Critical transitions in a game theoretic model of tumour metabolism

Colorectal cancer cells establish metabolic reprogramming with cancer-associated fibroblasts (CAFs) through lactate shuttle to enhance invasion, migration, and angiogenesis

Fibroblasts undergo metabolic reprogramming after contact with cancer cells in tumor microenvironment, producing lactate to provide a metabolic substrate for neighboring tumor cells. The exchange of lactate between cancer cells and fibroblasts via monocarboxylate transporters (MCTs) is known as the lactate shuttle. Colorectal cancer cells may establish a metabolic coupling akin to the lactate shuttle in collaboration with cancer-associated fibroblasts (CAFs) to augment their invasive and migratory capabilities. However, the specific phenomena and underlying mechanisms are not clear. In this study, we investigated the phenomena and explored the correlation and possible mechanism between CAFs and the invasion and migration of colorectal cancer cells by using two different co-culture models. The results showed that colorectal cancer cells established a lactate metabolic coupling with fibroblasts through the oxidative stress effect, triggering the metabolic reprogramming process of themselves and those of fibroblasts. In addition, lactate enhanced the invasion and migration of colorectal cancer by stabilizing the protein expression levels of nuclear factor kappa-B (NF-κB) and hypoxia-inducible factor-1α (HIF-1α). Blocking oxidative stress and lactate metabolic coupling with reactive oxygen species removers and MCT1-specific inhibitors, respectively, could effectively suppress metastasis in colorectal cancer. These findings suggest that targeting the lactate metabolic coupling between tumor cells and CAFs will offer a new strategy to combat colorectal cancer.

Metabolic symbiosis between oxygenated and hypoxic tumour cells: An agent-based modelling study

Deregulated metabolism is one of the hallmarks of cancer. It is well-known that tumour cells tend to metabolize glucose via glycolysis even when oxygen is available and mitochondrial respiration is functional. However, the lower energy efficiency of aerobic glycolysis with respect to mitochondrial respiration makes this behaviour, namely the Warburg effect, counter-intuitive, although it has now been recognized as source of anabolic precursors. On the other hand, there is evidence that oxygenated tumour cells could be fuelled by exogenous lactate produced from glycolysis. We employed a multi-scale approach that integrates multi-agent modelling, diffusion-reaction, stoichiometric equations, and Boolean networks to study metabolic cooperation between hypoxic and oxygenated cells exposed to varying oxygen, nutrient, and inhibitor concentrations. The results show that the cooperation reduces the depletion of environmental glucose, resulting in an overall advantage of using aerobic glycolysis. In addition, the oxygen level was found to be decreased by symbiosis, promoting a further shift towards anaerobic glycolysis. However, the oxygenated and hypoxic populations may gradually reach quasi-equilibrium. A sensitivity analysis using Latin hypercube sampling and partial rank correlation shows that the symbiotic dynamics depends on properties of the specific cell such as the minimum glucose level needed for glycolysis. Our results suggest that strategies that block glucose transporters may be more effective to reduce tumour growth than those blocking lactate intake transporters.

LDHA and LDHB overexpression promoted the Warburg effect in malignantly transformed GES-1 cells induced by N-nitroso compounds

N-nitroso compounds (NOCs) exposure is a major risk factor for the development of gastric cancer. However, the carcinogenic mechanisms by which NOCs induce gastric and other cancers, especially the NOCs-induced Warburg effect, have not been comprehensively studied. Lactate dehydrogenase (LDH), which has two subunits (LDHA and LDHB), plays an important role in the Warburg effect of tumor cells. Therefore, we hypothesized that LDHA and LDHB could promote Warburg effect in malignant transformed GES-1 cells induced by Nmethyl-N'-nitro-N-nitrosoguanidine (MNNG). GES-1 cells were exposed to 1 μmol/L MNNG and cultured for 40 passages. During the culturing process, cell proliferation, migration, and soft agar colony formation significantly increased after 30 passages. Following MNNG exposure, lactate, LDH, glucose uptake, and the expression levels of key enzymes in glycolysis were significantly increased. Knocking down LDHA or LDHB alone reduced lactate secretion, inhibited cell viability, and impaired migratory capacities. Knocking down LDHA and LDHB together fully suppressed lactate secretion and effectively suppressed the malignant phenotype of cells transformed by long-term MNNG exposure. Finally, we demonstrated that overexpression of LDHA and LDHB promotes the malignant transformation of GES-1 cells by enhancing the Warburg effect during long-term exposure to NOCs.

