Modeling the dynamics of chromosomal alteration progression in cervical cancer: A computational model
Modeling the dynamics of chromosomal alteration progression in cervical cancer: A computational model
Augusto Cabrera-Becerril 0 1
Cruz Vargas-De-LeoÂ n 1
Sergio HernaÂ ndez 1
Pedro Miramontes 0 1
RauÂ l Peralta 1
0 Departamento de MatemaÂticas, Facultad de Ciencias, Universidad Nacional AutoÂnoma de MeÂxico, Ciudad de MeÂxico, MeÂxico, 2 Escuela Superior de Medicina, Instituto PoliteÂcnico Nacional, Ciudad de MeÂxico, MeÂxico, 3 Programa de DinaÂmica Nolineal, Universidad AutoÂnoma de la Ciudad de MeÂxico, Ciudad de MeÂxico, MeÂxico, 4 Centro de InvestigacioÂn en DinaÂmica Celular, Instituto de InvestigacioÂn en Ciencias BaÂsicas y Aplicadas, Universidad AutoÂnoma del Estado de Morelos , Cuernavaca, MeÂxico
1 Editor: Marcia Edilaine Lopes Consolaro, Universidade Estadual de Maringa , BRAZIL
Computational modeling has been applied to simulate the heterogeneity of cancer behavior. The development of Cervical Cancer (CC) is a process in which the cell acquires dynamic behavior from non-deleterious and deleterious mutations, exhibiting chromosomal alterations as a manifestation of this dynamic. To further determine the progression of chromosomal alterations in precursor lesions and CC, we introduce a computational model to study the dynamics of deleterious and non-deleterious mutations as an outcome of tumor progression. The analysis of chromosomal alterations mediated by our model reveals that multiple deleterious mutations are more frequent in precursor lesions than in CC. Cells with lethal deleterious mutations would be eliminated, which would mitigate cancer progression; on the other hand, cells with non-deleterious mutations would become dominant, which could predispose them to cancer progression. The study of somatic alterations through computer simulations of cancer progression provides a feasible pathway for insights into the transformation of cell mechanisms in humans. During cancer progression, tumors may acquire new phenotype traits, such as the ability to invade and metastasize or to become clinically important when they develop drug resistance. Non-deleterious chromosomal alterations contribute to this progression.
Data Availability Statement: All relevant data are
within the paper and its Supporting Information
Funding: This work was partially supported by
PRODEP-SEP, Mexico and our wages. The funders
had no role in study design, data collection and
analysis, decision to publish, or preparation of the
Competing interests: The authors have declared
that no competing interests exist.
The genome and chromosomal unbalance of a transformed cell is highly heterogeneous, with
a wide range of structural and copy number alterations. On the other hand, the behavior of the
tumor as a whole results from the accumulation of altered cells [
]. In particular, in Squamous
Cell Carcinomas (SCC), there is strong experimental evidence for a correlation between
copynumber unbalance and tumor aggressiveness [
]. In this regard, a large number of
chromosomal alterations could characterize an aggressive tumor, while a smaller number of
these alterations could be associated with a less aggressive tumor [
]. Therefore, finding the
progression of these alterations would allow us to address the cancer treatment based on the
profile of chromosomal alterations.
On the other hand, although all cells can undergo chromosomal alterations, only a small
number of such alterations have the potential to be deleterious to the cell, while the majority of
chromosomal alterations are not deleterious [
]. In this context, the development of cancer is
the result of the accumulation of several non-deleterious mutations. In the early stages of
cancer, non-deleterious alterations are few; however, in advanced stages, these alterations are
]. Several studies in molecular cytogenetics (e.g., comparative genomic
hybridization) have investigated chromosomal alterations in cancer. Some of the authors of
these studies correlate these chromosomal alterations with specific tumor behaviors [
Cervical Cancer (CC) is the second most common malignancy in women worldwide.
