this is
the suggestion by Burton (38) and Summers (39) that differ
ences in tumor growth rates can be due to vascular insufficiency
resulting in such conditions as lowered extracellular pH, local
hypoxia, and/or focal necrosis. Rofstad (40) demonstrated
strong correlations between morphometrically determined vas
cular parameters in human melanoma xenograft tumors and
parameters such as doubling time, growth fraction, and cell loss
factors. Also, Goldacre and Sylven (41), Lewis et ai. (42), and
Forschen et al. (43) have demonstrated that the presence of a
large volume of necrotic tissue within tumors can lead to volume
growth curves which overestimate the true viable tissue volume
by a large extent. This effect was particularly evident in large
tumors and therefore is relevant to our calculations of asymp
totic final volumes (Fig. 5) (22).
In summary, we have produced data indicating that the in
vivo growth kinetics of AHTs in this human colon adenocarci
noma model system is quite different from what would be
expected on the basis of the behavior of the individual A and D
subpopulations. We have indicated a number of processes
through which such unpredictable behavior may be produced,
which will be the basis for further research.
ACKNOWLEDGMENTS
We wish to thank Dr. Daniel L. Dexter and Dr. Arvin S. Glicksman
for helpful discussions and critical advice during the execution of these
experiments and in the preparation of the manuscript.
(32) has shown in heterogeneous mouse mammary tumors
qualitatively and quantitatively different T-lymphocyte popu
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Growth Properties of Artificial Heterogeneous Human Colon
Tumors
John T. Leith, Seth Michelson, Lynn E. Faulkner, et al.
Cancer Res 1987;47:1045-1051.
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