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Seminars in Cancer Biology xxx (2014) xxx–xxx

Contents lists available at ScienceDirect

Seminars in Cancer Biology

j o ur na l ho me page: www.elsev ier .com/ locate /semcancer

eview

ancer systems biology and modeling: Microscopic scale andultiscale approaches

li Masoudi-Nejada,∗, Gholamreza Bidkhoria, Saman Hosseini Ashtiania, Ali Najafia,oseph H. Bozorgmehra, Edwin Wangb,c

Laboratory of Systems Biology and Bioinformatics (LBB), Institute of Biochemistry and Biophysics, University of Tehran, Tehran, IranNational Research Council Canada, Montreal, QC H4P 2R2, CanadaCenter for Bioinformatics, McGill University, Montreal, QC H3G 0B1, Canada

r t i c l e i n f o

eywords:ancerystems biologyultiscale modeling

ell proliferation and survival

a b s t r a c t

Cancer has become known as a complex and systematic disease on macroscopic, mesoscopic and micro-scopic scales. Systems biology employs state-of-the-art computational theories and high-throughputexperimental data to model and simulate complex biological procedures such as cancer, which involvesgenetic and epigenetic, in addition to intracellular and extracellular complex interaction networks. Inthis paper, different systems biology modeling techniques such as systems of differential equations,stochastic methods, Boolean networks, Petri nets, cellular automata methods and agent-based systemsare concisely discussed. We have compared the mentioned formalisms and tried to address the span of
applicability they can bear on emerging cancer modeling and simulation approaches. Different scales ofcancer modeling, namely, microscopic, mesoscopic and macroscopic scales are explained followed by anillustration of angiogenesis in microscopic scale of the cancer modeling. Then, the modeling of cancercell proliferation and survival are examined on a microscopic scale and the modeling of multiscale tumorgrowth is explained along with its advantages.
© 2014 Elsevier Ltd. All rights reserved.

. Introduction

Cancer is a disease mainly derived from mutations in singleomatic cells that deviate from the normal routes of proliferation,igrate to adjacent normal tissues, and end in secondary tumors

metastasis) on sites different from the initial origin. In humaneings, cancer refers to at least 100 versions of a disease that canevelop in almost any tissue in the body. Despite the fact that eachancer type has unique attributes, all these different tumors evolveccording to a common scheme of progression that includes geneticnd epigenetic incidents in addition to a complex network of inter-ctions between cells and the extracellular matrix in the host tissue.ancerous cells communicate with their micro-environment in aay that can promote their growth, survival and the manifestation

Please cite this article in press as: Masoudi-Nejad A, et al. Cancer syapproaches. Semin Cancer Biol (2014), http://dx.doi.org/10.1016/j.sem

f distant metastasis [1].Successful treatments for cancer stems from an iterative pro-

ess that depends on experimental research advances as well as

∗ Corresponding author. Tel.: +98 21 6695 9256; fax: +98 21 6640 4680.E-mail addresses: [email protected], [email protected]

A. Masoudi-Nejad).URL: http://LBB.ut.ac.ir (A. Masoudi-Nejad).

ttp://dx.doi.org/10.1016/j.semcancer.2014.03.003044-579X/© 2014 Elsevier Ltd. All rights reserved.

feedback from clinical trials in which it is feasible to learn whetherfundamental ideas and related theoretical and biological modelsare demonstrating a therapeutic benefit [2]. Due to the complex-ity of biological systems it is hard to merely rely on experimentalobservations in order to predict the behavior of such systems [3].Therefore, an increased use of mathematical modeling to under-stand tumor progression, directs the design of new experiments byintroducing likely candidates for further clinical investigation, andpresents novel approaches to cancer therapy. Consequently, it isnecessary to generate appropriate models for simulation purposes[3]. Models are based on various levels of abstraction, for instance torepresent DNA, Protein or RNA, the sequences of predefined lettersare used. Chemical structures are depicted as graphs and complexprotein structures are represented by graph-theoretical descrip-tions [4,5]. For network depiction, wireframe graphs are used. Suchgraphs are differentiated using various definitions of vertices, edgesand corresponding labels. For dynamic properties, mathematicaltheorems are used at distinct levels of abstraction. In this regardlogical formalisms are usually used for Boolean modeling, differen-

stems biology and modeling: Microscopic scale and multiscalecancer.2014.03.003

tial equations are often applied for continuous properties, discreteformalisms are utilized for Petri net modeling and stochastic prin-ciples are mainly employed to deal with the stochastic propertiesof chemical reaction networks.

dx.doi.org/10.1016/j.semcancer.2014.03.003


http://www.sciencedirect.com/science/journal/1044579X

http://www.elsevier.com/locate/semcancer

mailto:[email protected]

mailto:[email protected]

http://LBB.ut.ac.ir


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ARTICLESCBI-1123; No. of Pages 10

A. Masoudi-Nejad et al. / Seminar

Recently, data-driven cancer modeling has emerged as anmportant field in cancer research [6,7]. Especially, some of the cur-ent cancer models that include an array of different time-spacecales, i.e. multiscale cancer models have become in the lime-ight. This is mainly because such multiscale models are capablef using diverse patient data to make exclusive predictions forach patient [8]. From another angle of view, such formalismsre divided into two main categories. A bottom-up (bottom–top)pproach investigates the constituent elements to prepare theecessary foundation to predict the whole system behavior. Theottom-up formalisms are appropriate to simulate cancer-relatedraits caused by cell–host and cell–cell interactions including sig-aling pathways [9]. Conversely, a top-down approach tries toropose detailed explanations on an observed behavior or char-cteristic [10].

