Supplemental Text and Methods
Christopher D McFarland, Julia A Yaglom, Jonathan W Wojtkowiak, Jacob G
Scott, David L Morse, Michael Y Sherman, Leonid A Mirny
Table of Contents
Predictions of the Deleterious Passenger Model and their evidences
Deleterious passengers slow and can reverse cancer progression
Fitness reduction is ~0.1 – 1% per passenger
Clinical cancers are dominated by driver events
High mutation rates increase the passenger:driver ratio & inhibit carcinogenesis
Deleterious passengers especially limit metastatic progression
2
2
3
3
4
6
Generation of human breast cell lines with various passenger loads
8
Fitness assays
Measuring proliferative fitness
Measuring metastatic fitness
8
8
8
Mouse models of breast cancer with differing mutation rates
9
Genotyping and Genetic Analysis
Human cell line genotyping
Mouse tumor genotyping
Identification of driver CNAs in cell lines and mouse tumors
9
10
11
11
References
13
1
Predictions of the Deleterious Passenger Model and their
evidences
Here, we briefly justify the predictions of the Deleterious Passenger Model tested
in this manuscript. For a rigorous description of dynamics, please refer to 1 and 2.
Other researchers also preformed a meta-analysis of evolutionary models of
tumor progression, including this model, that tested each model’s ability to
predict the temporal order of driver events3.
Deleterious passengers slow and can reverse cancer progression
We found that a lesion’s stationary population size N can be approximately
described as follows:
(
dN
» N 2 m Td sdp (sd , N, m ) - Tp spp (-sp , N, m )
dt
)
(1)
Here, t denotes the time of progression in cell generations,  denotes the
mutation rate, Td/p denotes the number of mutable driver/passenger loci in the
cancer genome, sd/p denotes the change in cell fitness (proliferative potential) due
to a driver/passenger, and  (s, N, ) denotes the probability that a mutation
fixates in the population (i.e. the effect of natural selection). Overall, this equation
summarizes the ‘balance’ or tug-of-war that we observe between the
accumulating drivers (left term) and deleterious passengers (right term) in
simulations. The effect of drivers N2 Tdsd (s, N, ) denotes the rate at which new
driver mutations enter the population (NTd), multiplied by a driver’s effect on
population size if fixated (Nsd—i.e. ‘hard selection’), multiplied by the driver
fixating  (sd, N, ). The effect of passengers is, essentially, the same except their
effect on population size is negative (Nsd).
Natural selection  (s, N, ) is a profoundly complicated force and depends upon
many properties of the mutation and population, including: (1) the selective
benefit or costs of the mutation s, (2) the current population size N, and (3) the
mutation rate  or, more specifically, the number of segregating mutations
already in the population. In a previous publication2, we present several
approximations for the effects of natural selection.
This equation demonstrates that deleterious passengers slow tumor growth
dN
and will reverse the mean growth rate when
dt
Tp spp (-sp , N, m ) > Td sdp (sd , N, m ) . Because selection against passengers is minimal
near this tipping-point (i.e.  (sp, N, ) ~ 1/N, population collapse occurs when the
Ts
tumor population declines below a critical size: N * = p p2 identified earlier 2 and
Td sd
explained in somewhat greater detail below.
2
Fitness reduction is ~0.1 – 1% per passenger
Eq. 1 can be solved in terms of the number of accumulated drivers
nd = ò mTdp (sd , N, m )dt and number of accumulated passengers
np = ò mTpp (sp , N, m )dt as follows:
(
N(nd ,np ) = N 0 sd nd - sp np
)
(2)
Here, N0 is the initial population size of the lesion. This very simple relationship
can then be compared to tallies of drivers and passengers in real human cancers
to infer values of sd and sp. This was first done in a previous publication2 that
found sp ~ 0.001 – 0.01. However, this estimate assumed that all passengers have
similar values of sp, whereas in the main text we show that passenger alteration
length and ploidy affect deleteriousness. Hence, we repeated our analysis using
the improved metric of passenger load.
As with our analysis of passenger load metrics in the main text, we found that
human tumor genomes were best fit by a model that assessed passenger load
using a “Capped CNA Volume” measure (Figure S1). We fit observed quantities
of {nd, np} in sequenced breast cancers4 to Eq. 2 using all three measures of
passenger load described in the main text. Somatic driver CNAs were reported in
Table S4 of the initial sequencing study4. These tallies were then compared to
Capped CNA Volume (which correlated most strongly), CNA Volume, and a
simply tally (which correlated least strongly; Figure S1). From this analysis, we
estimate the wpsp:sd ratio to be 0.0038 95% CI [0.0033, 0.0045] per capped MB.