Infection with high-risk Human Papillomavirus (HR HPV) is the major etiological factor for this
]. HR HPV can transform infected cells through the direct action of the products of
two of its early genes: E6 and E7. The E6 and E7 proteins of HR HPV are able to interact with
molecules important to growth regulation and cell replication and can repair damage to the
DNA of healthy cells. The E6 protein of HR HPV binds with high affinity to the molecule
known as p53, inducing its degradation. The p53 protein is an important regulator of cell
replication and is known as the main tumor repressor in humans; p53 is able to detect damage to
DNA and arrest cell replication. A high proportion of human cancers have been shown to
have damage in the gene encoding the p53 protein; CC is an exception to this because in this
case, the gene is intact, but the protein is not present in the cells infected by HR HPV, and E6
has been responsible for removing it. In this case, the cell cannot repair DNA errors and will
experience tumor development when the number of mutations increases. On the other hand,
the E7 protein binds specifically to the tumor repressor gene product Rb. This gene was
discovered and characterized in retinoblastoma [
]. This is a cell-cycle regulatory factor and is
directly linked with the E2F transcription factor that, in turn, induces the transcription of
elements involved in cell replication. The E7 protein of HR HPV possesses a high affinity for
RbE2F. When the E7 protein binds to Rb, E2F is released and induces cell proliferation. Thus, E6
and E7 cooperate efficiently in cell transformation, stimulating chromosomal alterations in the
uterine cervix. The profile of chromosomal alterations is very heterogeneous in precursor
lesions (cervical intraepithelial neoplasms 1, 2, and 3), but this heterogeneity decreases in CC.
In advanced tumors, we observe a profile of chromosomal alterations induced by HPV
]. Using computational tools, it is possible to obtain a model of the progression
of chromosomal alterations from the appearance of precursor lesions until CC ±[
Within the context of a cancer, these models help in determining the global behavior of the
]. The aim of this study is to determine the progression of chromosomal
alterations, including deleterious or non-deleterious alterations, from precursor lesions to CC,
using a computational model.
Computational model of cervical cancer
The molecular biology methods applied to study chromosomal alterations in CC indicate a
great heterogeneity of such alterations. Thus, CC behaves as a complex system, rendering
computational tools ideal for the study of the behavior of this tumor.
Agent-Based Modeling (ABM) is a computational modeling technique for the study of
complex systems, i.e., systems that are composed of many interacting elements. The main idea
of ABM is to replicate, with a stimulus, some of the interactions among individual components
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of the system. ABM consists of the following three main components: agents, rules that govern
interactions among agents, and the environment in which agents interact. Currently, there are
many options and platforms for developing ABM; however, it has only recently been applied
in the study of cancer [21±23]. For example, in a biological system such as tissue, each cell can
be represented as an agent, and these agents may receive signals and input from the
environment and their neighboring agents, providing output to the environment and their neighbors
and making decisions based on input from their surrounding environment and from their
internal signals. Within this context, the dynamics of chromosomal alterations, from precursor
lesions to CC, can be modeled by ABM. Under conditions in which a deleterious mutation is
present, cells enter into an apoptotic state. If a non-deleterious mutation is active, the cell
progresses to the development of advanced lesions and cancer. There are at least three advantages
of utilizing ABM as a mechanism for modeling cellular cancer: multi-scale modeling,
randomness, and emergent behavior. Additionally, we can employ a random distribution to simulate
external stimuli and to account for stochastic effects, which are always present in biological
On the other hand, with Cellular Automata (CA), it is possible make idealizations of
physical systems, as they are discrete dynamical systems both in time and in space. For example, a
single cellular automaton consists of a line of cells, each with a value of 0 or 1 (true or false).
These values are updated in a sequence of discrete time steps according to a definite, fixed rule
]. CA produce complex behavior even with the simplest defining rules. In general, cells
have a finite number k of possible values and may be arranged on a regular lattice in any
number of dimensions. Some defining characteristics of CA are as follows: they are discrete in
space and in time; they have discrete states; they are homogeneous; and they allow for
synchronous updating. The rule of each cell depends solely on the values of a local neighborhood of
cells around it, and its state depends only on its values in the preceding steps. Many biological
systems have been modeled using CA [
]. The development of structure and patterns in
the growth of organisms often appears to be governed by very simple and local rules; therefore,
they are well-described by CA. The advantages of using CA for modeling is that this method
may be treated as parallel processing computers; thus, complex behavior that involves many
individual cells can be properly modeled with CA. Cervical cancer has been modeled in
different works using CA combined with another techniques . In this work, we model cellular
behavior using CA and cellular dynamics with ABM to determine the dynamics of deleterious
and non-deleterious alterations in cervical tissue; therefore, our agents are autonomous,
probabilistic-state cellular automata.
Overview of the model
The ªABM-Cervical-Cancerº model is a hybrid, two-Dimensional (2D) computational model
implemented in the Netlogo framework [
]. This model consists of a set of agents that
simulate cell behavior. We decided to construct each cell with a minimal chromosome that is
subjected to two possible alterations, deleterious and non-deleterious mutations, and each gene
has three possible states: silenced; normal, or overexpressed. Fig 1.
