Modeling metabolism: a window toward a comprehensive interpretation of networks in cancer.

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Contents lists available at ScienceDirect

Seminars in Cancer Biology journal homepage: www.elsevier.com/locate/semcancer

Review

Modeling metabolism: A window toward a comprehensive interpretation of networks in cancer ˜ a,b , Osbaldo Resendis-Antonio a,∗ , Carolina González-Torres a , Gustavo Jaime-Munoz a,c a,b ˜ ˜ Claudia Erika Hernandez-Patino , Carlos Felipe Salgado-Munoz a

Laboratory of Human Systems Biology, Instituto Nacional de Medicina Genómica (INMEGEN), México, DF, Mexico Facultad de Medicina-UNAM, Mexico c Undergraduate Program in Genomic Sciences-UNAM, Cuernavaca, Mexico b

a r t i c l e

i n f o

Keywords: Cancer metabolism Mathematical models Systems biology: Constraint-based modeling P4 medicine

a b s t r a c t Given the multi-factorial nature of cancer, uncovering its metabolic alterations and evaluating their implications is a major challenge in biomedical sciences that will help in the optimal design of personalized treatments. The advance of high-throughput technologies opens an invaluable opportunity to monitor the activity at diverse biological levels and elucidate how cancer originates, evolves and responds under drug treatments. To this end, researchers are confronted with two fundamental questions: how to interpret high-throughput data and how this information can contribute to the development of personalized treatment in patients. A variety of schemes in systems biology have been suggested to characterize the phenotypic states associated with cancer by utilizing computational modeling and high-throughput data. These theoretical schemes are distinguished by the level of complexity of the biological mechanisms that they represent and by the computational approaches used to simulate them. Notably, these theoretical approaches have provided a proper framework to explore some distinctive metabolic mechanisms observed in cancer cells such as the Warburg effect. In this review, we focus on presenting a general view of some of these approaches whose application and integration will be crucial in the transition from local to global conclusions in cancer studies. We are convinced that multidisciplinary approaches are required to construct the bases of an integrative and personalized medicine, which has been and remains a fundamental task in the medicine of this century. © 2014 The Authors. Published by Elsevier Ltd. This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/3.0/).

1. Introduction Multiple roads lead to cancer, it can emerge as the result of mutations in regulatory or signaling proteins [1], as well as the imbalance of oxidative stress and anti-oxidative mechanisms [2], or by the continuous exposition of cells to a given stimulus [3]. There are a myriad of causes for cancer, and the compounds or conditions that stop or delay its progress in some circumstances do not work in others. A variety of factors contribute to this complex behavior, including the heterogeneity in cancer cell populations, even in tumors from the same patient, a fact that directly reduces the effectiveness and reliability of the drugs for treating the disease [4,5]. Furthermore, with the advent of high-throughput (HT) and Next Generation Sequencing (NGS) technologies, new biological mechanisms that are typical of cancer cells have been discovered

∗ Corresponding author. Tel.: +52 01 55 5350 1900. E-mail address: [email protected] (O. Resendis-Antonio).

[6]. This scenery has created the need to develop new ways to interpret these data and elucidate their role in human diseases in a coherent and systematic fashion. At this stage, a biological system can be considered an interactive set of networks with components and relations at different biological levels that are the causes by which certain phenotype, functional or dysfunctional, emerges, see Fig. 1. Currently, understanding how these biological networks orchestrate their activities to support cancer phenotypes is a great challenge in medical science to prevent, suggest and predict strategies with direct implications in clinical stages. Despite this astonishing complexity – which involves biological processes such as signaling, regulation and metabolic networks, – hallmark traits have been suggested to characterize key processes in all human cancers, such as proliferation, invasion and metastasis [1,7,8]. Arguably the most fundamental trait of cancer cells is their ability to sustain chronic uncontrolled proliferation [1]. Although it is well accepted that this dysfunctional state is accompanied by a rewiring of metabolic activity in the cell [9], it is not completely

http://dx.doi.org/10.1016/j.semcancer.2014.04.003 1044-579X/© 2014 The Authors. Published by Elsevier Ltd. This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/3.0/).