Here, wp is the mean weight of a passenger, or 4.5 Capped MB. If we borrow our
estimate of wpsp in the main text of -0.027 per Capped MB, 95% CI [-0.0213, 0.056], then we obtain a rough estimate of sd = 0.14 95% CI [0.06, 0.21]. Because
this value is actually fairly similar other estimates and measurements of sd 2,5,6,
our calculations suggest that the value of sp for cells grown on a glass plate may
actually be somewhat similar to values of sp within a human breast.
Clinical cancers are dominated by driver events
Natural selection tips the evolutionary balance towards driver accumulation
events in larger tumor populations. Because our predictions are only qualitative
in nature, it is sufficient to consider several limiting situations of natural selection:
lim p (s, N, m ) ® 0
N®¥
s<0
m <<1
lim p (s, N, m ) ®
N>>1
s>0
m <<1
s
1+ s
lim p (s, N, m ) = lim p (s, N, m ) ®
m ®¥
p (s1 > 0, N, m ) ¥
s®0
1
N
1
¥ p (s2 < 0, N, m ) : "N, m
N
3
Several important properties of natural selection are evident: (i) if a mutation is
deleterious and the mutation rate is relatively small, then natural selection will
prevent it from fixating in the population, given sufficient size; (ii) if a mutation is
advantageous and the mutation rate is relatively small, then it will fixate in the
population once the advantageous clone grows to sufficient size to overcome
genetic drift (thereby making the fixation probability independent of population
size); (iii) extreme mutation rates and mutations with extremely mild effects will
not be affected by natural selection—mutation fixate at a neutral rate: 1 N .
Hence, when population sizes are large, and mutation rates tractable (as is the
case in a typical clinical tumor) advantageous drivers continue to fixate at a rate
proportional to the population size (because more cells are introducing more
drivers and fixation events are independent of population size), yet deleterious
passengers will eventually be weeded-out by natural selection ( p ® 0 )—
eliminating their impact.
High mutation rates increase the passenger:driver ratio & inhibit
carcinogenesis
From the limits above, it is clear that increasing mutation rates interfere with
natural selection. Cells with very high mutation rates contain many segregating
mutations of varying fitness effect. Selection, however, must act on entire cells,
not each mutation, hence deleterious hitchhiking mutations reduce the
advantageousness of a driver mutation and its fixation probability, while
advantageous mutations carry deleterious mutations (that would otherwise be
weeded out) to fixation with them. In effect, elevated mutation rates attenuate the
effect of natural selection; because natural selection increases the accumulation
of drivers and prevents the accumulation of passengers, this change benefits
passenger accumulation and hurts driver accumulation.
As mentioned above, once the mutation rate increases to the extent that
Tp spp (-sp , N, m ) > Td sdp (sd , N, m ) , then population size will decline. However, before
this point growth is positive and proportional to . Hence, increases in mutation
dN
rate can be beneficial to growth to a point. We find this by maximizing
with
dt
respect to :
0=
¶ 2
N m Td sdp (sd , N, m ) - Tp spp (-sp , N, m )
¶m
(
(
)
0 = Td sd (p (sd , N, m ) + mp '(sd , N, m )) - Tp sp p (-sp , N, m ) + mp '(-sp , N, m )
)
Finding the optimal mutation rate now requires a quantitative description of
p (s, N, m ) . For high mutation rates, previous analysis2 found that the following
assumptions worked well:
4
p (+sd , N, m ) » sd - mTp
p (-sp , N, m ) »
1
(i.e. passengers are neutral)
N
With these assumptions, we can identify an optimal mutation rate for tumor
progression (opt):
m (opt) »
sd æ 1 æ
N
1- æ : n = *
æ
2Tp æ n æ
N
This solution is defined using the characteristic population size of the population
identified earlier2. Near the critical population size, this approximation is
unreasonable because (i) it ignores the stochastic properties of progression that
are critical2 and (ii) selection against passengers that would become relevant as
s
m ® 0 . Nonetheless, for large tumors (the focus of this discussion) m (opt) ~ d .
