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.

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.

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.

From Experiment to Theory: What Can We Learn from Growth Curves?

Finding an appropriate functional form to describe population growth based on key properties of a described system allows making justified predictions about future population development. This information can be of vital importance in all areas of research, ranging from cell growth to global demography. Here, we use this connection between theory and observation to pose the following question: what can we infer about intrinsic properties of a population (i.e., degree of heterogeneity, or dependence on external resources) based on which growth function best fits its growth dynamics? We investigate several nonstandard classes of multi-phase growth curves that capture different stages of population growth; these models include hyperbolic-exponential, exponential-linear, exponential-linear-saturation growth patterns. The constructed models account explicitly for the process of natural selection within inhomogeneous populations. Based on the underlying hypotheses for each of the models, we identify whether the population that it best fits by a particular curve is more likely to be homogeneous or heterogeneous, grow in a density-dependent or frequency-dependent manner, and whether it depends on external resources during any or all stages of its development. We apply these predictions to cancer cell growth and demographic data obtained from the literature. Our theory, if confirmed, can provide an additional biomarker and a predictive tool to complement experimental research.

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.

Escape from tumor dormancy and time to angiogenic switch as mitigated by tumor-induced stimulation of stroma.

A variety of mechanisms have been proposed to explain "cancer without disease", the state of tumor dormancy, characterized by balance in cell proliferation and cell death within a tumor. Here we have investigated a theoretical construct, whereby one of such mechanisms, the time to induction of angiogenesis, or "angiogenic switch", is mitigated by the degree of stromal stimulation by the tumor. We tested this hypothesis and its implications by introducing a mathematical model that captures how angiogenesis regulators, released from the platelet clot, contribute to formation of normal vasculature. We then modified the model to introduce tumor-induced increase in production of angiogenesis regulators and were able to simulate pathological angiogenesis. Through varying parameters governing the degree of tumor-induced stromal stimulation, we were able to qualitatively replicate experimentally observed growth curves for both dormant and actively growing tumors of breast cancer and liposarcoma. In fact, variation of very few parameters was sufficient to replicate any experimentally observed time to angiogenic switch in the available data. Finally, we investigated the effects of tighter binding isoforms of angiogenesis stimulators on neovasculature formation and tumor growth, which may provide an explanation for variations in angiogenesis -dependence in tumors of different tissue origin.

Immune evasion through competitive inhibition: the shielding effect of cancer non-stem cells.

It has been recently proposed that the two emerging hallmarks of cancer, namely altered glucose metabolism and immune evasion, may in fact be fundamentally linked. This connection comes from up-regulation of glycolysis by tumor cells, which can lead to active competition for resources in the tumor microenvironment between tumor and immune cells. Here it is further proposed that cancer stem cells (CSCs) can circumvent the anti-tumor immune response by creating a "protective shield" of non-stem cancer cells around them. This shield can protect the CSCs both by creating a physical barrier between them and cytotoxic lymphocytes (CTLs), and by promoting competition for the common resources, such as glucose, between non-stem cancer cells and CTLs. The implications of this hypothesis are investigated using an agent-based model, leading to a prediction that relative CSC to non-CSC ratio will vary depending on the strength of the host immune response. A discussion of possible therapeutic approaches concludes the paper, suggesting that a chemotherapeutic regimen consisting of regular pulsed doses, i.e., metronomic chemotherapy, would yield the best clinical outcome by removing the "protective shield" and thus allowing CTLs to most effectively reach and eliminate CSCs.

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

It is a well-established fact that tumors up-regulate glucose consumption to meet increasing demands for rapidly available energy by upregulating a purely glycolytic mode of glucose metabolism. What is often neglected is that activated cytotoxic cells of the immune system, integral players in the carcinogenesis process, also come to rely on glycolysis as a primary mode of glucose metabolism. Moreover, while cancer cells can revert back to aerobic metabolism, rapidly proliferating cytotoxic lymphocytes are incapable of performing their function when adequate resources are lacking. Consequently, it is likely that in the tumor microenvironment there may exist competition for shared resources between cancer cells and the cells of the immune system, which may underlie much of tumor-immune dynamics. Proposed here is a model of tumor-immune-glucose interactions, formulated as a predator-prey-common resource type system. The outcome of these interactions ranges from tumor elimination, to tumor dormancy, to unrestrained tumor growth. It is also predicted that the process of tumor escape can be preceded by periods of oscillatory tumor growth. A detailed bifurcation analysis of three subsystems of the model suggest that oscillatory regimes are a result of competition for shared resource (glucose) between the predator (immune cells) and the prey (cancer cells). Existence of competition for nutrients between cancer and immune cells may provide additional mechanistic insight as to why the efficacy of many immunotherapies may be limited.