Comparing mechanism-based and machine learning models for predicting the effects of glucose accessibility on tumor cell proliferation

Glucose plays a central role in tumor metabolism and development and is a target for novel therapeutics. To characterize the response of cancer cells to blockade of glucose uptake, we collected time-resolved microscopy data to track the growth of MDA-MB-231 breast cancer cells. We then developed a mechanism-based, mathematical model to predict how a glucose transporter (GLUT1) inhibitor (Cytochalasin B) influences the growth of the MDA-MB-231 cells by limiting access to glucose. The model includes a parameter describing dose dependent inhibition to quantify both the total glucose level in the system and the glucose level accessible to the tumor cells. Four common machine learning models were also used to predict tumor cell growth. Both the mechanism-based and machine learning models were trained and validated, and the prediction error was evaluated by the coefficient of determination (R²). The random forest model provided the highest accuracy predicting cell dynamics (R² = 0.92), followed by the decision tree (R² = 0.89), k-nearest-neighbor regression (R² = 0.84), mechanism-based (R² = 0.77), and linear regression model (R² = 0.69). Thus, the mechanism-based model has a predictive capability comparable to machine learning models with the added benefit of elucidating biological mechanisms.

Emerging role of substance and energy metabolism associated with neuroendocrine regulation in tumor cells

Cancer is the second most common cause of mortality in the world. One of the unresolved difficult pathological mechanism issues in malignant tumors is the imbalance of substance and energy metabolism of tumor cells. Cells maintain life through energy metabolism, and normal cells provide energy through mitochondrial oxidative phosphorylation to generate ATP, while tumor cells demonstrate different energy metabolism. Neuroendocrine control is crucial for tumor cells' consumption of nutrients and energy. As a result, better combinatorial therapeutic approaches will be made possible by knowing the neuroendocrine regulating mechanism of how the neuroendocrine system can fuel cellular metabolism. Here, the basics of metabolic remodeling in tumor cells for nutrients and metabolites are presented, showing how the neuroendocrine system regulates substance and energy metabolic pathways to satisfy tumor cell proliferation and survival requirements. In this context, targeting neuroendocrine regulatory pathways in tumor cell metabolism can beneficially enhance or temper tumor cell metabolism and serve as promising alternatives to available treatments.

The role of evolutionary game theory in spatial and non-spatial models of the survival of cooperation in cancer: a review

Evolutionary game theory (EGT) is a branch of mathematics which considers populations of individuals interacting with each other to receive pay-offs. An individual’s pay-off is dependent on the strategy of its opponent(s) as well as on its own, and the higher its pay-off, the higher its reproductive fitness. Its offspring generally inherit its interaction strategy, subject to random mutation. Over time, the composition of the population shifts as different strategies spread or are driven extinct. In the last 25 years there has been a flood of interest in applying EGT to cancer modelling, with the aim of explaining how cancerous mutations spread through healthy tissue and how intercellular cooperation persists in tumour-cell populations. This review traces this body of work from theoretical analyses of well-mixed infinite populations through to more realistic spatial models of the development of cooperation between epithelial cells. We also consider work in which EGT has been used to make experimental predictions about the evolution of cancer, and discuss work that remains to be done before EGT can make large-scale contributions to clinical treatment and patient outcomes.

Development and Validation of a 6-Gene Hypoxia-Related Prognostic Signature For Cholangiocarcinoma

Cholangiocarcinoma (CHOL) is highly malignant and has a poor prognosis. This study is committed to creating a new prognostic model based on hypoxia related genes. Here, we established a novel tumor hypoxia-related prognostic model consisting of 6 hypoxia-related genes by univariate Cox regression and the least absolute shrinkage and selection operator (LASSO) algorithm to predict CHOL prognosis and then the risk score for each patient was calculated. The results showed that the patients with high-risk scores had poor prognosis compared with those with low-risk scores, which was verified as an independent predictor by multivariate analysis. The hypoxia-related prognostic model was validated in both TCGA and GEO cohorts and exhibited excellent performance in predicting overall survival in CHOL. The PPI results suggested that hypoxia-related genes involved in the model may play a central role in regulating the hypoxic state. In addition, the presence of IDH1 mutations in the high-risk group was high, and GSEA results showed that some metabolic pathways were upregulated, but immune response processes were generally downregulated. These factors may be potential reasons for the high-risk group with worse prognosis. The analysis of different immune regulation-related processes in the high- and low-risk groups revealed that the expression of genes related to immune checkpoints would show differences between these two groups. We further verified the expression of the oncogene PPFIA4 in the model, and found that compared with normal samples, CHOL patients were generally highly expressed, and the patients with high-expression of PPFIA4 had a poor prognosis. In summary, the present study may provide a valid prognostic model for bile duct cancer to inform better clinical management of patients.

