Kathleen Sprouffske,C.Athena Aktipis,Jerald P.Radich,Martin Carroll, Aurora M. Nedelcu and 
CarloC.Maley.Anevolutionaryexplanationforthepresenceofcancernonstem cellsin
neoplasms
 
 
Supplementary Material   
 
 
 
Tableof Contents 
 
SupplementaryFigures.............................................................................................................2 
SupplementaryMethods...........................................................................................................6 
Stage structured population model...........................................................................................6 
Individual-basedmodeldesignandimplementation ................................................................8 
SupplementaryTables ............................................................................................................11
SupplementaryText ................................................................................................................15
SupplementaryReferences....................................................................................................16
 
 
 SupplementaryInformation. Sprouffske et al.An evolutionary explanation forcancernonstem cells 2 of 16 
Supplementary Figures 
 
 
 
Fig.S1.The effect of varying the probability for symmetric division and the number of differentiation 
stages on the finalpercentof tumor-propagating cells and the proportion of tumor-propagating cell
symmetric divisions. 
(A) In the absence of evolution, increasing the probability for symmetric division is sufficient to increase 
the percent of tumor-propagating cells in a neoplasm.Simulations in which the probability of symmetric 
division could notevolve show thathigh levels of symmetric division resultin high numbers of tumor-
propagating cells.Values of less than 0.5 for the probability of symmetric division led to neoplasm 
extinction (n=[0,0,0,50,50,50,50] for probability of symmetric division=[0.05,0.2,0.35,0.5,0.65,0.8,0.95]).
Theprobability ofsymmetricdivision and thefinalpercentoftumor-propagating cells is highly correlated 
(Pearson’s correlation R=0.97).  (B) In the absence of evolution, increasing the number of differentiation 
stages decreases the percent of tumor-propagating cells in the neoplasm forpopulations with a fixed 
symmetric division probability of 0.5 (n=[49,50,49,26] for number transientcellstages=[2,4,8,16]).The 
numberof transientstages and the finalpercentof tumor-propagating cells are negatively correlated 
(Pearson’s correlation R=0.88). (C) In evolving populations,the number of differentiation stages did not
affectthe finalpercentof tumor-propagating cells or(D)the proportion of tumor-propagating cell
symmetric divisions reached by naturalselection (n=[50,50,47,29] for number transientcell
stages=[2,4,8,16]). The proportion of tumor-propagating cellsymmetric divisions was significantly higher
than control simulations conducted in the absence of evolution (p=[3x10-164,2x10-167,1x10-153,3x10-79] for 
numbertransientcellstages=[2,4,8,16]).Errorbars show standard error of the mean,50 simulations were 
initialized per condition.  Replicate simulations from each condition were similarand led to small error 
bars;in some cases the errorbars are indistinguishable from the top of the data bar.
0.5 0.65 0.8 0.95
Initial probability of symmetric division
Final percent of tumor
−propagating cells
0
20
40
60
80
100
2 4 8 16
Number of transient stages
Final percent of tumor
−propagating cells
0
20
40
60
80
100
2 4 8 16
Number of transient stages
Final propor
tion of symmetr
ic divisions
0.0
0.2
0.4
0.6
0.8
1.0
2 4 8 16
Number of transient stages
Final percent of tumor
−propagating cells
0
20
40
60
80
100
A B
C DSupplementaryInformation. Sprouffske et al.An evolutionary explanation forcancernonstem cells 3 of 16 
 
 
Fig.S2.Evolution ofthetumor-propagating cellsymmetric division traitrequires sufficientvariability for
naturalselection to actin 10 simulated years.
Therewassufficientvariability fortheevolution of(A)high tumor-propagating celland (B)symmetric
division levels forthe standard deviation of the symmetric division trait.The proportion of tumor-
propagating cellsymmetric divisions was significantly higherthan controlsimulations conducted in the 
absence of evolution (p=[5x10-28,2x10-36,6x10-120,2x10-169,6x10-166,4x10-155,3x10-169] for standard 
deviation=[0.01,0.02,0.04,0.08,0.16,0.32,0.64]).While the proportion of symmetric divisions did evolve 
underconditions of low traitvariability,its rate of evolution was slow enough thatthere was insufficient
time for the population to reach the high levels observed once it exceeded 0.04 (n=[48,47,47,48,47,48,48] 
forstandard deviation=[0.01,0.02,0.04,0.08,0.16,0.32,0.64]).There was insufficientvariability forthe 
evolution of (C) high tumor-propagating celland (D)symmetric division levels atlow mutation rates as 
compared to controlsimulations conducted in the absence of evolution using a t-test with significance 
levels adjusted using the Bonferroni correction for multiple-testing (p=[0.08,0.002], n=[48,48]formutation 
rate=[1x10-7,1x10-6]).  .  However, the mutation rate did not affect the final percent of tumor-propagating 
cells or the proportion of tumor-propagating cellsymmetric divisions reached by naturalselection once it
exceeded 1x10-4 mutations in the asymmetric / symmetric division gene set per cell division (p=[4x10-
21,1x10-112,3x10-161] n=[48,48,50] for mutation rate=[1x10-5,1x10-4,1x10-3]).  Together, the mutation rate 
and the standard deviation of new mutations in the probability of symmetric division can define whether 
the symmetric division trait can evolve quickly enough for tumor-propagating cells to take overthe 
neoplasm.Due to computationallimitations,we did notrun the simulation atrealistic population sizes (109-
1012), however,withlargerpopulations,lowermutationratesresultintheevolutionofhighsymmetric
division probabilities and tumor-propagating cells willcontinue to dominate the neoplasm.Errorbars show 
standard error of the mean,50 simulations were initialized per condition. 
 