2Tp
2
7
For point mutations, earlier estimates of sd ~ 0.2 and Tp ~ 10 nucleotides suggest
(opt) ~ 10-8 nucleotide-1generation-1—a value that is consistent with prior
simulations7. Mutation rates of this level are observed in cells with a mutator
phenotype7; however, our analyses of both point mutations and copy-number
alterations suggests that Tp is most likely larger than 107 nucleotides (as this
estimate assumes deleterious mutations can only arise within housekeeping
genes, yet all genes seems to be relevant for predicting passenger load, 1 and
Figure S2B). Hence, the optimal mutation rate is mostly likely less than 10-8
nucleotide-1generation-1.
Extending this estimate of the optimal point mutation rate to an optimal copynumber alteration rate is difficult for two reasons:
1. The error threshold should depend on the aggregate rate of deleterious
mutations. Accordingly, the copy-number alteration rate and point
mutation rate form a hyperbolic relationship that is very consistent with our
hypothesis of a maximum tolerable combined mutation rate8.
2. Our assumption that sp is constant (while imperfect for point mutations) is
egregiously inappropriate for CNAs, as we’ve found that CNA fitness cost
is proportional to CNA length, which is power-law distributed. Because the
main term in our solution (sd / 2Tp) results entirely from Robertson-Hill
Interference, and ignores selection against passengers, this solution is
almost certainly inappropriate. Moreover, the Robertson-Hill correction
assumes that passengers are in mutation-selection balance, which
conveniently predicts a mean mutational load that is independent of sp, yet
equilibration time to this balance decreases exponentially with sp.
These concerns are in addition to the specific issues (listed above) that arise
when n ~ 1 and the intrinsic limitations of our mathematical model. For these
reasons, we chose to not make a quantitative prediction for the optimal CNA
mutation rate, and instead search for this optimal rate experimentally. We still
expect the optimal CNA mutation rate to exist, if passengers are deleterious,
5
because both Robertson-Hill Interference and Muller’s Ratchet increase with
increasing mutation rates. Given the hyperbolic relationship between CNAs and
point mutations8 and given the fact that cancers are a rarefied set of
evolutionarily-successful populations, it seemed reasonable to assume that CNA
mutation rates in observed cancers are near optimality (not precisely so, but
within an order-of-magnitude).
Deleterious passengers especially limit metastatic progression
Metastases acquire deleterious passengers during (i) dissemination and (ii) their
evolution from micrometastases to clinical metastases. These two events, in
addition to the deleterious passengers already fixated within the primary tumor,
collectively add to the deleterious passenger load in metastases, enhancing their
effects.
Deleterious passengers acquired during dissemination are akin to hitchhiking
passengers—the subclonal (private) mutations within a disseminating metastatic
clone will automatically fixate in the metastasis, just as subclonal mutations
within a new driver clone hitchhike and fixate during the hard sweep. Thus, the
passenger load acquired during these two events is approximately the same. As
mentioned in the previous section, a population in mutation selection balance
conveniently has a mean number of unfixed passengers of Tp/sp and mean
fitness cost of Tp, so a mutagenic load of this quantity will fixate during
dissemination.
Most passenger, however, are added during micrometastatic evolution. There
are few evolutionary models that speculate about the evolutionary events of
micrometastatic evolution, despite evidence that micrometastatic evolution is the
most inefficient step in metastatic progression9. We previously proposed a
model10 where evolutionary dynamics are identical to dynamics at the primary
site, except either (i) a fraction s of the drivers that accumulated at the primary
site become inert in the environment of the secondary stroma, or (ii) the initial
carrying capacity of secondary stroma is less hospitable than the initial carrying
capacity of the primary site
. Note that drivers can be genetic in origin or
epigenetic (e.g. an Epithelial to Mesenchymal transition). We find dynamics are
mathematically equivalent in either scenario. Because the dynamics are identical
to the dynamics of primary tumors, after a translation in the carrying capacity,
and because the properties of this model of primary tumor evolution was
explored previously2, the number of accumulating deleterious passengers during
micrometastatic evolution np, micrometastasis is2:
6
np, micrometastasis = mTpTcancer (nmetastasis ) , where nmetastasis =
np, micrometastasis » mTp
np, micrometastasis »
N primary N S
Log [ nmetastasis ]
, when nmetastasis << 1
vp
N* N 0
Log [ nmetastasis ]
, when vp = mTp sp
sp
Here, n metastasis denotes the population size of the metastasis relative to the
critical population size of the metastasis (see Deleterious passengers slow and
can reverse cancer progression from above for an explanation of the critical
population size) and is a function of the size of the primary tumor when a seeding
cell disseminates N primary, along with the relative carrying capacities of the
primary and secondary stromal environments. This result is asymptotically valid
only when micrometastatic progression is inefficient (i.e. <<50% of
micrometastases progress to clinical size) and when passenger accumulate at an
effectively neutral rate (see above). Although these approximations are roughly
correct, the explicit, non-asymptotic formalism was specified previously2.
