Mathematical model approach to describe tumour response in mice after vaccine administration and its applicability to immune-stimulatory cytokine-based strategies

A Comprehensive review on Pharmacokinetic Studies of Vaccines: Impact of delivery route, carrier-and its modulation on immune response

The lack of knowledge about the absorption, distribution, metabolism, and excretion (ADME) of vaccines makes former biopharmaceutical optimization difficult. This was shown during the COVID-19 immunization campaign, where gradual booster doses were introduced.. Thus, understanding vaccine ADME and its effects on immunization effectiveness could result in a more logical vaccine design in terms of formulation, method of administration, and dosing regimens. Herein, we will cover the information available on vaccine pharmacokinetics, impacts of delivery routes and carriers on ADME, utilization and efficiency of nanoparticulate delivery vehicles, impact of dose level and dosing schedule on the therapeutic efficacy of vaccines, intracellular and endosomal trafficking and in vivo fate, perspective on DNA and mRNA vaccines, new generation sequencing and mathematical models to improve cancer vaccination and pharmacology, and the reported toxicological study of COVID-19 vaccines. Altogether, this review will enhance the reader's understanding of the pharmacokinetics of vaccines and methods that can be implied in delivery vehicle design to improve the absorption and distribution of immunizing agents and estimate the appropriate dose to achieve better immunogenic responses and prevent toxicities.

Semi-Mechanistic Model for the Antitumor Response of a Combination Cocktail of Immuno-Modulators in Non-Inflamed (Cold) Tumors

Simple Summary

The clinical efficacy of immunotherapies when treating cold tumors is still low, and different treatment combinations are needed when dealing with this challenging scenario. In this work, a middle-out strategy was followed to develop a model describing the antitumor efficacy of different immune-modulator combinations, including an antigen, a toll-like receptor-3 agonist, and an immune checkpoint inhibitor in mice treated with non-inflamed tumor cells. Our results support that clinical response requires antigen-presenting cell activation and also relies on the amount of CD8 T cells and tumor resistance mechanisms present. This mathematical model is a very useful platform to evaluate different immuno-oncology combinations in both preclinical and clinical settings.

Abstract

Immune checkpoint inhibitors, administered as single agents, have demonstrated clinical efficacy. However, when treating cold tumors, different combination strategies are needed. This work aims to develop a semi-mechanistic model describing the antitumor efficacy of immunotherapy combinations in cold tumors. Tumor size of mice treated with TC-1/A9 non-inflamed tumors and the drug effects of an antigen, a toll-like receptor-3 agonist (PIC), and an immune checkpoint inhibitor (anti-programmed cell death 1 antibody) were modeled using Monolix and following a middle-out strategy. Tumor growth was best characterized by an exponential model with an estimated initial tumor size of 19.5 mm³ and a doubling time of 3.6 days. In the treatment groups, contrary to the lack of response observed in monotherapy, combinations including the antigen were able to induce an antitumor response. The final model successfully captured the 23% increase in the probability of cure from bi-therapy to triple-therapy. Moreover, our work supports that CD8⁺ T lymphocytes and resistance mechanisms are strongly related to the clinical outcome. The activation of antigen-presenting cells might be needed to achieve an antitumor response in reduced immunogenic tumors when combined with other immunotherapies. These models can be used as a platform to evaluate different immuno-oncology combinations in preclinical and clinical scenarios.

The Role of Mathematical Models in Immuno-Oncology: Challenges and Future Perspectives

Immuno-oncology (IO) focuses on the ability of the immune system to detect and eliminate cancer cells. Since the approval of the first immune checkpoint inhibitor, immunotherapies have become a major player in oncology treatment and, in 2021, represented the highest number of approved drugs in the field. In spite of this, there is still a fraction of patients that do not respond to these therapies and develop resistance mechanisms. In this sense, mathematical models offer an opportunity to identify predictive biomarkers, optimal dosing schedules and rational combinations to maximize clinical response. This work aims to outline the main therapeutic targets in IO and to provide a description of the different mathematical approaches (top-down, middle-out, and bottom-up) integrating the cancer immunity cycle with immunotherapeutic agents in clinical scenarios. Among the different strategies, middle-out models, which combine both theoretical and evidence-based description of tumor growth and immunological cell-type dynamics, represent an optimal framework to evaluate new IO strategies.