Please cite this article in press as: Resendis-Antonio O, et al. Modeling metabolism: A window toward a comprehensive interpretation of networks in cancer. Semin Cancer Biol (2014), http://dx.doi.org/10.1016/j.semcancer.2014.04.003

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Fig. 1. Mechanisms of metabolic regulation in cancer cells. Cancer cells display a variety of alterations in metabolic pathways for building the precursors that cells need to proliferate and sustain the anomalous state. Glycolysis, the TCA cycle and glutaminolysis, are a few pathways that guide the malignant transformation by covering the metabolic demand of nucleotides, amino acids, lipids and other building materials that cancer cells need to proliferate. Enzymes with an important role in cancer are depicted in the upper level of the figure (gray ovals), and metabolites participating in anabolic pathways are depicted in pink and orange arrows. These metabolic alterations are modulated by a variety of mechanisms that involve other molecules, such as oncogenes, tumor suppressors and microRNAs. Examples falling in the first category are given by c-MYC, HIF-1 and P53, with activities that directly affect metabolic activity (green circles). c-Myc and HIF act in complexes with other proteins to modulate the expression of glycolytic genes or enzymes. c-Myc specifically stimulates glutaminolysis. P53 regulates the suppression of glycolysis through TIGAR and increases mitochondrial metabolism via SCO2 (yellow circle), as depicted by the dashed blue arrows. In turn, these regulators modulate the expression of other target genes to enhance the cancer phenotype. c-MYC and HIF-1 promote the expression of cell cycle proteins, and mutations in P53, denoted as P53* , inhibit apoptotic genes, as depicted by the dashed green arrows. Moreover, the transcription of oncogenes and tumor suppressors can be controlled by the up-regulation of oncogenic miRNAs (red) or inhibitory miRNAs, see green arrows. Simultaneously, metabolites can play an important role in epigenetic regulation, see yellow arrow. Furthermore, the stromal cells induce important metabolic changes to favor cancer proliferation thought metabolic cross-talk (cyan arrow). GLUT1 – Glucose transporter 1, HK-hexokinase, GLC – Glucose, G6P – Glucose-6 phosphate, F6P – Fructose 1,6phosphate, PFK – Phosphofructokinase, G3P – Glyceraldehyde-3phosphate, 3PG – 3-Phosphoglycerate, PEP – Phosphoenol pyruvate, LDH – Lactate dehydrogenase, PYR – Pyruvate, LAC – Lactate, MCT1 – Monocarboxylate transporter 1, MCT4 – Monocarboxylate transporter 4, SLC1A5 – Glutamine transporter, GLN–Glutamine, GLU – Glutamate, CIT – Citrate, ICIT – Isocitrate, ␣-KG-␣-Ketoglutarate, SuCoA – Succinylcoenzyme A, SUC – Succinate, FUM – Fumarate, MAL – Malate.

clear how and which metabolic pathways differentially alters their activities in cancer versus normal tissues [10,11]. The most studied metabolic alteration in cancer is the degradation of glucose via aerobic glycolysis, a less efficient pathway for generating ATP compared with oxidative phosphorylation, despite

oxygen availability. This finding was reported almost a century ago by Otto Warburg in his seminal studies of metabolism in cancer cells [12]. Notably, studies in cancer biology have demonstrated that cancer genes are intimately linked to the Warburg effect and other metabolic alterations [13,14], see Fig. 1. There is evidence