Resource consumption, sustainability, and cancer.

Preserving a system's viability in the presence of diversity erosion is critical if the goal is to sustainably support biodiversity. Reduction in population heterogeneity, whether inter- or intraspecies, may increase population fragility, either decreasing its ability to adapt effectively to environmental changes or facilitating the survival and success of ordinarily rare phenotypes. The latter may result in over-representation of individuals who may participate in resource utilization patterns that can lead to over-exploitation, exhaustion, and, ultimately, collapse of both the resource and the population that depends on it. Here, we aim to identify regimes that can signal whether a consumer-resource system is capable of supporting viable degrees of heterogeneity. The framework used here is an expansion of a previously introduced consumer-resource type system of a population of individuals classified by their resource consumption. Application of the Reduction Theorem to the system enables us to evaluate the health of the system through tracking both the mean value of the parameter of resource (over)consumption, and the population variance, as both change over time. The article concludes with a discussion that highlights applicability of the proposed system to investigation of systems that are affected by particularly devastating overly adapted populations, namely cancerous cells. Potential intervention approaches for system management are discussed in the context of cancer therapies.

Mitigating non-genetic resistance to checkpoint inhibition based on multiple states of immune exhaustion.

Despite the revolutionary impact of immune checkpoint inhibition on cancer therapy, the lack of response in a subset of patients, as well as the emergence of resistance, remain significant challenges. Here we explore the theoretical consequences of the existence of multiple states of immune cell exhaustion on response to checkpoint inhibition therapy. In particular, we consider the emerging understanding that T cells can exist in various states: fully functioning cytotoxic cells, reversibly exhausted cells with minimal cytotoxicity, and terminally exhausted cells. We hypothesize that inflammation augmented by drug activity triggers transitions between these phenotypes, which can lead to non-genetic resistance to checkpoint inhibitors. We introduce a conceptual mathematical model, coupled with a standard 2-compartment pharmacometric (PK) model, that incorporates these mechanisms. Simulations of the model reveal that, within this framework, the emergence of resistance to checkpoint inhibitors can be mitigated through altering the dose and the frequency of administration. Our analysis also reveals that standard PK metrics do not correlate with treatment outcome. However, we do find that levels of inflammation that we assume trigger the transition from the reversibly to terminally exhausted states play a critical role in therapeutic outcome. A simulation of a population that has different values of this transition threshold reveals that while the standard high-dose, low-frequency dosing strategy can be an effective therapeutic design for some, it is likely to fail a significant fraction of the population. Conversely, a metronomic-like strategy that distributes a fixed amount of drug over many doses given close together is predicted to be effective across the entire simulated population, even at a relatively low cumulative drug dose. We also demonstrate that these predictions hold if the transitions between different states of immune cell exhaustion are triggered by prolonged antigen exposure, an alternative mechanism that has been implicated in this process. Our theoretical analyses demonstrate the potential of mitigating resistance to checkpoint inhibitors via dose modulation.

Minimally sufficient experimental design using identifiability analysis.

Mathematical models are increasingly being developed and calibrated in tandem with data collection, empowering scientists to intervene in real time based on quantitative model predictions. Well-designed experiments can help augment the predictive power of a mathematical model but the question of when to collect data to maximize its utility for a model is non-trivial. Here we define data as model-informative if it results in a unique parametrization, assessed through the lens of practical identifiability. The framework we propose identifies an optimal experimental design (how much data to collect and when to collect it) that ensures parameter identifiability (permitting confidence in model predictions), while minimizing experimental time and costs. We demonstrate the power of the method by applying it to a modified version of a classic site-of-action pharmacokinetic/pharmacodynamic model that describes distribution of a drug into the tumor microenvironment (TME), where its efficacy is dependent on the level of target occupancy in the TME. In this context, we identify a minimal set of time points when data needs to be collected that robustly ensures practical identifiability of model parameters. The proposed methodology can be applied broadly to any mathematical model, allowing for the identification of a minimally sufficient experimental design that collects the most informative data.