Lactate shuttle: from substance exchange to regulatory mechanism

Lactate, as the product of glycolytic metabolism and the substrate of energy metabolism, is an intermediate link between cancer cell and tumor microenvironment metabolism. The exchange of lactate between the two cells via mono-carboxylate transporters (MCTs) is known as the lactate shuttle in cancer. Lactate shuttle is the core of cancer cell metabolic reprogramming between two cells such as aerobic cancer cells and hypoxic cancer cells, tumor cells and stromal cells, cancer cells and vascular endothelial cells. Cancer cells absorb lactate by mono-carboxylate transporter 1 (MCT1) and convert lactate to pyruvate via intracellular lactate dehydrogenase B (LDH-B) to maintain their growth and metabolism. Since lactate shuttle may play a critical role in energy metabolism of cancer cells, components related to lactate shuttle may be a crucial target for tumor antimetabolic therapy. In this review, we describe the lactate shuttle in terms of both substance exchange and regulatory mechanisms in cancer. Meanwhile, we summarize the difference of key proteins of lactate shuttle in common types of cancer.

An experimental-mathematical approach to predict tumor cell growth as a function of glucose availability in breast cancer cell lines

We present the development and validation of a mathematical model that predicts how glucose dynamics influence metabolism and therefore tumor cell growth. Glucose, the starting material for glycolysis, has a fundamental influence on tumor cell growth. We employed time-resolved microscopy to track the temporal change of the number of live and dead tumor cells under different initial glucose concentrations and seeding densities. We then constructed a family of mathematical models (where cell death was accounted for differently in each member of the family) to describe overall tumor cell growth in response to the initial glucose and confluence conditions. The Akaikie Information Criteria was then employed to identify the most parsimonious model. The selected model was then trained on 75% of the data to calibrate the system and identify trends in model parameters as a function of initial glucose concentration and confluence. The calibrated parameters were applied to the remaining 25% of the data to predict the temporal dynamics given the known initial glucose concentration and confluence, and tested against the corresponding experimental measurements. With the selected model, we achieved an accuracy (defined as the fraction of measured data that fell within the 95% confidence intervals of the predicted growth curves) of 77.2 ± 6.3% and 87.2 ± 5.1% for live BT-474 and MDA-MB-231 cells, respectively.

Modeling and Analyzing Stem-Cell Therapy toward Cancer: Evolutionary Game Theory Perspective

BACKGROUND

Immunotherapy is a recently developed method of cancer therapy, aiming to strengthen a patient's immune system in different ways to fight cancer. One of these ways is to add stem cells into the patient's body.

METHODS

The study was conducted in Kermanshah, western Iran, 2016-2017. We first modeled the interaction between cancerous and healthy cells using the concept of evolutionary game theory. System dynamics were analyzed employing replicator equations and control theory notions. We categorized the system into separate cases based on the value of the parameters. For cases in which the system converged to undesired equilibrium points, "stem-cell injection" was employed as a therapeutic suggestion. The effect of stem cells on the model was considered by reforming the replicator equations as well as adding some new parameters to the system.

RESULTS

By adjusting stem cell-related parameters, the system converged to desired equilibrium points, i.e., points with no or a scanty level of cancerous cells. In addition to the theoretical analysis, our simulation results suggested solutions were effective in eliminating cancerous cells.

CONCLUSION

This model could be applicable to different types of cancer, so we did not restrict it to a specific type of cancer. In fact, we were seeking a flexible mathematical framework that could cover different types of cancer by adjusting the system parameters.

Anticipating critical transitions in epithelial-hybrid-mesenchymal cell-fate determination