that reprogramming signaling or regulatory networks in normal cells induces the expression and activation of several enzymes that form part of the metabolic pathways that promote proliferation and survival in cancer cells [15–17]. For instance, c-Myc regulates the expression of glycolytic genes, particularly enzymes such as hexokinase (HK), phosphofructokinase (PFK), lactate dehydrogenase A (LDHA) and extracellular glucose transporter [18–20]. Furthermore, c-Myc controls glutaminolytic pathways that promote the expression of glutamine transporters such as SLC1A5 and the expression of glutaminase (GLS) [21]. c-Myc has also been implicated in the regulation of genes participating in mitochondrial biogenesis [22]. Similarly, HIF-1 modulates the activity of some enzymes involved in glycolytic metabolism at hypoxic conditions [23,24]. Moreover, mutations in many types of cancer disrupt the functional role of some tumor suppressors. For example, mutations in P53 simultaneously promote glycolysis and inhibit mitochondrial respiration in cancer cells through genes such as TIGAR [25] and SCO2 [26], see Fig. 1.c-Myc, HIF-1 and P53 are together involved in other biological processes that sustain cancer. c-Myc and HIF1 form a complex with the protein MAX, and consequently, this complex up-regulates the expression of cyclins (proteins involved in of cell cycle). Conversely, mutated P53 promotes cancer by down-regulating apoptotic genes [24,27]. In turn, the transcription factors mentioned above are regulated by microRNAs (miRNAs), small-noncoding RNAs of 18–25 nucleotides in length [28]. miRNAs typically reduce the translation and stability of target mRNAs by specific base-pairing interactions, but in some cases, they can promote translation by indirect mechanisms [28–30]. Some elements of metabolic networks can affect other levels of regulation, which adds another layer of complexity; for example, there is evidence that metabolites can play an important role in epigenetic regulation [31], see Fig. 1. The above examples represent only a small fraction of many cross-linking interactions at different biological levels that are together responsible for cancer phenotype. These different levels of biological information constitute one aspect that determines metabolic capabilities in cancer cells, however the microenvironment also plays a relevant role in supporting cancer phenotypes. Epithelial cancer cells have been shown to induce a type of aerobic glycolysis in neighboring fibroblasts [32]. The proposed mechanism considers that cancer associated fibroblasts (CAF) produce high-energy metabolites such as lactate and export them to the microenvironment. Then, epithelial cancer cells can use these metabolites to fuel mitochondrial activity. This biochemical crosstalk between cell types is called the reverse Warburg effect and induces a higher proliferative capacity in epithelial cancer cells [32]. These findings reveal that the classical Warburg Effect and the reverse Warburg effect are only the top of the iceberg on metabolic alterations in cancer; there is thus an increased need to understand how metabolic pathways in cancer can be altered by environmental cells in a tissue specific context. To construct a holistic view of this phenomenon, it is necessary to develop systemic schemes capable of simultaneously: (1) representing biological knowledge in a mathematical language; (2) integrating HT data; and (3) formulating and assessing metabolic predictions in silico [33]. Significant advances have been reported in understanding cancer metabolism through two parallel branches: experimentally and computationally. A variety of biological assays in cancer have discovered new metabolic changes that support growth and proliferation [10,34–37]. Additionally, new theoretical schemes have been suggested to analyze, describe and predict cellular metabolism at a genome scale level [38]. Although both branches have been evolving, there remains a significant challenge in integrating them and improving our understanding of cancer metabolism. In this review, we present some of the standard formalisms to approach this problem. These methods represent

