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

Abstract

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.

Optimal control of combination immunotherapy for a virtual murine cohort in a glioblastoma-immune dynamics model

“…A combination immunotherapy regimen with anti-PD-1 and a CCR2 antagonist showed efficacy in preclinical murine models (Flores-Toro et al (2020)). In this paper, we extend the GBM-immune dynamics model from Anderson et al (2023) to include treatment with the combination immunotherapy and formulate a treatment optimization problem in terms of optimal control theory. The aim of this study was to obtain optimized, personalized treatment regimens for virtual subjects and predict markers of treatment success and failure.…”

“…Lastly, Corollary 4.1 (Fleming and Rishel (2012)) requires that where c 1 > 0 and β > 1. Since C ≥ 0 (Anderson et al (2023)), this lower bound for L ( t, y, u ) is trivially fulfilled by. Thus, an optimal pair, ( u 1 , u 2 ), exists that minimizes the Hamiltonian (B.1).…”

“…Using the average tumor size at each time point, we re-estimated the five practically identifiable parameters ( λ C , η, ρ, r , and d M ) for the treatment-free groups and set all other parameters to the “Best Fit” values listed in Table 1. Given that the tumor sizes were an order of magnitude larger than the glioma data in Anderson et al (2023), we also re-estimated the carrying capacity, C max . In each of the eight scenarios (2 without treatment, 6 with treatment), we obtained parameter distributions (Appendix E) by accepting 20,000 parameter sets of lowest error from a set of 100,000 samples using the approximate Bayesian computation (ABC) rejection method (Sunnåker et al (2013); Liepe et al (2014); Anderson et al (2023)).…”

“…Survival analysis for the cohort of 10,000 virtual GBM mice after receiving a personalized optimal treatment regimen with anti-PD-1 and the CCR2 antagonist. The virtual cohort was sampled using the GBM-specific distributions of the 5 practically identifiable parameters from Anderson et al (2023)[Table 2].…”

“…We use a sparse and noisy data set consisting of total cell counts of cancer cells, T cells, and MDSCs in murine gliomas reported in Anderson et al (2023) to conduct practical identifiability analysis. Mice were orthotopically implanted with 35,000 KR158 high-grade glioma cells and then euthanized on days 7, 13, 20, 24, 27, and 34 following glioma implantation.…”