In the vicinity of a tipping point, critical transitions occur when small changes in an input condition cause sudden, large, and often irreversible changes in the state of a system. Many natural systems ranging from ecosystems to molecular biosystems are known to exhibit critical transitions in their response to stochastic perturbations. In diseases, an early prediction of upcoming critical transitions from a healthy to a disease state by using early-warning signals is of prime interest due to potential application in forecasting disease onset. Here, we analyze cell-fate transitions between different phenotypes (epithelial, hybrid-epithelial/mesenchymal [E/M], and mesenchymal states) that are implicated in cancer metastasis and chemoresistance. These transitions are mediated by a mutually inhibitory feedback loop-microRNA-200/ZEB-driven by the levels of transcription factor SNAIL. We find that the proximity to tipping points enabling these transitions among different phenotypes can be captured by critical slowing down-based early-warning signals, calculated from the trajectory of ZEB messenger RNA level. Further, the basin stability analysis reveals the unexpectedly large basin of attraction for a hybrid-E/M phenotype. Finally, we identified mechanisms that can potentially elude the transition to a hybrid-E/M phenotype. Overall, our results unravel the early-warning signals that can be used to anticipate upcoming epithelial-hybrid-mesenchymal transitions. With the emerging evidence about the hybrid-E/M phenotype being a key driver of metastasis, drug resistance, and tumor relapse, our results suggest ways to potentially evade these transitions, reducing the fitness of cancer cells and restricting tumor aggressiveness.

Metabolic reprogramming and its clinical application in thyroid cancer

Warburg found that tumor cells exhibit high-level glycolysis, even under aerobic condition, which is known as the ‘Warburg effect’. As systemic changes in the entire metabolic network are gradually revealed, it is recognized that metabolic reprogramming has gone far beyond the imagination of Warburg. Metabolic reprogramming involves an active change in cancer cells to adapt to their biological characteristics. Thyroid cancer is a common endocrine malignant tumor whose metabolic characteristics have been studied in recent years. Some drugs targeting tumor metabolism are under clinical trial. This article reviews the metabolic changes and mechanisms in thyroid cancer, aiming to find metabolic-related molecules that could be potential markers to predict prognosis and metabolic pathways, or could serve as therapeutic targets. Our review indicates that knowledge in metabolic alteration has potential contributions in the diagnosis, treatment and prognostic evaluation of thyroid cancer, but further studies are needed for verification as well.

Natural Selection Between Two Games with Applications to Game Theoretical Models of Cancer

Evolutionary game theory has been used extensively to study single games as applied to cancer, including in the context of metabolism, development of resistance, and even games between tumor and treatment. However, the situation when several games are being played against each other at the same time has not yet been investigated. Here, we describe a mathematical framework for analyzing natural selection not just between strategies, but between games. We provide theoretical analysis of situations of natural selection between the games of Prisoner's dilemma and Hawk-Dove, and demonstrate that while the dynamics of cooperators and defectors within their respective games is as expected, the distribution of games changes over time due to natural selection. We also investigate the question of mutual invasibility of games with respect to different strategies and different initial population composition. We conclude with a discussion of how the proposed approach can be applied to other games in cancer, such as motility versus stability strategies that underlie the process of metastatic invasion.

Cooperation among cancer cells: applying game theory to cancer

Cell cooperation promotes many of the hallmarks of cancer via the secretion of diffusible factors that can affect cancer cells or stromal cells in the tumour microenvironment. This cooperation cannot be explained simply as the collective action of cells for the benefit of the tumour because non-cooperative subclones can constantly invade and free-ride on the diffusible factors produced by the cooperative cells. A full understanding of cooperation among the cells of a tumour requires methods and concepts from evolutionary game theory, which has been used successfully in other areas of biology to understand similar problems but has been underutilized in cancer research. Game theory can provide insights into the stability of cooperation among cells in a tumour and into the design of potentially evolution-proof therapies that disrupt this cooperation.

Multi-scale computational study of the Warburg effect, reverse Warburg effect and glutamine addiction in solid tumors

Cancer metabolism has received renewed interest as a potential target for cancer therapy. In this study, we use a multi-scale modeling approach to interrogate the implications of three metabolic scenarios of potential clinical relevance: the Warburg effect, the reverse Warburg effect and glutamine addiction. At the intracellular level, we construct a network of central metabolism and perform flux balance analysis (FBA) to estimate metabolic fluxes; at the cellular level, we exploit this metabolic network to calculate parameters for a coarse-grained description of cellular growth kinetics; and at the multicellular level, we incorporate these kinetic schemes into the cellular automata of an agent-based model (ABM), iDynoMiCS. This ABM evaluates the reaction-diffusion of the metabolites, cellular division and motion over a simulation domain. Our multi-scale simulations suggest that the Warburg effect provides a growth advantage to the tumor cells under resource limitation. However, we identify a non-monotonic dependence of growth rate on the strength of glycolytic pathway. On the other hand, the reverse Warburg scenario provides an initial growth advantage in tumors that originate deeper in the tissue. The metabolic profile of stromal cells considered in this scenario allows more oxygen to reach the tumor cells in the deeper tissue and thus promotes tumor growth at earlier stages. Lastly, we suggest that glutamine addiction does not confer a selective advantage to tumor growth with glutamine acting as a carbon source in the tricarboxylic acid (TCA) cycle, any advantage of glutamine uptake must come through other pathways not included in our model (e.g., as a nitrogen donor). Our analysis illustrates the importance of accounting explicitly for spatial and temporal evolution of tumor microenvironment in the interpretation of metabolic scenarios and hence provides a basis for further studies, including evaluation of specific therapeutic strategies that target metabolism.

