Mathematical modeling of an immune checkpoint inhibitor and its synergy with an immunostimulant

Nikolopoulou, Elpiniki; Eikenberry, Steffen E.; Gevertz, Jana L.; Kuang, Yang

doi:10.3934/dcdsb.2020138

Cited by 13 publications

(28 citation statements)

References 30 publications

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“…Finally, the last two terms describe how CTLs can die. Specifically, interaction with tumor cells can result in death at a rate

δ_{2}

as was done in [19], but which sets our model apart from [18, 20, 21]. CTLs can also die naturally at a rate

δ_{Y}

.…”

Section: Model Formulation and Experimental Datamentioning

confidence: 99%

“…where is the cell rate of expression of PD-1 on T cells. Again, following [18,20,21], the molar concentration of PD-L1 ( ) within the tumor micro-environment is given by…”

Section: +2mentioning

confidence: 99%

“…An anti-PD-L1 antibody ( ) binds to PD-L1 and inhibits the formation of the PD-1-PD-L1 complex. Following [18,20,21], the equation for the change in anti-PD-L1 antibody is given by:…”

Section: Model Formulation With Fgfr3 Immune Checkpoints and Combination Therapymentioning

confidence: 99%

“…Following [18,20,21,24], we assume that the association and dissociation of are fast, so applying a quasi-steady-state argument, we can approximate using the equation:…”

Section: A C K N O W L E D G M E N T Smentioning

confidence: 99%

“…where YQ = TQ (described in Table 2) [18,20,21,24]. In order to achieve agreement between the units for and in Equation (A-3), we converted the dosage of anti-PD-L1 in the experiment from μg to nmol/L using the following formula:…”

Section: A C K N O W L E D G M E N T Smentioning

confidence: 99%

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

et al. 2021

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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.

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“…Finally, the last two terms describe how CTLs can die. Specifically, interaction with tumor cells can result in death at a rate

δ_{2}

as was done in [19], but which sets our model apart from [18, 20, 21]. CTLs can also die naturally at a rate

δ_{Y}

.…”

Section: Model Formulation and Experimental Datamentioning

confidence: 99%

“…where is the cell rate of expression of PD-1 on T cells. Again, following [18,20,21], the molar concentration of PD-L1 ( ) within the tumor micro-environment is given by…”

Section: +2mentioning

confidence: 99%

“…An anti-PD-L1 antibody ( ) binds to PD-L1 and inhibits the formation of the PD-1-PD-L1 complex. Following [18,20,21], the equation for the change in anti-PD-L1 antibody is given by:…”

Section: Model Formulation With Fgfr3 Immune Checkpoints and Combination Therapymentioning

confidence: 99%

“…Following [18,20,21,24], we assume that the association and dissociation of are fast, so applying a quasi-steady-state argument, we can approximate using the equation:…”

Section: A C K N O W L E D G M E N T Smentioning

confidence: 99%

Section: A C K N O W L E D G M E N T Smentioning

confidence: 99%

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

et al. 2021

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Global stability and parameter analysis reinforce therapeutic targets of PD-L1-PD-1 and MDSCs for glioblastoma

Anderson,

Takacs,

Harris

et al. 2023

J. Math. Biol.

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Glioblastoma (GBM) is an aggressive primary brain cancer that currently has minimally effective treatments. Like other cancers, immunosuppression by the PD-L1-PD-1 immune checkpoint complex is a prominent axis by which glioma cells evade the immune system. Myeloid-derived suppressor cells (MDSCs), which are recruited to the glioma microenviroment, also contribute to the immunosuppressed GBM microenvironment by suppressing T cell functions. In this paper, we propose a GBM-specific tumor-immune ordinary differential equations model of glioma cells, T cells, and MDSCs to provide theoretical insights into the interactions between these cells. Equilibrium and stability analysis indicates that there are unique tumorous and tumor-free equilibria which are locally stable under certain conditions. Further, the tumor-free equilibrium is globally stable when T cell activation and the tumor kill rate by T cells overcome tumor growth, T cell inhibition by PD-L1-PD-1 and MDSCs, and the T cell death rate. Bifurcation analysis suggests that a treatment plan that includes surgical resection and therapeutics targeting immune suppression caused by the PD-L1-PD1 complex and MDSCs results in the system tending to the tumor-free equilibrium. Using a set of preclinical experimental data, we implement the approximate Bayesian computation (ABC) rejection method to construct probability density distributions that estimate model parameters. These distributions inform an appropriate search curve for global sensitivity analysis using the extended fourier amplitude sensitivity test. Sensitivity results combined with the ABC method suggest that parameter interaction is occurring between the drivers of tumor burden, which are the tumor growth rate and carrying capacity as well as the tumor kill rate by T cells, and the two modeled forms of immunosuppression, PD-L1-PD-1 immune checkpoint and MDSC suppression of T cells. Thus, treatment with an immune checkpoint inhibitor in combination with a therapeutic targeting the inhibitory mechanisms of MDSCs should be explored.

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Dynamic Analysis of a Model on Tumor-Immune System with Regulation of PD-1/PD-L1 and Stimulation Delay of Tumor Antigen

Liu²,

Chen³

et al. 2022

Qual. Theory Dyn. Syst.

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Mathematical modeling of an immune checkpoint inhibitor and its synergy with an immunostimulant

Cited by 13 publications

References 30 publications

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

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

Global stability and parameter analysis reinforce therapeutic targets of PD-L1-PD-1 and MDSCs for glioblastoma

Dynamic Analysis of a Model on Tumor-Immune System with Regulation of PD-1/PD-L1 and Stimulation Delay of Tumor Antigen

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