. Modeling algorithms

Biological pathways are naturally versatile. To understand thenteractions of these pathways, beside the need for the identifi-ation of the constituent elements and their interactions, we alsoeed to know how their dynamics evolve over the time. Differentodeling and simulation techniques used in systems biology are

he systems of differential equations, stochastic methods, Booleanetworks, Petri nets, �-calculus, cellular automata methods, agent-ased systems, and hybrid approaches.

Methodologies for computational analysis encompass a wideange depending on the problem to be dealt and the exper-mental data at hand, ranging from highly abstracted modelsenerated by correlative regression to highly deterministic mod-ls on the basis of differential equations. Network componentnteraction and logic modeling techniques lie between the ones

entioned above [11]. Main modeling formalisms are brieflyxplained below.

. Petri nets

Petri nets denote a refinement of monopartite graph modelso bipartite directed graphs that are employed to model concur-ent causal systems. This formalism has been satisfactorily appliedn many areas of biology, e.g. to simulate metabolic networks12–15], signal transduction pathways [16] and also gene reg-latory systems [17,18]. The pivotal ideas in Petri nets are theonsecutive distinction between active and passive nodes and thetilization of discrete movable objects to define system’s dynam-

cs. The set of nodes includes places for the passive part, indicatingiochemical species, and transitions as the active part, denot-

ng chemical reactions. The movable objects are named tokens.ccording to firing rules, tokens are transferred by means of

he PN from one place to another. Originally, PNs were limitedo qualitative simulation within discrete time steps. However,dvanced PNs are capable of mimicking Boolean, timed-discrete19], Bayesian, Fuzzy [20], stochastic [21–23], continuous systemsf ordinary differential equations [24], and even hybrid systems25,26].

. Bayesian networks

Another computational formalism for modeling, based on graph representation, is Bayesian network (BNs). Bayesianetworks that describe both direct and indirect pathway interac-


ions in terms of stochastic influences of specific components onther components, have been proved useful for disclosing the oper-tion of cell signaling networks but has not been widely appliedo cancer biology problems [27]. Bayesian modeling is beneficial

PRESSncer Biology xxx (2014) xxx–xxx

because biology is intricate and biological data are accompa-nied with noise. Bayesian network models explain the effects ofpathway elements upon each other in an influence diagram for-mat. Boolean networks can only manage discrete values, however,the Bayesian formalism can handle continuous values as well. InBayesian network, a node denotes a random variable for the condi-tional probability distribution of each pathway element. Bayesianmodeling provides the possibility to describe stochastic processesand to handle uncertainty, incomplete knowledge and also noisyobservations. In such networks, restrictions are the static and theacyclic nature of Bayesian networks [28]. In BNs, the relationshipsbetween variables, e.g. proteins and genes are represented by con-ditional probability distributions (CPDs) of the form p (G2|G1), i.e.the probability of G2 given G1. Regarding discrete variables, proba-bility distributions are represented as conditional probability tables(CPTs) including probabilities that are the model parameters. ForBNs using continuous variables, conditional probability densities areused in a similar manner as CPTs [29].

5. Cellular automata

Cellular automata (CA) is a discrete dynamical system thatmeans time, space and the space of the system are discrete. Anypoint assumed in a regular spatial lattice, i.e. a cell, may have eachone of a finite number of states. The states of the cells in the men-tioned lattice are updated in accordance with a local rule. In otherwords, the state of a cell at a particular time is merely dependent onits own state and the states of its nearby neighbors at the previoustime step. Every cell on the lattice is updated synchronously.

Extensive studies of CA have been carried out by S. Wolframcommencing in the 1980s [30]. Use of CA in biology is primarilyfocused on systems biology subjects, such as shape space simula-tions of the immune system [31], artificial brain development [32],the study of morphogenesis in simple cellular systems [33], model-ing the competitive growth of two underwater species Chara asperaand Potamogeton pectinatus [34] and the modeling of an enzymaticreaction [35].

Additionally, there is another type of CA, named Dynamic CA(DCA), which varies from conventional CA in that the DCA modeltries to simulate real motions by using Brownian dynamics [36],that is to say, the motions of particles are intended to imitatethe motions found in real macromolecules. Consequently, randomobjects cannot be taken up and randomly scattered over the lat-tice in each time step as they are in the majority of CA models.Instead, DCA needs regular time steps in which the lattice sizeand time steps could be small enough to fulfill physical laws orexperimentally measured parameters such as diffusion rates.

6. Multi-agent systems

An agent is an interactive computer system, which is put insome environment conditions and is autonomously able to per-form in such conditions to satisfy its design objectives. Agentsare autonomous and interactive entities and may be mobile. Theyhave the potentiality for adaptation and learning. Multi-agent sys-tems (MAS) are a set of agents that undergo interactions in acertain dynamic environment. A comprehensive introduction toMAS can be found in [37]. MASs are able to handle the complexityof solutions through modeling, decomposition and managing theinterrelationships between components [38]. Multi-agent systems


cal system to a set of agents; multi-agent systems are inherentlypowerful tools when it comes to modeling complex systems [38].Modeling complex systems necessitates a profound understandingof the system both regarding its structure and its behavior.


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. Ordinary differential equations

One of the most ubiquitously used formalisms for modelingiological systems is based on ODEs. A differential equation isefined as an equation declaring the relationship between a func-ion and some of the first or higher order derivatives of it. Basically,

differential equation defines how a variable, such as the initialoncentration of a substance, changes by the passing of time. Thisappens through interrelating the rates of changes with respect tohe simultaneous concentrations [39–42].