Cancer metabolism is an emerging hallmark of cancer. In the past decade, a renewed focus on cancer metabolism has led to several distinct hypotheses describing the role of metabolism in cancer. To complement experimental efforts in this field, a scale-bridging computational framework is needed to allow rapid evaluation of emerging hypotheses in cancer metabolism. In this study, we present a multi-scale modeling platform and demonstrate the distinct outcomes in population-scale growth dynamics under different metabolic scenarios: the Warburg effect, the reverse Warburg effect and glutamine addiction. Within this modeling framework, we confirmed population-scale growth advantage enabled by the Warburg effect, provided insights into the symbiosis between stromal cells and tumor cells in the reverse Warburg effect and argued that the anaplerotic role of glutamine is not exploited by tumor cells to gain growth advantage under resource limitations. We point to the opportunity for this framework to help understand tissue-scale response to therapeutic strategies that target cancer metabolism while accounting for the tumor complexity at multiple scales.

Rate of recovery from perturbations as a means to forecast future stability of living systems

Anticipating critical transitions in complex ecological and living systems is an important need because it is often difficult to restore a system to its pre-transition state once the transition occurs. Recent studies demonstrate that several indicators based on changes in ecological time series can indicate that the system is approaching an impending transition. An exciting question is, however, whether we can predict more characteristics of the future system stability using measurements taken away from the transition. We address this question by introducing a model-less forecasting method to forecast catastrophic transition of an experimental ecological system. The experiment is based on the dynamics of a yeast population, which is known to exhibit a catastrophic transition as the environment deteriorates. By measuring the system's response to perturbations prior to transition, we forecast the distance to the upcoming transition, the type of the transition (i.e., catastrophic/non-catastrophic) and the future equilibrium points within a range near the transition. Experimental results suggest a strong potential for practical applicability of this approach for ecological systems which are at risk of catastrophic transitions, where there is a pressing need for information about upcoming thresholds.

Extinction rates in tumour public goods games

Cancer evolution and progression are shaped by cellular interactions and Darwinian selection. Evolutionary game theory incorporates both of these principles, and has been proposed as a framework to understand tumour cell population dynamics. A cornerstone of evolutionary dynamics is the replicator equation, which describes changes in the relative abundance of different cell types, and is able to predict evolutionary equilibria. Typically, the replicator equation focuses on differences in relative fitness. We here show that this framework might not be sufficient under all circumstances, as it neglects important aspects of population growth. Standard replicator dynamics might miss critical differences in the time it takes to reach an equilibrium, as this time also depends on cellular turnover in growing but bounded populations. As the system reaches a stable manifold, the time to reach equilibrium depends on cellular death and birth rates. These rates shape the time scales, in particular, in coevolutionary dynamics of growth factor producers and free-riders. Replicator dynamics might be an appropriate framework only when birth and death rates are of similar magnitude. Otherwise, population growth effects cannot be neglected when predicting the time to reach an equilibrium, and cell-type-specific rates have to be accounted for explicitly.

Microenvironmental cooperation promotes early spread and bistability of a Warburg-like phenotype

We introduce an in silico model for the initial spread of an aberrant phenotype with Warburg-like overflow metabolism within a healthy homeostatic tissue in contact with a nutrient reservoir (the blood), aimed at characterizing the role of the microenvironment for aberrant growth. Accounting for cellular metabolic activity, competition for nutrients, spatial diffusion and their feedbacks on aberrant replication and death rates, we obtain a phase portrait where distinct asymptotic whole-tissue states are found upon varying the tissue-blood turnover rate and the level of blood-borne primary nutrient. Over a broad range of parameters, the spreading dynamics is bistable as random fluctuations can impact the final state of the tissue. Such a behaviour turns out to be linked to the re-cycling of overflow products by non-aberrant cells. Quantitative insight on the overall emerging picture is provided by a spatially homogeneous version of the model.