Under these assumptions, the number of accumulated deleterious passengers is
inversely proportional to their deleteriousness and only subtly (logarithmically)
dependent upon other factors. For the value of sp estimated here (~0.01) and a
tumor that grows to 106 cells before spawning a micrometastasis with a critical
carrying capacity of 103, we would expect ~300 deleterious passengers to
accumulate during the evolution of this micrometastasis.
Note that, in our formulation, micrometastases disseminate as only 1 cell, but
then quickly bloom to several hundred (or thousands) of cells at the stromal site.
This assumption, however, disagrees with evidence that small, polyclonal
clusters (>1 cell) can seed metastases11. From a genetic perspective, the clonal
diversity of cells in these seeding cohorts is most important in determining the
success of the metastasis—more diverse seeds should lead to a less stringent
bottleneck and greater likelihood of metastatic success. Consistent with our
paradigm, polyclonal seeds exhibit a greater likelihood of metastatic success in
mouse models11. However, without comprehensive information on the genetic
diversity of seeds it is difficult to make more quantitative statements about
seeding probabilities in polyclonal models. Because many metastases appear to
be monoclonal12 and because this is a topic of scientific debate, we believe it is
still useful to explore a monoclonal model of seeding in quantitative detail.
Micrometastatic evolution takes decades in our model because, after blooming to
a small population, the metastasis must then acquire new drivers that are
beneficial in the new stroma10. This behavior follows naturally from a minimalistic
model of metastatic progression where selection is hard, growth is logistic, and
mutations are rarely beneficial, yet often mildly deleterious; nonetheless, it is also
fully consistent with existing observations of micrometastatic progression 9,13.
7
Generation of human breast cell lines with various passenger
loads
MCF-10A cells (a spontaneously-immortalized, genomically-stable, human breast
epithelial cell line) were used to create our cell lines of varying passenger loads.
A single clone was chosen from this cell line to ensure genomic consistency for
experimentation. Any alterations within this clone were identified as “Ancestral”
and removed from analysis (see Genotyping and Genomic Analysis and Figure
S1). Tumorigenic properties were induced using an activated form of Her2,
NeuT, transmitted via retrovirus and control empty virus (under blasticidin
selection), as in our prior publications14. Her2 expression was confirmed. Two
days post-infection, mild blastocidin (10µg/ml) selection was used to ensure
transformation.
Next, we tested whether Her2-transformed cells exhibit increased level of
induced DNA instability by exposing both a parental MCF10A clone and one of
the MCF10A/NeuT clones to low-dose (sub-therapeutic) doxorubicin, thereby
introducing DNA damage. To accomplish this, cells were treated overnight with 0,
10, 20, and 30nM of doxorubicin, then grown in normal media for 4 days and
then cloned. DNA from these clones was isolated and hybridized on SNP-arrays
(analysis described below). We expected DNA damage to only occur within
Her2-activated cell lines exposed to sufficient doxorubicin because prior analyses
had shown that Her2-activation reduces the expression of major DNA repair
factors, including H2AX15.
Fitness assays
Measuring proliferative fitness
Growth rates, inverse doubling time, were measured by cell counting on a glass
plate for two days.
Measuring metastatic fitness
MCF-10A/Her2-activated cells were treated in-vitro with sub-lethal doses of
doxorubicin to increase mutation load for in-vivo experimental metastatic fitness
studies. Cells were treated with 10 or 20 nM doxorubicin for 16 hours followed
by a 6-day drug free recovery period. Growth rates for both treatment groups (10
nM – 20.38 h and 20 nM – 20.81 h) post recovery were lower than the untreated
control line (18.90 h), as seen in earlier assays.