We introduce the global variable ªHPVº as a Boolean variable. When HPV is true, there is
infection with HPV, integration in the genome, and the triggering of random alterations,
behaviors that are suggested by the literature [
The variable P simulates the clinical manifestation of HPV infection, and P is the outcome
of the roll of a pair of dice: if the result is greater than or equal to 2 (P 2), the HPV-infected
host will probably exhibit a Cervical Intraepithelial Neoplasia (CIN)1 lesion; if the result of the
roll of the dice is greater than or equal to 5 (P 5), it is more probable that a CIN1 lesion will
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Fig 1. Minimal chromosome alterations in a cell.
evolve into a CIN2 lesion; and if P 6 7, it is highly probable that the host will develop a CIN3
lesion and, once in this state, develop Cervical Cancer (CC) with probability η.
The evolution from HPV infection to CC is simulated by counting the number of cells that
present early-stage cervical intraepithelial neoplasia lesions. A second roll of the dice yields the
probability for progressing from CIN1 to CIN2, although some of the cells with CIN1 lesions
will likely recover, with probability β = 0.01. If some deleterious alterations are present, cell
death will be more probable and cancer will not develop. The ªnaturalº cell-death rate is μ.
Individual cells have two forms of interaction: Each cell breeds a new cell when it reaches a
ªmatureº stage (when it passes a fixed time τ), and the offspring will inherit the chromosome
of the ªparent-cellº. When a large number of cell neighbors are cancerous, the probability of
Fig 2. The ABM-Cervical-Cancer model.
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Fig 3. Chromosomal alteration dynamics.
progressing from CIN2 to CIN3 or to cancer is increased Fig 2. In the S1 Appendix, we have
included a detailed description of the model using the ODD (Overview, Design concepts and
Details) protocol and the full code for the implementation in NetLogo in S1 File.
In our model, the Clinical Intervention variable is an external stimulus that randomly
selects a patch of cancer cells and deletes it in one step of the simulation; this allows us to
simulate real clinical intervention. In the next step, the dynamics repeat; thus, cancer cells remain
present after Clinical Intervention, but their growth is being bound. The mechanism produces
loops in the simulation, as depicted in Figs 3 and 4. Additionally, the randomness produces
oscillations in the dynamics of the model.
The cells possess two means of interaction: ªhorizontalº interaction and ªverticalº
interaction. Vertical Interaction refers to the inheritance of characteristics or mitotic transmission.
Horizontal Interaction occurs with the nearest cells in a De Moore neighborhood. Horizontal
Interaction is governed by a random process; thus, the probability for a single cell to develop
cancer increases when cancer cells are nearby in its neighborhood (Figs 5, 6 and 7).
The condition for halting the program consists either of the tissue comprising 75% cancer
cells or reaching 20,000 steps in the simulation. It is worth noting that in this model, we do not
pretend to simulate the growth of cancer masses; rather, we simulate chromosomal variations
as the cancer cells grow. Therefore, the movement of the agents does not correspond to the
natural dynamics of tissue growth, but rather, chromosomal alterations are simulated
Simulation and results
We define two different experiments, each consisting of 100 runs with 20,000 iterations of the
ABM-Cancer model in the NetLogo framework, with some initial conditions for the density of
cell growth and cell death rate set at fixed values. For the initial experiments E1 and E2, the
Clinical Intervention variable has been set as false. For experiments E11 and E21 , this variable
has been set as true. The main difference between the E1 and E2 experiments is the choice of
values for cell density and death rate, as shown in the Table 1.
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Fig 4. Dynamics of the ABM-Cervical-Cancer model with the Clinical Intervention variable.
Fig 5. Neighborhood in the ABM-Cervical-Cancer model.
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Fig 6. ªHorizontalº interaction.
Fig 7. ªVerticalº interaction or mitotic transmission.
Experiments E1 and E2 showed similar statistical behavior. In 18% of the runs of experiment
E1, CIN1 lesions appear, which is consistent with the 16% prevalence of cervical cancer due to
HPV infection, as reported in the literature [
]. Experiment E2 reveals a 12% prevalence
of CIN1 lesions. Both experiments showed a different mean duration, while nearly all of the
CIN1-positive cases in E1 had invasive cancer. In experiment E2, almost none of the runs
presented invasive cancer (Table 1).
