Cancer immunoediting: A process driven by metabolic competition as a predator-prey-shared resource type model

A Cancer Subpopulation Competition Model Reveals Optimal Levels of Immune Response that Minimize Tumor Size

Breast cancer is a complex disease with significant phenotypic heterogeneity of cells, even within a single breast tumor. Emerging evidence underscores the significance of intratumoral competition, which can serve as a key contributor to cancer drug resistance, imparting substantial clinical implications. Understanding the competitive dynamics is paramount as it can significantly influence disease progression and treatment outcomes. In the present work, a mathematical model was developed using a system of differential equations to describe the dynamic interactions between two cancer subtypes (each further classified into cancer stem cells and tumor cells) and innate immune cells. The purpose of the model is to comprehensively understand the competitive interactions between the heterogeneous subpopulations. The equilibrium points and stability analysis for each equilibrium point were established. Model simulations showed that the competition between two cancer subtypes directly affects the number of both species. When competition between two cancer subtypes is strong, increasing the immune response rate specific to the more competitive species effectively reduces the tumor size. However, if the competition is relatively weak, an optimal immune response rate is required to minimize the total number of tumor cells. Rates below the optimal level fail to reduce the population of the stronger species, whereas rates above the optimal level can lead to the recurrence of the weaker species. Overall, this model provides insights into breast cancer dynamics and guides the development of effective treatment strategies.

Mechanistic characterization of oscillatory patterns in unperturbed tumor growth dynamics: The interplay between cancer cells and components of tumor microenvironment

Mathematical modeling of unperturbed and perturbed tumor growth dynamics (TGD) in preclinical experiments provides an opportunity to establish translational frameworks. The most commonly used unperturbed tumor growth models (i.e. linear, exponential, Gompertz and Simeoni) describe a monotonic increase and although they capture the mean trend of the data reasonably well, systematic model misspecifications can be identified. This represents an opportunity to investigate possible underlying mechanisms controlling tumor growth dynamics through a mathematical framework. The overall goal of this work is to develop a data-driven semi-mechanistic model describing non-monotonic tumor growth in untreated mice. For this purpose, longitudinal tumor volume profiles from different tumor types and cell lines were pooled together and analyzed using the population approach. After characterizing the oscillatory patterns (oscillator half-periods between 8-11 days) and confirming that they were systematically observed across the different preclinical experiments available (p<10-9), a tumor growth model was built including the interplay between resources (i.e. oxygen or nutrients), angiogenesis and cancer cells. The new structure, in addition to improving the model diagnostic compared to the previously used tumor growth models (i.e. AIC reduction of 71.48 and absence of autocorrelation in the residuals (p>0.05)), allows the evaluation of the different oncologic treatments in a mechanistic way. Drug effects can potentially, be included in relevant processes taking place during tumor growth. In brief, the new model, in addition to describing non-monotonic tumor growth and the interaction between biological factors of the tumor microenvironment, can be used to explore different drug scenarios in monotherapy or combination during preclinical drug development.

A PDE Model of Breast Tumor Progression in MMTV-PyMT Mice

The evolution of breast tumors greatly depends on the interaction network among different cell types, including immune cells and cancer cells in the tumor. This study takes advantage of newly collected rich spatio-temporal mouse data to develop a data-driven mathematical model of breast tumors that considers cells' location and key interactions in the tumor. The results show that cancer cells have a minor presence in the area with the most overall immune cells, and the number of activated immune cells in the tumor is depleted over time when there is no influx of immune cells. Interestingly, in the case of the influx of immune cells, the highest concentrations of both T cells and cancer cells are in the boundary of the tumor, as we use the Robin boundary condition to model the influx of immune cells. In other words, the influx of immune cells causes a dominant outward advection for cancer cells. We also investigate the effect of cells' diffusion and immune cells' influx rates in the dynamics of cells in the tumor micro-environment. Sensitivity analyses indicate that cancer cells and adipocytes' diffusion rates are the most sensitive parameters, followed by influx and diffusion rates of cytotoxic T cells, implying that targeting them is a possible treatment strategy for breast cancer.

