Indian Academy of Sciences Conference Series (2020) 3:1 © Indian Academy of Sciences DOI: 10.29195/iascs.03.01.0031 The Warburg effect: A computational cancer modeling approach UGO H. P. SILVA1,2,∗ and FERNANDO F. FERREIRA2,3 1 Department of Informatics and Tourism, Federal Institute of Education, Science and Technology of São Paulo, 01109-010 São Paulo, SP, Brazil 2 Center for Interdisciplinary Research on Complex Systems, University of Sao Paulo, Av. Arlindo Bettio 1000, 03828-000 São Paulo, Brazil 3 Department of Physics, School of Philosophy, Sciences and Letters, University of São Paulo, 14040-901 Ribeirão Preto, SP, Brazil ∗Corresponding author. E-mail: [email protected] Abstract. The approach of complex systems has been increasingly used by the different areas of knowledge, such as physics, biology, social sciences, and economy. In studies started in the 1920s that resulted in the pub- lication of a paper in 1956, Warburg was one of the first to study the origin of tumorigenic cells, changing the metabolic process of oxidative phosphorylation to glycolysis in cellular respiration, and its implications in the control and proliferation of tumor cells. In this report, we propose a computational method to study the Warburg effect; the competitive advantage of different strains; and cooperation mechanisms in the uptake of nutrients used for energy generation. The objective here is to discuss the trade-off between high-yielding organ- isms and high reproduction rate. We propose a model to study the competition between normal and tumor cells exposed to hypoxia, or low presence of oxygen, and a more acidic environment. We qualitatively predict the invasion of tumor cells for a broad range of parameter values. This is useful to calibrate a model with real data. Keywords. The Warburg effect; equilibrium dynamics of cancer; stability. PACS Nos 02.70.-c; 05.45.-a; 64.60.Ht; 87.19.xj 1. Introduction cell must undergo multiple mutations. Later, mathe- matical modeling of cancer began with a statistical Cancer is the result of a dynamic evolutionary process analysis of age patterns of incidence, in which the that can lead to improvements or innovations. The evo- emergence of cancer requires multiple probabilistic lutionary process that leads to cancer is different from events [1]. other processes because many genes can be inactivated In this context, changes in metabolism play a fun- or modified without any loss of fitness for the cells, and damental role in the progression and maintenance sometimes a gain (in this way their progression is seen of tumor cells, which causes the scientific commu- as ‘destructive evolution’) as Nowak explains [1]. nity to investigate the actions of oncogenes, proto- Ernest Tyzzer was the first to use the term ‘somatic oncogenes and tumor suppressor genes, transcription mutation’ meaning that cancer is a genetic disease factors that can explain the altered state, metabolism, caused by somatic developments, approximately one and possible therapies that can be applied to fight the hundred years ago. Then, other experts, like David disease. von Hansemann and Theodor Boveri, already had stud- In this section, we briefly review and discuss the pro- ied abnormal cell division and observed that there cesses associated with the Warburg effect, which has was something wrong with the cancer cells chromo- already been extensively studied but are not satisfacto- somes [2]. His studies showed that ionizing radiation, rily and precisely understood in terms of determining besides being carcinogenic, was also mutagenic. This the causes or effects of this change in the state of cells corroborates the idea that for cancer to occur a single with tumor. 54 Indian Academy of Sciences Conference Series (2020) 3:1 2. Cancer as a complex system The release of O2, as a result of photosynthe- sis, altered the environment in which cells developed 2.1 Evolution of metabolism and possibly led to the development of an oxidative According to [3], metabolism is the set of chemi- metabolic model that currently occurs in cells for energy cal processes by which living organisms use energy generation [4, 5]. from food, air, or sunlight to maintain all the func- Cellular respiration is a characteristic process of tions necessary to live. These chemical processes occur both normal and tumor cells. The mechanisms that largely within cells, through currents of chemical reac- make tumor cells the preferred choice of a less effi- tions called metabolic pathways. In an organism’s body cient metabolic pathway in ATP generation are widely the transformation of nutrients is processed to produce studied by the scientific community. energy-generating molecules and cellular components 2.2 Cell cycle and tumor progression are constructed through parallel metabolic pathways. In general, metabolic pathways are complex sequences of In general, cancer is caused by mutations in genes that chemical reactions controlled by self-regulatory feed- regulate the cell cycle. For a better understanding of back. Metabolism