On the other hand, runs in which Clinical Intervention was set as true exhibited a minor
prevalence of CIN1 lesions, as expected. In experiment E11 , there was an 11% prevalence, but
in experiment E21 , we obtained a 12% prevalence, the same as in E2 with the absence of Clinical
Intervention. Experiment E21 exhibits interesting behavior: although Clinical Intervention is
present, in cases where CIN1 lesions appear, invasive cervical cancer is more likely to develop;
therefore, the simulation does not reach 20,000 steps, which may be a pattern caused by
reaching the charge capacity of the system.
In Table 2, we show the arithmetical means of the results of the numerical experiments in
the ABM-Cervical-Cancer model, summarizing the statistical behavior of the model.
Dispersion analysis shows that there is a correlation between the heterogeneity of
chromosomal alterations and cancer progression. An analysis of the time series shows that in cases
where CC has developed, non-deleterious transformed cells are more prevalent than
deleterious transformed cells. In subsequent figures, we depict some runs of experiment E1. Fig 8
In experiments E2 and E11 , simulations reached 20,000 steps, and in both cases, we can
observe that an oscillation occurs in both deleterious and non-deleterious alterations. In
experiment E1, we have a more interesting behavior: we have a noisy oscillation in both alterations,
although in the case of E11 , the oscillations are bound due to Clinical Intervention. On the
other hand, E2 exhibits an initial spike in both alterations, produced by the fast spread of the
Fig 8. Time series for run 39 of experiment E1.
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Fig 9. Histograms of frequencies and recounts in run 8 of experiment E11 . ND stands for non-deleterious, and DEL stands for deleterious.
cancer cells, but eventually, the number of transformed cells reaches a stationary state. The
main difference among these three experiments is that only in experiment E1 were we able to
reproduce invasive cancer. Therefore, it is in this experiment that we expected to find the
more interesting behavior.
In Fig 9, we present the histograms of the frequencies and recounts of deleterious and
nondeleterious alterations for run 8 of E11 .
The progression of chromosomal alteration when non-deleterious mutations is present will
probably drive the development of CC, acting as a selective mechanism; however, when
deleterious mutations are present, cell death will probably rise. This can be observed in the results of
our simulation. In the figure below, we illustrate the progression of CIN1 and CIN3 lesions
and the progression of cervical cancer in run 39 of experiment E1 (we choose run 39
The development of cancer can be seen as a process of accumulating mutations and
chromosomal alterations, with the selection of cells that, to the best of their ability, adapt to their
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Fig 10. CIN lesion progression with deleterious alteration.
perturbed environment. The survival of the transformed cells is driven by the sequential
accumulation of genetic alterations in sets of genes that control cell proliferation and the
differentiation of signal transduction pathways. The number and types of somatic mutations
accumulated during cancer progression are variable among different cancer types. Alterations
typically include allele loss, point mutations, amplifications, and others, but these alterations
are essentially divided between alterations that are deleterious and those that are
non-deleterious to the cell [
In the oncology literature, the terms ªdriver genesº and ªpassenger genesº are widely used.
Oncogenes and tumor suppressors are considered to be driver genes. Mutations in these genes
result in the gain or loss of function and stimulate, either directly or indirectly, cellular survival
and proliferation. Mutations that promote cancer development are considered driver
mutations, and those that are not relevant in cellular transformation are called passenger mutations
]. Most of the mutations present in the cell are passengers. However, as the rate of
mutations increases, the cell acquires a mutator phenotype that promote cellular transformation.
During this stage, the increase in the number of mutations in driver genes is evident [
the other hand, in systems biology, specifically in the study of networks, the term ªhubº is
introduced as a central node. In this context, Palaniapan et al. defined hubs as highly
connected nodes in a network, which can have a deleterious effect on the cell in the event that they
are removed, whereas driver genes are those that promote tumor progression through the gain
or loss of function (oncogenes and tumor suppressors, respectively) [
]. The human genome
has drivers and passenger genes that can regulate the cell cycle, programmed cell death or
apoptosis and other cellular processes that determine cellular fate. These genes fulfill the
conditions of driver genes; mutations such as the loss or gain of function in driver genes are not
deleterious to the cell. In this context, we can consider these mutations as non-deleterious in
the same way as mutations are in passenger genes. Alterations in these genes change the
genetic and epigenetic networks in cancer cells and reflect changes in the cellular processes
defined above. In this framework, networks can be identified as the hubs or regions whose
removal could be deleterious to the cell [30±32].
