Mathematical modeling of cancer metabolism
Introduction
Globally cancer represents one of the greatest challenges of the 21st century biomedicine, since cancer is one of the three main causes of death in the developed world. In fact, it is estimated that up to almost a half of population will develop some kind of cancer along life (World Health Organization cancer factsheet, www.who.int/mediacentre/factsheets/fs297/en/). Nonetheless, cancer is a very complex system, since the term “cancer” integrates around two hundred different diseases with very different etiology, evolution, diagnosis, prognosis and treatments loosely coupled by the emerging and integrating concept of hallmarks of cancer (Hanahan and Weinberg, 2000, Hanahan and Weinberg, 2011). Furthermore, every kind of cancer is an intrinsically heterogeneous and complex disease at different scales (Burrell et al., 2013). Firstly, in spite of the popular clonal theory of the origin of cancer, not all the tumor cells within a tumor mass have the same genetic landscape or exhibit the same biological behavior. For instance, within a cancer mass there are many highly proliferative tumor cells but also a small subpopulation of undifferentiated cancer stem cells with very low proliferative potential and exhibiting the property of self-renewal (Kaiser, 2015). On the other hand, in a tumor mass with a diameter greater than a few mm, the biological and metabolic behaviors of tumor cells within its core are extremely different from those exhibited by tumor cells at the surface of the tumor mass (Floor et al., 2012). Secondly, it is frequent that most of the cells within a tumor mass are not cancer cells, but a complex set of accompanying non-tumor cells, including endothelial cells, fibroblasts, T cells and macrophages, among other, linked by complex signaling and metabolic cross-talks supporting the properties of the so-called cancer microenvironment (Vaupel et al., 1989; Quesada et al., 2007; Balkwill et al., 2012; Hanahan and Coussens, 2012; Ghesquière et al., 2014). Third, cancers grow within the context of specific tissues and organs of the host and complex inter-relationships between cancer cells and the host are key not only in the carcinogenesis process but also in cancer progression, invasion and metastasis (Medina, 2014; Ruiz-Pérez et al., 2014; Ocaña et al., 2017).
Therefore, cancers as a whole are complex systems amenable to the systemic approaches provided by modern systems biology (Oltvai and Barabasi, 2002; Medina, 2013). Systems biology understands the emergence of complex cellular, tissue and organismic functions as systems-level properties that arise from the dynamic interactions of many biomolecules, both gene-derived products and their low molecular weight substrates, ligands and modulators (Alberghina and Westerhoff, 2005). As a matter of fact, it has been proposed that cancer cell properties can be redefined from a systems biology approach (Alberghina et al., 2012). The aim of this and other systems biology approaches is to get insight of the behavior of the studied system as a whole.
Section snippets
Modeling at the heart of systems biology
From its beginning, the efforts to build a conceptual framework for systems biology have assumed that the study of a biological system as a whole entails the goals established by Kitano (2002), namely, to know the structure and the dynamics of the system, to identify the design principles that can justify both the structure and the dynamics of the system and to identify the rules governing the regulation of the behavior of the system. This conceptual framework places the modeling process at the
Metabolic reprogramming as a pervading hallmark of cancer
Traditionally metabolism was understood as the whole set of biochemical reactions within a cell allowing the transformation of certain metabolites in others. This view is no longer acceptable, since a modern view of metabolism also integrates the whole set of physicochemical processes allowing the exchange of matter (transport) and energy (bioenergetics) of every cell or alive being with their environment as an open thermodynamic system.
During the first half of the 20th century, an important
Mathematical modeling of metabolism: bottom-up and top-down approaches
As other tasks within the systems biology framework, mathematical modeling can be carried out by either top-down or bottom-up approaches. According to Shahzad and Loor (2012), the top-down approach involves a workflow in five stages: i) Sample collection and laboratory experiments to obtain the initial set of data. ii) High-throughput “omic” assays to expand the set of data to be analyzed. iii) Statistical analysis of the collected data. iv) The use of bioinformatics application for functional
The modularity of metabolism
Network science offers new approaches that have become increasingly popular and have demonstrated to be useful within the framework of systems biology. Metabolism is the paradigm of a biological network. The metabolic network has been shown to be hierarchical and modular (Ravasz et al., 2002). The modularity of metabolism opens the possibility to “grow” mathematical models of metabolic pathways by connecting independent model of pathways sharing at least a metabolite or a biochemical reaction.