is the heart of cell biology, and under- tumor formation, a basic understanding of this process standing how cancer cells deal with metabolic needs has is necessary. been the focus of cancer research for many years. Under normal conditions, within a cooperative model, Since the molecules were originated from a set of cells undergo selective pressures and occasional muta- organic molecules, they were able to obtain food and tions that do not affect the functioning of the organ- energy directly from the environment. However, this ism, because the function of the cell is to maintain is very limiting, which led them to develop their own the machinery as a whole, and, when necessary, the mechanisms to generate energy and synthesize the nec- apoptosis-induced death of some defective individuals essary molecules for their replication. The generation occur to keep the system in balance. and controlled use of metabolic energy is essential for Cancer is the result of a system failure in a cellular all cellular activities, and the main pathways of energy society in which a single cell (due to a mutation or set metabolism are largely conserved in today’s cells. All of mutations) begins to exhibit uncontrolled growth, the cells use adenosine triphosphate (ATP) as a source of cooperation that maintains the integrity of a multicel- metabolic energy to control the synthesis of cellular lular organism is then interrupted. Abnormal cells can constituents and perform other activities that require be identified through interactions with other cells by energy. cellular signaling mechanisms [5, 6]. It is assumed that the mechanism used by cells for ATP generation evolves in three stages, correspond- 2.3 Cancer cycle ing to the evolution of glycolysis, photosynthesis, and Dated from 1911, the first recognition that the tumor oxidative metabolism (figure 1)[4]. develops in stages is attributed to Haaland by Foulds in The first reactions of energy generation involved the studies of breast and lung tumors in mice. Three stages breakdown of organic molecules in the absence of oxy- were considered to be virtually axiomatic, but standard gen. They were probably very similar to current gly- terminology was introduced by Friedewald and Rous in colysis, the anaerobic breakdown of glucose to produce 1944: lactic acid with a net gain of two molecules of ATP and • Initiation. State of neoplasia, a form of prolifera- its use as an energy source intracellular chemistry. tion not controlled by the organism. The different types of genetic alterations are mutations that activate function gain, gene amplification, point mutations, and promoter mutations that change an allele from a proto-oncogene to an oncogene. • Promotion. Tumor cells are stimulated to prolif- erate to form a visible tumor. • Progression. Development of the malignant tumor from tissues bearing a benign tumor, through the accumulation of additional genetic damage, through mutations or epigenetic silenc- ing of the genes that shaved the DNA and the altered expression of genes that promote the vas- Figure 1. Generation of energy metabolism. Adapted cularization and spread of the tumor through local from [4]. invasion or distant metastases. Indian Academy of Sciences Conference Series (2020) 3:1 55 From the point of view of cell biology, a tumor needs Not only can the tumor’s micro-environment select to acquire the following properties to develop: a metabolism more appropriate to its conditions, but • uncontrolled proliferation, the status of the oncogene can also lead to metabolic • insensitivity to antiproliferative signs, changes. The signaling molecule of Ras – rat sarcoma • evasion of programmed cell death, virus, a potent oncogene that when mutated pro- • motes glycolysis, and the Akt kinase – family of unlimited replicative capacity, 2 • angiogenesis, serine/threonine protein kinases, an effector down- • handling. stream well characterized by insulin signaling, resumes its role in glucose uptake and use in the cancer 2.4 Oncogenes environment [8]. Consider a compartment of replicating cells. During The discovery that tumor-causing oncogenes are related each cell division there is a small probability that an to normal genes raised several questions about the role error will be made during DNA replication, a mutant of these genes in growth and development (differentia- daughter cell with a better adaptive advantage in the tion) of normal and tumor cells. existing function or even the appearance of a new func- It seems certain to say that stages of tumor initia- tion will be produced. Alternatively, the mutation can tion and promotion and the existence of a malignant impair important cellular functions with a negative apti- neoplasm itself depends on the increased expression tude for the cell, causing it to proliferate more slowly or (manifestation of the effect) of oncogenes, caused by die more quickly than its neighbors [1]. The dynamics of amplification (increased number of copies of the gene), a specific mutation within a compartment is discussed.