Integrating evolutionary game theory into an agent-based model of ductal carcinoma in situ: Role of gap junctions in cancer progression

BACKGROUND AND OBJECTIVE

There are many cells with various phenotypic behaviors in cancer interacting with each other. For example, an apoptotic cell may induce apoptosis in adjacent cells. A living cell can also protect cells from undergoing apoptosis and necrosis. These survival and death signals are propagated through interaction pathways between adjacent cells called gap junctions. The function of these signals depends on the cellular context of the cell receiving them. For instance, a receiver cell experiencing a low level of oxygen may interpret a received survival signal as an apoptosis signal. In this study, we examine the effect of these signals on tumor growth.

METHODS

We make an evolutionary game theory component in order to model the signal propagation through gap junctions. The game payoffs are defined as a function of cellular context. Then, the game theory component is integrated into an agent-based model of tumor growth. After that, the integrated model is applied to ductal carcinoma in situ, a type of early stage breast cancer. Different scenarios are explored to observe the impact of the gap junction communication and parameters of the game theory component on cancer progression. We compare these scenarios by using the Wilcoxon signed-rank test.

RESULTS

The Wilcoxon signed-rank test succeeds in proving a significant difference between the tumor growth of the model before and after considering the gap junction communication. The Wilcoxon signed-rank test also proves that the tumor growth significantly depends on the oxygen threshold of turning survival signals into apoptosis.

CONCLUSIONS

In this study, the gap junction communication is modeled by using evolutionary game theory to illustrate its role at early stage cancers such as ductal carcinoma in situ. This work indicates that the gap junction communication and the oxygen threshold of turning survival signals into apoptosis can notably affect cancer progression.

Lactate promotes glutamine uptake and metabolism in oxidative cancer cells

Oxygenated cancer cells have a high metabolic plasticity as they can use glucose, glutamine and lactate as main substrates to support their bioenergetic and biosynthetic activities. Metabolic optimization requires integration. While glycolysis and glutaminolysis can cooperate to support cellular proliferation, oxidative lactate metabolism opposes glycolysis in oxidative cancer cells engaged in a symbiotic relation with their hypoxic/glycolytic neighbors. However, little is known concerning the relationship between oxidative lactate metabolism and glutamine metabolism. Using SiHa and HeLa human cancer cells, this study reports that intracellular lactate signaling promotes glutamine uptake and metabolism in oxidative cancer cells. It depends on the uptake of extracellular lactate by monocarboxylate transporter 1 (MCT1). Lactate first stabilizes hypoxia-inducible factor-2α (HIF-2α), and HIF-2α then transactivates c-Myc in a pathway that mimics a response to hypoxia. Consequently, lactate-induced c-Myc activation triggers the expression of glutamine transporter ASCT2 and of glutaminase 1 (GLS1), resulting in improved glutamine uptake and catabolism. Elucidation of this metabolic dependence could be of therapeutic interest. First, inhibitors of lactate uptake targeting MCT1 are currently entering clinical trials. They have the potential to indirectly repress glutaminolysis. Second, in oxidative cancer cells, resistance to glutaminolysis inhibition could arise from compensation by oxidative lactate metabolism and increased lactate signaling.

Cell population heterogeneity and evolution towards drug resistance in cancer: Biological and mathematical assessment, theoretical treatment optimisation

BACKGROUND

Drug-induced drug resistance in cancer has been attributed to diverse biological mechanisms at the individual cell or cell population scale, relying on stochastically or epigenetically varying expression of phenotypes at the single cell level, and on the adaptability of tumours at the cell population level.

SCOPE OF REVIEW

We focus on intra-tumour heterogeneity, namely between-cell variability within cancer cell populations, to account for drug resistance. To shed light on such heterogeneity, we review evolutionary mechanisms that encompass the great evolution that has designed multicellular organisms, as well as smaller windows of evolution on the time scale of human disease. We also present mathematical models used to predict drug resistance in cancer and optimal control methods that can circumvent it in combined therapeutic strategies.

MAJOR CONCLUSIONS

Plasticity in cancer cells, i.e., partial reversal to a stem-like status in individual cells and resulting adaptability of cancer cell populations, may be viewed as backward evolution making cancer cell populations resistant to drug insult. This reversible plasticity is captured by mathematical models that incorporate between-cell heterogeneity through continuous phenotypic variables. Such models have the benefit of being compatible with optimal control methods for the design of optimised therapeutic protocols involving combinations of cytotoxic and cytostatic treatments with epigenetic drugs and immunotherapies.

GENERAL SIGNIFICANCE

Gathering knowledge from cancer and evolutionary biology with physiologically based mathematical models of cell population dynamics should provide oncologists with a rationale to design optimised therapeutic strategies to circumvent drug resistance, that still remains a major pitfall of cancer therapeutics. This article is part of a Special Issue entitled "System Genetics" Guest Editor: Dr. Yudong Cai and Dr. Tao Huang.

