esicancer: evolutionary in silico cancer simulator · 18/12/2018 · like survival curves of...

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Resource Report 2

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esiCancer: Evolutionary in Silico Cancer Simulator 5

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Darlan Conterno Minussi1,4¶; Bernardo Henz2¶; Mariana dos Santos Oliveira1,4¶, Eduardo C. Filippi-7

Chiela3, Manuel M. Oliveira2; Guido Lenz1,4* 8

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1Departamento de Biofísica, 2Instituto de Informática, 3Departamento de Ciências Morfológicas, 10

4Centro de Biotecnologia, Universidade Federal do Rio Grande do Sul (UFRGS), Porto Alegre, 11

RS, Brazil 12

* Corresponding author: Guido Lenz, Av. Bento Goncalves, n. 9500, CEP: 91801970, Porto 13

Alegre, RS, Brazil, +55 51 33087613, [email protected] 14

¶ These authors contributed equally to this work 15

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Keywords: Cancer Evolution; Computational Modeling; Cancer Fitness; Cancer Clonality 17

Running title: esiCancer: Evolutionary in Silico Cancer Simulator 18

The authors declare no potential conflicts of interest 19

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Research. on November 13, 2020. © 2018 American Association for Cancercancerres.aacrjournals.org Downloaded from

Author manuscripts have been peer reviewed and accepted for publication but have not yet been edited. Author Manuscript Published OnlineFirst on December 18, 2018; DOI: 10.1158/0008-5472.CAN-17-3924

http://cancerres.aacrjournals.org/

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Abstract 22

The evolution of cancer is inferred mainly from samples taken at discrete points that represent 23

glimpses of the complete process. In this study, we present esiCancer as a cancer-evolution 24

simulator. It uses a branching process, randomly applying events to a diploid oncogenome, 25

altering probabilities of proliferation and death of the affected cells. Multiple events that occur over 26

hundreds of generations lead to a gradual change in cell fitness and the establishment of a fast-27

growing population. esiCancer provides a platform to study the impact of several factors on tumor 28

evolution, including dominance, fitness, event rate, and interactions among genes as well as 29

factors affecting the tumor microenvironment. The output of esiCancer can be used to reconstruct 30

clonal composition and Kaplan-Meier-like survival curves of multiple evolutionary stories. 31

esiCancer is an open-source, standalone software to model evolutionary aspects of cancer 32

biology. 33

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Introduction 35

Despite immense advances in the study of the molecular biology of cancer (1-3), it remains 36

dependent on biopsies, restricted to specific time points and to a fraction of the whole tumor. Thus, 37

they fail to capture a complete picture of cancer heterogeneity offering only a snapshot of tumor 38

evolution. The evolutionary story of a normal cell to a heterogeneous population of billions of cells 39

is complex and, therefore, requires new theoretical insights to better understand the process. 40

Several models have been developed to study cancer in silico (4), each focusing on a 41

specific characteristic of cancer biology. These include the hallmarks of cancer (5), the rate of 42

clonal expansion (6), stem-cell driven tumor initiation (7), the effect of cell migration on tumor 43

growth (8), and the impact of the microenvironment on tumor evolution (9). With esiCancer, we 44

provide a fully-customizable tool designed to help stitch together genetic events during cancer 45

clonal evolution. esiCancer follows a stochastic branching model. Its simulations generate 46

evolutionary paths with events that modify the fitness of cancer cells leading to the selection of the 47

fittest cells. 48

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Methodology 50

esiCancer 51

esiCancer simulates a population of esiCells, each containing a diploid representation of its 52

genome as two independent lists, a probability of death, a probability of division, and a maximum 53

number of divisions (Fig. 1a). This genome can be hit by genetic events, representing point 54

mutations, translocations, indels, etc., with a defined probability and dominance. These events 55

alter the fitness and other aspects of the affected esiCell (Video 1). 56

esiCancer applies events to a predefined number of esiCells, each one independently 57

subjected to four possible outcomes: no alteration; death; senescence; or cell division (Fig. 1a). If 58

an esiCell divides, the two daughter cells receive, at random sites, a number of genetic events, 59

defined by the user. Each event is associated with a change in the probability of division, death, 60

mutation, and/or maximum divisions, thus impacting the population of esiCells over time. For all 61

stochastic decisions, esiCancer uses a pseudorandom number generator initialized with a seed 62

value. Different seeds create different evolutionary stories, which can be automatically iterated 63

over multiple seeds to grant high throughput simulations. A given seed will re-create the same 64

sequence of events thus guaranteeing reproducibility (Video 2). esiCancer exports data about the 65

cell lineages, the sequence, and frequency of events that gave rise to specific groups of esiCells, 66

providing a complete analysis of the clonal composition of an esiTumor (Fig 1a, Video 3). 67