2.5 x 106 cells with stable expression of firefly luciferase were injected into the tail
vein of female SCID mice (ten per group) and imaged once per week for seven
weeks. Bioluminescent signal was determined for the thoracic region and
reported as mean lung bioluminescence (photons/sec ± SEM). In agreement with
an initial pilot study of MCF-10A/Her2-activated cell lines, increased
bioluminescence was observed by week 4 in control mice representing
successful metastatic tumor formation (Figure 4D). At the conclusion of the
8
study (week 7), lung bioluminescence of control mice was significantly greater (p
< 0.002) than both treatment groups, which were not statistically different from
each other (Figure 4E, p = 0.0923). To better quantify lung metastases in each
group, ex-vivo bioluminescence of surgically resected tumors was collected and
individual metastases counted (Figure 4E, right). A metastatic lesion was
defined as isolated bioluminescent foci. Control lungs averaged 3.3 ± 0.34
metastases compared to 0.11 ± 0.33 and 0.44 ± 0.53 metastases in 10 nM and
20 nM groups respectively. Confirming in-vivo measurements, the number of
metastases in control lungs was statistically greater than both control groups (p <
0.0001).
Mouse models of breast cancer with differing mutation rates
We used a MMTV-neu mouse model of Her2-positive breast cancer to test the
effects of elevated passenger loads on tumor progression. Mutagenic load was
increased by haploinsufficiency in histone H2AX that leads to multiple defects in
repair of single and double strand DNA breaks. This was achieved by crossing
MMTV-neu (F) mice with homozygous H2AX-/- (M) mice to generate neuT+/H2AX+/- progeny, along with control FVB/NJ (M) mice to generate neuT+/-H2AX+/+
progeny.
After tumors had grown to appreciable size, animals were sacrificed and tumors
removed. DNA, for low-coverage DNA sequencing was prepared using methods
described in our previous publication15.
Animal care, experimentation, and sacrifice were conducted humanely in
compliance with ethical standards.
Genotyping and Genetic Analysis
DNA was isolated from individual clones and mouse tumors for genotyping. Most
cell lines were genotyped using Affymetrix Genome-wide Human SNP Array 6.0
(Cat. #901150) courtesy of the Broad Institute’s Genome Sequencing and
Analysis Program, while mouse tumor alterations (and a few cell lines, see Table
S1) were characterized using low-coverage DNA sequencing (Illumina HiSeq
2000) courtesy of the BioMicro Center at MIT.
Metastatic samples were not genotype because, after the first experiment, we
found that growth rate correlated more closely with [Doxorubicin] exposure (R = 0.89) than even our best-calibrated passenger metric (Capped CNV volume, R =
-0.73). Hence, Doxorubicin exposure alone can be used to estimate the load of
passenger mutations in precancerous populations more effectively than modern
genotyping measurements. Presumably, this is either because modern
genotyping methods introduce significant errors or because many CNAs are subclonal and undetectable when sampling entire population.
9
Human cell line genotyping
SNP probe intensities were quantified and DNA copy number was determined by
segmenting SNP probes along the genome into tracks of equal copy number
using the GLAD software package, an adaptive weights smoothing algorithm16.
CNAs were then identified from these tracks using a simplified calling rubric.
Histograms of background-subtracted Log2 mean segment intensity were
generated and then smoothed using a Gaussian kernel. Each sample’s
histogram exhibited 3-4 well-defined peaks, separated by approximately integer
distances. Hence, these peaks correspond to the various ploidy levels that an
alteration could have. Mean track intensities were scaled by a multiplicative
constant such that the second peak, always the sample mode, was assigned a
ploidy value of 2.0 (diploid). No signs of aneuploidy were evident in the samples.
All track were then assigned ploidy by rounding their intensity to the nearest
integer, baring one exception. If a track (1) contained only 1-2 probes, (2) was
flanked on the left and right by tracks with the same ploidy, and (3) was within 1.0
intensity of its flanking assignment, the track was merged with its flanking
assignments (e.g. a very short track with a scaled signal intensity of 3.72, and
neighboring tracks assigned a ploidy of 3, would be merged with its neighboring
tracks to forge one long CNA of ploidy 3, rather than rounded to a ploidy of 4.
CNA were then defined as uninterrupted tracks of ploidy other than diploid.
Two calling parameter sets were then used to call CNAs: a high specificity set
and a high sensitivity set. The later proved more reproducible and consistent with
mutagen exposure (Figure S1). In the high specificity condition, at least three
continuous non-diploid probes of mean intensity >2.75 or <1.25 were required to
define a CNA. In the high sensitivity condition, only two continuous non-diploid
probes of mean intensity >2.5 or <1.5 were required.