Preventing the tragedy of the commons through punishment of over-consumers and encouragement of under-consumers.

The conditions that can lead to the exploitative depletion of a shared resource, i.e., the tragedy of the commons, can be reformulated as a game of prisoner's dilemma: while preserving the common resource is in the best interest of the group, over-consumption is in the interest of each particular individual at any given point in time. One way to try and prevent the tragedy of the commons is through infliction of punishment for over-consumption and/or encouraging under-consumption, thus selecting against over-consumers. Here, the effectiveness of various punishment functions in an evolving consumer-resource system is evaluated within a framework of a parametrically heterogeneous system of ordinary differential equations (ODEs). Conditions leading to the possibility of sustainable coexistence with the common resource for a subset of cases are identified analytically using adaptive dynamics; the effects of punishment on heterogeneous populations with different initial composition are evaluated using the reduction theorem for replicator equations. Obtained results suggest that one cannot prevent the tragedy of the commons through rewarding of under-consumers alone--there must also be an implementation of some degree of punishment that increases in a nonlinear fashion with respect to over-consumption and which may vary depending on the initial distribution of clones in the population.

Tumors induce complex DNA damage in distant proliferative tissues in vivo.

That tumors cause changes in surrounding tissues is well documented, but whether they also affect distant tissues is uncertain. Such knowledge may be important in understanding the relationship between cancer and overall patient health. To address this question, we examined tissues distant to sites of implanted tumors for genomic damage using cohorts of C57BL/6 and BALB/c mice with early-stage subcutaneous syngeneic grafts, specifically, B16 melanoma, MO5076 sarcoma, and COLON26 carcinoma. Here we report that levels of two serious types of DNA damage, double-strand breaks (DSBs) measured by γ-H2AX focus formation and oxidatively induced non-DSB clustered DNA lesions (OCDLs), were elevated in tissues distant from the tumor site in tumor-bearing mice compared with their age- and sex-matched controls. Most affected were crypts in the gastrointestinal tract organs and skin, both highly proliferative tissues. Further investigation revealed that, compared with controls, tumor-bearing mice contained elevated amounts of activated macrophages in the distant gastrointestinal tissues, as well as elevated serum levels of several cytokines. One of these cytokines, CCL2/MCP-1, has been linked to several inflammation-related conditions and macrophage recruitment, and strikingly, CCL2-deficient mice lacked increased levels of DSBs and OCDLs in tissues distant from implanted tumors. Thus, this study is unique in being a direct demonstration that the presence of a tumor may induce a chronic inflammatory response in vivo, leading to increased systemic levels of DNA damage. Importantly, these findings suggest that tumors may have more profound effects on their hosts than heretofore expected.

Guiding model-driven combination dose selection using multi-objective synergy optimization.

Despite the growing appreciation that the future of cancer treatment lies in combination therapies, finding the right drugs to combine and the optimal way to combine them remains a nontrivial task. Herein, we introduce the Multi-Objective Optimization of Combination Synergy - Dose Selection (MOOCS-DS) method for using drug synergy as a tool for guiding dose selection for a combination of preselected compounds. This method decouples synergy of potency (SoP) and synergy of efficacy (SoE) and identifies Pareto optimal solutions in a multi-objective synergy space. Using a toy combination therapy model, we explore properties of the MOOCS-DS algorithm, including how optimal dose selection can be influenced by the metric used to define SoP and SoE. We also demonstrate the potential of our approach to guide dose and schedule selection using a model fit to preclinical data of the combination of the PD-1 checkpoint inhibitor pembrolizumab and the anti-angiogenic drug bevacizumab on two lung cancer cell lines. The identification of optimally synergistic combination doses has the potential to inform preclinical experimental design and improve the success rates of combination therapies. Jel classificationDose Finding in Oncology.

Different costs of therapeutic resistance in cancer: Short- and long-term impact of population heterogeneity.