Pre-compiled Linux, Windows and MacOS GUI-based versions of esiCancer, as well as 68

examples of esiTables, outputs, and video tutorials outlining how to use the system and analyze its 69

output data are available at http://www.ufrgs.br/labsinal/esiCancer/. There one can also find 70

detailed documentation about esiCancer, which includes pipelines to assist users in selecting the 71

oncogenome and the parameters for their simulations. A guide for the production of the figures 72

presented in this report is also provided. Source code and additional information can be found at 73

https://github.com/bernardohenz/esiCancer. esiCancer is under GNU Public License v3.0. 74

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Randomness of the Population Fitness 77

Fitness in evolutionary biology is defined by the number of individuals in the nth generation 78

(GENn) divided by the number of individuals in the previous generation (GENn-1). In esiCancer, 79

fitness is directly defined by the probability of division minus the probability of death (Fig1b). If the 80

probability of division and death are both set to 0.01, fitness value calculated with the input data 81

(equation 1) is similar to the value calculated with the output values (equation 2), and this 82

continues to be true after alteration in fitness produced by events. An event that affects the 83



http://www.ufrgs.br/labsinal/esiCancer/

https://github.com/bernardohenz/esiCancer


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probability of division increases the average fitness, which is further increased by a second event. 84

If an event increases the probability of division and decreases the probability of death, the impact 85

of this event on the fitness reflects the impact on both division and death (Fig. 1b). As expected 86

with exponential growth, this produces a final number of esiCells that is about 8 times higher when 87

compared to the impact of only increasing the probability of division. 88

Escape from replicative senescence is another important hallmark of cancer. esiCancer 89

allows the user to limit the number of divisions, resulting in a gradual reduction in the population 90

since cells retain their probability of death (Fig. 1c). Events that lead to an increase in the 91

maximum number of divisions model an escape from replicative senescence. esiCancer can also 92

be used to generate Kaplan-Meier-like plots by plotting the number of generations required to 93

achieve a defined threshold. Increasing the number of events per division also increases the 94

number of simulations that reach the threshold while reducing the number of generations required 95

to reach such condition (Fig 1d). 96

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Survival of the fittest 98

In esiCancer, different simulations produce unique frequencies in gene events, but the 99

frequency after 1100 generation of a given event on average directly correlates with its dominance 100

(Fig 2a, i), probability (iii), and impact on the fitness (ii) as predicted by evolutionary biology. Highly 101

dominant events will appear more frequently than events with low dominance, as the impact of a 102

mutation on the first allele of a highly dominant gene is much stronger than on genes with low 103

dominance values (i). Gene frequency also directly correlates with fitness (ii) and the probability of 104

the event (iii). Therefore, these parameters will affect the probability of an event occurring and will 105

alter the number of descendants that contain the event. A given gene can have two events, which 106

interact allelically and, if all other conditions are the same, their frequency is higher than a gene 107

with a single event (iv) 108

An event can also impact several genes, resembling copy number variation (CNV). An 109

event affecting gene A and B, but not C, will have a frequency equal to gene A, if gene A does not 110

receive any additional event by itself. Frequency of gene B will be the sum of the frequencies due 111

to event AB and an additional event on gene B. Event C will not be affected by event AB (Fig. 2a, 112

right). Lastly, the relative frequency of events at different time points indicates that the same 113

conditions, when modeled with different seeds, can produce variable population dynamics 114

recapitulating different models of tumorigenesis (Fig. 2b). 115

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Gene and cell interactions in esiCancer 118