Modulation of intratumoural myeloid cells, the hallmark of the anti-tumour efficacy induced by a triple combination: tumour-associated peptide, TLR-3 ligand and α-PD-1

BACKGROUND

Anti-programmed cell death 1 (PD-1)/programmed death-ligand 1 (PD-L1) monoclonal antibodies (mAbs) show remarkable clinical anti-tumour efficacy. However, rational combinations are needed to extend the clinical benefit to primary resistant tumours. The design of such combinations requires the identification of the kinetics of critical immune cell populations in the tumour microenvironment.

METHODS

In this study, we compared the kinetics of immune cells in the tumour microenvironment upon treatment with immunotherapy combinations with different anti-tumour efficacies in the non-inflamed tumour model TC-1/A9. Tumour-bearing C57BL/6J mice were treated with all possible combinations of a human papillomavirus (HPV) E7 long peptide, polyinosinic-polycytidylic acid (PIC) and anti-PD-1 mAb. Tumour growth and kinetics of the relevant immune cell populations were assessed over time. The involvement of key immune cells was confirmed by depletion with mAbs and immunophenotyping with multiparametric flow cytometry.

RESULTS

The maximum anti-tumour efficacy was achieved after intratumoural administration of HPV E7 long peptide and PIC combined with the systemic administration of anti-PD-1 mAb. The intratumoural immune cell kinetics of this combination was characterised by a biphasic immune response. An initial upsurge of proinflammatory myeloid cells led to a further rise in effector CD8⁺ T lymphocytes at day 8. Depletion of either myeloid cells or CD8⁺ T lymphocytes diminished the anti-tumour efficacy of the combination.

CONCLUSIONS

The anti-tumour efficacy of a successful immunotherapy combination in a non-inflamed tumour model relies on an early inflammatory process that remodels the myeloid cell compartment.

Accelerating the Development of Personalized Cancer Immunotherapy by Integrating Molecular Patients' Profiles with Dynamic Mathematical Models

We review the evolution, achievements, and limitations of the current paradigm shift in medicine, from the "one-size-fits-all" model to "Precision Medicine." Precision, or personalized, medicine-tailoring the medical treatment to the personal characteristics of each patient-engages advanced statistical methods to evaluate the relationships between static patient profiling (e.g., genomic and proteomic), and a simple clinically motivated output (e.g., yes/no responder). Today, precision medicine technologies that have facilitated groundbreaking advances in oncology, notably in cancer immunotherapy, are approaching the limits of their potential, mainly due to the scarcity of methods for integrating genomic, proteomic and clinical patient information. A different approach to treatment personalization involves methodologies focusing on the dynamic interactions in the patient-disease-drug system, as portrayed in mathematical modeling. Achievements of this scientific approach, in the form of algorithms for predicting personal disease dynamics in individual patients under immunotherapeutic drugs, are reviewed as well. The contribution of the dynamic approaches to precision medicine is limited, at present, due to insufficient applicability and validation. Yet, the time is ripe for amalgamating together these two approaches, for maximizing their joint potential to personalize and improve cancer immunotherapy. We suggest the roadmap toward achieving this goal, technologically, and urge clinicians, pharmacologists, and computational biologists to join forces along the pharmaco-clinical track of this development.