Therapeutic resistance continues to undercut long-term success of many promising cancer treatments. At times, development of therapeutic resistance can come at a fitness cost for the cancer cell population, which could potentially be leveraged to the patient's advantage. A mathematical formulation of such a situation was proposed by Pressley et al. (2020), who discussed two scenarios, namely, when developing therapeutic resistance can come at a cost to proliferative capacity (such as when a drug targets a growth receptor), or to the total tumor carrying capacity (such as when a drug targets neovascularization). Here we expand the analysis of the two models and evaluate both short- and long-term dynamics of a population heterogeneous with respect to resistance. We analyze four initial distributions with respect to resistance at the time of treatment initiation: uniform, bell-shaped, exponential, and U-shaped. We show that final population composition is invariant to the initial distribution, with a single clone eventually dominating within the population; the value of the resistance parameter of the final clone depends on other system parameters but not on the initial distribution. Transitional behaviors, however, which may have more significant implications for immediate treatment decisions, depend critically on the initial distribution. Furthermore, we show that depending on the mechanism for the cost of resistance (i.e., proliferation vs carrying capacity), increase in natural cell death rate has opposite effects, with higher natural death rate selecting for less resistant cell clones in the long term for proliferation-dependent model, and selecting for more resistant cell clones for carrying capacity-dependent model, a prediction that may have implications for combination therapy with cytotoxic agents. We conclude with a discussion of strengths and limitations of using modeling for understanding treatment trajectory, as well as the promise of model-informed evolutionary steering for improved long-term therapeutic outcomes.

Understanding Metabolic Alterations in Cancer Cachexia through the Lens of Exercise Physiology.

Cancer cachexia is one of the leading causes of mortality for late-stage cancer patients. One of its key characteristics is abnormal metabolism and loss of metabolic flexibility, i.e., loss of ability to switch between use of fats and carbohydrates as needed. Here, it is hypothesized that late-stage systemic cancer creates a chronic resource drain on the body that may result in the same metabolic adaptations that occur during intense endurance exercise, activating some of the same mechanisms of nutrient consumption that are supposed to be transient during strenuous physical activity. This hypothesis is evaluated by creating a mathematical model that characterizes the relationships between increased exercise intensity and carbohydrate and fat oxidation. The model is parametrized using published data on these characteristics for a group of professional athletes, moderately active individuals, and individuals with metabolic syndrome. Transitions between different zones of relative nutrient consumption as a function of increased effort are captured through explicitly modeling ventilatory thresholds, particularly VT1 and VT2, where fat is primarily used below VT1, both carbohydrates and fats are used between VT1 and VT2, and where carbohydrates become the primary source of fuel above VT2. A simulation is conducted of projected patterns of nutrient consumption when simulated "effort" remains between VT1 and VT2, or above VT2, and it is proposed that it is the scenario when the simulated effort is maintained primarily above VT2 that most closely resembles metabolic patterns characteristic of cachexia. A discussion of a broader framework for understanding cachectic metabolism using insights from exercise physiology, including potential intervention strategies, concludes this paper.

Mathematical model of a cytokine storm.

Cytokine storm is a life-threatening inflammatory response that is characterized by hyperactivation of the immune system, and which can be caused by various therapies, autoimmune conditions, or pathogens, such as respiratory syndrome coronavirus 2 (SARS-CoV-2), which causes coronavirus disease COVID-19. While initial causes of cytokine storms can vary, late-stage clinical manifestations of cytokine storm converge and often overlap, and therefore a better understanding of how normal immune response turns pathological is warranted. Here we propose a theoretical framework, where cytokine storm phenomenology is captured using a conceptual mathematical model, where cytokines can both activate and regulate the immune system. We simulate normal immune response to infection, and through variation of system parameters identify conditions where, within the frameworks of this model, cytokine storm can arise. We demonstrate that cytokine storm is a transitional regime, and identify three main factors that must converge to result in storm-like dynamics, two of which represent individual-specific characteristics, thereby providing a possible explanation for why some people develop CRS, while others may not. We also discuss possible ecological insights into cytokine-immune interactions and provide mathematical analysis for the underlying regimes. We conclude with a discussion of how results of this analysis can be used in future research.

Mathematical modeling of SARS-CoV-2 viral dynamics and treatment with monoclonal antibodies.