Tumour immunotherapy: lessons from predator-prey theory

With the burgeoning use of immune-based treatments for cancer, never has there been a greater need to understand the tumour microenvironment within which immune cells function and how it can be perturbed to inhibit tumour growth. Yet, current challenges in identifying optimal combinations of immunotherapies and engineering new cell-based therapies highlight the limitations of conventional paradigms for the study of the tumour microenvironment. Ecology has a rich history of studying predator-prey dynamics to discern factors that drive prey to extinction. Here, we describe the basic tenets of predator-prey theory as applied to 'predation' by immune cells and the 'extinction' of cancer cells. Our synthesis reveals fundamental mechanisms by which antitumour immunity might fail in sometimes counterintuitive ways and provides a fresh yet evidence-based framework to better understand and therapeutically target the immune-cancer interface.

A Fractional Analysis of Hyperthermia Therapy on Breast Cancer in a Porous Medium along with Radiative Microwave Heating

Cancer is a prominent source of mortality and morbidity globally, but little is known about how it develops and spreads. Tumor cells are unable to thrive in high-temperature environments, according to recent research. Hyperthermia is the name for this therapy method. This study provides insights into hyperthermia therapy on breast cancer in the presence of a porous material with fractional derivative access when using radiative microwave heating. The mathematical model is formulated by PDE, while the time-fractional Caputo derivative is applied to make our equation more general as compared to the classical model. To produce a more efficient analysis of blood temperature distributions inside the tissues of the breast, the unsteady state is calculated by using the Laplace transform technique. The Laplace inversion is found by Durbin’s and Zakian’s algorithms. The treatment involves mild temperature hyperthermia, which causes cell death by enhancing cell sensitivity to radiation therapy and blood flow in the tumor. The variations of different parameters to control the temperate profile during therapy are discussed; we can also see how a fractional parameter makes our study more realistic for further experimental study.

Imaging the Rewired Metabolism in Lung Cancer in Relation to Immune Therapy

Metabolic reprogramming is recognized as one of the hallmarks of cancer. Alterations in the micro-environmental metabolic characteristics are recognized as important tools for cancer cells to interact with the resident and infiltrating T-cells within this tumor microenvironment. Cancer-induced metabolic changes in the micro-environment also affect treatment outcomes. In particular, immune therapy efficacy might be blunted because of somatic mutation-driven metabolic determinants of lung cancer such as acidity and oxygenation status. Based on these observations, new onco-immunological treatment strategies increasingly include drugs that interfere with metabolic pathways that consequently affect the composition of the lung cancer tumor microenvironment (TME). Positron emission tomography (PET) imaging has developed a wide array of tracers targeting metabolic pathways, originally intended to improve cancer detection and staging. Paralleling the developments in understanding metabolic reprogramming in cancer cells, as well as its effects on stromal, immune, and endothelial cells, a wave of studies with additional imaging tracers has been published. These tracers are yet underexploited in the perspective of immune therapy. In this review, we provide an overview of currently available PET tracers for clinical studies and discuss their potential roles in the development of effective immune therapeutic strategies, with a focus on lung cancer. We report on ongoing efforts that include PET/CT to understand the outcomes of interactions between cancer cells and T-cells in the lung cancer microenvironment, and we identify areas of research which are yet unchartered. Thereby, we aim to provide a starting point for molecular imaging driven studies to understand and exploit metabolic features of lung cancer to optimize immune therapy.

Predator-Prey in Tumor-Immune Interactions: A Wrong Model or Just an Incomplete One?