Deleterious regions may be important hubs that make multiple (functional or physical)
connections with nodes that control tumor-cell behavior. It is currently not clear how the
products of deleterious regions are organized into networks. However, recent evidence
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suggests that they may be organized as critical hubs in clusters among networks, with some of
these mutated in the majority of cancers [
25, 31, 33
Some mutations are potentially deleterious to the cell, and in cancer progression, these do
not accumulate. A cell with mutations could have both desirable (non-deleterious) and
undesirable (deleterious) consequences. Cells with lethal deleterious mutations would be
eliminated, which would mitigate cancer progression. However, cells with non-deleterious
mutations would become dominant, which could predispose them to cancer progression.
During cancer progression, it becomes increasingly harder to eliminate deleterious mutations and
to fix beneficial mutations [
The types and number of documented somatic mutations in cancer are variable. The
mutations that are selected promote tumor progression. These non-deleterious mutations help to
explain why passenger and driver mutations are common in carcinomas. Interestingly, the
frequencies of non-deleterious mutations accumulate in the transformed cells [
]. However, in
our results, we found that deleterious mutations are more frequent in the early stages of cell
transformation. Multiple deleterious mutations are most frequently found in the precursor
lesion, which is invasive cancer [
]. Given the impossibility of human experimental
manipulations, the analysis of somatic alterations using computer simulations during cancer
progression provides a feasible pathway for generating insights into the transformation of cell
mechanisms in humans. Somatic alterations can reveal much about the cancer cell during
progression. During cancer progression, tumors may acquire new phenotype traits, such as the
ability to invade and metastasize, or may become clinically important when they develop drug
resistance. Acquired chromosomal alterations contribute to this progression [
The etiologic factor in cervical cancer and associated lesions is HPV infection. Two of the
oncogenes of HPV, E6 and E7, induce cell transformation. At the clinical level, lesions
associated with HPV infection are heterogeneous, and only one group progresses to invasive cancer.
In this context, the HPV type that infects the cell is important in the malignant progression of
the epithelium. HPV 16 infection is more likely to progress to cancer than infection with
another genotype [
]. The introduction of different specific HPV genotypes in our model
could potentially modulate the progression of precursor lesions to CC.
Computational models such as Cellular Automata (CA), Agent Based Modeling (ABM),
and their hybrids are in silico techniques for studying a variety of cancer behavior. Through
computational programming, it is possible to simulate cellular behavior according to the type
of mutations they present. Therefore, both CA and ABM have become powerful methods of
modeling that are widely used by cancer researchers. There are many altered cellular processes
in cancer, as well as the effects of different treatments, that have been modeled in
computational systems [
19, 39, 40
]. Other mathematical-computational methods important in cancer
research are network models. Network science has provided theoretical tools for
understanding how the interaction of cellular components gives rise to cancer as an outcome of such
interaction, such as in [
]. However, our approach does not consider all possible protein
interactions but instead explores a plausible mechanism that relates chromosomal alterations
to cancer development via emergent behavior of the cancerous cells.
In a hybrid model, each cell is often represented as an agent that behaves locally as a CA.
Agents can receive signals from the environment and neighboring agents and make decisions
based on these signals. In the context of cancer, an agent that simulates a transformed cell can
grow or undergo apoptosis in response to surrounding environmental signals [
cancer progression, cellular proliferation requires genomic stability; if not, the cell will
undergo apoptosis. In this regard, the dynamics of deleterious and non-deleterious mutations
can be simulated as a manifestation of cell death mediated by apoptosis; i.e., deleterious
mutations in precursor lesions are lethal to the cells. Thus, the latter do not progress to advanced
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lesions and cancer, while non-deleterious mutations in precursor lesions induce cellular
transformations and cancer, rendering hybrid modeling an ideal tool to model this process.
In this paper, we focused our efforts on the progression of chromosomal alterations in cervical
cancer by employing a hybrid computational model and especially focused on the manner in
which deleterious and non-deleterious alterations affect cancer behavior across different
precursor lesions in CC.
Interestingly, this study revealed a significantly high frequency of deleterious mutations in
precursor lesions and a low frequency in the mutations in CC. Precursor lesions of the cervix
are well defined, and their progression to CC shows that it can be seen as an accumulation of
deleterious mutations. Deleterious mutations are more common in precursor lesions, but
these do not occur in later or advanced stages of cancer.