Tools and data sources
An ever-increasing number of biocomputational tools are made available to help researchers in the task of metabolic modeling. They include BioPP (Viswanathan et al., 2007), CellDesigner, (Funahashi et al., 2003), COPASI (Hoops et al., 2006), Payao (Matsuoka et al., 2010), sycamore (Weidermann et al., 2008), SBMM Assistant (Reyes-Palomares et al., 2009) and WikiPathways (Kutmon et al., 2016), among many others. There are also several useful databases containing valuable data regarding metabolic
Modeling metabolic interchanges in tumor microenvironment and other future challenges
As mentioned above, tumor cells are in a continuous exchange with other cell types within its microenvironment. The metabolic features of these cells are being studied extensively in the last few years, as reviewed elsewhere (De Bock et al., 2013; Ghesquiére et al., 2014; Ho and Liu, 2016). A number of models of tumor microenvironment signaling and biological features are already currently available (for instance, see Hartung et al., 2014; Norton and Popel, 2014; Shirinifard et al., 2009; Tran
Conflicts of interest
I declare that I have no actual or potential competing financial interest.
Acknowledgements
Supported by grants BIO2014-56092-R (MINECO and FEDER), P12-CTS-1507 (Andalusian Government and FEDER) and funds from group BIO-267 (Andalusian Government). The “CIBER de Enfermedades Raras” is an initiative from the ISCIII (Spain). The funders had no role in the study design, data collection and analysis, decision to publish or preparation of the manuscript.
References (63)
- et al.
Carbon metabolism and the sign of control coefficients in metabolic adaptations underlying K-ras transformation
Biochim. Biophys. Acta
(2011) - et al.
Role of endothelial cell metabolism in vessel sprouting
Cell Metab.
(2013) - et al.
Hallmarks of cancer: of all cancer cells, all the time?
Trends Mol. Med.
(2012) - et al.
CellDesigner: a process diagram editor for gene-regulatory and biochemical networks
Biosilico
(2003) - et al.
Accesories to the crime: functions of cells recruited to the tumor microenvironment
Cancer Cell
(2012) - et al.
Hallmarks of cancer
Cell
(2000) - et al.
Hallmarks of cancer: the next generation
Cell
(2011) - et al.
Genetically altered expression of spermidine/spermine N1-acetyltransferase affects fat metabolism in mice via acetyl-CoA
J. Biol. Chem.
(2007) - et al.
Modeling cancer glycolysis
Biochim. Biophys. Acta
(2011) - et al.
Genome scale metabolic modeling of cancer
Metab. Eng.
(2017)
Mathematical modeling of polyamine metabolism in mammals
J. Biol. Chem.
Biochemical systems analysis, I. Some mathematical properties of the rate law for the components enzymatic reactions
J. Theor. Biol.
Polyamines: fundamental characters in chemistry and biology
Amino Acids
Systems Biology: Definitions and Perspectives
Cancer cell growth and survival as a system-level property sustained by enhanced glycolysis and mitochondrial
Front. Physiol.
A systems biology roadmap for the discovery of drugs targeting cancer cell metabolism
Curr. Pharm. Des.
The tumor microenvironment at a glance
J. Cell Sci.
The causes and consequences of genetic heterogeneity in cancer evolution
Nature
Metabolomics and fluxomics approaches
Essays Biochem.
Global reconstruction of the human metabolic network based on genomic and bibliomic data
Proc. Natl. Acad. Sci. U. S. A.
Understanding the Control of Metabolism
Oncogenic K-Ras decouples glucose and glutamine metabolism to support cancer cell growth
Mol. Syst. Biol.
Metabolism of stromal and immune cells in health and disease
Nature
Mathematical modeling of tumor growth and metastatic spreading: validation in tumor-bearing mice
Cancer Res.
Metabolic communication in tumors: a new layer of immunoregulation for immune evasion
J. Immunother. Cancer
COPASI: a COmplex PAthway SImulator
Bioinformatics
The cáncer stem cell gamble
Science
Systems biology: a brief overview
Science
Modulation of polyamine biosynthetic activity by S-adenosylmethionine depletion
Biochem. J.
WikiPathways: capturing the full diversity of pathway knowledge
Nucl. Acids Res.
BioModels database: a free, centralized database of curated, published, quantitative kinetic models of biochemical and cellular systems
Nucleic Acids Res.
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