 
 
 
 
Mutation rate (log)
Final percent of tumor
−propagating cells
0
20
40
60
80
100
−7 −6 −5 −4 −3
Mutation rate (log)
Final propor
tion of symmetr
ic divisions
0.0
0.2
0.4
0.6
0.8
1.0
−7 −6 −5 −4 −3
0.01 0.04 0.16 0.64
Probability symmetric division std dev
Final percent of tumor
−propagating cells
0
20
40
60
80
100
0.01 0.04 0.16 0.64
Probability symmetric division std dev
Final propor
tion of symmetr
ic divisions
0.0
0.2
0.4
0.6
0.8
1.0
A B
C DSupplementaryInformation. Sprouffske et al.An evolutionary explanation forcancernonstem cells 4 of 16 
 
 
Fig.S3.All maximum possible neoplasm sizes, or tissue carrying capacities, resulted in the evolution of 
(A) high tumor-propagating celllevels and (B)high tumor-propagating cellsymmetric division 
probabilities,and was significantly higher than control simulations conducted in the absence of evolution 
(p=[4x10-155,3x10-161,3x10-161] and n=[48,50,50] for maximum neoplasm size=[1x105,5x105,1x106]). Error 
bars show standard errorof the mean,50 simulations were initialized percondition.
 
 
 
 
 
 
 
Fig.S4.Flow chart depicting the order of events that occurs each day during a simulation. Each box is 
described in detailin the SupplementaryMethods Submodels section.
 
 
 
A B
Maximum neoplasm size
Final percent of tumor
−propagating cells
0
20
40
60
80
100
100,000 500,000 1,000,000
Maximum neoplasm size
Final propor
tion of symmetr
ic divisions
0.0
0.2
0.4
0.6
0.8
1.0
100,000 500,000 1,000,000
Start Time Step
Each cell can die
Each cell can 
divide
EndTime Step
Divide
Allow dividing cells 
to mutate
Decide daughters'
stages
Impose limits on 
neoplasm sizeSupplementaryInformation. Sprouffske et al.An evolutionary explanation forcancernonstem cells 5 of 16 
1
8
ph(1 + ph)3
 
 
Fig.S5.A graphical representation of the transitions between stages associated with the analyticalstage-
structured population model.Tumor-propagating cells with high symmetric division rates,ph, are labeled 
0H and those with lowersymmetric division rates,pl, are labeled 0L. Transient cells, labelled 1-3, 
differentiate atcelldivision untilthey terminally differentiate and reach stage 4.Theapoptosisratepa and 
the cell division rate pc are constant across all stages. Note that one cell in transient stage s-1 divides to 
become 2 cells in stage s, which is notdepicted graphically butis included in the population projection 
matrixA in the Materials and Methods.
 
 
 
 
 
 
 
 
Fig.S6. Increasing the symmetric division rate for the fast-dividing tumor-propagating cells causes an 
increase in the proportion of tumor-propagating cells.The proportion of tumor-propagating cells in the 
neoplasm is given by   and is plotted here. 
 
0H
pc ph
1 2 3 4
paOLpc pl pc (1-pl )
2 pc
papapa
pa
pa
pc (1-ph )
2 pc 2 pc
0.0 0.2 0.4 0.6 0.8 1.0
0.0
0.2
0.4
0.6
0.8
1.0
Symmetric division rate (ph) for
fast-dividing tumor-propagating cells
Pro
po
rti
on
 o
f
tu
mo
r-p
ro
pa
ga
tin
g 
ce
llsSupplementaryInformation. Sprouffske et al.An evolutionary explanation forcancernonstem cells 6 of 16 
Supplementary Methods 
Stage structured population model  
In ouranalytical, deterministic approach, we constructed a stage-structured population model (Lefkovitch 
1965;Caswell2001)to characterize the stable stage distributionof differentiation states. To do so, we split 
the tumor-propagating cells into two groups:stages 0H and 0L and assigned stage 0H a highersymmetric 
divisionrate ph than stage 0L pl, such that ph > pl. We then observed the outcome on the asymptotic 
population composition of “competition” between clones of tumor-propagating cells with different
symmetric division rates. Transient and differentiated cells were defined as depicted in Fig.S5.
 