Some extensions of the model may include new variables, for instance, a vaccination
variable. Vaccination could be simulated as another external stimulus that modulates the clinical
manifestation of HPV infection; therefore, it would be a weight function of the P variable. We
can also extend the model to simulate interactions among scales; thus, we can begin to
elucidate how chromosomal alteration is connected to other phenomenological manifestations of
cervical cancer by constructing a multi-scale version of the ABM-Cervical-Cancer model.
S1 File. Code for the NetLogo implementation of the ABM-CC model.
S1 Appendix. ODD for ABM-Cervical-Cancer ODD protocol for the ABM-CC model.
RP wishes to thank PRODEP-SEP 6986 for the support. The authors also wish to thank Dr.
Mauricio Salcedo for his constructive comments and suggestions.
Writing ± original draft: RP.
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1. Ojesina AI , Lichtenstein L , Freeman SS , Pedamallu CS , Imaz-Rosshandler I , Pugh TJ , et al. Landscape of genomic alterations in cervical carcinomas . Nature . 2014 , 506 ( 7488 ): 371 ±5. https://doi.org/10.1038/ nature12881 PMID: 24390348
2. Costa JL , Meijer G , Ylstra B , Caldas C . Comparative genomic hybridization copy number profiling: a new tool for translational research in solid malignancies . Semin Radiat Oncol . 2008 , 18 ( 2 ): 98 ± 104 . https://doi.org/10.1016/j.semradonc. 2007 . 10 .005 PMID: 18314064
3. Gandolfi G , Longo C , Moscarella E , Zalaudek I , Sancisi V , Raucci M , et al. The extent of whole-genome copy number alterations predicts aggressive features in primary melanomas . Pigment Cell Melanoma Res . 2016 Mar; 29 ( 2 ): 163 ± 75 . https://doi.org/10.1111/pcmr.12436 PMID: 26575206
4. Ma L , Cui P , Zhu J , Zhang Z , Zhang Z. Translational selection in human: more pronounced in housekeeping genes . Biol Direct . 2014 , 9 ( 1 ): 17 . https://doi.org/10.1186/ 1745 -6150-9-17 PMID: 25011537
5. Bignell GR , Greenman CD , Davies H , Butler AP , Edkins S , Andrews JM , et al. Signatures of mutation and selection in the cancer genome . Nature . 2010 ; 463 ( 7283 ): 893 ±8. https://doi.org/10.1038/ nature08768 PMID: 20164919
6. Albertson DG , Pinkel D. Genomic microarrays in human genetic disease and cancer . Hum Mol Genet . 2003 , 12 ( 2 ):R145± 52 . https://doi.org/10.1093/hmg/ddg261 PMID: 12915456
7. Laczmanska I , Skiba P , Karpinski P , Bebenek M , Sasiadek MM . Customized Array Comparative Genomic Hybridization Analysis of 25 Phosphatase-encoding Genes in Colorectal Cancer Tissues . Cancer Genomics Proteomics . 2017 Jan 2 ; 14 ( 1 ): 69 ± 74 . https://doi.org/10.21873/cgp.20019 PMID: 28031238
8. Policht FA , Song M , Sitailo S , O'Hare A , Ashfaq R , Muller CY ,et al. Analysis of genetic copy number changes in cervical disease progression . BMC Cancer . 2010 , 10 : 432 . https://doi.org/10.1186/ 1471 - 2407-10-432 PMID: 20712890
9. Hidalgo A , Baudis M , Petersen I , Arreola H , Piña P , VaÂzquez-Ortiz G , et al. Microarray comparative genomic hybridization detection of chromosomal imbalances in uterine cervix carcinoma . BMC Cancer . 2005 , 5 : 77 . https://doi.org/10.1186/ 1471 -2407-5-77 PMID: 16004614
10. Rositch AF , Soeters HM , Offutt-Powell TN , Wheeler BS , Taylor SM , Smith JS . The incidence of human papillomavirus infection following treatment for cervical neoplasia: a systematic review . Gynecol Oncol . 2014 , 132 ( 3 ): 767 ± 79 . https://doi.org/10.1016/j.ygyno. 2013 . 12 .040 PMID: 24412508
11. Mighty KK , Laimins LA . The role of human papillomavirus in oncogenesis . Recent Results Cancer Res . 2014 , 193 : 135 ± 48 . https://doi.org/10.1007/978-3- 642 -38965- 8 _8 PMID: 24008297
12. Caraway NP , Khanna A , Dawlett M , Guo M , Guo N , Lin E , Katz RL . Gain of the 3q26 region in cervicovaginal liquid-based pap preparations is associated with squamous intraepithelial lesions ans squamous cell carcinoma . Gynecol Oncol . 2008 , 110 ( 1 ): 37 ± 42 . https://doi.org/10.1016/j.ygyno. 2008 . 01 . 040 PMID: 18433848
13. Araujo A , Baum B , Bentley P. The role of chromosome missegregation in cancer development: A theoretical approach using agent±based modelling . PLoS One . 2013 , 8 ( 8 ): e72206. https://doi.org/10.1371/ journal.pone. 0072206 PMID: 23991060
14. Giaretta A , Di Camillo B , Barzon L , Toffolo GM . Modeling HPV early promoter regulation . Conf Proc IEEE Eng Med Biol Soc . 2015 ; 2015 : 6493±6 . PMID: 26737780