Tumor-immune interactions are often framed as predator-prey. This imperfect analogy describes how immune cells (the predators) hunt and kill immunogenic tumor cells (the prey). It allows for evaluation of tumor cell populations that change over time during immunoediting and it also considers how the immune system changes in response to these alterations. However, two aspects of predator-prey type models are not typically observed in immuno-oncology. The first concerns the conversion of prey killed into predator biomass. In standard predator-prey models, the predator relies on the prey for nutrients, while in the tumor microenvironment the predator and prey compete for resources (e.g. glucose). The second concerns oscillatory dynamics. Standard predator-prey models can show a perpetual cycling in both prey and predator population sizes, while in oncology we see increases in tumor volume and decreases in infiltrating immune cell populations. Here we discuss the applicability of predator-prey models in the context of cancer immunology and evaluate possible causes for discrepancies. Key processes include "safety in numbers", resource availability, time delays, interference competition, and immunoediting. Finally, we propose a way forward to reconcile differences between model predictions and empirical observations. The immune system is not just predator-prey. Like natural food webs, the immune-tumor community of cell types forms an immune-web of different and identifiable interactions.

How Should Cancer Models Be Constructed?

Choosing and optimizing treatment strategies for cancer requires capturing its complex dynamics sufficiently well for understanding but without being overwhelmed. Mathematical models are essential to achieve this understanding, and we discuss the challenge of choosing the right level of complexity to address the full range of tumor complexity from growth, the generation of tumor heterogeneity, and interactions within tumors and with treatments and the tumor microenvironment. We discuss the differences between conceptual and descriptive models, and compare the use of predator-prey models, evolutionary game theory, and dynamic precision medicine approaches in the face of uncertainty about mechanisms and parameter values. Although there is of course no one-size-fits-all approach, we conclude that broad and flexible thinking about cancer, based on combined modeling approaches, will play a key role in finding creative and improved treatments.

Dormant Tumor Cell Vaccination: A Mathematical Model of Immunological Dormancy in Triple-Negative Breast Cancer

Simple Summary

Triple-negative breast cancer (TNBC) is the most aggressive subtype of breast cancer, particularly affecting young women. Chemotherapy is the main choice for the treatment of these patients. It has been shown that some chemotherapies induce immunogenic cell death and elicit an adaptive cytotoxic T cell immune response through the activation of the type I interferon pathway. We made an evolutionary mathematical model based on the recently reported in vivo induction of immunological tumor dormancy of a murine TNBC cell line upon in vitro treatment with chemotherapy. Our model replicates the previously obtained experimental results and predicts a prophylactic and therapeutic vaccination effect by injecting dormant cells with active type I interferon signaling, before or after challenge with the aggressive parental tumor cells, respectively. These results show the potential of a dormant tumor cell-based therapy inducing an adaptive immune response, suppressing tumor growth.

Abstract

Triple-negative breast cancer (TNBC) is a molecular subtype of breast malignancy with a poor clinical prognosis. There is growing evidence that some chemotherapeutic agents induce an adaptive anti-tumor immune response. This reaction has been proposed to maintain the equilibrium phase of the immunoediting process and to control tumor growth by immunological cancer dormancy. We recently reported a model of immunological breast cancer dormancy based on the murine 4T1 TNBC model. Treatment of 4T1 cells in vitro with high-dose chemotherapy activated the type I interferon (type I IFN) signaling pathway, causing a switch from immunosuppressive to cytotoxic T lymphocyte-dependent immune response in vivo, resulting in sustained dormancy. Here, we developed a deterministic mathematical model based on the assumption that two cell subpopulations exist within the treated tumor: one population with high type I IFN signaling and immunogenicity and lower growth rate; the other population with low type I IFN signaling and immunogenicity and higher growth rate. The model reproduced cancer dormancy, elimination, and immune-escape in agreement with our previously reported experimental data. It predicted that the injection of dormant tumor cells with active type I IFN signaling results in complete growth control of the aggressive parental cancer cells injected at a later time point, but also of an already established aggressive tumor. Taken together, our results indicate that a dormant cell population can suppress the growth of an aggressive counterpart by eliciting a cytotoxic T lymphocyte-dependent immune response.