Regarding signal transduction network models, analytical meth-ds indicate the more realistic moiety of the model spectrum. Theentioned models involve nonlinear systems of ordinary differen-

ial equations, where each variable represents the concentration of certain gene product [43]. As an instance, assume the succeeding

eaction in which the product P1 is produced: ∅k1−→P1. This ordi-

ary reaction does not include any catalyst and can be modeled bysing mass action kinetics. Mass action describes the behavior ofeactants and products in a simple chemical reaction. Mass actioninetics explains such a behavior through an equation by whichhe rate of a chemical reaction is directly kept in proportion to theoncentrations of the reactants, where k1 symbolizes the reactionate constant. The above reaction is called a zero-order reaction.n a first-order reaction, the reaction rates are proportional to theoncentration of one reactant, here S. As an example, assume theeaction below in which the substrate S is changed into the prod-

ct P: S2k2−→P2. The reaction rate goes on as follows: v = k2[S2]. It

s clear that the reaction rate (v) is directly proportional to someactors such as [S2], i.e. the more the concentration of the S2, theigher the reaction rate. According to the mentioned equation, ithould not be difficult to present differential equations to define theate of change in [S2] and [P2]: d[S2]/dt = − K2[S2] ; d[P2]/dt = K2[S2].n order to model and simulate reactions, it is indispensable tonow substrates’ and products’ initial concentrations. A second-rder reaction is proportional to the square of the concentrationsf an individual reactant or both reactants. It is possible to modeleversible reactions by two specific reactions or by one reaction.or example: A + B < k3/kr3 > C. The reaction rate of C production is:

= k3[A][B] − kr3[C], where k3 denotes the rate constant of the for-ard direction and kr3 is related to the reverse one. The above


nzymatic reaction rate, with respect to the Michaelis–Mentenquation is: V = Vmax[S]/(Km + [S]), where, [S] presents the concen-ration of substrate, Vmax denotes the maximum rate. The Michaelisonstant Km indicates the substrate concentration at which the

able 1ystems biology simulation tools.

Name Category Model representation

MATLAB, withSimBiologyToolbox

Continuous and stochastic Mathematical (e.g. ODE)

XPPAut Continuous and stochastic ODE

Copasi Continuous and stochastic ODE

Virtual Cell Continuous and stochastic ODE-based, PDE

Systems BiologyWorkbench,including Jarnac andJDesigner

Discrete, continuous andstochastic

ODE/SBML

Narrator Continuous and stochastic Graphical, ODE-based

E-CELL Continuous Object-oriented

SPiM Stochastic Calculus

BioSigNet Discrete Graphical

BIOCHAM Discrete and continuous Logical + kinetic models

PRISM Discrete Stochastic process algebra

PEPAWorkbench Discrete Stochastic process algebra

PRESSncer Biology xxx (2014) xxx–xxx 3

reaction rate approaches half the Vmax [44]. Different models whichare usually employed in the literature can be classified from the cal-culus point of view as: ordinary differential equations (ODEs) [44],delay differential equations (DDEs), Fredholm integral equations(FIES) (in the estimation of parameter problem), stochastic differ-ential equations (SDEs), partial differential equations (PDES) andintegro-differential equations (IDEs) [45]. Different software pack-ages can be applied for different types of models for simulations andnumerical analysis. Table 1 illustrates some of the systems biologysimulation tools concisely.

8. Cancer modeling

Tumors are notable examples of complex systems that canundergo self-organization. Because of their intrinsic complexity, itis essential to analyze their growth at different scales. It involvesa number of phenomena that take place over a variety of spatialscales encompassing from tissue (for instance, tissue invasion andangiogenesis) up to molecular length scales (for example, genesilencing, mutations and signal transduction). The timescales rangefrom seconds for signaling to years for prostate cancer.

The complexity of cancer development expresses itself at least inthree scales that can be distinguished and described using mathe-matical models, namely, microscopic, mesoscopic and macroscopicscales [46] as described further below:

1) The microscopic scale represents molecular and sub-cellularphenomena taking place within the cell or at its plasma mem-brane. Instances are gene mutations or modifications in geneexpression patterns, variations of signaling cascades and/ormetabolic pathways, cytoskeleton rearrangements and alteredmembrane activities, protein traffic within the cell, cell cycleprogression and the control of the cell cycle, etc. Biologicalnetworks can be categorized into four main types: Metabolicnetworks, gene regulatory networks (GRN), protein–proteininteraction (PPI) networks and signal transduction networks.Metabolic networks are applied to describe the basic bio-chemistry in a cell. Biologically important reactions have beenexplained in terms of reaction pathways catalyzed by enzymes,and metabolic networks are systematic collections of such


biochemical data. The metabolic process can be defined as arepertoire of biochemical transformations ending in the con-sumption as well as the production of one or more metabolites[47]. GRNs are characterized as directed graphs. They involve