Engineered 3D Model of Cancer Stem Cell Enrichment and Chemoresistance

Intraperitoneal dissemination of ovarian cancers is preceded by the development of chemoresistant tumors with malignant ascites. Despite the high levels of chemoresistance and relapse observed in ovarian cancers, there are no in vitro models to understand the development of chemoresistance in situ. Method: We describe a highly integrated approach to establish an in vitro model of chemoresistance and stemness in ovarian cancer, using the 3D hanging drop spheroid platform. The model was established by serially passaging non-adherent spheroids. At each passage, the effectiveness of the model was evaluated via measures of proliferation, response to treatment with cisplatin and a novel ALDH1A inhibitor. Concomitantly, the expression and tumor initiating capacity of cancer stem-like cells (CSCs) was analyzed. RNA-seq was used to establish gene signatures associated with the evolution of tumorigenicity, and chemoresistance. Lastly, a mathematical model was developed to predict the emergence of CSCs during serial passaging of ovarian cancer spheroids. Results: Our serial passage model demonstrated increased cellular proliferation, enriched CSCs, and emergence of a platinum resistant phenotype. In vivo tumor xenograft assays indicated that later passage spheroids were significantly more tumorigenic with higher CSCs, compared to early passage spheroids. RNA-seq revealed several gene signatures supporting the emergence of CSCs, chemoresistance, and malignant phenotypes, with links to poor clinical prognosis. Our mathematical model predicted the emergence of CSC populations within serially passaged spheroids, concurring with experimentally observed data. Conclusion: Our integrated approach illustrates the utility of the serial passage spheroid model for examining the emergence and development of chemoresistance in ovarian cancer in a controllable and reproducible format.

Quantitative Systems Pharmacology: An Exemplar Model-Building Workflow With Applications in Cardiovascular, Metabolic, and Oncology Drug Development

Quantitative systems pharmacology (QSP), a mechanistically oriented form of drug and disease modeling, seeks to address a diverse set of problems in the discovery and development of therapies. These problems bring a considerable amount of variability and uncertainty inherent in the nonclinical and clinical data. Likewise, the available modeling techniques and related software tools are manifold. Appropriately, the development, qualification, application, and impact of QSP models have been similarly varied. In this review, we describe the progressive maturation of a QSP modeling workflow: a necessary step for the efficient, reproducible development and qualification of QSP models, which themselves are highly iterative and evolutive. Furthermore, we describe three applications of QSP to impact drug development; one supporting new indications for an approved antidiabetic clinical asset through mechanistic hypothesis generation, one highlighting efficacy and safety differentiation within the sodium‐glucose cotransporter‐2 inhibitor drug class, and one enabling rational selection of immuno‐oncology drug combinations.

Quantitative Mechanistic Modeling in Support of Pharmacological Therapeutics Development in Immuno-Oncology

Following the approval, in recent years, of the first immune checkpoint inhibitor, there has been an explosion in the development of immuno-modulating pharmacological modalities for the treatment of various cancers. From the discovery phase to late-stage clinical testing and regulatory approval, challenges in the development of immuno-oncology (IO) drugs are multi-fold and complex. In the preclinical setting, the multiplicity of potential drug targets around immune checkpoints, the growing list of immuno-modulatory molecular and cellular forces in the tumor microenvironment-with additional opportunities for IO drug targets, the emergence of exploratory biomarkers, and the unleashed potential of modality combinations all have necessitated the development of quantitative, mechanistically-oriented systems models which incorporate key biology and patho-physiology aspects of immuno-oncology and the pharmacokinetics of IO-modulating agents. In the clinical setting, the qualification of surrogate biomarkers predictive of IO treatment efficacy or outcome, and the corresponding optimization of IO trial design have become major challenges. This mini-review focuses on the evolution and state-of-the-art of quantitative systems models describing the tumor vs. immune system interplay, and their merging with quantitative pharmacology models of IO-modulating agents, as companion tools to support the addressing of these challenges.

Importance of Feedback and Feedforward Loops to Adaptive Immune Response Modeling

The human adaptive immune system is a very complex network of different types of cells, cytokines, and signaling molecules. This complex network makes it difficult to understand the system level regulations. To properly explain the immune system, it is necessary to explicitly investigate the presence of different feedback and feedforward loops (FFLs) and their crosstalks. Considering that these loops increase the complexity of the system, the mathematical modeling has been proved to be an important tool to explain such complex biological systems. This review focuses on these regulatory loops and discusses their importance on systems modeling of the immune system.

