Quantification of endothelial cell-targeted anti-Bcl-2 therapy and its suppression of tumor growth and vascularization

A validated mathematical model of FGFR3-mediated tumor growth reveals pathways to harness the benefits of combination targeted therapy and immunotherapy in bladder cancer

Bladder cancer is a common malignancy with over 80,000 estimated new cases and nearly 18,000 deaths per year in the United States alone. Therapeutic options for metastatic bladder cancer had not evolved much for nearly four decades, until recently, when five immune checkpoint inhibitors were approved by the U.S. Food and Drug Administration (FDA). Despite the activity of these drugs in some patients, the objective response rate for each is less than 25%. At the same time, fibroblast growth factor receptors (FGFRs) have been attractive drug targets for a variety of cancers, and in 2019 the FDA approved the first therapy targeted against FGFR3 for bladder cancer. Given the excitement around these new receptor tyrosine kinase and immune checkpoint targeted strategies, and the challenges they each may face on their own, emerging data suggest that combining these treatment options could lead to improved therapeutic outcomes. In this paper, we develop a mathematical model for FGFR3-mediated tumor growth and use it to investigate the impact of the combined administration of a small molecule inhibitor of FGFR3 and a monoclonal antibody against the PD-1/PD-L1 immune checkpoint. The model is carefully calibrated and validated with experimental data before survival benefits, and dosing schedules are explored. Predictions of the model suggest that FGFR3 mutation reduces the effectiveness of anti-PD-L1 therapy, that there are regions of parameter space where each monotherapy can outperform the other, and that pretreatment with anti-PD-L1 therapy always results in greater tumor reduction even when anti-FGFR3 therapy is the more effective monotherapy.

Mathematical model of STAT signalling pathways in cancer development and optimal control approaches

In various diseases, the STAT family display various cellular controls over various challenges faced by the immune system and cell death programs. In this study, we investigate how an intracellular signalling network (STAT1, STAT3, Bcl-2 and BAX) regulates important cellular states, either anti-apoptosis or apoptosis of cancer cells. We adapt a mathematical framework to illustrate how the signalling network can generate a bi-stability condition so that it will induce either apoptosis or anti-apoptosis status of tumour cells. Then, we use this model to develop several anti-tumour strategies including IFN-β infusion. The roles of JAK-STATs signalling in regulation of the cell death program in cancer cells and tumour growth are poorly understood. The mathematical model unveils the structure and functions of the intracellular signalling and cellular outcomes of the anti-tumour drugs in the presence of IFN-β and JAK stimuli. We identify the best injection order of IFN-β and DDP among many possible combinations, which may suggest better infusion strategies of multiple anti-cancer agents at clinics. We finally use an optimal control theory in order to maximize anti-tumour efficacy and minimize administrative costs. In particular, we minimize tumour volume and maximize the apoptotic potential by minimizing the Bcl-2 concentration and maximizing the BAX level while minimizing total injection amount of both IFN-β and JAK2 inhibitors (DDP).

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.

Cancer Stem Cells in Head and Neck Squamous Cell Carcinoma: Identification, Characterization and Clinical Implications

Head and neck squamous cell carcinoma (HNSCC) is the sixth most commonly diagnosed cancer worldwide. Despite advances in the treatment management, locally advanced disease has a poor prognosis, with a 5-year survival rate of approximately 50%. The growth of HNSCC is maintained by a population of cancer stem cells (CSCs) which possess unlimited self-renewal potential and induce tumor regrowth if not completely eliminated by therapy. The population of CSCs is not only a promising target for tumor treatment, but also an important biomarker to identify the patients at risk for therapeutic failure and disease progression. This review aims to provide an overview of the recent pre-clinical and clinical studies on the biology and potential therapeutic implications of HNSCC stem cells.

Modeling head and neck cancer stem cell-mediated tumorigenesis

A large body of literature has emerged supporting the importance of cancer stem cells (CSCs) in the pathogenesis of head and neck cancers. CSCs are a subpopulation of cells within a tumor that share the properties of self-renewal and multipotency with stem cells from normal tissue. Their functional relevance to the pathobiology of cancer arises from the unique properties of tumorigenicity, chemotherapy resistance, and their ability to metastasize and invade distant tissues. Several molecular profiles have been used to discriminate a stem cell from a non-stem cell. CSCs can be grown for study and further enriched using a number of in vitro techniques. An evolving option for translational research is the use of mathematical and computational models to describe the role of CSCs in complex tumor environments. This review is focused discussing the evidence emerging from modeling approaches that have clarified the impact of CSCs to the biology of cancer.