Weconstructedastage-classified matrix model,in which n(t+1) = A n(t),wheren(t)is a vector of stage 
abundances attime t and A is the population projection matrix. We depict our model both graphically (Fig. 
S5)and mathematically using the population projection matrix A, 
 
. 
 
Thisaccountsforboth therateoftransition between stagesand thenumberofindividualsaffected.A 
matrixentryaijcan be interpreted as the contribution of cellabundances from stage j at time t to the cell 
abundances in stage i at time t + 1.  For example, the number of cells in stage 1 at time t+1 is given by,
n1(t+1) = noH(t) pc (1-ph) + noL(t) pc (1-pl) + n1(t) (1 - pc - pa). The rest of the parameters in A are as 
previously defined (Table S2), where pa is the rate of apoptosis per day and pc is the rate of cell division per 
day.
 
Thedominanteigenvalueλ1 of matrix A corresponds to the change in population size over time and is 
constantwhen λ1 = 1. When λ1 > 1, the tumor size increasesand when λ1 < 1, the tumor shrinks. The 
dominanteigenvalue λ1 of the characteristic equation of A is  λ1 = 1- pa - pcph, since ph > pl. Thus, tumor 
growth depends on the apoptosis and celldivision rates and only the highersymmetric division rate.Using 
ourdefaultparametervalues forapoptosis and celldivision (Table S2),the tumorsize is constantwhen ph 
= 0.41176, grows exponentially when ph > 0.41176, and shrinks to extinction when ph < 0.41176. This is 
consistentwith the observation in our agent-based modelthatsmallinitialprobabilities of symmetric 
divisions could not sustain a tumor population (Fig. S1).
 
Therighteigenvectorofλ1 gives the asymptotic distribution of cells in the stage classes and in the general 
case is 
. 
 
From this,weobserve that the asymptotic population distribution value for stage 0L is 0 for all values of pa, 
pc, ph, and pl, and thus cells with the lower symmetric division rates do not survive.  This is consistent with 
the evolutionary simulations from our individual-based model,in which mutantclones with lower
symmetric division rates eventually reached extinction.Theactualdynamicsofthiscellpopulation depend 
on the initialconditions,in thatthere mustbe cells in stage 0H.
 
Wecancalculatetheproportion of the neoplasm thatcomprises tumor-propagating cells from the 
aymptotic population distribution by dividing the fraction of the cells thatare in stage 0H by the sum of the 
€ 
A =
1− pa − pcph 0 0 0 0 0
0 1− pa − pcpl 0 0 0 0
pc(1− ph) pc(1− pl) 1− pc − pa 0 0 0
0 0 2pc 1− pc − pa 0 0
0 0 0 2pc 1− pc − pa 0
0 0 0 0 2pc 1− pa
#
$
%
%
%
%
%
%
%
&
'
(
(
(
(
(
(
(SupplementaryInformation. Sprouffske et al.An evolutionary explanation forcancernonstem cells 7 of 16 
fraction of cells in any stage.Doing this,we find thatthe fraction of tumor-propagating cells in the 
neoplasm depends only on the symmetric division rate forfast-dividing tumor-propagating cells and is 
given by 
  .   
Thus,theproportion oftumor-propagating cells in the neoplasm increases as the tumor-propagating cell’s 
rate of symmetric division, ph, increases (Fig. S6).   
 
 
1
8
ph(1 + ph)3SupplementaryInformation. Sprouffske et al.An evolutionary explanation forcancernonstem cells 8 of 16 
Individual-basedmodeldesignandimplementation
Thesemethodsarepresented in ODD protocolstandard formatforindividual-based models (Grimm etal.
2006). Briefly, tumor-propagating cells and transientcells were modeled using NetLogo 4.0.4 (Wilensky
1999). Each day in the simulation, a cell had the opportunity to die,divide,ordo nothing.Transientcells 
could divide symmetrically a parameterized number of times before undergoing apoptosis or senescence.
Exceptwherenoted,transientcellscould notdedifferentiateinto tumor-propagating cells.The probability 
that a tumor-propagating celldivided symmetrically orasymmetrically was determined by a mutable cell
intrinsic trait that could evolve.  
 