Global Dynamics of a Breast Cancer Competition Model

In this paper, we present a system of five ordinary differential equations which consider population dynamics among cancer stem cells, tumor cells, and healthy cells. Additionally, we consider the effects of excess estrogen and the body's natural immune response on the aforementioned cell populations. Employing a variety of analytical methods, we study the global dynamics of the full system, along with various submodels. We find sufficient conditions on parameter values to ensure cancer persistence in the absence of immune cells, and cancer eradication when an immune response is included. We conclude with a discussion on the biological implications of the resulting global dynamics.

Dynamics of Breast Cancer under Different Rates of Chemoradiotherapy

A type of cancer which originates from the breast tissue is referred to as breast cancer. Globally, it is the most common cause of death in women. Treatments such as radiotherapy, chemotherapy, hormone therapy, immunotherapy, and gene therapy are the main strategies in the fight against breast cancer. The present study aims at investigating the effects of the combined radiotherapy and chemotherapy as a way to treat breast cancer, and different treatment approaches are incorporated into the model. Also, the model is fitted to data on patients with breast cancer in Tanzania. We determine new treatment strategies, and finally, we show that when sufficient amount of chemotherapy and radiotherapy with a low decay rate is used, the drug will be significantly more effective in combating the disease while health cells remain above the threshold.

Metabolism and Gut Microbiota in Cancer Immunoediting, CD8/Treg Ratios, Immune Cell Homeostasis, and Cancer (Immuno)Therapy: Concise Review

The concept of immunoediting, a process whereby the immune system eliminates immunogenic cancer cell clones, allowing the remaining cells to progress and form a tumor, has evolved with growing appreciation of the importance of cancer ecology on tumor progression. As cancer cells grow and modify their environment, they create spatial and nutrient constraints that may affect not only immune cell function but also differentiation, tipping the balance between cytotoxic and regulatory immunity to facilitate tumor growth. Here, we review how immunometabolism may contribute to cancer escape from the immune system, as well as highlight an emerging role of gut microbiota, its effects on the immune system and on response to immunotherapy. We conclude with a discussion of how these pieces can be integrated to devise better combination therapies and highlight the role of computational approaches as a potential tool to aid in combination therapy design. Stem Cells 2019;37:1273-1280.

Illuminating the Numbers: Integrating Mathematical Models to Optimize Photomedicine Dosimetry and Combination Therapies

Cancer photomedicine offers unique mechanisms for inducing local tumor damage with the potential to stimulate local and systemic anti-tumor immunity. Optically-active nanomedicine offers these features as well as spatiotemporal control of tumor-focused drug release to realize synergistic combination therapies. Achieving quantitative dosimetry is a major challenge, and dosimetry is fundamental to photomedicine for personalizing and tailoring therapeutic regimens to specific patients and anatomical locations. The challenge of dosimetry is perhaps greater for photomedicine than many standard therapies given the complexity of light delivery and light-tissue interactions as well as the resulting photochemistry responsible for tumor damage and drug-release, in addition to the usual intricacies of therapeutic agent delivery. An emerging multidisciplinary approach in oncology utilizes mathematical and computational models to iteratively and quantitively analyze complex dosimetry, and biological response parameters. These models are parameterized by preclinical and clinical observations and then tested against previously unseen data. Such calibrated and validated models can be deployed to simulate treatment doses, protocols, and combinations that have not yet been experimentally or clinically evaluated and can provide testable optimal treatment outcomes in a practical workflow. Here, we foresee the utility of these computational approaches to guide adaptive therapy, and how mathematical models might be further developed and integrated as a novel methodology to guide precision photomedicine.