Mathematical models of breast and ovarian cancers

Women constitute the majority of the aging United States (US) population, and this has substantial implications on cancer population patterns and management practices. Breast cancer is the most common women's malignancy, while ovarian cancer is the most fatal gynecological malignancy in the US. In this review, we focus on these subsets of women's cancers, seen more commonly in postmenopausal and elderly women. In order to systematically investigate the complexity of cancer progression and response to treatment in breast and ovarian malignancies, we assert that integrated mathematical modeling frameworks viewed from a systems biology perspective are needed. Such integrated frameworks could offer innovative contributions to the clinical women's cancers community, as answers to clinical questions cannot always be reached with contemporary clinical and experimental tools. Here, we recapitulate clinically known data regarding the progression and treatment of the breast and ovarian cancers. We compare and contrast the two malignancies whenever possible in order to emphasize areas where substantial contributions could be made by clinically inspired and validated mathematical modeling. We show how current paradigms in the mathematical oncology community focusing on the two malignancies do not make comprehensive use of, nor substantially reflect existing clinical data, and we highlight the modeling areas in most critical need of clinical data integration. We emphasize that the primary goal of any mathematical study of women's cancers should be to address clinically relevant questions. WIREs Syst Biol Med 2016, 8:337-362. doi: 10.1002/wsbm.1343 For further resources related to this article, please visit the WIREs website.

A phase II trial of the BCL-2 homolog domain 3 mimetic AT-101 in combination with docetaxel for recurrent, locally advanced, or metastatic head and neck cancer

BACKGROUND

AT-101 is a BCL-2 Homolog domain 3 mimetic previously demonstrated to have tumoricidal effects in advanced solid organ malignancies. Given the evidence of activity in xenograft models, treatment with AT-101 in combination with docetaxel is a therapeutic doublet of interest in metastatic head and neck squamous cell carcinoma.

PATIENTS AND METHODS

Patients included in this trial had unresectable, recurrent, or distantly metastatic head and neck squamous cell carcinoma (R/M HNSCC) not amenable to curative radiation or surgery. This was an open label randomized, phase II trial in which patients were administered AT-101 in addition to docetaxel. The three treatment arms were docetaxel, docetaxel plus pulse dose AT-101, and docetaxel plus metronomic dose AT-101. The primary endpoint of this trial was overall response rate.

RESULTS

Thirty-five patients were registered and 32 were evaluable for treatment response. Doublet therapy with AT-101 and docetaxel was well tolerated with only 2 patients discontinuing therapy due to treatment related toxicities. The overall response rate was 11 % (4 partial responses) with a clinical benefit rate of 74 %. Median progression free survival was 4.3 months (range: 0.7-13.7) and overall survival was 5.5 months (range: 0.4-24). No significant differences were noted between dosing strategies.

CONCLUSION

Although met with a favorable toxicity profile, the addition of AT-101 to docetaxel in R/M HNSCC does not appear to demonstrate evidence of efficacy.

Vascular phenotype identification and anti-angiogenic treatment recommendation: A pseudo-multiscale mathematical model of angiogenesis

The development of anti-angiogenic drugs for cancer therapy has yielded some promising candidates, but novel approaches for interventions to angiogenesis have led to disappointing results. In addition, there is a shortage of biomarkers that are predictive of response to anti-angiogenic treatments. Consequently, the complex biochemical and physiological basis for tumour angiogenesis remains incompletely understood. We have adopted a mathematical approach to address these issues, formulating a spatially averaged multiscale model that couples the dynamics of VEGF, Ang1, Ang2 and PDGF, with those of mature and immature endothelial cells and pericyte cells. The model reproduces qualitative experimental results regarding pericyte coverage of vessels after treatment by anti-Ang2, anti-VEGF and combination anti-VEGF/anti-Ang2 antibodies. We used the steady state behaviours of the model to characterise angiogenic and non-angiogenic vascular phenotypes, and used mechanistic perturbations representing hypothetical anti-angiogenic treatments to generate testable hypotheses regarding transitions to non-angiogenic phenotypes that depend on the pre-treatment vascular phenotype. Additionally, we predicted a synergistic effect between anti-VEGF and anti-Ang2 treatments when applied to an immature pre-treatment vascular phenotype, but not when applied to a normalised angiogenic pre-treatment phenotype. Based on these findings, we conclude that changes in vascular phenotype are predicted to be useful as an experimental biomarker of response to treatment. Further, our analysis illustrates the potential value of non-spatial mathematical models for generating tractable predictions regarding the action of anti-angiogenic therapies.