Modeloverview 
Purpose
Thisindividual-based modeltests how the probability forsymmetric division evolves in tumor-propagating 
cells,or cancer stem cells,given the cancer stem cellhypothesis of cancer. 
Entities, statevariables, and scales 
Each cellin asimulation hasvaluesforthestatevariablesdefined in TableS2.
Process overview and scheduling
Themodelisbroken into timesteps, each of which is equivalent to 1 day. The flow chart in Fig. S4 outlines 
the decisions that a cell makes each timestep. Details of the implementation are described in the Submodels 
below.
Adaptation
Cellsinthismodelarenotexplicitly encoded with adaptive behavior.Instead,increasing propensity of 
symmetric division implicitly increases the fitness of the cellby decreasing the rate atwhich cells become 
fully differentiated and are removed from the population. 
Sensing 
Cellsarenot encoded with any sensing ability.
Interaction 
Thereareno directinteractionsorcommunication between cellsin themodel.
Stochasticity 
Celldivision,celldeath,andmutationarestochastic in the model.They are constrained by parameterized 
probabilities.  
Observation 
Forallsimulations,summary dataarerecorded attheend ofthesimulation.Forcertain simulations,
summary data are written to a file every 10 days.These data include the number of tumor-propagating 
cells,the number of transientcells,the observed average propensity for symmetric division by tumor-
propagating cells,and the time atwhich simulation crossed the 90% tumor-propagating cells threshold.
 
Modeldetails  
Initialization
SeeTableS2 fortheparametervaluesand theirranges used in the simulations.Simulations are initialized 
withns tumor-propagating cells and nt transient cells. A cell i is a tumor-propagating cellattime t if its 
stage is 0,si(t) = 0. A cell i is a transient cell at time t if its stage is not 0, si(t) > 0. All cells have the same SupplementaryInformation. Sprouffske et al.An evolutionary explanation forcancernonstem cells 9 of 16 
propensity forcelldivision pc and apoptosis pa. Tumor-propagating cells can divide symmetrically or
asymmetrically.Both daughter cells from a symmetric division remain tumor-propagating cells.When a 
tumor-propagating cell divides asymmetrically, one daughter cell remains a tumor-propagating celland the 
otherdifferentiates into a transientcell(Fig.1A-C).Initially,eachcelli has probability psd,i(0) = psd of 
symmetric division if itis a tumor-propagating cell.Eachcell’s probability of symmetric division psd,i(t)is 
allowed to evolve over time.Because a tumor-propagating cellcan only divide symmetrically or
asymmetrically,allowing the probabilities of symmetric division or asymmetric division to evolve is 
equivalent. 
 
Submodels 
Each submodelcorrespondsto adecision in theflowchart(Fig.S4).
Each cellcan die
Formostofthesimulations,acelldiesfrom background mortality ifitdrawsarandom numberfrom a
uniform distribution between 0 and 1 thatis less than the probability forapoptosis,pa.  
 
In a subset of the simulations that test the effects of feedback from transient cells to stem cells, transient 
cells die as before while stem cells with higher numbers of clonaltransientcells die less often than those 
withfewer.Thenumberofclonaltransientcellsforastem celli at time t, or nc,i(t), is defined as the number 
of transientcells thatarise from the mostrecentcommon stem cellancestor(as such,the stem celland its 
clonaltransientcells have common mutational state).  Specifically, a stem cells dies if it draws a random 
numberfrom a uniform distribution between 0 and 1 thatis less than paf(t), the probability for apoptosis 
underfeedback attime t, where paf(t)is obtained from the sigmoidfunction 
  , 
and r is an arbitrary constant (r = -0.0001).Varying negative values of r had no effect on the outcome of 
the simulations.  
 