Cancer genes act within complex interaction networks during tumor development. A given 119

event can affect the impact of another event, either by decreasing its impact leading to mutual 120

exclusivity, or increasing its impact, resulting in co-occurrence (10). In a simulation containing 3 121

genes with equal settings and no interactions, a similar frequency of event 1 in gene 2 and 3 122

occurs (Fig 2c, grey). If the impact of gene 1 and 2 are mutually exclusive, gene 2 will appear less 123

frequently altered when compared to non-interacting genes and the contrary occurs in the case of 124

co-occurrence (Fig 2b, red and green). esiCancer also permits the modeling of interactions among 125

cells, in which events can have impacts on the whole tumor, resulting in alterations that impact the 126

microenvironment positively or negatively (Fig 2d). 127

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Conclusion 129 130

esiCancer provides a platform for simulating the genetics of tumor evolution. It was 131

designed from the ground up to model important aspects of evolutionary biology applied to cancer 132

using real genetic data. The unique strategy of modeling individual cells and applying single-cell 133

decisions of division, senescence, or death reproduces key aspects of tumorigenesis. This results 134

in the survival of the fittest, where each simulation yields a unique outcome, thereby resembling 135

the rise of cancer in humans and capable of modeling the response to mutagens or genetic 136

alterations. In this way, esiCancer can become an important tool to better understand the hidden 137

aspects of tumor evolution. 138

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Acknowledgment: This work was supported by FAPERGS/PRONEX (16-2551). All authors are or 140

were recipients of fellowships from CNPq. We wish to thank Dr. Franscisco M. Salzano (in 141

memoriam) and Francisco Ivanio for critical reading of the manuscript and Maria Julia Oliveira for 142

video and sound editing. 143

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REFERENCES 146 147 1. Kandoth C, McLellan MD, Vandin F, Ye K, Niu B, Lu C, et al. Mutational landscape and 148

significance across 12 major cancer types. Nature 2013;502:333-9 149

2. Lawrence MS, Stojanov P, Mermel CH, Robinson JT, Garraway LA, Golub TR, et al. 150

Discovery and saturation analysis of cancer genes across 21 tumour types. Nature 151

2014;505:495-501 152

3. McGranahan N, Swanton C. Clonal Heterogeneity and Tumor Evolution: Past, Present, and 153

the Future. Cell 2017;168:613-28 154

4. Beerenwinkel N, Schwarz RF, Gerstung M, Markowetz F. Cancer evolution: mathematical 155

models and computational inference. Syst Biol 2015;64:e1-25 156

5. Spencer SL, Gerety RA, Pienta KJ, Forrest S. Modeling somatic evolution in tumorigenesis. 157

PLoS Comput Biol 2006;2:e108 158

6. Bozic I, Antal T, Ohtsuki H, Carter H, Kim D, Chen S, et al. Accumulation of driver and 159

passenger mutations during tumor progression. Proc Natl Acad Sci U S A 2010;107:18545-50 160

7. Gentry SN, Jackson TL. A mathematical model of cancer stem cell driven tumor initiation: 161

implications of niche size and loss of homeostatic regulatory mechanisms. PLoS One 162

2013;8:e71128 163

8. Waclaw B, Bozic I, Pittman ME, Hruban RH, Vogelstein B, Nowak MA. A spatial model 164

predicts that dispersal and cell turnover limit intratumour heterogeneity. Nature 2015;525:261-165

4 166

9. Lloyd, M, Cunning, JJ., Bui, MM, Gilles, RJ, Brown, JS, Gatenby, RA, Darwinian Dynamics of 167

Intratumoral Heterogeneity: Not Solely Random Mutations but Also Variable Environmental 168

Selection Forces. Cancer Res 2016; 76:3136-44 169

10. Mina, M et al. Conditional Selection of Genomic Alterations Dictates Cancer Evolution and 170

Oncogenic Dependencies. Cancer Cell 2017;32:155-68. 171

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Legends: 174

Fig. 1 Overview of esiCancer: (a) Modeling starts with normal esiCells pre-defined probabilities of 175

division and death, and a number of maximum divisions; if an esiCell divides, it receives a number 176

of events and if an event hits a gene, characteristics defined in the esiTable are changed. Number 177

of esiCells, their mutations and fitness are recorded (b) Stochasticity of fitness of the esiCell 178

population. Fitness in esiCancer is defined (1) by the number of esiCells in generation n divided by 179

the number of cells at generation n-1 or (2) by the difference between the probability of cell division 180

and death. Fitness using formula (1) (light grey and red line) and the number of esiCells (blue) are 181

shown for a simulation with the conditions indicated in the boxes. Average fitness as calculated by 182