An integrated cellular and sub-cellular model of cancer chemotherapy and therapies that target cell survival

Apoptosis resistance is a hallmark of human cancer, and tumor cells often become resistant due to defects in the programmed cell death machinery. Targeting key apoptosis regulators to overcome apoptotic resistance and promote rapid death of tumor cells is an exciting new strategy for cancer treatment, either alone or in combination with traditionally used anti-cancer drugs that target cell division. Here we present a multiscale modeling framework for investigating the synergism between traditional chemotherapy and targeted therapies aimed at critical regulators of apoptosis.

Computational systems biology approaches to anti-angiogenic cancer therapeutics

Angiogenesis is an exquisitely regulated process that is required for physiological processes and is also important in numerous diseases. Tumors utilize angiogenesis to generate the vascular network needed to supply the cancer cells with nutrients and oxygen, and many cancer drugs aim to inhibit tumor angiogenesis. Anti-angiogenic therapy involves inhibiting multiple cell types, molecular targets, and intracellular signaling pathways. Computational tools are useful in guiding treatment strategies, predicting the response to treatment, and identifying new targets of interest. Here, we describe progress that has been made in applying mathematical modeling and bioinformatics approaches to study anti-angiogenic therapeutics in cancer.

Exploiting the synergy between carboplatin and ABT-737 in the treatment of ovarian carcinomas

Platinum drug-resistance in ovarian cancers mediated by anti-apoptotic proteins such as Bcl-xL is a major factor contributing to the chemotherapeutic resistance of recurrent disease. Consequently, concurrent inhibition of Bcl-xL in combination with chemotherapy may improve treatment outcomes for patients. Here, we develop a mathematical model to investigate the potential of combination therapy with ABT-737, a small molecule inhibitor of Bcl-xL, and carboplatin, a platinum-based drug, on a simulated tumor xenograft. The model is calibrated against in vivo experimental data, wherein xenografts established in mice were treated with ABT-737 and/or carboplatin on a fixed periodic schedule. The validated model is used to predict the minimum drug load that will achieve a predetermined level of tumor growth inhibition, thereby maximizing the synergy between the two drugs. Our simulations suggest that the infusion-duration of each carboplatin dose is a critical parameter, with an 8-hour infusion of carboplatin given weekly combined with a daily bolus dose of ABT-737 predicted to minimize residual disease. The potential of combination therapy to prevent or delay the onset of carboplatin-resistance is also investigated. When resistance is acquired as a result of aberrant DNA-damage repair in cells treated with carboplatin, drug delivery schedules that induce tumor remission with even low doses of combination therapy can be identified. Intrinsic resistance due to pre-existing cohorts of resistant cells precludes tumor regression, but dosing strategies that extend disease-free survival periods can still be identified. These results highlight the potential of our model to accelerate the development of novel therapeutics such as BH3 mimetics.

Computational model of VEGFR2 pathway to ERK activation and modulation through receptor trafficking

Vascular Endothelial Growth Factor (VEGF) signal transduction is central to angiogenesis in development and in pathological conditions such as cancer, retinopathy and ischemic diseases. We constructed and validated a computational model of VEGFR2 trafficking and signaling, to study the role of receptor trafficking kinetics in modulating ERK phosphorylation in VEGF-stimulated endothelial cells. Trafficking parameters were optimized and validated against four previously published in vitro experiments. Based on these parameters, model simulations demonstrated interesting behaviors that may be highly relevant to understanding VEGF signaling in endothelial cells. First, at moderate VEGF doses, VEGFR2 phosphorylation and ERK phosphorylation are related in a log-linear fashion, with a stable duration of ERK activation; but with higher VEGF stimulation, phosphoERK becomes saturated, and its duration increases. Second, a large endosomal fraction of VEGFR2 makes the ERK activation reaction network less sensitive to perturbations in VEGF dosage. Third, extracellular-matrix-bound VEGF binds and activates VEGFR2, but by internalizing at a slower rate, matrix-bound VEGF-induced intracellular ERK phosphorylation is predicted to be greater in magnitude and more sustained, in agreement with experimental evidence. Fourth, different endothelial cell types appear to have different trafficking rates, which result in different levels of endosomal receptor localization and different ERK response profiles.