A cellthatisfullydifferentiateddies.Thenumberofdifferentiationstagesisaparameters to the model, 
and each celli has a state variable that tracks its differentiation level at time t, si(t). Thus, cells with si(t) = s
die.The qualitative results of the modeldo notchange if terminally differentiated cells are allowed to 
remain as quiescent cells in the modeland are slowly cleared by background apoptosis.
Each cellcan divide 
A celldividesifitdrawsarandom numberfrom theuniform distributionbetween0and1thatislessthan
the probability for cell division, pc. 
Allow dividingcellstomutate
A cell i acquires a mutation in its probability for its tumor-propagating symmetric celldivision traitif it
draws a numberfrom a uniform distribution between 0 and 1 thatis less than the mutation rate,µ.  Once it 
gets a new mutation,the currentprobability forsymmetric division forits daughters,cells j and k, are 
updated to psd,j(t+1) = psd,k(t+1) = N(psd,i(t),σ), where the mean of the normal distribution is the parental 
probability of symmetric division,psd,i(t), and σ is the standard deviation parameter. The updated 
probabilities forsymmetric division are bounded by 0 and 1.
Decidedaughters’differentiation level
Recallthatthedifferentiationstageforacelli at time t is stored in its local variable si(t). Here, we 
determine the differentiation stage fordaughtercells j and k. In most simulations, a tumor-propagating cell
can divide symmetrically or asymmetrically. It divides symmetrically if it draws a random number from a 
uniform distribution between 0 and 1 thatis less thatits currentprobability forsymmetric division psd,i(t), 
and asymmetrically otherwise.When a tumor-propagating celldivides symmetrically,both of its daughters 
remain tumor-propagating cells,sj(t+1) = sk(t+1) = 0.  When a tumor-propagating celldivides SupplementaryInformation. Sprouffske et al.An evolutionary explanation forcancernonstem cells 10 of 16 
asymmetrically,one daughter remains a tumor-propagating cell,sj(t+1) = 0, and the other differentiates 
into a transient cell,sk(t+1) = 1.  
 
A transientcelldividessymmetrically.Mostofthesimulationswererununderanormal,orforward-only 
differentiation regime,in which the progeny from transientcells were always more differentiated,sj(t+1) = 
sk(t+1) = si(t) +1. In a subset of the simulations, transient cells were allowed to dedifferentiate according to 
a parameterized probability,such thatboth daughters became tumor-propagating cells,sj(t+1) = sk(t+1) = 
0.  
Impose limits on neoplasm size 
If the total number of cells in the neoplasm N exceeds the maximum possible carrying capacity of the tissue 
nmax, then N - nmax cells are chosen at random for death until the total population is nmax. The total number 
of cells in a simulation fluctuates overthe course of each timestep, typically decreasing when the cell death 
submodels are executed and increasing when the cellbirth submodels is executed. 
 
Niche-determination of tumor-propagatingcells 
Weextendedthebasicmodeltoexploretheeffectsofmicroenvironmentally-determined “stemness”,in 
whichthedifferentiationstructureremains,andanycellthatmovesintothenichebecomesatumor-
propagating cell.Tumor-propagating cellself-renewal is defined as a symmetric division in which both 
daughtercells remain tumor-propagating cells,and has a probability of occurring in celliat time t of psr,i(t). 
Here,weimplementthemutationandevolutionofself-renewal just as we implemented mutation of 
symmetric division in the basic model.Allcells are placed on the neoplasm at(0,0) in a 32x32 torus,and 
the niche is located at (0,0).  At cell division, one daughter remains in place and the other moves 1 niche-
widthinarandom direction.Anytransientcelli that moves into the niche becomes a tumor-propagating 
cell,such thatsi(t+1) = 0.Both daughters for a tumor-propagating cellin the niche remain tumor-
propagating cells.Tumor-propagating cells notin the niche can only divide symmetrically,and so both 
daughters j and k are either tumor-propagating cells sj(t+1) = sk(t+1) = 0or transient cells sj(t+1) = sk(t+1) 
= 1. A tumor-propagating cellnotin the niche self-renews if it draws a random number from a uniform 
distribution between 0 and 1 thatis less thatits currentprobability forself-renewing division psr,i(t), and 
differentiates otherwise.The initialprobability fortumor-propagating cellself-renewing division is zero for 
allcells.Allother transientcells differentiate as previously defined. SupplementaryInformation. Sprouffske et al. An evolutionary explanation for cancer nonstem cells 11 of 16 
Supplementary Tables 
TableS1.Summarydataforalloftheexperimentalconditionssimulated. 
 
Meanfinalprobabilityforsymmetricdivisionandpercentoftumor-propagating cells.Fifty simulations were initiated foreach experimentalcondition,including 
the default parameter values (see Table S2), control experiments in which the default parameters were used but mutation was not allowed, and varying each of 
the parameter values.  The percent of tumor-propagating cells,the population’s mean probability forsymmetric division,and the time to 90% tumorpropagating 
cells were recorded.The mean and standard error are reported for these metrics.Mostparameter values resulted in symmetric division rates thatwere 
statistically greater than the controlsimulation cases (marked *).Significance was obtained using a t-test with the Bonferroni multiple-testing correction 
(significant at p < 0.0016). Due to the nature of stochastic simulation modeling, sometimes populations went extinct before the simulation completed. The 
numberof simulations perexperimentthatsurvived for10 years is reported.
 