15. Ulam S. Some prospects and ideas in biomathematics . Ann Rev Bio . 1974 , 255 .
16. Escobar Ospina ME , Perdomo JG . A growth model of human papillomavirus type 16 designed from cellular automata and agent-based models . Artif Intell Med . 2013 Jan; 57 ( 1 ): 31 ± 47 . https://doi.org/10. 1016/j.artmed. 2012 . 11 .001 PMID: 23207013
17. Chiacchio F , Pennisi M , Russo G , Motta S , Pappalardo F. Agent-Based Modeling of the Immune System: NetLogo, a Promising Framework . BioMed Research International. 2014 ; 2014 :907171. https:// doi.org/10.1155/ 2014 /907171 PMID: 24864263
18. Beerenwinkel N , Schwarz RF , Gerstung M , Markowetz F . Cancer evolution: mathematical models and computational inference . Sys Biol . 2015 ; 64 ( 1 ):e1± 25 . https://doi.org/10.1093/sysbio/syu081
19. Wang Z , Butner JD , Kerketta R , Cristini V , Deisboeck TS . Simulating cancer growth with multiscale agent-based modeling . Semin Cancer Biol . 2015 , 30 : 70 ± 78 . https://doi.org/10.1016/j.semcancer. 2014 . 04 .001 PMID: 24793698
20. SzaboÂ A , Merks RM . Cellular potts modeling of tumor growth, tumor invasion, and tumor evolution . Front Oncol . 2013 , 3 : 87 .
21. Zhang Le , Wang Zhihui, Sagotsky Jonathan A ,Deisboeck Thomas S. Multiscale agent-based cancer modeling . J Math Biol . 2009 , 58 ( 4-5 ): 545 ± 59 .
22. Pepper John W., Vydelingum Nadarajen A. , Dunn Barbara K. , and Fagerstrom Richard M.. Agentbased Models in Cancer Prevention Research in Advances in Computational Modeling Research, editor: Anna Belya Kora. Nova Science Publishers, Inc.
23. Brown BN , Price IM , Toapanta FR , DeAlmeida DR , Wiley CA , Ross TM , et al. An agent-based model of inflammation and fibrosis following particulate exposure in the lung . Math Biosci . 2011 Jun; 231 ( 2 ): 186 ± 96 . https://doi.org/10.1016/j.mbs. 2011 . 03 .005 PMID: 21385589
24. Zhang YX , Zhao YL . Pathogenic Network Analysis Predicts Candidate Genes for Cervical Cancer . Comput Math Methods Med . 2016 ; 2016 :3186051. https://doi.org/10.1155/ 2016 /3186051 PMID: 27034707
25. Rambaldi D , Giorgi FM , Capuani F , Ciliberto A , Ciccarelli FD . Low duplicability and network fragility of cancer genes . Trends Genet . 2008 ; 24 ( 9 ): 427 ± 30 . https://doi.org/10.1016/j.tig. 2008 . 06 .003 PMID: 18675489
26. Bruni L , Diaz M , CastellsagueÂ M , Ferrer E , Bosch FX and de SanjoseÂ S. Cervical Human Papillomavirus Prevalence in 5 Continents: Meta-Analysis of 1 Million Women with Normal Cytological Findings . J Infect Dis . ( 2010 ) 202 ( 12 ) https://doi.org/10.1086/657321 PMID: 21067372
27. Peralta-RodrÂõguez R , Romero-Morelos P , Villegas-Ruiz V , Mendoza-RodrÂõguez M , Taniguchi-Ponciano K , GonzaÂlez-Yebra B , et al. Prevalence of human papillomavirus in the cervical epithelium of Mexican women: meta-analysis . Infect Agent Cancer . 2012 , 7 : 34 . https://doi.org/10.1186/ 1750 -9378-7-34 PMID: 23199368
28. Beroukhim R , Mermel CH , Porter D , Wei G , Raychaudhuri S , Donovan J ,et al. The landscape of somatic copy±number alterations across human cancers . Nature . 2010 , 463 ( 7283 ): 899 ± 905 . https:// doi.org/10.1038/nature08822 PMID: 20164920