Function URL

General-purpose mathematicalenvironments, simulation andanalysis

www.mathworks.com

General purpose; simulation,analysis

www.math.pitt.edu/ bard/xpp/xpp.html

Simulation and analysis www.copasi.orgSimulation and parametersensitivity analysis

www.nrcam.uchc.edu

Data-exchange framework forData-exchange framework formodeling, simulation and analysis

sbw.kgi.edu

Modeling and simulation www.narrator-tool.orgModeling and simulation www.e-cell.orgSimulation http://www.doc.ic.ac.uk/ anp/spim/Reasoning, hypothesis testing www.public.asu.edu/ cbaral/biosignetSimulation and analysis contraintes.inria.fr/BIOCHAMGeneral purpose; Analysis((modelchecking))

www.cs.bham.ac.uk/ dxp/prism

General purpose; Analysis www.dcs.ed.ac.uk/pepa/tools


http://www.mathworks.com/

http://www.math.pitt.edu/_bard/xpp/xpp.html

http://www.copasi.org/

http://www.nrcam.uchc.edu/

http://sbw.kgi.edu/

http://www.narrator-tool.org/

http://www.e-cell.org/

http://www.doc.ic.ac.uk/_anp/spim/

http://www.public.asu.edu/_cbaral/biosignet

http://contraintes.inria.fr/BIOCHAM

http://www.cs.bham.ac.uk/_dxp/prism

http://www.dcs.ed.ac.uk/pepa/tools

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interrelated genes by directed edges in such way that one generegulates the transcription of the other one [48]. PPI networksare depicted as undirected graphs. In these networks, an undi-rected edge is drawn between each couple of proteins for whichthere is evidence of physical or biochemical interactions. A PPInetwork mainly embraces information about how different pro-teins operate in coordination with others to facilitate biologicalprocesses within the cell. Protein function prediction is still abottleneck in computational biology research and many exper-imental and computational methods have been devised to inferprotein function from its interactions with other biomolecules[49]. In signal transduction networks, reactions mainly denotecomplex formation, phosphorylation, dephosphorylation, acti-vation, deactivation and so forth. The processes involved inthis complex system comprise many interacting molecules andcannot be deduced by the reductionism approach alone. Infact, signal transduction networks perform as a bridge betweenthe extracellular environment and the intracellular response[50,51].

) The mesoscopic scale indicates cellular interactions betweenhost and tumor cells such as endothelial cells, lymphocytes,macrophages and also the local components of the extracellu-lar matrix (ECM) [52]. Moreover, this level includes cell–matrixand cell–cell adhesion mechanisms that determine the invasivetraits of cancer cells, tumor growth and so forth.

) The macroscopic scale deals with processes happening at thetissue level such as cell migration, convection and diffusion ofchemical factors and nutrients, mechanical stress, invasion ofnearby tissues, rupture of capsules or basement membranes andso forth.

Therefore, cancer growth is indeed a multiscale, nonlinearynamical problem whose basic evolution is impossible to beuantitatively explained without the aid of mathematical mod-ls [1]. Models usually fall into two main categories; they areither discrete or continuum with respect to the fact that howhe tumor tissue is represented. Discrete models represent distinctells on the basis of a specific set of biophysical and biochemical


ules, which is especially useful for studying genetic instabil-ty, carcinogenesis, natural selection and cell–cell in addition toell–microenvironment interactions. Continuum models look uponumors as an assemblage of tissue and herein, the principles from

ig. 1. The connection between macrosocopic, mesoscopic and microscopic scales. The arrof cancer growth, indicating that models (subsystems) at a specific scale apply informatio


continuum mechanics are used to describe cancer-related variables(e.g. cell volume fractions, nutrients and concentrations of oxygen)as continuous fields by using PDEs and IDEs [53]. On a micro-scopic scale ODEs are commonly applied for continuum modelingwhere quantitative data are available. The third modeling methodemploys a hybrid combination of both discrete and continuous rep-resentations of tumor cells and microenvironment components, inorder to develop multiscale models.

Fig. 1 shows that three scales, namely, macroscopic, mesoscopicand microscopic are interrelated because the tumor growth isdependent to cell population density, nutrient concentration andchemical factors, cell–cell communication, cell behavior, intracel-lular mechanisms, pressure, etc. each of the mentioned items aremodeled on specific scales.

Biological networks in subcellular compartments are modeledon a microscopic scale. These networks are often modeled usingODE, Petri net, Boolean network and hybrid methods. Cellularautomata and agent-based approaches are used as well.

The produced output and the calculated parameters throughsubcellular modeling are used in cellular, cellular communicationsand tissues models on a mesoscopic or macroscopic scale. More-over, the production of the proteins that are involved in the celljunctions and the cell–matrix connections and the production ofthe molecules to be secreted and diffused on the tissues are alsoconsidered as important modeling parameters for the mesoscopicand macroscopic scales. The mentioned parameters are obtainedfrom microscopic models.

As an instance, assume the functional state (F) of a cell is definedby the molecular concentrations of EGFR, PLC gamma and EGF suchthat the cell immigration, proliferation and apoptosis are depend-ent on the increase or the decrease of the mentioned factors in thecell [54]. Suppose that a cell population size is N and for each cell thefunctional state (F) exists. The rate of the cell number change, thecells being of a specific type, and in the F state at the time ‘t’ dependson: (1) Li that denotes the sum of all cellular processes such as theincrease and the decrease of the gene expression, mutation, inter-action alterations, etc. which change the F. (2) Ji indicates cell–cellconnections which lead to the F in one or more interacting cells


and the proliferative interactions (Pi) or deadly interactions (Di)are observed. (3) Si that is related to the external sources and leadsto the formation of I cells. Herein, the assessment of the cell inter-nal changes which end in the determination of the F, manifested

ws show the reciprocal interdependence between the levels in multiscale modelingn from other scales [60].


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n microscopic scale. The evaluation of the cell population changesith size N occurs on a mesoscopic scale which is fully dependent

n the changes to F. This fact demonstrates that there’s a mutualependency between the mesoscopic and the microscopic scales.