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a cornerstone for quantitatively interpreting and understanding how cells alter their metabolism to acquire their malignant phenotype, an aim that could have strong implications for the design of combined medical treatments in cancer that achieve more efficient results [39–41]. 1.1. Conceptual schemes in cancer systems biology Complexity in cancer is astonishing, and understanding the metabolic mechanisms involved in this disease requires qualitative and quantitative methods for systematically elucidating their principles [42–45]. To this end, a variety of theoretical frameworks have been suggested in the literature. These frameworks can be classified into a few categories: Topological, classical, stochastic, Boolean and Constraint-based modeling, see Table 1. Although there is no rule for the selection of the approach, it can be guided by at least two criteria: (1) the type of biological question to be addressed; and (2) the information that is available for the biological system. In this section, we present some examples of different formalisms that one can find in the literature to analyze pathways in cancer. This formalism represents schemes that are capable of uncovering and highlighting some mechanisms in cancer at diverse levels of detail and complexity. 2. Balancing complexity, biological detail and physiological knowledge in cancer modeling Given the complexity of biological systems, mathematical models are invaluable tool for integrating knowledge, understanding mechanisms and predicting phenotypic behavior. In the construction of a model the balance between the degree of complexity and the biological detail required should be addressed, Fig. 2. The strategy is guided by criteria such as the nature of the question and the available data to validate the outputs and predictions of the model. A variety of schemes have been applied to explore the behavior of cancer cells in a broad spectrum of biological processes, such as tumor growth, metabolism and treatment response [45–49]. To classify these schemes is not a trivial task, however they can be distinguished in terms of the mathematical formalisms used, the level of its biological detail and the scopes of their predictions. Considering these items, we suggest the classification in Table 1 in which at least six approaches are identified: Topological, Classical, Boolean, Stochastic, Constraint-Based and Hybrid modeling. 2.1. Networks topology: unveiling structural organization in metabolic networks Cancer is a network disease resulting from alterations at diverse biological levels, and topological analysis is a primary strategy to survey the organization of the biological components and how dysfunctional mechanisms can emerge. Thus, topological properties such as robustness, centrality, modularity, motif discovery or minimal path-length provide clues concerning how organization in biological networks can be associated with functional states [50–54]. Genome-scale metabolic reconstruction of human cells is a fastmoving area in which a framework can be established to distinguish functional and dysfunctional states associated with diseases [38]. For instance, the most current version of the human metabolic reconstruction (Recon) contains approximately 7400 reactions of human metabolism, representing 123 metabolic pathways with experimental and bioinformatics evidence in human cells [55,56]. Notably, this curated metabolic reconstruction constitutes a computational platform to explore in silico the metabolic phenotypes that characterize human diseases, such as cancer, obesity, diabetes


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Table 1 Modeling approaches in systems with applications in cancer systems biology. This table summarizes some properties associated with each approach. The square colors in the first column label approach classification in concordance with Fig. 2. Approach

Description

Characteristics

Limitations

Examples

Network topology

Mathematical scheme to uncover the organizing principles in biological network

This approach has been able to elucidate organizing principles in biology by taking into account a large number of biological entities

Topological analysis is independent of time and physiological context

Protein–Protein interaction networks Gene co-expression networks

Classical models

Basic models based on ODE or PDE for analyzing biological systems with few parameters

Consider few parameters of the system generally macroscopic properties. Those parameters are related by simple equations

The resolution of the information is restricted to the scale used for the calculations

Lokta–Volterra competition model Gompertz growth rate

Boolean models

Biological networks whose components can be in one of two states (0,1) and whose dynamic are given by logical rules

It is a proper framework to analyze biological circuits where parameters are not well characterized

The computational cost may rise depending upon the complexity of the network

Transcriptional regulatory networks Signaling networks

Stochastic models

Models describing phenomena in a probabilistic approach due to significative fluctuations in the system

Eliminate the deterministic view of the system and consider that noise is fundamental to drive the phenotype of a biological circuit

Computational simulation is a time consuming process, it increases according the number of component rises

Master equation systems

Constraint-based models

Models based on genomic base information (omics technologies) and physiological information.

With the combination of the omics information model can be built for exploring the relationship between genotype with phenotype.

The quality of the results depends of the metabolic reconstruction, which in turn depend on available omics data and physiological information.

Flux balance analysis Flux variability analysis

Hybrid models

Combine two or more type of models and mixes different levels of information.

These models become more detailed and will be more accurate with the

Some limitations can be solved mixing models, but instead others can appear.