Probability for symmetric 
division
 
Percentoftumor-
propagating cells 
 
Timeto 90% tumor
propagating cells (years) 
Number of simulations  
 
Experiment
number Parameter value Mean
Standard 
error 
P-value 
(* denotes 
significance) Mean
Standard 
error Mean
Standard 
error 
Reached
90% Completed 
Default parameters (see Table S2)           
 
ns=50
nt=99,950
pc=0.17
pa=0.07
µ=1x10-3 
psd=0.5
σ=0.08
pd=0
d=8 
nmax=100,000 0.99892 0.00003 3 x 10-164  * 99.6 0.01 2.97 0.07 49 49
Controlusing defaultparameters(seeTableS2)          
2 µ=0 0.5 0 control  12.42 0.03 N/A 0 /49 0 49
 SupplementaryInformation. Sprouffske et al. An evolutionary explanation for cancer nonstem cells 12 of 16 
 
Probability for symmetric 
division
 
Percentoftumor-
propagating cells 
 
Timeto 90% tumor
propagating cells (years) 
Number of simulations  
 
Experiment
number Parameter value Mean
Standard 
error 
P-value 
(* denotes 
significance) Mean
Standard 
error Mean
Standard 
error 
Reached
90% Completed 
Probability of dedifferentiation           
3 pd=0 0.99888 0.00004 4 x 10-155  * 99.6 0.02 2.97 0.07 48 48
4 pd=0.2 0.97323 0.0025 4 x 10-72  * 94.88 0.45 8.36 0.13 47 50
5 pd=0.4 0.52914 0.00113 2 x 10-30  * 63.32 0.06 N/A N/A 0 50
6 pd=0.6 0.50636 0.00095 1 x 10-08  * 70.86 0.05 N/A N/A 0 50
7 pd=0.8 0.50309 0.00092 8 x 10-04  * 76.31 0.04 N/A N/A 0 50
8 pd=1 0.50302 0.00082 3 x 10-04  * 80.09 0.03 N/A N/A 0 50
Relativequiescenceof tumor-propagating cells          
9 pc-tpc / pc-trans = 0.425 0.9989 0.00003 8 x 10-126  * 99.04 0.03 3.75 0.11 36 37
10 pc-tpc / pc-trans = 0.567 0.99895 0.00003 2 x 10-151  * 99.29 0.02 3.66 0.09 45 45
11 pc-tpc / pc-trans =  1 0.99894 0.00002 5 x 10-176  * 99.62 0.01 2.8 0.07 50 50
Number of stages            
12 d=2 0.99893 0.00003 3 x 10-164  * 99.93 0.002 2.17 0.04 49 49
13 d=4 0.99892 0.00003 2 x 10-167  * 99.82 0.005 2.51 0.06 50 50
14 d=8 0.99889 0.00005 1 x 10-153  * 99.59 0.02 3.02 0.07 49 49
15 d=16 0.99875 0.00008 3 x 10-79  * 99.03 0.06 4.31 0.17 26 26
 SupplementaryInformation. Sprouffske et al. An evolutionary explanation for cancer nonstem cells 13 of 16 
 
Probability for symmetric 
division
 
Percentoftumor-
propagating cells 
 
Timeto 90% tumor
propagating cells (years) 
Number of simulations  
 
Experiment
number Parameter value Mean
Standard 
error 
P-value 
(* denotes 
significance) Mean
Standard 
error Mean
Standard 
error 
Reached
90% Completed 
Standard deviation of probability symmetricdivision          
16 σ=0.01 0.5527 0.00223 5 x 10-28  * 15.9 0.17 N/A N/A 0 48
17 σ=0.02 0.73384 0.00627 2 x 10-36  * 35.59 0.99 N/A N/A 0 47
18 σ=0.04 0.99777 0.0002 6 x 10-120  * 99.17 0.08 6.58 0.11 47 47
19 σ=0.08 0.99895 0.00002 2 x 10-169  * 99.61 0.01 2.95 0.06 48 48
20 σ=0.16 0.99894 0.00002 6 x 10-166  * 99.62 0.01 1.8 0.06 47 47
21 σ=0.32 0.99895 0.00004 4 x 10-155  * 99.62 0.01 1.18 0.06 48 48
22 σ=0.64 0.99899 0.00002 2 x 10-169  * 99.64 0.01 0.74 0.05 48 48
Mutationrate            
23 µ=1x10-7 0.50272 0.00193 8 x 10-02 12.55 0.14 N/A N/A 0 48
24 µ=1x10-6 0.53212 0.01084 2 x 10-03 15.47 1.25 N/A N/A 0 48
25 µ=1x10-5 0.80144 0.01867 4 x 10-21  * 51.7 3.69 8.42 0.43 7 48
26 µ=1x10-4 0.99865 0.00032 1 x 10-112  * 99.5 0.12 5.45 0.18 48 48
27 µ=0.001 0.99892 0.00004 3 x 10-161  * 99.6 0.02 2.99 0.08 50 50
Maximumneoplasmsize            
28 nmax=100,000 0.99894 0.00004 4 x 10-155  * 99.62 0.02 3.06 0.06 48 48
29 nmax=500,000 0.99891 0.00004 3 x 10-161  * 99.6 0.01 2.49 0.04 50 50
30 nmax=1,000,000 0.99887 0.00004 3 x 10-161  * 99.59 0.02 2.3 0.03 50 50
Microenvironmentalmodulationoftumor-propagatingcells (niche model)         
31
  0.99816 0.00014 
1 x 10-134  * 
98.66 0.1 
6.9 0.16 50 50
Fitness increaseto tumor-propagating cells from clonally-related transient cells        
32   0.502 0.002 2 x 10-01   33 0.2 N/A N/A 0 50Supporting Information.Sprouffske etal.An evolutionary explanation forcancernonstem cells 14 of 16 
TableS2.Parametervaluesforourmodel of tumor-propagating cellsymmetricdivision.
 