Utilization of data below the analytical limit of quantitation in pharmacokinetic analysis and modeling: promoting interdisciplinary debate

Traditionally, bioanalytical laboratories do not report actual concentrations for samples with results below the LOQ (BLQ) in pharmacokinetic studies. BLQ values are outside the method calibration range established during validation and no data are available to support the reliability of these values. However, ignoring BLQ data can contribute to bias and imprecision in model-based pharmacokinetic analyses. From this perspective, routine use of BLQ data would be advantageous. We would like to initiate an interdisciplinary debate on this important topic by summarizing the current concepts and use of BLQ data by regulators, pharmacometricians and bioanalysts. Through introducing the limit of detection and evaluating its variability, BLQ data could be released and utilized appropriately for pharmacokinetic research.

Multivariate analysis of cytokine profiles in pregnancy complications

PROBLEM

The immunoregulation to tolerate the semiallogeneic fetus during pregnancy includes a harmonious dynamic balance between anti- and pro-inflammatory cytokines. Several earlier studies reported significantly different levels and/or ratios of several cytokines in complicated pregnancy as compared to normal pregnancy. However, as cytokines operate in networks with potentially complex interactions, it is also interesting to compare groups with multi-cytokine data sets, with multivariate analysis. Such analysis will further examine how great the differences are, and which cytokines are more different than others.

METHODS

Various multivariate statistical tools, such as Cramer test, classification and regression trees, partial least squares regression figures, 2-dimensional Kolmogorov-Smirmov test, principal component analysis and gap statistic, were used to compare cytokine data of normal vs anomalous groups of different pregnancy complications.

RESULTS

Multivariate analysis assisted in examining if the groups were different, how strongly they differed, in what ways they differed and further reported evidence for subgroups in 1 group (pregnancy-induced hypertension), possibly indicating multiple causes for the complication.

CONCLUSION

This work contributes to a better understanding of cytokines interaction and may have important implications on targeting cytokine balance modulation or design of future medications or interventions that best direct management or prevention from an immunological approach.

Radiation and PD-(L)1 treatment combinations: immune response and dose optimization via a predictive systems model

BACKGROUND

Numerous oncology combination therapies involving modulators of the cancer immune cycle are being developed, yet quantitative simulation models predictive of outcome are lacking. We here present a model-based analysis of tumor size dynamics and immune markers, which integrates experimental data from multiple studies and provides a validated simulation framework predictive of biomarkers and anti-tumor response rates, for untested dosing sequences and schedules of combined radiation (RT) and anti PD-(L)1 therapies.

METHODS

A quantitative systems pharmacology model, which includes key elements of the cancer immunity cycle and the tumor microenvironment, tumor growth, as well as dose-exposure-target modulation features, was developed to reproduce experimental data of CT26 tumor size dynamics upon administration of RT and/or a pharmacological IO treatment such as an anti-PD-L1 agent. Variability in individual tumor size dynamics was taken into account using a mixed-effects model at the level of tumor-infiltrating T cell influx.

RESULTS

The model allowed for a detailed quantitative understanding of the synergistic kinetic effects underlying immune cell interactions as linked to tumor size modulation, under these treatments. The model showed that the ability of T cells to infiltrate tumor tissue is a primary determinant of variability in individual tumor size dynamics and tumor response. The model was further used as an in silico evaluation tool to quantitatively predict, prospectively, untested treatment combination schedules and sequences. We demonstrate that anti-PD-L1 administration prior to, or concurrently with RT reveal further synergistic effects, which, according to the model, may materialize due to more favorable dynamics between RT-induced immuno-modulation and reduced immuno-suppression of T cells through anti-PD-L1.

CONCLUSIONS

This study provides quantitative mechanistic explanations of the links between RT and anti-tumor immune responses, and describes how optimized combinations and schedules of immunomodulation and radiation may tip the immune balance in favor of the host, sufficiently to lead to tumor shrinkage or rejection.

