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.

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.

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.

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.

Identifying key questions in the ecology and evolution of cancer.

The application of evolutionary and ecological principles to cancer prevention and treatment, as well as recognizing cancer as a selection force in nature, has gained impetus over the last 50 years. Following the initial theoretical approaches that combined knowledge from interdisciplinary fields, it became clear that using the eco-evolutionary framework is of key importance to understand cancer. We are now at a pivotal point where accumulating evidence starts to steer the future directions of the discipline and allows us to underpin the key challenges that remain to be addressed. Here, we aim to assess current advancements in the field and to suggest future directions for research. First, we summarize cancer research areas that, so far, have assimilated ecological and evolutionary principles into their approaches and illustrate their key importance. Then, we assembled 33 experts and identified 84 key questions, organized around nine major themes, to pave the foundations for research to come. We highlight the urgent need for broadening the portfolio of research directions to stimulate novel approaches at the interface of oncology and ecological and evolutionary sciences. We conclude that progressive and efficient cross-disciplinary collaborations that draw on the expertise of the fields of ecology, evolution and cancer are essential in order to efficiently address current and future questions about cancer.

Quantitative Systems Pharmacology Approaches for Immuno-Oncology: Adding Virtual Patients to the Development Paradigm.

Drug development in oncology commonly exploits the tools of molecular biology to gain therapeutic benefit through reprograming of cellular responses. In immuno-oncology (IO) the aim is to direct the patient's own immune system to fight cancer. After remarkable successes of antibodies targeting PD1/PD-L1 and CTLA4 receptors in targeted patient populations, the focus of further development has shifted toward combination therapies. However, the current drug-development approach of exploiting a vast number of possible combination targets and dosing regimens has proven to be challenging and is arguably inefficient. In particular, the unprecedented number of clinical trials testing different combinations may no longer be sustainable by the population of available patients. Further development in IO requires a step change in selection and validation of candidate therapies to decrease development attrition rate and limit the number of clinical trials. Quantitative systems pharmacology (QSP) proposes to tackle this challenge through mechanistic modeling and simulation. Compounds' pharmacokinetics, target binding, and mechanisms of action as well as existing knowledge on the underlying tumor and immune system biology are described by quantitative, dynamic models aiming to predict clinical results for novel combinations. Here, we review the current QSP approaches, the legacy of mathematical models available to quantitative clinical pharmacologists describing interaction between tumor and immune system, and the recent development of IO QSP platform models. We argue that QSP and virtual patients can be integrated as a new tool in existing IO drug development approaches to increase the efficiency and effectiveness of the search for novel combination therapies.

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.

Delicate Balances in Cancer Chemotherapy: Modeling Immune Recruitment and Emergence of Systemic Drug Resistance.

Metronomic chemotherapy can drastically enhance immunogenic tumor cell death. However, the mechanisms responsible are still incompletely understood. Here, we develop a mathematical model to elucidate the underlying complex interactions between tumor growth, immune system activation, and therapy-mediated immunogenic cell death. Our model is conceptually simple, yet it provides a surprisingly excellent fit to empirical data obtained from a GL261 SCID mouse glioma model treated with cyclophosphamide on a metronomic schedule. The model includes terms representing immune recruitment as well as the emergence of drug resistance during prolonged metronomic treatments. Strikingly, a single fixed set of parameters, adjusted neither for individuals nor for drug schedule, recapitulates experimental data across various drug regimens remarkably well, including treatments administered at intervals ranging from 6 to 12 days. Additionally, the model predicts peak immune activation times, rediscovering experimental data that had not been used in parameter fitting or in model construction. Notably, the validated model suggests that immunostimulatory and immunosuppressive intermediates are responsible for the observed phenomena of resistance and immune cell recruitment, and thus for variation of responses with respect to different schedules of drug administration.

Immune Suppression in Pregnancy and Cancer: Parallels and Insights.

Immune system has evolved to maintain homeostatic balance between effector and regulatory immunity, which is critical to both elicit an adequate protective response to fight pathogens and disease, such as cancer, and to prevent damage to healthy tissues. Transient immune suppression can occur under normal physiological conditions, such as during wound healing to enable repair of normal tissue, or for more extended periods of time during fetal development, where the balance is shifted towards regulatory immunity to prevent fetal rejection. Interestingly, tumors can exhibit patterns of immune suppression very similar to those observed during fetal development. Here some of the key aspects of normal patterns of immune suppression during pregnancy are reviewed, followed by a discussion of parallels that exist with tumor-related immune suppression and consequent potential therapeutic implications.

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.

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.

Guiding principles for mechanistic modeling of bispecific antibodies.

System based pharmacokinetic (PK) models can be used to study and predict the distribution of antibody based drugs into target tissues and assess the pharmacobinding (PB) of the drug to the target and the subsequent pharmacodynamic (PD) changes. In the absence of relevant PD readouts, compounded in cases of novel mechanisms, one can rely on binding between the drug and the target, computed as target occupancy (TO), as a relevant biomarker. This approach assumes that at maximum TO across the dosing interval, the drug-target interaction must demonstrate the intended pharmacology. Such analysis can help set laboratory objectives for protein engineers and chemists and guide them to the appropriate design and binding affinity of the molecule. Analysis of mechanistic models to guide affinity optimization against soluble and membrane-bound targets has been done for monoclonal antibodies (mAbs) (Tiwari et al., The AAPS Journal, 2017). However, comparable understanding of bispecific antibodies (BsAb; drugs with two targets, which are either soluble, membrane-bound, or a combination of the two) is still lacking. We propose to extend the work done by Tiwari et al. (2017) to BsAb. We focus on describing a generic BsAb with two membrane-bound targets, and explore the impact of various parameters on the TO of the BsAb to each target. Performed analysis can guide the optimization of dissociation constant (KD) of the BsAb, and can also help in identifying druggable targets. Proposed model can be modified and tailored to specific biologics as needed.

Evolved Dependence in Response to Cancer.

Evolved dependence is a process through which one species becomes 'dependent' on another following a long evolutionary history of interaction. This happens when adaptations selected in the first species for interacting lead to fitness costs when the second species is not encountered. Evolved dependence is frequent in host-parasite interactions, where hosts may achieve a higher fitness in the presence of the parasite than in its absence. Since oncogenic manifestations are (i) ubiquitous across multicellular life, (ii) involved in parasitic-like interactions with their hosts, and (iii) have effectively driven the selection of numerous adaptations, it is possible that multicellular organisms display evolved dependence in response to oncogenic processes. We provide a comprehensive overview of the topic, including the implications for cancer prevention and treatment.