Novel agent base models Multi-scale models

and mental disorders. Given the relevance of this reconstruction, community strategies have recently been accomplished for improving data quality and, consequently, the predictive scope of in silico models [55]. Although topology is independent of time and physiological context, this approach can elucidate the organizing principles that govern biological functions in cells [57]. For example, the presence of functional modules has been reported at different levels of biological information, ranging from regulatory to metabolic networks [58,59]. The concept of modules has a variety of connotations: in gene expression analysis a module is understood as a co-expressed set of genes, whereas in a networks context, a module is a set of nodes that have strong

Cellular automaton models Agent base models

interconnections among them, characterized by a high clustering coefficient [60]. Notably, although these concepts arise from different criteria, there have been some efforts to combine them and explore their relationships [42,57,59]. One such approach is based on the reconstruction of co-expression networks that allows to study how genes coordinate their expression to sustain a specific biological state [42,61–64]. These methods have been applied in a variety of tissues to elaborate hypotheses and identify drug targets [65–70]. Notable observations have been made with this type of analysis, such as the finding that up-regulated genes in lung cancer present a high degree of connection and centrality [71]. Although the representation of biological data through networks

Fig. 2. Theoretical approaches used in cancer modeling. This figure depicts some theoretical schemes that have been applied to analyze different aspects of cancer by combining different levels of complexity and detail. Models that represent high biological complexity and a low level of detail (reduced number of variables) are located to the left of the figure. Conversely, models that represent low biological level of complexity and a high level of detail are located on the right side. The colors of the examples are in concordance with those in the classification proposed in Table 1.


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Input data

Algorithm

Method classification

Biological reconstructions

MBA

Generic metabolic reconstruction Human curated tissue specific pathways transcriptomic, proteomic, metabolomic

Heuristic

Liver model General cancer metabolism Hereditary Leiomyomatosis and Renal-Cell

INIT

Generic metabolic reconstruction Protein information Optional Metabolome transcriptome

Mixed integer-linear problem (MILP)

16 cancer models like breast, cervical, colorectal, prostate, thyroid, liver, lung. 70 normal tissue/cell type brain (3 structures each divided in different kind of cells), stomach, skin, among others

mCADRE

Generic metabolic reconstruction Transcriptome Optional metabolome

Optimization with topology

26 cancers including breast, lung, ovary, pancreas, uterus, among others 100 normal tissue type including 30 distinct brain structures, kidney, ovary, cervix, thyroid, among others

iMAT

Generic metabolic reconstruction Proteome, transcriptomic

The human curated tissue specific pathways reactions are classified as high probability core reaction (CH ),and those reported by omics data as medium probability core reactions (CM ).The idea behind it is to find a model that has all the CH , a maximal CM with minimal amount of extra reactions to fill the gaps. These characteristics are represented in a score. Reactions are removed from a generic model unless its exclusion prevent the activation of Chor reduces the score. Given that the order in which reactions are removed might affect the reconstruction, multiple candidate models are made. Then the reactions are ranked according to the fraction of candidate models in which they were present. Then a new model is made adding reactions accordingly to this rank until a consistent model is reached The proteome and/or transcriptome data is transformed to weights. Evidence of expression will give a positive weight while absence will give a negative weight. This enable to make a constraint based model optimization where the number of flux-carrying reactions associated with highly expressed enzymes is maximized. Unlike the others method If the metabolite is present in the tissue it allows a small positive net accumulation The expression data is used to infer genes (reactions) that are present or absent. Those reactions that are constantly present in the samples form a core that should be able to carry flux. The rest of the genes then are ranked according to a combination of expression data and topology. For example if a reaction is connected to a highly expressed reaction with few others connections it probably should be included in the model. Then the generic network is pruned given that ranking, unless its exclusion inactive a core reaction or doesn’t allow the cell to create key metabolites from glucose The proteome and/or transcriptome data is transformed to numerical weights. Evidence of expression will give a positive weight while absence will give a negative weight. This enable to make a constraint based model optimization where the number of flux-carrying reactions associated with highly expressed enzymes is maximized. This algorithm assumes steady state, unlike INIT

Mixed integer-linear problem (MILP)

10 healthy tissues brain, heart, kidney, liver, lung, pancreas, prostate, spleen, skeletal muscle and thymus

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Table 2 Algorithms used to reconstruct tissue-specific metabolic networks. Different strategies have been used in the literature to construction of metabolic networks. These computational methods use a genome-scale reconstruction and high-throughput data for finding the most coherent sub-network and are more consistent with HT data. This table describes some distinctive properties associated with some of these methods (IMAT, INIT, mCADRE and MBA). Global properties on input data, the algorithm used, its classification and some applications are listed in this table.