In macroscopic scale, for obtaining the rate of the cell concen-rations changes, the cell generation parameters are needed as wells those related to the cell death, the lack of the cell conditionsuctuations from one state to another, cell migration, materialsistribution and absorption. The materials distribution pertainso the materials such as oxygen, nutrients and so forth [55,56].hese items disclose the relationships between the three scales arenevitably woven together.

. Angiogenesis in microscopic scale of the cancer modeling

Angiogenesis is defined as the development of new bloodapillaries with the origin of preexisting vessels, which is a pivotaltep in tumor growth and metastasis. Many growth factor com-lexes take part in angiogenesis regulation, involving the vascularndothelial growth factor (VEGF) system of minimum five ligands,.e. VEGF-A, PlGF, VEGF-B, VEGF-C and VEGF-D, in addition to threeeceptors, i.e. VEGFR1, VEGFR2 and VEGFR3, the fibroblast growthactor (FGF) system including at least 18 ligands, namely, FGF1o FGF10 and FGF16 to FGF23, and four receptors, i.e. FGFR1 toGFR4, the angiopoietin (Ang) system involving at least four lig-nds, i.e. ANG1 to ANG4 and two receptors, i.e. TIE1 and TIE2, thelatelet-derived growth factor (PDGF) system comprising at leastour ligands, i.e. PDGF-A to PDGF-D and two receptors (PDGFR-lpha and PDGFR-beta), and the insulin-like growth factor (IGF)ystem embracing at least two ligands, i.e. IGF1 and IGF2 and twoeceptors, i.e. IGF1R and IGF2R [57].

An ODE simulation of the result of the mentioned vascularemodeling on tumor growth has been performed [58]. This modelncluded starvation-induced VEGF expression in tumors as thenly angiogenic factor, while considering the destabilization of theature vessels and the regression of the immature vessels by Ang2.ypoxic cells secrete angiogenic factors in the vicinity of the cen-

er of the necrotic region of the tumor. The alpha subunit of theIF1 largely regulates the cellular response to hypoxia. In a hypoxic

ituation the cytosolic HIF1� skips being hydroxylated and pene-rates into the nucleus. Then it binds HIF1�/ARNT and triggers thengiogenic pathway, involving VEGF and its receptor VEGFR2/Flk1.

The hypoxic response pathway has been modeled using a sys-em of ODEs indicating the molecular kinetics of 17 compounds andhe data have been validated from several other [59]. The modelroved both a rapid, switch-like response to low oxygen concen-rations as well as a slower one, depending on the existence ofytosolic iron, ascorbate and PHD2 [60]. Finley et al. proposed aodel of VEGF transport and kinetics in the mice that had devel-

ped tumor, which gave a simulation of the interactions betweenhe VEGF isoforms and receptors, i.e. VEGFR1 and VEGFR2, in addi-ion to co-receptors, i.e. NRP1 and NRP2. This is perceived as aomplementary study along with experimental investigations inice and brings a framework with which it is feasible to examine

he effects of anti-VEGF agents. It can lead to the optimization ofnti-angiogenic therapeutics parallel to clinical data analysis [61].

In another study, an experiment-based model of VEGF kineticsnd transport was suggested to examine the distribution of theajor VEGF isoforms, i.e. VEGF121 and VEGF 165 in the body. Theodel has predicted that the free VEGF in the tumor interstitium

s seven to 13 times higher than that of plasma and is mainly in


he form of VEGF121 (more than 70%). These predictions were val-dated by experimental data. The model has additionally predictedhat the tumor VEGF would increase or decrease with anti-VEGFreatment being contingent upon tumor microenvironment,


denoting the significance of personalized medicine. The studysuggested that the rate of VEGF secreted by the tumor cells couldserve as a biomarker in order to predict the number of patientsthat were probable to respond to anti-VEGF treatment [62].

The VEGF–Bcl-2–CXCL8 pathway introduces new targets for thecreation of anti-angiogenic approaches involving short interferingRNA (siRNA) that can silence the CXCL8 gene and small moleculeinhibitors of Bcl-2 [63]. Jain et al. presented a validated mathe-matical model to predict the result of the therapeutic blockage ofVEGF, CXCL8 and Bcl-2 at various stages of the tumor progression.In accord with the experimental evidence, the model predictedthat reducing the production of CXCL8 in the early stages of devel-opment can lead to a lag in the tumor growth rate and vasculardevelopment, however, it had no significant effect when put to useat the late stages of the tumor progression. Moreover, numericalsimulations have demonstrated that blocking Bcl-2 up-regulation,be it at early stages or after the full tumor development, confirmsthat both tumor cells and microvascular density are stabilized atlow values indicating growth control. These findings have provideda deeper understanding of the facets of the VEGF–Bcl-2–CXCL8pathway, which are crucial mediators of tumor growth and vasculardevelopment both independently and in combination [64].