Prediction of the Optimal Dosing Regimen Using a Mathematical Model of Tumor Uptake for Immunocytokine-Based Cancer Immunotherapy

Purpose: Optimal dosing is critical for immunocytokine-based cancer immunotherapy to maximize efficacy and minimize toxicity. Cergutuzumab amunaleukin (CEA-IL2v) is a novel CEA-targeted immunocytokine. We set out to develop a mathematical model to predict intratumoral CEA-IL2v concentrations following various systemic dosing intensities.Experimental Design: Sequential measurements of CEA-IL2v plasma concentrations in 74 patients with solid tumors were applied in a series of differential equations to devise a model that also incorporates the peripheral concentrations of IL2 receptor-positive cell populations (i.e., CD8⁺, CD4⁺, NK, and B cells), which affect tumor bioavailability of CEA-IL2v. Imaging data from a subset of 14 patients were subsequently utilized to additionally predict antibody uptake in tumor tissues.Results: We created a pharmacokinetic/pharmacodynamic mathematical model that incorporates the expansion of IL2R-positive target cells at multiple dose levels and different schedules of CEA-IL2v. Model-based prediction of drug levels correlated with the concentration of IL2R-positive cells in the peripheral blood of patients. The pharmacokinetic model was further refined and extended by adding a model of antibody uptake, which is based on drug dose and the biological properties of the tumor. In silico predictions of our model correlated with imaging data and demonstrated that a dose-dense schedule comprising escalating doses and shortened intervals of drug administration can improve intratumoral drug uptake and overcome consumption of CEA-IL2v by the expanding population of IL2R-positive cells.Conclusions: The model presented here allows simulation of individualized treatment plans for optimal dosing and scheduling of immunocytokines for anticancer immunotherapy. Clin Cancer Res; 24(14); 3325-33. ©2018 AACRSee related commentary by Ruiz-Cerdá et al., p. 3236.

Current mathematical models for cancer drug discovery

INTRODUCTION

Pharmacometric models represent the most comprehensive approaches for extracting, summarizing and integrating information obtained in the often sparse, limited, and less-than-optimally designed experiments performed in the early phases of oncology drug discovery. Whilst empirical methodologies may be enough for screening and ranking candidate drugs, modeling approaches are needed for optimizing and making economically viable the learn-confirm cycles within an oncology research program and anticipating the dose regimens to be investigated in the subsequent clinical development. Areas covered: Papers appearing in the literature of approximately the last decade reporting modeling approaches applicable to anticancer drug discovery have been listed and commented. Papers were selected based on the interest in the proposed methodology or in its application. Expert opinion: The number of modeling approaches used in the discovery of anticancer drugs is consistently increasing and new models are developed based on the current directions of research of new candidate drugs. These approaches have contributed to a better understanding of new oncological targets and have allowed for the exploitation of the relatively sparse information generated by preclinical experiments. In addition, they are used in translational approaches for guiding and supporting the choice of dosing regimens in early clinical development.

Third-Kind Encounters in Biomedicine: Immunology Meets Mathematics and Informatics to Become Quantitative and Predictive

The understanding of the immune response is right now at the center of biomedical research. There are growing expectations that immune-based interventions will in the midterm provide new, personalized, and targeted therapeutic options for many severe and highly prevalent diseases, from aggressive cancers to infectious and autoimmune diseases. To this end, immunology should surpass its current descriptive and phenomenological nature, and become quantitative, and thereby predictive.Immunology is an ideal field for deploying the tools, methodologies, and philosophy of systems biology, an approach that combines quantitative experimental data, computational biology, and mathematical modeling. This is because, from an organism-wide perspective, the immunity is a biological system of systems, a paradigmatic instance of a multi-scale system. At the molecular scale, the critical phenotypic responses of immune cells are governed by large biochemical networks, enriched in nested regulatory motifs such as feedback and feedforward loops. This network complexity confers them the ability of highly nonlinear behavior, including remarkable examples of homeostasis, ultra-sensitivity, hysteresis, and bistability. Moving from the cellular level, different immune cell populations communicate with each other by direct physical contact or receiving and secreting signaling molecules such as cytokines. Moreover, the interaction of the immune system with its potential targets (e.g., pathogens or tumor cells) is far from simple, as it involves a number of attack and counterattack mechanisms that ultimately constitute a tightly regulated multi-feedback loop system. From a more practical perspective, this leads to the consequence that today's immunologists are facing an ever-increasing challenge of integrating massive quantities from multi-platforms.In this chapter, we support the idea that the analysis of the immune system demands the use of systems-level approaches to ensure the success in the search for more effective and personalized immune-based therapies.