Computational Model of Gab1/2-Dependent VEGFR2 Pathway to Akt Activation

Vascular endothelial growth factor (VEGF) signal transduction is central to angiogenesis in development and in pathological conditions such as cancer, retinopathy and ischemic diseases. However, no detailed mass-action models of VEGF receptor signaling have been developed. We constructed and validated the first computational model of VEGFR2 trafficking and signaling, to study the opposing roles of Gab1 and Gab2 in regulation of Akt phosphorylation in VEGF-stimulated endothelial cells. Trafficking parameters were optimized against 5 previously published in vitro experiments, and the model was validated against six independent published datasets. The model showed agreement at several key nodes, involving scaffolding proteins Gab1, Gab2 and their complexes with Shp2. VEGFR2 recruitment of Gab1 is greater in magnitude, slower, and more sustained than that of Gab2. As Gab2 binds VEGFR2 complexes more transiently than Gab1, VEGFR2 complexes can recycle and continue to participate in other signaling pathways. Correspondingly, the simulation results show a log-linear relationship between a decrease in Akt phosphorylation and Gab1 knockdown while a linear relationship was observed between an increase in Akt phosphorylation and Gab2 knockdown. Global sensitivity analysis demonstrated the importance of initial-concentration ratios of antagonistic molecular species (Gab1/Gab2 and PI3K/Shp2) in determining Akt phosphorylation profiles. It also showed that kinetic parameters responsible for transient Gab2 binding affect the system at specific nodes. This model can be expanded to study multiple signaling contexts and receptor crosstalk and can form a basis for investigation of therapeutic approaches, such as tyrosine kinase inhibitors (TKIs), overexpression of key signaling proteins or knockdown experiments.

Mathematical modeling predicts synergistic antitumor effects of combining a macrophage-based, hypoxia-targeted gene therapy with chemotherapy

Tumor hypoxia is associated with low rates of cell proliferation and poor drug delivery, limiting the efficacy of many conventional therapies such as chemotherapy. Because many macrophages accumulate in hypoxic regions of tumors, one way to target tumor cells in these regions could be to use genetically engineered macrophages that express therapeutic genes when exposed to hypoxia. Systemic delivery of such therapeutic macrophages may also be enhanced by preloading them with nanomagnets and applying a magnetic field to the tumor site. Here, we use a new mathematical model to compare the effects of conventional cyclophosphamide therapy with those induced when macrophages are used to deliver hypoxia-inducible cytochrome P450 to locally activate cyclophosphamide. Our mathematical model describes the spatiotemporal dynamics of vascular tumor growth and treats cells as distinct entities. Model simulations predict that combining conventional and macrophage-based therapies would be synergistic, producing greater antitumor effects than the additive effects of each form of therapy. We find that timing is crucial in this combined approach with efficacy being greatest when the macrophage-based, hypoxia-targeted therapy is administered shortly before or concurrently with chemotherapy. Last, we show that therapy with genetically engineered macrophages is markedly enhanced by using the magnetic approach described above, and that this enhancement depends mainly on the strength of the applied field, rather than its direction. This insight may be important in the treatment of nonsuperficial tumors, where generating a specific orientation of a magnetic field may prove difficult. In conclusion, we demonstrate that mathematical modeling can be used to design and maximize the efficacy of combined therapeutic approaches in cancer.

The molecular basis of synergism between carboplatin and ABT-737 therapy targeting ovarian carcinomas

Resistance to standard chemotherapy (carboplatin + paclitaxel) is one of the leading causes of therapeutic failure in ovarian carcinomas. Emergence of chemoresistance has been shown to be mediated in part by members of the Bcl family of proteins including the antiapoptotic protein Bcl-x(L), whose expression is correlated with shorter disease-free intervals in recurrent disease. ABT-737 is an example of one of the first small-molecule inhibitors of Bcl-2/Bcl-x(L) that has been shown to increase the sensitivity of ovarian cancer cells to carboplatin. To exploit the therapeutic potential of these two drugs and predict optimal doses and dose scheduling, it is essential to understand the molecular basis of their synergistic action. Here, we build and calibrate a mathematical model of ABT-737 and carboplatin action on an ovarian cancer cell line (IGROV-1). The model suggests that carboplatin treatment primes cells for ABT-737 therapy because of an increased dependence of cells with DNA damage on Bcl-x(L) for survival. Numerical simulations predict the existence of a threshold of Bcl-x(L) below which these cells are unable to recover. Furthermore, co- plus posttreatment of ABT-737 with carboplatin is predicted to be the best strategy to maximize synergism between these two drugs. A critical challenge in chemotherapy is to strike a balance between maximizing cell-kill while minimizing patient drug load. We show that the model can be used to compute minimal doses required for any desired fraction of cell kill. These results underscore the potential of the modeling work presented here as a valuable quantitative tool to aid in the translation of novel drugs such as ABT-737 from the experimental to clinical setting and highlight the need for close collaboration between modelers and experimental scientists.

Dissecting cancer through mathematics: from the cell to the animal model

This Timeline article charts progress in mathematical modelling of cancer over the past 50 years, highlighting the different theoretical approaches that have been used to dissect the disease and the insights that have arisen. Although most of this research was conducted with little involvement from experimentalists or clinicians, there are signs that the tide is turning and that increasing numbers of those involved in cancer research and mathematical modellers are recognizing that by working together they might more rapidly advance our understanding of cancer and improve its treatment.