Nutrient deprivation-related OXPHOS/glycolysis interconversion via HIF-1α/C-MYC pathway in U251 cells

Although the Warburg effect is a dominant metabolic phenotype observed in cancers, the metabolic changes and adaptation occurring in tumors have been demonstrated to extend beyond the Warburg effect and thus considered a secondary effect to the transformation process of carcinogenesis, including nutritional deficiencies. However, the role of nutritional deficiencies in this metabolic reprogramming (e. g., oxidative phosphorylation (OXPHOS)/glycolysis interconversion) is not completely known yet. Here, we showed that under regular culture condition, the proliferation of U251 cells, but not other tumor cell lines, preferentially performed the Warburg effect and was remarkably inhibited by oxamic acid which can inhibit the activity of lactate dehydrogenase (LDH); whereas under serum starvation, glycolysis was depressed, tricarboxylic acid cycle (TCA) was enhanced, and the activity of OXPHOS was reinforced to maintain cellular ATP content in a high level, but interestingly, we observed a decreased expression of reactive oxygen species (ROS). Moreover, the upregulated activity of mitochondrial complex I was confirmed by Western blots and showed that the mitochondrial-related protein, NDUFA9, NDUFB8, ND1, and VDAC1 were remarkably increased after serum starved. Mechanistically, nutritional deficiencies could reduce hypoxia-inducible factor α (HIF-1α) protein expression to increase C-MYC protein level, which in turn increased nuclear respiratory factor 1 (NRF1) and mitochondrial transcription factor A (TFAM) transcription to enhance the activity of OXPHOS, suggesting that metabolic reprogramming by the changes of microenvironment during the carcinogenesis can provide some novel therapeutic clues to traditional cancer treatments.

The mathematics of cancer: integrating quantitative models

Mathematical modelling approaches have become increasingly abundant in cancer research. The complexity of cancer is well suited to quantitative approaches as it provides challenges and opportunities for new developments. In turn, mathematical modelling contributes to cancer research by helping to elucidate mechanisms and by providing quantitative predictions that can be validated. The recent expansion of quantitative models addresses many questions regarding tumour initiation, progression and metastases as well as intra-tumour heterogeneity, treatment responses and resistance. Mathematical models can complement experimental and clinical studies, but also challenge current paradigms, redefine our understanding of mechanisms driving tumorigenesis and shape future research in cancer biology.

Quantitative constraint-based computational model of tumor-to-stroma coupling via lactate shuttle

Cancer cells utilize large amounts of ATP to sustain growth, relying primarily on non-oxidative, fermentative pathways for its production. In many types of cancers this leads, even in the presence of oxygen, to the secretion of carbon equivalents (usually in the form of lactate) in the cell’s surroundings, a feature known as the Warburg effect. While the molecular basis of this phenomenon are still to be elucidated, it is clear that the spilling of energy resources contributes to creating a peculiar microenvironment for tumors, possibly characterized by a degree of toxicity. This suggests that mechanisms for recycling the fermentation products (e.g. a lactate shuttle) may be active, effectively inducing a mutually beneficial metabolic coupling between aberrant and non-aberrant cells. Here we analyze this scenario through a large-scale in silico metabolic model of interacting human cells. By going beyond the cell-autonomous description, we show that elementary physico-chemical constraints indeed favor the establishment of such a coupling under very broad conditions. The characterization we obtained by tuning the aberrant cell’s demand for ATP, amino-acids and fatty acids and/or the imbalance in nutrient partitioning provides quantitative support to the idea that synergistic multi-cell effects play a central role in cancer sustainment.

Heterogeneity and proliferation of invasive cancer subclones in game theory models of the Warburg effect

OBJECTIVES

The Warburg effect, a switch from aerobic energy production to anaerobic glycolysis, promotes tumour proliferation and motility by inducing acidification of the tumour microenvironment. Therapies that reduce acidity could impair tumour growth and invasiveness. I analysed the dynamics of cell proliferation and of resistance to therapies that target acidity, in a population of cells, under the Warburg effect.

MATERIALS AND METHODS

The dynamics of mutant cells with increased glycolysis and motility has been assessed in a multi-player game with collective interactions in the framework of evolutionary game theory. Perturbations of the level of acidity in the microenvironment have been used to simulate the effect of therapies that target glycolysis.