Immune Checkpoint inhibitors: An introduction to the next-generation cancer immunotherapy

Activating the immune system to eliminate cancer cells and produce clinically relevant responses has been a long-standing goal of cancer research. Most promising therapeutic approaches to activating antitumor immunity include immune checkpoint inhibitors. Immune checkpoints are numerous inhibitory pathways hardwired in the immune system. They are critical for maintaining self-tolerance and modulating the duration and amplitude of physiological immune responses in peripheral tissues to minimize collateral tissue damage. Tumors regulate certain immune checkpoint pathways as a major mechanism of immune resistance. Because immune checkpoints are initiated by ligand-receptor interactions, blockade by antibodies provides a rational therapeutic approach. Although targeted therapies are clinically successful, they are often short-lived due to rapid development of resistance. Immunotherapies offer one notable advantage. Enhancing the cell-mediated immune response against tumor cells leads to generation of a long-term memory lymphocyte population patrolling the body to attack growth of any new tumor cells, thereby sustaining the therapeutic effects. Furthermore, early clinical results suggest that combination immunotherapies offer even more potent antitumor activity. This review is intended to provide an introduction to immune checkpoint inhibitors and discusses the scientific overview of cancer immunotherapy, mechanisms of the inhibitors, clinical pharmacology considerations, advances in combination therapies, and challenges in drug development.

Challenges and Opportunities for Quantitative Clinical Pharmacology in Cancer Immunotherapy: Something Old, Something New, Something Borrowed, and Something Blue

Cancer immunotherapy (CIT) initiates or enhances the host immune response against cancer. Following decades of development, patients with previously few therapeutic options may now benefit from CIT. Although the quantitative clinical pharmacology (qCP) of previous classes of anticancer drugs has matured during this time, application to CIT may not be straightforward since CIT acts via the immune system. Here we discuss where qCP approaches might best borrow or start anew for CIT.

A review of mixed-effects models of tumor growth and effects of anticancer drug treatment used in population analysis

Population modeling of tumor size dynamics has recently emerged as an important tool in pharmacometric research. A series of new mixed-effects models have been reported recently, and we present herein a synthetic view of models with published mathematical equations aimed at describing the dynamics of tumor size in cancer patients following anticancer drug treatment. This selection of models will constitute the basis for the Drug Disease Model Resources (DDMoRe) repository for models on oncology.

Modeling tumor response after combined administration of different immune-stimulatory agents

The aims of this work were as follows: 1) to develop a semimechanistic pharmacodynamic model describing tumor shrinkage after administration of a previously developed antitumor vaccine (CyaA-E7) in combination with CpG (a TLR9 ligand) and/or cyclophosphamide (CTX), and 2) to assess the translational capability of the model to describe tumor effects of different immune-based treatments. Population approach with NONMEM version 7.2 was used to analyze the previously published data. These data were generated by injecting 5 × 10(5) tumor cells expressing human papillomavirus (HPV)-E7 proteins into C57BL/6 mice. Large and established tumors were treated with CpG and/or CTX administered alone or in combination with CyaA-E7. Applications of the model were assessed by comparing model-based simulations with preclinical and clinical outcomes obtained from literature. CpG effects were modeled: 1) as an amplification of the immune signal triggered by the vaccine and 2) by shortening the delayed response of the vaccine. CTX effects were included through a direct decrease of the tumor-induced inhibition of vaccine efficacy over time, along with a delayed induction of tumor cell death. A pharmacodynamic model, built based on plausible biologic mechanisms known for the coadjuvants, successfully characterized tumor response in all experimental scenarios. The model developed was satisfactory applied to reproduce clinical outcomes when CpG or CTX was used in combination with different vaccines. The results found after simulation exercise indicated that the contribution of the coadjuvants to the tumor response elicited by vaccines can be predicted for other immune-based treatments.