Parameter Description Biologicalvalue Modelvalue(defaultvalue) 
Number tumor-propagating 
cells (ns) 
Initial number of tumor-
propagating cells
13,250 - 353,000 cells 
(Rubinow and Lebowitz
1976) 
50 - 500 cells (50)
Numbertransient cells (nt) Initial number of transient cells ≈ 5x1010 cells (Rubinow and 
Lebowitz 1976) 
99,950 - 999,500 cells 
(99,950) 
Probability of celldivision (pc)  The probability a given cell
divides each day
0.173 divisions /day 
(Rubinow and Lebowitz
1976) 
0.17 celldivisions /day 
(0.17) 
Probability of apoptosis (pa) The probability a given celldies 
each day 
0.071 deaths /day (Rubinow 
and Lebowitz 1976; Mundle
et al. 1994) 
0.07 deaths /day (0.07)
Mutationrate(µ) The chance of a cellacquiring a 
mutationeachcelldivision 
1.6x10-8 - 1x10-3 mutations / 
cell division (Araten et al. 
2005; Bielasand Loeb 2005; 
Siegmund etal.2009; 
Ushijima et al. 2005) 
1x10-7- 1x10-3 mutations/
cell division  
(1x10-3) 
Probability of symmetric
division (psd) 
Initial probability that a given 
tumor-propagating cell’s 
daughters are both tumor-
propagating cells,each cell
division 
Unknown 0.05 - 0.95 symmetric / cell 
division (0.5)
Standard deviation (σ) Standard deviation of 
probability of tumor-
propagating cellsymmetric 
division 
Unknown 0.01 - 0.64 (0.08) 
Probability of dedifferentiation 
(pd) 
Probability thatagiven 
transient cell’s daughters are 
both tumor-propagating cells,
each cell division  
Unknown 0 - 1 / cell division (0)
Number of stages (d) Number of possible 
differentiation stages 
Minimum8stages,ifAML
mimicshematopoiesis 
(Khanna-Gupta and Berliner 
2005; Ansker et al. 2005) 
2 - 16 stages (8) 
Maximumneoplasmsize (nmax) Maximumsize possible for a 
neoplasm
Model-specific 100,000 - 1,000,000 cells 
(100,000) 
 
 
 
TableS3.Statevariablesforourmodel of tumor-propagating cellsymmetricdivision.
 
Parameter Description 
Stage (si(t))  Differentiation stage of cell i at time t, characterizes if cell i is a tumor-
propagating cellor any stage of transientcell
Probability of tumor-propagating celldivision 
(psd,i(t)) 
The probability thata tumor-propagating celli divides symmetrically at time t, 
once itdivides 
 Supporting Information.Sprouffske etal.An evolutionary explanation forcancernonstem cells 15 of 16 
Supplementary Text  
Naturalselectioncontinues tofavor a high tumor-propagatingcellsymmetricdivision
probability,regardlessofthe numberofdifferentiationstages.
In normal hematopoiesis, there are at least 8 distinct maturation stages, or levels of differentiation, in the 
neutrophillineage (Khanna-GuptaandBerliner2005). It is not known if the levels of differentiation in 
AMLmimicthat of hematopoiesis,orhow many times a transientcellin AML may divide before it
terminally differentiates.  Thus, we varied the number of times a cell could divide before terminal 
differentiation.Inexperiments with constant probability for tumor-propagating symmetric divisions (i.e.,
no evolution),we found thatincreasing the numberof differentiation stages decreases the percentof tumor-
propagating cells in the neoplasm (Fig. S1B). Showing the robustness of ourmodelby varying the number 
of differentiation stages, wefoundthatnaturalselection still favored high chances of tumor-propagating 
cellsymmetric divisions (Fig.S1D),and thus high levels of tumor-propagating cells (Fig.S1C).
 