29. Pon JR , Marra MA . Driver and passenger mutations in cancer . Annu Rev Pathol . 2015 ; 10 : 25 ± 50 . https://doi.org/10.1146/annurev-pathol- 012414 -040312 PMID: 25340638
30. Palaniappan A , Ramar K , Ramalingam S . Computational Identification of Novel Stage-Specific Biomarkers in Colorectal Cancer Progression . PLoS One . 2016 ; 11 ( 5 ):e0156665. https://doi.org/10.1371/ journal.pone. 0156665 PMID: 27243824
31. Koutsogiannouli E , Papavassiliou AG , Papanikolaou NA . Complexity in cancer biology: is systems biology the answer? . Cancer Med . 2013 ; 2 ( 2 ): 164 ± 77 . https://doi.org/10.1002/cam4.62 PMID: 23634284
32. Jalan S , Kanhaiya K , Rai A , Bandapalli OR , Yadav A . Network Topologies Decoding Cervical Cancer . PLoS One . 2015 ; 10 ( 8 ):e0135183. https://doi.org/10.1371/journal.pone. 0135183 PMID: 26308848
33. Wang N , Xu Z , Wang K , Zhu M , Li Y . Construction and analysis of regulatory genetic networks in cervical cancer based on involved microRNAs, target genes, transcription factors and host genes . Oncol Lett . 2014 ; 7 ( 4 ): 1279 ± 1283 . https://doi.org/10.3892/ol. 2014 . 1814 PMID: 24944708
34. Bauer B , Siebert R , Traulsen A . Cancer initiation with epistatic interactions between driver and passenger mutations . J Theor Biol . 2014 , 358C: 52 ± 60 . https://doi.org/10.1016/j.jtbi. 2014 . 05 .018
35. Thomas LK , Bermejo JL , Vinokurova S , Jensen K , Bierkens M , Steenbergen R , Bergmann M , et al. Chromosomal gains and losses in human papillomavirus-associated neoplasia of the lower genital tractÐa systematic review and meta-analysis . Eur J Cancer . 2014 ; 50 ( 1 ): 85 ± 98 . https://doi.org/10. 1016/j.ejca. 2013 . 08 .022 PMID: 24054023
36. Martincorena I , Luscombe NM . Non-random mutation: the evolution of targeted hypermutation and hypomutation . Bioessays . 2013 , 35 ( 2 ): 123 ± 30 . https://doi.org/10.1002/bies.201200150 PMID: 23281172
37. Alloza E , Al-Shahrour F , Cigudosa JC , Dopazo J. A large scale survey reveals that chromosomal copynumber alterations significantly affect gene modules involved in cancer initiation and progression . BMC Med Genomics . 2011 , 4 : 37 . https://doi.org/10.1186/ 1755 -8794-4-37 PMID: 21548942
38. Kang H , Shibata D. Direct measurements of human colon crypt stem cell niche genetic fidelity: the role of chance in non-darwinian mutation selection . Front Oncol . 2013 ; 3 : 264 . https://doi.org/10.3389/fonc. 2013 .00264 PMID: 24133655
39. Wang J , Zhang L , Jing C , Ye G , Wu H , Miao H ,et al. Multi-scale agent-based modeling on melanoma and its related angiogenesis analysis . Theor Biol Med Model . 2013 , 10 : 41 . https://doi.org/10.1186/ 1742 -4682-10-41 PMID: 23800293
40. Chapa J , Bourgo RJ , Greene GL , Kulkarni S , An G . Examining the pathogenesis of breast cancer using a novel agent-based model of mammary ductal epithelium dynamics . PloS One . 2013 ; 8 ( 5 ):e64091. https://doi.org/10.1371/journal.pone. 0064091 PMID: 23704974
41. Poleszczuk J , Hahnfeldt P , Enderling H . Biphasic modulation of cancer stem cell-driven tumour dynamics in response to reactivated replicative senescence . Cell Prolif . 2014 , 47 ( 3 ): 267 ± 76 . https://doi.org/ 10.1111/cpr.12101 PMID: 24666838