The novel coronavirus (SARS-CoV-2) affects primarily the respiratory tract, and if left unchecked can cause a spectrum of pathological manifestations such as pneumonia, acute respiratory distress syndrome, myocardial injury, thromboembolism, and acute kidney injury. Medication strategies have involved minimizing the spread of the virus through antiviral medications (monoclonal antibodies or nucleotide reverse transcriptase inhibitors). Here, we develop a mathematical model that simulates viral dynamics in an untreated individual, and the evaluate the impact that a monoclonal antibody can have on slowing viral replication. Drug pharmacokinetics (PK) was informed by a typical two-compartment PK model with parameters typical of a monoclonal antibody, with a third compartment for the lung included as the drug site of action. The viral dynamics were captured using a simplified model describing uninfected target cells, infected target cells, and viral load in the body. The mechanism of action of the simulated antiviral is based on binding to the virus, thereby preventing it from infecting healthy cells. The model is used to project dosages needed to prevent severe disease under a variety of simulated conditions and subject to realistic constraints. The proposed model can capture a variety of scenarios of longitudinal viral dynamics and assess the impact of antiviral therapy on disease severity and duration. The described approach can be easily adapted to rapidly assess the dosages needed to affect duration and outcome of other viral infections and can serve as part of a fast and efficient scientific and modeling response strategy in the future as needed.

Bispecific antibodies: A guide to model informed drug discovery and development.

Affinity (KD) optimization of monoclonal antibodies is one of the factors that impacts the stoichiometric binding and the corresponding efficacy of a drug. This impacts the dose and the dosing regimen, making the optimum KD a critical component of drug discovery and development. Its importance is further enhanced for bispecific antibodies, where affinity of the drug needs to be optimized with respect to two targets. Mathematical modeling can have critical impact on lead compound optimization. Here we build on previous work of using mathematical models to facilitate lead compound selection, expanding analysis from two membrane bound targets to soluble targets as well. Our analysis reveals the importance of three factors for lead compound optimization: drug affinity to both targets, target turnover rates, and target distribution throughout the body. We describe a method that leverages this information to help make early stage decisions on whether to optimize affinity, and if so, which arm of the bispecific should be optimized. We apply the proposed approach to a variety of scenarios and illustrate the ability to make improved decisions in each case. We integrate results to develop a bispecific antibody KD optimization guide that can be used to improve resource allocation for lead compound selection, accelerating advancement of better compounds. We conclude with a discussion of possible ways to assess the necessary levels of target engagement for affecting disease as part of an integrative approach for model-informed drug discovery and development.

Identifying Safety Thresholds for Immunosuppressive Drugs: Applying Insights from Primary Antibody Deficiencies to Mitigate Adverse Events in Secondary Antibody Deficiencies Using Mathematical Modeling of Preclinical and Early Clinical Data.

Immunosuppressive drugs can alleviate debilitating symptoms of autoimmune diseases, but, by the same token, excessive immune suppression can result in an increased risk of infection. Despite the dangers of a compromised immune system, clear definitions of what constitutes excessive suppression remain elusive. Here we review the most common infections associated with primary antibody deficiencies (PADs), such as agammaglobulinemia, common variable immunodeficiency (CVID), and IgA deficiency, as well as infections that are associated with drug-induced or secondary antibody immunodeficiencies (SADs). We identify a number of bacterial, viral, and fungal infections (e.g., Listeria monocytogenes, Staphylococcus sp., Salmonella spp., Escherichia coli, influenza, varicella zoster virus, and herpes simplex virus) associated with both PADs and SADs, and suggest that diagnostic criteria for PADs could be used as a first-line measure to identify potentially unsafe levels of immune suppression in SADs. Specifically, we suggest that, based on PAD diagnostic criteria, IgG levels should remain above 2-3 g/L, IgA levels should not fall below 0.07 g/L, and IgM levels should remain above 0.4 g/L to prevent immunosuppressive drugs from inducing mimicking PAD-like effects. We suggest that these criteria could be used in the early stages of drug development, and that pharmacokinetic and pharmacodynamic modeling could help guide patient selection to potentially improve drug safety. We illustrate the proposed approach using atacicept as an example and conclude with a discussion of the applicability of this approach for other drugs that may induce excessive immune suppression.