Natural Killer Cell Education Is Associated With a Distinct Glycolytic Profile

NK cells expressing self-inhibitory receptors display increased functionality compared to NK cells lacking those receptors. The acquisition of functional competence in these particular NK-cell subsets is termed education. Little is known about the underlying mechanisms that lead to the functional differences between educated and uneducated NK cells. An increasing number of studies suggest that cellular metabolism is a determinant of immune cell functions. Thus, alterations in cellular metabolic pathways may play a role in the process of NK-cell education. Here, we compared the glycolytic profile of educated and uneducated primary human NK cells. KIR-educated NK cells showed significantly increased expression levels of the glucose transporter Glut1 in comparison to NKG2A-educated or uneducated NK cells with and without exposure to target cells. Subsequently, the metabolic profile of NK-cell subsets was determined using a Seahorse XF Analyzer. Educated NK cells displayed significantly higher rates of cellular glycolysis than uneducated NK cells even in a resting state. Our results indicate that educated and uneducated NK cells reside in different metabolic states prior to activation. These differences in the ability to utilize glucose may represent an underlying mechanism for the superior functionality of educated NK cells expressing self-inhibitory receptors.

Mathematical Modeling of the Function of Warburg Effect in Tumor Microenvironment

Tumor cells are known for their increased glucose uptake rates even in the presence of abundant oxygen. This altered metabolic shift towards aerobic glycolysis is known as the Warburg effect. Despite an enormous number of studies conducted on the causes and consequences of this phenomenon, little is known about how the Warburg effect affects tumor growth and progression. We developed a multi-scale computational model to explore the detailed effects of glucose metabolism of cancer cells on tumorigenesis behavior in a tumor microenvironment. Despite glycolytic tumors, the growth of non-glycolytic tumor is dependent on a congruous morphology without markedly interfering with glucose and acid concentrations of the tumor microenvironment. Upregulated glucose metabolism helped to retain oxygen levels above the hypoxic limit during early tumor growth, and thus obviated the need for neo-vasculature recruitment. Importantly, simulating growth of tumors within a range of glucose uptake rates showed that there exists a spectrum of glucose uptake rates within which the tumor is most aggressive, i.e. it can exert maximal acidic stress on its microenvironment and most efficiently compete for glucose supplies. Moreover, within the same spectrum, the tumor could grow to invasive morphologies while its size did not markedly shrink.

A Combination of Immune Checkpoint Inhibition with Metronomic Chemotherapy as a Way of Targeting Therapy-Resistant Cancer Cells

Therapeutic resistance remains a major obstacle in treating many cancers, particularly in advanced stages. It is likely that cytotoxic lymphocytes (CTLs) have the potential to eliminate therapy-resistant cancer cells. However, their effectiveness may be limited either by the immunosuppressive tumor microenvironment, or by immune cell death induced by cytotoxic treatments. High-frequency low-dose (also known as metronomic) chemotherapy can help improve the activity of CTLs by providing sufficient stimulation for cytotoxic immune cells without excessive depletion. Additionally, therapy-induced removal of tumor cells that compete for shared nutrients may also facilitate tumor infiltration by CTLs, further improving prognosis. Metronomic chemotherapy can also decrease the number of immunosuppressive cells in the tumor microenvironment, including regulatory T cells (Tregs) and myeloid-derived suppressor cells (MDSCs). Immune checkpoint inhibition can further augment anti-tumor immune responses by maintaining T cells in an activated state. Combining immune checkpoint inhibition with metronomic administration of chemotherapeutic drugs may create a synergistic effect that augments anti-tumor immune responses and clears metabolic competition. This would allow immune-mediated elimination of therapy-resistant cancer cells, an effect that may be unattainable by using either therapeutic modality alone.

Linking tumor glycolysis and immune evasion in cancer: Emerging concepts and therapeutic opportunities

Metabolic reprogramming and immune evasion are two hallmarks of cancer. Metabolic reprogramming is exemplified by cancer's propensity to utilize glucose at an exponential rate which in turn is linked with "aerobic glycolysis", popularly known as the "Warburg effect". Tumor glycolysis is pivotal for the efficient management of cellular bioenergetics and uninterrupted cancer growth. Mounting evidence suggests that tumor glycolysis also plays a key role in instigating immunosuppressive networks that are critical for cancer cells to escape immune surveillance ("immune evasion"). Recent data show that induction of cellular stress or metabolic dysregulation sensitize cancer cells to antitumor immune cells implying that metabolic reprogramming and immune evasion harmonize during cancer progression. However, the molecular link between these two hallmarks of cancer remains obscure. In this review the molecular intricacies of tumor glycolysis that facilitate immune evasion has been discussed in the light of recent research to explore immunotherapeutic potential of targeting cancer metabolism.