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has contributed to understanding the organization of dysfunctional pathways in cancer, some elements require more attention to ensure proper interpretations. For instance, the topological analysis of metabolic networks is usually performed with only one type of element as node, i.e. either reactions or metabolites, as a consequence, there is a loss of information in these approaches. To overcome this fact, the representation of metabolism through bipartite networks and the development of methods to explore their architecture are needed to uncover more general organizing principles [72]. In a more general context, the proper networks representation and coherent interpretation of heterogeneous HT data is a major challenge in the field, achieving that will advance our understanding of cancer in at least two ways: (1) uncovering organization principles by which cancer cells response and evolve in tissues, and (2) applying this knowledge to contribute to the design of optimal treatments for cancer. Both goals are closely linked to the purposes of P4 medicine: predictive, preventive, personalized, and participatory [46]. 2.2. Classical mathematical models In classical models of cancer, ordinary differential equations (ODE) or partial differential equations (PDE) play important roles in describing processes in cancer. A myriad of ODE models have analyzed cancer from different points of view that range from modeling the growth rate to calculating radiation doses in therapy [45]. In this classification, we include all those models whose description is characterized by simplifying the biological system through a reduced number of mathematical variables associated with biological macroscopic properties (such as cell growth). A seminal example falling into this classification is the Gompertz model that reproduces growth rate measurements of cancer cells in vitro [73]. Some other models based on ODE focus on analyzing drug responses in cancer cultures, which is an essential point for the optimal design of therapeutic strategies [74]. A detailed description of these methods and a broader number of examples can be found in the literature [45]. Although these schemes have contributed significantly to understanding global mechanisms in cancer – such as growth rate, angiogenesis or metastasis – they do not include detailed information regarding specific alterations in signaling, regulatory or metabolic networks underlying the phenotype. To integrate this latter information one necessary step is to move toward genome-scale modeling, which allows us to explore the relationship among topology, dynamic and biological functionality [42,75,76]. 2.3. Boolean models Another option for mathematical modeling in cancer is the Boolean formalism, a proper scheme for analyzing the dynamic behavior of transcriptional regulatory (TRN) or signaling networks without the need to include kinetic parameters of the processes involved. Given a network, this approach assumes that the expression of each biological element can be in one of two states (zero or one) whose selection depends on a set of Boolean rules defined by the state of the elements that regulate it. Hence, with network topology and Boolean rules, the dynamic behavior of genes can be obtained by applying the rules at discrete intervals of time in a synchronic or asynchronic fashion. As a result, the state of the entire network changes at a discrete interval of time until it reaches a fixed or cyclic state associated with a phenotype state, known as an attractor [77,78]. To ensure a proper simulation, one should define Boolean rules in terms of physiological knowledge [79]; however, this information is often absent, and the combinatory effects of the possible mechanisms significantly increase as a function of the number of regulators involved. Nevertheless, this approach is an