10. Cancer cell proliferation and survival in microscopicscale modeling

EGFR overexpression has been reported in neck and head, colon,non small cell lung cancer (NSCLC), breast, bladder, stomach, esoph-agus, cervix, ovary and endometrium cancers which is consideredas an indication for cancer prediction. EGFR mutations in kinasedomain are commonly known as activating mutations as they seemto trigger an increase in the kinase activity of the receptor. It hasbeen shown that ligand induced EGFR phosphorylation kineticsamong wild type and mutant EGFR are dissimilar. More over, itis confirmed that activation-kinetics of downstream factors suchas ERK, Akt and STAT3/5 are also different. EGFR signaling setsoff Ras/ERK, PI3K/Akt and STAT activation pathways (Fig. 2). Thesethree pathways are the main ones for cell proliferation and survival.Accordingly, mutations that lead to excessive activation of the men-tioned pathways may lead to cancer. In one of our previous studiesmathematical (ODE-based) models were developed representingEGFR signaling in normal and NSCLC EGFR signaling pathways, anddifferent dynamics and behaviors of these models were examined.For the first time we have simultaneously analyzed the mutationin both EGFR and PTEN and over-expression of PI3K, EGFR, Akt,STAT3 and Ras in NSCLC EGFR signaling in one study. Our simula-tion denoted the effect of EGFR mutations and increased expressionof certain factors in NSCLC EGFR signaling on each of three path-ways where levels of pERK, pSTAT and pAkt are increased. Theover activation of ERK, Akt and STAT3 that are the main cell pro-liferation and survival factors act as promoting factors for tumorprogression in NSCLC. In case of the loss of PTEN, Akt activity levelis considerably increased. Simulation results showed that in thepresence of erlotinib, downstream factors, i.e. pAkt, pSTAT3 andpERK are inhibited. However, in case of the loss of PTEN expressionin the presence of erlotinib, pAkt level would not decrease whichdemonstrates that these cells are resistant to erlotinib [44].

Comparable to the EGFR family members, insulin-like growthfactor type 1 (IGF1R) is a transmembrane tyrosine kinase receptor,which is encoded by the IGF1R gene [65]. Both activated EGFR andIGF1R prompt the signal transduction events involving the Ras/ERK


and PI3K/Akt pathways. The biological relationship between theproteins existing in EGFR and IGF1R signaling pathways and thedownstream PIK3 and MAPK networks has been modeled apply-ing a set of ordinary differential equations (ODEs) to study the


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Fig. 2. EGFR signaling pathways. Through EGF and EGFR interaction, the receptors undergo homo- or hetero dimerization causing auto phosphorylation of specific tyrosineresidues at the cytoplasmic end. After the phosphorylation of C-terminal tail, the Shc adaptor attaches to its site and Grb2 binds Shc, consequently, SOS is applied by Grb2.Moreover, Grb2 directly binds its receptor and accordingly SOS binds Grb2. Then, SOS converts Ras-GDP into Ras-GTP (the activated form of Ras). Ras in its activated forminduces Raf phosphorylation and activation. Raf is a kind of Serine/Threonine kinase with the capability of phosphorylation and activation of MEK. The activated MEK, canphosphorylate and activate ERKs (MAPKs). PI3K binds phosphorylated EGFR. Under such circumstances, PI3K is activated and then converts PIP2 into phosphatidyl inositolPIP3. PIP3 triggers Akt activation in such a way that PDK1 attaches to membrane PIP3, afterwards, PDK1 phosphorylates and activates Akt. Phospholipase C� directly bindsthe receptor and is activated and after being activated converts PIP2 by means of DAG and IP3. After the attachment of STAT to the receptor, the receptor phosphorylates ita us ands

tpwtitagamta

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nd STAT becomes a dimer. The mentioned activated dimer STAT3 enters the nucleurvival (depicted using “Pathway Builder Tool 2.0”).

ime behavior of the overall system, and the functional interde-endencies between the receptors, the proteins and kinases thatere involved. Bianconi et al. suggested a systems biology approach

o model EGFR and IGF1R pathways in NSCLC. They proposed ann silico model (on the basis of ordinary differential equations) ofhe pathways and examined the dynamic effects of receptor alter-tions on the time behavior of the MAPK cascade down to ERK thatoverns proliferation and cell migration. Moreover, a sensitivitynalysis of the proposed model was carried out and a simplifiedodel was proposed which allowed them to infer a similar rela-

ionship between EGFR and IGF1R activities and disease the diseaseftermath [66].

In 2004, Brown et al. established computational models of theGF and NGF activated ERK pathway in PC12 cells [67]. The topo-ogical structure of the model was initially constructed and then aovel ensemble method was used to automatically assign values


o model parameters on the basis of accessible experimental timeourse data. By means of this approach, models of the EGF and NGFctivated ERK pathway were generated and afterwards were usedo make a number of interesting predictions; for example the fact

promotes the expression of some necessary genes related to proliferation and cell

that knocking out Akt would have little effect on ERK activationwas predicted. The study by Orton et al. was focused on investigat-ing what effects different cancerous alterations exert on signalingthrough the EGF activated ERK pathway [68]. They generated a newmodel of the EGFR activated ERK pathway, which was verified bytheir own experimental data. Afterwards, they altered their modelto represent various cancerous situations such as Ras, B-Raf andEGFR mutations, as well as EGFR overexpression. Analysis of themodels demonstrated that different cancerous situations ended indifferent signaling patterns through the ERK pathway, particularlywhen compared with the normal EGF signal patterns. Moreover,the model points out the importance of receptor degradation innormal and cancerous EGFR signaling, and indicates that receptordegradation is a key contrast between the signaling from the EGFand nerve growth factor (NGF) receptors [68].