Concise Review: An (Im)Penetrable Shield: How the Tumor Microenvironment Protects Cancer Stem Cells

Cancer stem cells (CSCs) are defined by their unlimited self-renewal ability and their capacity to initiate and maintain malignancy, traits that are not found in most cells that comprise the tumor. Although current cancer treatments successfully reduce tumor burden, the tumor will likely recur unless CSCs are effectively eradicated. This challenge is made greater by the protective impact of the tumor microenvironment (TME), consisting of infiltrating immune cells, endothelial cells, extracellular matrix, and signaling molecules. The TME acts as a therapeutic barrier through immunosuppressive, and thereby tumor-promoting, actions. These factors, outside of the cancer cell lineage, work in concert to shelter CSCs from both the body's intrinsic anticancer immunity and pharmaceutical interventions to maintain cancer growth. Emerging therapies aimed at the TME offer a promising new tool in breaking through this shield to target the CSCs, yet definitive treatments remain unrealized. In this review, we summarize the mechanisms by which CSCs are protected by the TME and current efforts to overcome these barriers. Stem Cells 2017;35:1123-1130.

Mathematical models for explaining the Warburg effect: a review focussed on ATP and biomass production

For producing ATP, tumour cells rely on glycolysis leading to lactate to about the same extent as on respiration. Thus, the ATP synthesis flux from glycolysis is considerably higher than in the corresponding healthy cells. This is known as the Warburg effect (named after German biochemist Otto H. Warburg) and also applies to striated muscle cells, activated lymphocytes, microglia, endothelial cells and several other cell types. For similar phenomena in several yeasts and many bacteria, the terms Crabtree effect and overflow metabolism respectively, are used. The Warburg effect is paradoxical at first sight because the molar ATP yield of glycolysis is much lower than that of respiration. Although a straightforward explanation is that glycolysis allows a higher ATP production rate, the question arises why cells do not re-allocate protein to the high-yield pathway of respiration. Mathematical modelling can help explain this phenomenon. Here, we review several models at various scales proposed in the literature for explaining the Warburg effect. These models support the hypothesis that glycolysis allows for a higher proliferation rate due to increased ATP production and precursor supply rates.

Primary and metastatic tumor dormancy as a result of population heterogeneity

Existence of tumor dormancy, or cancer without disease, is supported both by autopsy studies that indicate presence of microscopic tumors in men and women who die of trauma (primary dormancy), and by long periods of latency between excision of primary tumors and disease recurrence (metastatic dormancy). Within dormant tumors, two general mechanisms underlying the dynamics are recognized, namely, the population existing at limited carrying capacity (tumor mass dormancy), and solitary cell dormancy, characterized by long periods of quiescence marked by cell cycle arrest. Here we focus on mechanisms that precede the avascular tumor reaching its carrying capacity, and propose that dynamics consistent with tumor dormancy and subsequent escape from it can be accounted for with simple models that take into account population heterogeneity. We evaluate parametrically heterogeneous Malthusian, logistic and Allee growth models and show that 1) time to escape from tumor dormancy is driven by the initial distribution of cell clones in the population and 2) escape from dormancy is accompanied by a large increase in variance, as well as the expected value of fitness-determining parameters. Based on our results, we propose that parametrically heterogeneous logistic model would be most likely to account for primary tumor dormancy, while distributed Allee model would be most appropriate for metastatic dormancy. We conclude with a discussion of dormancy as a stage within a larger context of cancer as a systemic disease.

Reviewers: This article was reviewed by Heiko Enderling and Marek Kimmel.