(1) in red or (2) in green. GEN – generation. (c) Population of esiCells with 15 or 30 maximum 183

divisions for 100 different seeds. (d) Kaplan-Meier-like plots for runs with different event rates. For 184

these runs, 10k esiCells from an initial population of 1,000 esiCells were considered an esiTumor. 185

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Fig. 2 (a) Frequency of events with the indicated dominance, fitness, interaction and probability 187

after 1100 generations with 20 events per generation. Each point represents a simulation with a 188

different seed. Median ± quartiles. Numbers indicate the comparisons mentioned in the text. (b) 189

Dynamics in the frequency of events during esiCancer simulation. (c) Impact of ME or CO between 190




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gene1 and 2 on the frequency of events in gene2 and 3. (d) Impact of the environment on the total 191

population of a defined seed. Maximal Tumor Growth Rate (MTGR) can be set to restrict tumor 192

growth, which can be impacted by events that increase or decrease this value. 193




Normal esiCell

- Probability of Division: 0.01- Probability of Death: 0.01- Maximum Divisions: 30

CTGCATCTGACTGA...TACGTAGACTGACT... 00000000000000...

00000000000000...

00X0000000000000000000000..000000000000000000000000000..00

Events occur at sites chosenthrouhg a seed-based process

Gene 1 Gene 2Event 1

Gene 3Event 1 Event 2 Probability of Division: 0.01 x 1.2

Probability of Death: 0.01

noitalupoP

Generations

noitalupoP

Generations

noitalupoP

Generations

Gene 1Fitness increase

event

Gene 2amp

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xNot altered

Divides

Dies

Senesces

Event Frequency at end of evolution

KM-like survival plot

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a

.CSV Files _ancestralResults_eventsMutationResults_sequenceEachCell

Figure 1

1234

events00

5

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snuR fo noitroporPslleCise k01> hti

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Generations

Gene 3del

esiCells GENn esiCells GENn-1 (2)Fitness = 1 + (Prob. Division-Prob Death) (1) Fitnessn =

0.98

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Fitn

ess

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Gene1 AffectedMULT Div 1.2

Gene2 AffectedMULT Div 1.5

Prob Div: 0.01Prob Death: 0.01

1.000 1.002

1.008

1.000 1.002

1.008esiCells

Fitness

esiC

ells

/ 10

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0.98

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1.02

1.000 1.007

1.014

1.000 1.004

1.012

esiCells0102030405060708090

Prob Div: 0.01Prob Death: 0.01

Gene1 AffectedMULT Div 1.2MULT Death 0.8

Gene2 AffectedMULT Div 1.5MULT Death 0.5

AverageFitness

Threshold for esiTumor formation

0

50

100

0 200 400 600 800 1000Generations

Perc

ent o

f Sim

ulat

ions

with

out e

siTu

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c d

Maximum Divisions

200 400 600 800 1000 1200 1400Generations

0

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esiC

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opul

atio

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eeds

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_genesMutationResults

events

Event 1

CTGCATCTGACTGA...TACGTAGACTGACT...

Allele 1

Allele 2

Simulation

Decision based on seeds

NormalesiCell

AlteredesiCell

Event Frequency at the end of Simulation0 25 50 75 100

Gene 3Event 1

Gene 2Event 1

Gene 1Event 1

Fitness: 1 Fitness: 1.002Iteraten generations




DominanceFitness

ProbEvents

11.51

11.12

11.11

0.31.51

01.51

0.31.51

0.51.51

1

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11.1

11.1

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11.1 1.1

GenesAB A B C

a

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stnevE detceffA fo ycneuqerF 25

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Gene1event1

Gene2event1

Gene3event1

Gene3event2

Gene4event1

Gene5event1

Gene6event1

i (dominance)ii (fitness)

iii (Prob)iv (interaction)

Figure 2

Generation

slleCise detceffa fo

%

g6 − e g5 − e1

g3 − e2 g3 − e1 g2 − e1 g1 − e1

g4 − e1

Gene - event

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Freq

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CO - Co-Occurrence

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pro/anti-tumoractivation

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no M

TGR

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TGR

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ro-tu

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MTG

R =

1.00

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MTGR +

anti-tumor 0.9998

MTGR + anti-tumor 0.9995

anti-tumor 0.9995

activation

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Published OnlineFirst December 18, 2018.Cancer Res Darlan Conterno Minussi, Bernardo Henz, Mariana dos Santos Oliveira, et al. esiCancer: Evolutionary in silico Cancer Simulator

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