Tumor genome sequencing has generated many genomic alter-


ations, it is a big challenge to dissect, prioritize and uncoverthe functional importance of the genomic alterations and theunderlying mechanism that drive cancer development, pro-gression and metastasis. Zaman et al. have constructed breast


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ancer subtype-specific (i.e. luminal and basal subtypes) survivaletworks by integrating genome-wide RNAi screening data andxome-sequencing data [69]. These networks elucidate underlyingignaling mechanisms governing cancer cell survival and prolifera-ion, and imply selective pressures for evolutionary convergencef cancer genomic alterations. Differential network modeling ofhese networks showed that signaling mechanisms of the twoubtypes are different. A set of network genes (i.e. genes are dif-erentially different between the two subtype-specific networks)hose genomic alteration profiles (amplification and mutating sta-

us) are able to significantly distinguish breast tumor samples intouminal and basal subtypes, and furthermore, these networks pre-icted subtype-specific drug targets. Importantly, most (∼80%) ofhe predicted drug targets have been experimentally validated [69].

1. Modeling of multiscale tumor growth

In spite of the astronomically increasing molecular data, therowth of tumors, the metastasis of tumors toward healthy tis-ues, and the response of tumors to therapies are not considerablynderstood [70]. Therefore, mesoscopic and macroscopic modelingllow us to examine the cancerous cells behavior in tissue and toodel the tumor growth and the whole tumor behavior in order to

btain the crucial parameters involved in different conditions.Delsanto et al. have investigated multicellular tumor spheroids

MTS) on mesoscopic and macroscopic scales and suggested anntermediate model to fill the gap between a macroscopic formula-ion of tumor growth and a mesoscopic one. In mesoscopic MTS

odel the space is divided into concentric isovolumetric shells = 0, . . ., N, where n = 0 labels the central sphere of radius r0, andhe growth is controlled by local nutrient availability and pursuesccording to reproduction, migration, death and feeding. Nutrientsre diffused from the nth shell to the ones in the vicinity at a ratef ˛�n (available nutrient units �n) per unit area. Applying the WBEodel (first proposed for tumors by Guiot et al. [71]), they assumed

hat the central core of the dead cells (region Z0) is surrounded by annner layer, Z1, of quiescent cells, and by an outer layer, Z2, of activeells. Their assumption temporarily neglected any wrong position-ng. It is important to emphasize that the central core Z0 and thether two layers Z1 and Z2 do not need to be spherical, which meansot only can the macroscopic model be used to describe MTS’s, but

t can also model almost any type of prevascular in vivo solid can-ers [72]. Ferreira et al. have integrated the cellular (mesoscopic)nd tissue (macroscopic) scales. Moreover, their study introducesn effective stochastic cell kinetics managed by local probabili-ies for cell division, migration and death to provide a strategy toonnect the macroscopic diffusion equations for nutrients and/orrowth factors to cell response and interactions at the microscopiccale. In this model each tumor cell was selected at random, withqual probability, and one of three actions was carried out: Division,igration, Cell death. The mentioned system comprised a tissue fed

y a single capillary vessel. The tissue was depicted as a squareattice of size (L + 1) × (L + 1) with the lattice constant of �. The cap-llary vessel, being localized at the top of the lattice at x = 0 is thenly source that acts as a nutrients diffusion center from the tis-ue toward individual cells. Only three cell types were considered:ormal, cancerous and tumor necrotic cells. As the initial “seed”, aingle cancerous cell in the middle of the lattice (x = L�/2) and at

distance Y from the capillary vessel was introduced in the nor-al tissue, which is in accord with the theory of the clonal origin

f cancer. Periodic boundary conditions down the horizontal axisere used. The row i = 0 indicated a capillary vessel and the sites


ith i = L + 1 showed the external border of the tissue. The simulatedumors comprise a spatial structure including a central necroticore, an inner rim containing quiescent cells and a thin outer rimf proliferating cells in accord with biological data [73].


Lymphoma tumor growth was modeled through merging theexperimental and the computational models in which the rate ofchange of the growth, apoptosis, necrosis, blood vessel density,the VEGF and oxygen diffusion as well as the cell velocity wereestimated in accord with the experimental data. Their method toconstrain the computational model comprises both cell and tumor-scale methods as described in Fig. 3. Then the model was calibratedon the basis of the mentioned cell scale parameters so that the tissuescale parameters such as size and growth rate could be estimated.Their model predicted that the tumor growth reaches 5.2 ± 0.5 mmup to the 21th day, which was in accord with in vivo data. Addi-tionally, the angiogenesis behavior in cancerous tissue was alsomodeled which showed that the simulated endothelial tissue den-sity was higher in tumor core and the results revealed that thedifference in spatio-localization of the cells and vasculature, as wellas in the transportation in the tumor microenvironment may havea serious role in the tumor behavior [74]. In a similar study butmore computational (using agent-based modeling) melanoma wasmodeled in a multiscale manner. They examined angiogenesis atthe level of the melanoma tumor by using the intracellular func-tional state and intercellular scale and with respect to the VEGFconcentration [75].