Natural selection continues tofavor a high tumor-propagatingcellsymmetric division 
probabilityas long as there is sufficient variability in the tumor-propagatingcell
symmetric divisiontrait.   
Mutationintheprobabilityofsymmetricdivision was modeledat cell division as a two-step process.Each 
cellcould either mutate or not,and if itdid then its currentprobability for symmetric division was updated 
by drawing a random numberfrom a normaldistribution centered on the parentalcell’s symmetric division 
rate with a parameterized standard deviation (see SupplementaryMethods). Because the standard deviation 
of the tumor-propagating cellsymmetric division rate is unknown, we tested a range of values. We also 
varied the mutation rate across physiologically reasonable ranges. We found that when the mutation rate or 
the effects of mutations are extremely small, the tumor-propagating cell’s symmetric division probability 
trait does not evolve during the 10-yearexperiment.However,with sufficientvariability in the symmetric 
division trait,naturalselection continues to favora high tumor-propagating cellsymmetric division 
probability and high levels of tumor-propagating cells (Fig.S2).
 
Naturalselectioncontinues tofavor a high tumor-propagatingcell symmetric division 
probability,regardlessofthe maximumneoplasmsize.
To keep themodelcomputationally tractable,default in silico neoplasms had resources to maintain 100,000 
cells.When a neoplasm reached this carrying capacity,cells were randomly selected to undergo apoptosis 
untilthe carrying capacity was again met.We varied the carrying capacity of the neoplasm and found that
the population size of the neoplasm has no effect on either the evolution of the probability of symmetric 
division,orthe finalproportion of tumor-propagating cells in the neoplasm (Fig.S3).Supporting Information.Sprouffske etal.An evolutionary explanation forcancernonstem cells 16 of 16 
Supplementary References 
Ansker,Y.,H.Leung,andC.Vergaillie.2005.Tumor-propagating cellmodelof hematopoeisis.In 
Hematology:basicprinciplesandpractices, edited by R.E.A. Hoffman. Philadelphia: Elsevier.
Araten,D.J.,D.W.Golde,R.H.Zhang,H.T.Thaler,L.Gargiulo,R.Notaro,andL.Luzzatto.2005.A 
quantitative measurementof the human somatic mutation rate.CancerResearch 65:8111-7.
Bielas,J.H.,andL.A.Loeb.2005.Quantificationofrandom genomicmutations.NatMethods2:285-90.
Caswell,H.20001.Matrixpopulationmodels. 2nd ed: Sinauer Associates, Sunderland, MA. 
Grimm,V.,U.Berger,F.Bastiansen,S.Eliassen,V.Ginot, J. Giske, J. Goss-Custardetal. 2006. A 
standard protocolfor describing individual-based and agent-based models.EcologicalModelling 
198:115-126.
Khanna-Gupta,A.,andN.Berliner.2005.Granulocytopoiesisandmonocytopoeisis.InHematology:Basic
Principlesand Practice, edited by R. E. A. Hoffman. Philadelphia: Elsevier.
Lefkovitch,L.1965.Thestudy ofpopulation growth in organismsgrouped by stages.Biometrics21:1-18.
Mundle,S.,A.Iftikhar,V.Shetty,S.Dameron,V.Wright-Quinones,B.Marcus,J.Loewetal. 1994. Novel 
in situ double labeling for simultaneous detection of proliferation and apoptosis. Journalof
Histochemistry and Cytochemistry 42:1533-7.
Rubinow,S.I.,andJ.L.Lebowitz.1976.A mathematicalmodeloftheacutemyeloblasticleukemicstatein
man.BiophysicalJournal16:897-910.
Siegmund,K.D.,P.Marjoram,Y.-J.Woo,S.Tavaré,and D.Shibata.2009.Inferring clonalexpansion and 
cancer stem celldynamics from DNA methylation patterns in colorectalcancers.Proceedingsof
the National Academy of Sciences of the United States of America 106:4828-33.
Ushijima,T.,N.Watanabe,K.Shimizu,K.Miyamoto,T.Sugimura,andA.Kaneda.2005.Decreased
fidelity in replicating CpG methylation patterns in cancercells.CancerResearch 65:11-7.
Wilensky,U.1999.NetLogo.http://ccl.northwestern.edu/netlogo/CenterforConnected Learning and 
Computer-BasedModeling,NorthwesternUniversity,Evanston,IL.