We chose somewhat ad hoc methods to call CNAs, rather than existing software
packages, because (i) our samples were clonal and did not need stromal
rectifications procedures that are intrinsic to existing software packages, (ii) we
were intently interested in developed a good passenger metric that considered
both specificity and sensitivity in approach, (iii) our objective (to identify genomewide passenger load for each sample) was significantly different from the goal of
existing methods (to identify specific driver alterations across cancer samples),
and (iv) existing methods were notoriously poor (with concordance <50%17) and
yielded poor results in preliminary analyses.
Ancestral CNA (existing in the cell lines prior to experimentation) were removed
by identifying an ancestral genome using a maximum parsimony approach. This
ancestral genome was defined by CNAs that were shared (equal ploidy and
≥75% overlap by genomic start/end sites) among all un-mutagenized and untransformed (0 nM Dox/pBABE) MCF-10A clones. If a CNA was shared (defined
above) between a sample of interest and the ancestral genome, then it was
excluded from our tally of DNA instability, as we concluded that this alteration
occurred prior to mutagenesis (Figure S2).
Analysis for the few cell lines processed via low-coverage HiSeq DNA
sequencing (identified in Table S1) was done in a similar manner as the mouse
10
tumor genotyping, described below. Reads were identified and mapped to the
human genome (HG19) using the BMC/BBC 1.3 pipeline18. On average, 16.8 ±
1.2 million reads were mapped. CNAs were then called using CNV-seq19. ‘High
specificity’ (i.e. stringent) mutation-calling parameters for these samples
corresponded to the algorithm’s default parameters (log2-threshold = 0.6, p =
0.001, minimum window = 2; adaptive window size), while ‘high sensitivity’ (i.e.
permissive) mutation-calling parameters were less stringent (log2-threshold =
0.5, p = 0.05, minimum window = 2). Once again, the high sensitivity parameters
correlated more strongly with doxorubicin concentration (Table S1). Finally,
ancestral CNAs were removed from these samples using the ancestral genome
defined above.
Mouse tumor genotyping
Mice breast tumor genomes were genotyped using HiSeq DNA sequencing and
the CNA-calling algorithm cn.MOPS20 (Table S2). HiSeq reads were identified
and mapped using the BMC/BCC 1.3 pipeline18. Reads were mapped to the
mouse genome (MM9) using Bowtie 221. On average, 26.0 ± 3.3 million reads
were mapped per sample (~0.4x coverage). Copy number variation was then
assessed using cn.MOPS20. Default calling parameters for cn.MOPS were used
because we sequenced fewer mouse tumors than human cell lines and we felt
that this was insufficient sample size to justify any deviation from the standard
approach. We did not expect to find any shared CNAs between samples because
the mice had stable diploid genomes and, as expected, did not find evidence of
excessively shared genotypes—on average, only 4% of CNAs overlapped for
any stretch between tumor sequence pairs. Hence, no ancestral CNAs were
removed from alteration tallies.
Identification of driver CNAs in cell lines and mouse tumors
We used data from human breast tumors to identify alterations that might be
drivers in our cell line and mouse model experiments. Genes that lead to driver
events when altered were identified by applying a alteration enrichment
algorithm, GISTICII, to existing surveys of human breast cancers22. Oncogenes
and tumor suppressors within alteration hotspots, expected to be drivers at a
threshold of p < 0.001, were identified in this previous study (Table S3). To be a
driver, an alteration in our samples had to (i) overlap a gene on Table S3 [partial
overlap was permitted because the resolution of our genotyping (~20 kb) is
approximately the length of a typical human gene (including introns)]; (ii) be an
amplification, if the alteration overlapped an oncogene, or be a deletion, if the
alteration overlapped a tumor suppressor. Driver events were rare in this study
(by intention) and reported in Tables S1 & S2.
Our theory suggests that total cell fitness should be a combination of passenger
and driver effects:
dN
= sd nd - sp np
dt
So we tested a multiple linear model of in vitro growth rate that considered both
11
nd and np. This multiple linear model did not significantly improve growth
predictions; the two-sided t-statistic of Capped Volume was highly significant (p <
0.001), while nd was insignificant (p = 0.73). Hence, we did not use this multiple
linear model elsewhere. The poor predictive power of nd is presumably a result of
our experimental setup generating so few drivers.
12
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