appealing formalism when one desires to explore global questions about the dynamic organization of the network without an accurate knowledge of mathematical parameters. In cancer studies, Boolean networks have an important role to elucidate the mechanisms that can sustain the cancer phenotype [81–83]. Hence, to characterize the biological profile in cancer, some methods applying a Boolean scheme have explored the physiological states of transcriptional regulatory networks (TRN) and its transition between normal and dysfunctional states [80,81]. For instance, Fumiã et al. constructed a regulatory protein network integrating signaling pathways relevant in cancer and characterized its phenotypes through Boolean states. The dynamic behavior of this network was such that the attractors identified were associated with one of these physiological states: proliferative, quiescent or apoptotic. Furthermore, gene mutation analysis carried out in silico evaluate the stability of cancer’s attractors, and their simulations concluded that perturbations in some nodes elicit transitions among physiological states. Notably, this finding suggest the possibility of controlling the disease evolution through the proper selection of targets along the network [82]. 2.4. Stochastic models Biological processes in cells are constantly subject to internal fluctuations that are induced by the fact that concentrations of some reacting species, such as transcriptional factors or metabolites, are extremely low inside the cell. Notably, biological circuits have the ability to control this noise to favor certain phenotypic states in cells according to the environmental conditions [83]. Noise functions at many levels of biological complexity, including genetic regulatory mechanisms, metabolism and cell populations [5,84,85]. Cancer cells are not excluded from this fundamental effect, and a clear consequence is observed at a population level where subspecies of cancer cells in a tumor coexist to potentially favor and sustain the malignant phenotype [5]. To describe the consequences that noise has on cell activity, a stochastic approach is more convenient than a deterministic one is more convenient to elucidate the cellular mechanism by which noise is controlled [86]. For simplicity, we subdivided stochastic models into two types: those that involve master equations; and those based on computational techniques such as cellular automaton or Monte Carlo simulations. The first scheme is frequently used to investigate analytically the statistical properties of biological circuits with a low number of components in a homogenized mixture [86], where as the second scheme overcomes these limits by computationally simulating interacting cells and biological networks subjected to diffusion and population effects. Thus, cellular automaton has been a central piece of the in silico models developed to simulate heterogeneities in tumors by considering vascularization, genetic mutations, metabolism and other biological processes [87]. For instance, computational models have simulated tumor growth in a set of interacting cancer cells in three dimensional space, where gradient effects of key metabolites, such as glucose or oxygen, play important factors in determining the disease. Overall, computational and mathematical models are complementary strategies for understanding the mechanisms by which cells regulate intrinsic and extrinsic noise and exploring how these biological mechanisms contribute to the cancer phenotype. 2.5. Constraint-based modeling New HT technologies have contributed significantly to move toward the integration and coherent interpretation of biological data. To this end, constraint-based modeling is a paradigm in systems biology that uses a biochemical, genetic and genomic (BiGG) knowledge base to explore the metabolic capabilities in


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microorganism and human tissues [88–90]. Constraint-based modeling integrates computational methods that contribute to link the fundamental relationship between the genotype and the phenotype such as the identification of gene essentiality in microorganisms [90]. One of the most applied methods is flux balance analysis (FBA) that calculate the flux through a metabolic networks that ensure an optimal production of a specific physiological objective function, such as biomass production in a cell [91,92]. FBA has been successful in exploring the metabolic capacities of cancer cell lines and identifying potential enzymes with therapeutic applications [33,93]. Given that most human diseases have consequences in metabolic activity, constraint-based modeling is considered a useful paradigm for understanding the mechanisms involved in human diseases [56]. 2.6. Hybrid models Computational or mathematical models based on previous schemes have guided our understanding of cancer at different levels of descriptions [44]. However, each approach has limits and to move toward more realistic models, there is an interest in combining more than one scheme simultaneously. In most cases, this integrative effort is propelled by the type of biological question to be explored and the experimental technologies that can be used to assess the conclusions. Currently, some strategies have been proposed to model metabolism in solid tumors by integrating different levels of complexity, such as metabolism and tumor development [94,95]. Advances in these types of modeling will create the opportunity to analyze the behavior of cancer cells with a greater level of detail, including additional processes such as cell cycle, angiogenesis, metastasis and the effect of metabolite gradients during the growth of solid tumors [95,96]. Overall, these paradigms constitute a valuable conceptual platform to characterize, understand and identify the mechanisms sustaining cancer [43,97]. As soon as these approaches increase their capacity to integrate biological information and heterogeneous high-throughput data, their role for moving toward an integrative analysis of diseases and the development of personalized, preventive and predictive medicine will become evident in clinical areas. 3. Tissue specific metabolism in cancer Metabolic alterations are important avenues to propitiate tumorigenesis and sustain cancer, these changes are heavily influenced by the physiological and microenvironmental conditions in human tissues. The human body integrates tissues with cells that are specialized in several processes, such as storing fat, transforming carbohydrates, creating hormones and covering energetic demands, among others functions. Tissues have physiological purposes, and when a disease emerges, its evolution is strongly influenced by tissue-specific metabolic ambiance [32,46,96,98]. For instance, prostate cancer appears to prefer fatty acid metabolism as a source of acetyl-CoA synthesis, whereas breast cancer appears to prefer the consumption of glucose as a main carbon source to sustain malignant phenotype [99,100]. Undoubtedly, the characterization of specific metabolic states in each tissue will contribute to improve the descriptive and predictive capacities of computational models in different types of cancer. To address this valuable and fundamental topic, there have been efforts to create manually curated networks (bottom-up scheme) for a couple of human tissues [101–104]. This type of reconstruction has the advantage of including high-quality curated information regarding biological networks. In recent years there has also been increased interest in implementing computational algorithms that integrate