Cell-based models incorporate a class of agent-based modelsthat imitate molecular and biophysical interactions between cells.One of the most common cell-based modeling approaches is thecellular Potts model (CPM), a multi particle cell- and lattice-basedformalism. The CPM has emerged as a popular and accessibleapproach for modeling mechanisms of multicellular processesinvolving cell sorting, angiogenesis or gastrulation. For a more com-prehensive review of the cellular Potts modeling of tumor growth,tumor invasion and tumor evolution, please refer to reference [70].Daub and Merks have modeled endothelial cells applying a cellu-lar Potts model (CPM) to examine the possible role of extracellularmatrix (ECM) guided cell motility in angiogenesis. The stochasticcell motility was simulated by iteratively contracting and expand-ing the defined domains with respect to a set of cell behavior rules.They used a partial-differential equation (PDE) representation forthe fields of extracellular matrix materials, diffusing growth factorsand proteolytic enzymes. Three PDEs described the concentrationsof VEGF, ECM and MMP components. The model explained thecell–matrix interactions at the level of distinct cells. They have dis-closed that an array of biologically-motivated cell behavioral rules,namely, haptokinesis, chemotaxis, haptotaxis and ECM-guidedproliferation is adequate for constructing sprouts and branchingvascular trees [76]. Sun et al. proposed a novel multiscale, agent-based computational model including both angiogenesis and EGFRmodules to investigate the brain cancer response under tyrosinekinase inhibitors (TKIs) treatment [77]. The angiogenesis module,which was integrated into the agent-based tumor model, consistedof a set of reaction–diffusion equations that explained the spatio-temporal evolution of the distributions of micro-environmentalfactors like glucose, TGFalpha, oxygen and fibronectin. The sim-ulations proved that the entire tumor growth profile is an integralbehavior of the cells, which is regulated by the cell cycle and EGFRsignaling pathway [77].

In epithelial tissue, a complex interplay between inhibitorymechanisms and growth stimulating signals regulates normalgrowth. Many tumors begin to develop when cells undergo atransition from stable epithelial behavior to expanding mes-enchymal growth [78]. A lattice-free DCA biophysical model hasfacilitated the simulation of cell- and tissue-shape changes underthe pressures of adhesion and deformation from surrounding cells


and underlying extra-cellular matrix. Displacement and deforma-tion forces were modeled applying Langevin equations throughthe coupling of both deterministic intercellular and stochasticforces with constants obtained from the literature or directly from


ARTICLE IN PRESSG ModelYSCBI-1123; No. of Pages 10

8 A. Masoudi-Nejad et al. / Seminars in Cancer Biology xxx (2014) xxx–xxx

Fig. 3. Schematic illustrating integrated computational/experimental modeling approach including both cell- and tumor-scale measurements. (A) Functional relationshipscontaining cell-scale parameters, i.e. proliferation (Ki-67), apoptosis (Caspase-3), and hypoxia (HIF-1a) are defined on the basis of experimental observations, as an instance,from immunohistochemistry the density of viable tissue is shown as a function of vascularization in the third panel (red: highest density; yellow: lowest; blue: vessels). Thementioned functional relationships in addiction to parameter values were measured experimentally and were used as the input for the model to simulate the lymphomagrowth. A sample was applied to simulate tumor cross-section depicting vascularized viable tissue, shown on the far right (highest density in red, lowest in yellow, withv size, mi odel sc ated to

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essel cross-sections as small blue dots). (B) Lymphoma observations related to then live mice specify part of the tumor-scale information used as validation of the menter, from which the tissue is provided with oxygen and nutrients (all the data rel

xperiments. Growth inhibitory cell–cell interactions were mod-led besides cell-substrate division inhibition and anoikis, a formf programmed cell death, commenced when cells lost contactith their own matrix. The strength of the cell-substrate adhesionas shown to be crucial in inhibiting the formation of spheroids

top the epithelial cells [79]. In a later paper, the model predictionsere juxtaposed to the growth patterns of cultured tumor cells

hat showed overexpression of the alternative isoforms of the EGFeceptor, CD97. The overexpression of one particular CD97 isoformEGF1,2,5) led to the stimulation of single-cell extracellular matrixroteolysis and motility. Nonetheless, it showed no effect onell-doubling times. Simulations demonstrated these findings androught about several other important observations: (1) directedigration away from the tumor center ended in much more rapid

nvasion of neighboring tissues, (2) induction of apoptosis withinormal cells or changing the endogenous rate of cell cycling hadinor effect on tumor invasion, however, slowing the cell cycle,

llowed more of them to evade contact inhibition and enter a rapidrowth phase which could be deemed as a paradox, and (3) If theate of migration rose as a result of decreased contact inhibitionrom adjacent tumor cells instead of being a result of growthnduction from adjacent tissues, the clonal population of theimulated tumor would match actual tumors more evidently [80].

2. Conclusion

Despite the fact that cancer is a complex disease with differ-


nt attributes and the potential to develop in various tissues, itollows a common plan of progression [1] making it feasible toeek for appropriate modeling approaches at various time andpace scales using extra- and intracellular contributing factors. The

orphology, and vasculature from macroscopic imaging of an inguinal lymph nodeimulations. Consider the pre-existing vasculature in the lymph node, being in the

this figure and the corresponding legend were taken from Frieboes HB, et al.) [74].

validation of the emerging models and simulations of cancer arechiefly dependent on mutual cooperation between experimentalresearches and clinical results [2]. Consequently, further improve-ment in mathematical modeling of cancer can lead to the designof more sophisticated cancer therapy approaches. In addition, themore accurate the raw data, i.e. transcriptional and/or transla-tional, the more actual and predictive the corresponding models. Topresent more actual models, there are different levels of abstractionand simplification. One should exercise great care to ensure that theformalisms along with their levels of abstraction and simplificationare chosen in a way that the least amounts of crucial data be lost.Lately, multiscale cancer models have proved to be more advanta-geous in that they can simultaneously incorporate more aspects ofcomplex diseases such as cancer, hence the improvement of morepredictive data-driven models. The mentioned approach along withthe experimental and clinical trial achievements can provide uswith the foundations that facilitate the future design of patient-specific cancer therapy, which could be perceived as great stridestoward entering an era of personalized medicine [81].

Conflict of interest

No conflict of interest exists.

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