RESULTS

The non-linear effects of glycolysis induce frequency-dependent clonal selection leading to coexistence of glycolytic and non-glycolytic cells within a tumour. Mutants with increased motility can invade such a polymorphic population and spread within the tumour. While reducing acidity may produce a sudden reduction in tumour cell proliferation, frequency-dependent selection enables it to adapt to the new conditions and can enable the tumour to restore its original levels of growth and invasiveness.

CONCLUSIONS

The acidity produced by glycolysis acts as a non-linear public good that leads to coexistence of cells with high and low glycolysis within the tumour. Such a heterogeneous population can easily adapt to changes in acidity. Therapies that target acidity can only be effective in the long term if the cost of glycolysis is high, that is, under non-limiting oxygen concentrations. Their efficacy, therefore, is reduced when combined with therapies that impair angiogenesis.

Critical transitions in chronic disease: transferring concepts from ecology to systems medicine

Ecosystems and biological systems are known to be inherently complex and to exhibit nonlinear dynamics. Diseases such as microbiome dysregulation or depression can be seen as complex systems as well and were shown to exhibit patterns of nonlinearity in their response to perturbations. These nonlinearities can be revealed by a sudden shift in system states, for instance from health to disease. The identification and characterization of early warning signals which could predict upcoming critical transitions is of primordial interest as prevention of disease onset is a major aim in health care. In this review, we focus on recent evidence for critical transitions in diseases and discuss the potential of such studies for therapeutic applications.

Disrupting the balance between tumor epithelia and stroma is a possible therapeutic approach for pancreatic cancer

Pancreatic ductal adenocarcinoma (PDAC) is a type of highly lethal malignant tumor. PDAC is locally invasive and is surrounded by a dense desmoplasia or fibrosis, which can involve adjacent vital structures. Previously, the effect of pancreatic stellate cells (PSCs) of stroma in the progression of PDAC has received more attention, and most in vitro and in vivo studies revealed that PSCs appear to confer biological aggressiveness. However, clinical trials targeting desmoplasia or PSCs showed disappointing results. Recent studies found that stromal components, especially activated PSCs, are able to inhibit the occurrence and progression of PDAC. Inhibition of the stroma or desmoplasia through genetic regulations or drugs accelerates the formation and progression of PDAC. Thus, we hypothesized that in various times and spaces, there is a balance between the tumor epithelia and stroma; once the balance is upset, the tumor traits may undergo certain changes. Therefore, finding the key changing points of this relationship to corrupt or influence it, instead of blindly inhibiting the stroma motivation or simply maintaining stroma activation, will destroy the cooperation or promote the competition and antagonism among cells. This approach may render tumors more vulnerable and thus unable to resist anti-cancer therapies.

Glucose-lactate metabolic cooperation in cancer: insights from a spatial mathematical model and implications for targeted therapy

A recent study has hypothesised a glucose-lactate metabolic symbiosis between adjacent hypoxic and oxygenated regions of a developing tumour, and proposed a treatment strategy to target this symbiosis. However, in vivo experimental support remains inconclusive. Here we develop a minimal spatial mathematical model of glucose-lactate metabolism to examine, in principle, whether metabolic symbiosis is plausible in human tumours, and to assess the potential impact of inhibiting it. We find that symbiosis is a robust feature of our model system-although on the length scale at which oxygen supply is diffusion-limited, its occurrence requires very high cellular metabolic activity-and that necrosis in the tumour core is reduced in the presence of symbiosis. Upon simulating therapeutic inhibition of lactate uptake, we predict that targeted treatment increases the extent of tissue oxygenation without increasing core necrosis. The oxygenation effect is correlated strongly with the extent of wild-type hypoxia and only weakly with wild-type symbiotic behaviour, and therefore may be promising for radiosensitisation of hypoxic, lactate-consuming tumours even if they do not exhibit a spatially well-defined symbiosis. Finally, we conduct in vitro experiments on the U87 glioblastoma cell line to facilitate preliminary speculation as to where highly malignant tumours might fall in our parameter space, and find that these experiments suggest a weakly symbiotic regime for U87 cells, thus raising the new question of what relationship might exist between symbiosis and tumour malignancy.

Metabolic asymmetry in cancer: a "balancing act" that promotes tumor growth

Profound metabolic differences between cancer cells and fibroblasts promote tumorigenesis. A study by Valencia and colleagues in this issue of Cancer Cell supports this assertion. They observed that metabolic asymmetry in prostate tumors drives aggressive disease with high p62 in anabolic cancer cells, but loss of p62 in catabolic fibroblasts.