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high-throughput data to reconstruct tissue-specific metabolic networks (top-down scheme). In the latter case, these computational methods start from a generic non-tissue-specific human metabolic reconstruction – such as Recon [55,56,100], EHMN [105] or HumanCyc [106] – and then select the subnetwork that better fits available biological data, such as microarrays, proteomics or metabolomics. Currently, a variety of methods are available in the literature, some of which have been applied to reconstruct the tissue-specific metabolism in cancer [38,107]. Conceptual foundations and properties of some of these methods are briefly described in Table 2. Some differences can be highlighted among them, for instance, INIT (Integrative Network Inference for Tissues) allows for a small net accumulation in the metabolic flux to have a network able to synthesize molecules such as NADH, rather than only being able to use such molecules as cofactors [108]. Although the final tissue-specific metabolic reconstruction in mCADRE (context-specificity assessed by deterministic reaction evaluation) is constrained to produce universally important metabolites from simple precursors such as glucose, INIT allows the model to use precursors that the cell is known to take up [109]. Remarkably, the achievements of these methods constitute a first step toward a human metabolic atlas that will serve as a platform to understand the metabolic alterations in cancer and potentially design drugs and more effective treatments for patients.

4. Outlook Mathematical models represent a simplified version of reality whose essential purpose is to help us handle and understand the complexity of biological phenomena. Systems biology enables the systematic analysis and coherent interpretation of highthroughput data, and this paradigm is fundamental to achieve a better understanding of metabolic mechanisms involved in cancer in a coherent and systematic fashion. The implications of this perspective should be reflected in practical aims oriented toward basic questions in biomedical sciences and clinical areas, such as the uncovering of metabolic alterations in cancer, discovering possible therapeutic targets or properly designing personalized treatments. However, these aims are not trivial tasks, and one important piece in the puzzle is the development of computational modeling methods that are capable of integrating information with HT data and physiological behavior in cancer. In this review, we present some theoretical schemes that have contributed to the understanding of key mechanisms in cancer. Each approach, whether mathematically or computationally, has its own scopes that are distinguished by their levels of complexity and the number of variables used to model the phenotype. Thus, systems biology schemes are a paradigm to advance our knowledge of how cancer emerges in tissues and how to design novel drugs treatments. Although there have been some important advances in this area, the practical implication of these findings for cancer therapy remains a challenge in systems biology. This challenges addresses additional problems, such as the building of a common language to communicate between the clinical and theoretical scientists and preparing a new generation of scientists with skills in mathematics, genomic and computational sciences. In our opinion, these strategies are required to move toward a quantitative description of cancer phenotype that contributes to the advent of a systemic and personalized medicine.

Funding The authors thank the financial support from the Research Chair on Systems Biology-INMEGEN-FUNTEL Mexico.




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Competing interests The authors have declared that no competing interests exist.

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