Tracy L. Stepien

During embryonic development of the retina of the eye, astrocytes, a type of glial cell, migrate over the retinal surface and form a dynamic mesh. This mesh then serves as scaffolding for blood vessels to form the retinal vasculature network that supplies oxygen and nutrients to the inner portion of the retina. Astrocyte spreading proceeds in a radially symmetric manner over the retinal surface. Additionally, astrocytes mature from astrocyte precursor cells (APCs) to immature perinatal astrocytes (IPAs) during this embryonic stage. We extend a previously-developed continuum model that describes tension-driven migration and oxygen and growth factor influenced proliferation and differentiation. Comparing numerical simulations to experimental data, we identify model equation components that can be removed via model reduction using approximate Bayesian computation (ABC). Our results verify experimental studies indicating that the choroid oxygen supply plays a negligible role in promoting differentiation of APCs into IPAs and in promoting IPA proliferation, and the hyaloid artery oxygen supply and APC apoptosis play negligible roles in astrocyte spreading and differentiation.

The immune checkpoint inhibitor anti-PD-1, commonly used in cancer immunotherapy, has not been successful as a monotherapy for the highly aggressive brain cancer glioblastoma. However, when used in conjunction with a CC-chemokine receptor-2 (CCR2) antagonist, anti-PD-1 has shown efficacy in preclinical studies. In this paper, we aim to optimize treatment regimens for this combination immunotherapy using optimal control theory. We extend a treatment-free glioblastoma-immune dynamics ODE model to include interventions with anti-PD-1 and the CCR2 antagonist. An optimized regimen increases the survival of an average mouse from 32 days post-tumor implantation without treatment to 111 days with treatment. We scale this approach to a virtual murine cohort to evaluate mortality and quality of life concerns during treatment, and predict survival, tumor recurrence, or death after treatment. A parameter identifiability analysis identifies five parameters suitable for personalizing treatment within the virtual cohort. Sampling from these five practically identifiable parameters for the virtual murine cohort reveals that personalized, optimized regimens enhance survival: 84% of the virtual mice survive to day 100, compared to 60% survival in a previously-studied experimental regimen. Subjects with high tumor growth rates and low T cell kill rates are identified as more likely to die during and after treatment due to their compromised immune systems and more aggressive tumors. Notably, the MDSC death rate emerges as a long-term predictor of either disease-free survival or death. Highlights A mathematical model of glioma-immune dynamics integrates combination immunotherapy. An optimized regimen extends survival in an average virtual mouse by 79 days. Quality of life and survival outcomes were evaluated for a virtual murine cohort. A high death rate of myeloid-derived suppressor cells predicts long-term survival.

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.

Bluetongue (BT) is a well-known vector-borne disease that infects ruminants such as sheep, cattle, and deer with high mortality rates. Recent outbreaks in Europe highlight the importance of understanding vector-host dynamics and potential courses of action to mitigate the damage that can be done by BT. We present an agent-based model, entitled ‘MidgePy’, that focuses on the movement of individual Culicoides spp. biting midges and their interactions with ruminants to understand their role as vectors in BT outbreaks, especially in regions that do not regularly experience outbreaks. The results of our sensitivity analysis suggest that midge survival rate has a significant impact on the probability of a BTV outbreak as well as its severity. Using midge flight activity as a proxy for temperature, we found that an increase in environmental temperature corresponded with an increased probability of outbreak after identifying parameter regions where outbreaks are more likely to occur. This suggests that future methods to control BT spread could combine large-scale vaccination programs with biting midge population control measures such as the use of pesticides. Spatial heterogeneity in the environment is also explored to give insight on optimal farm layouts to reduce the potential for BT outbreaks.

The May–Leonard model was introduced to examine the behavior of three competing populations where rich dynamics, such as limit cycles and nonperiodic cyclic solutions, arise. In this work, we perturb the system by adding the capability of global mutations, allowing one species to evolve to the other two in a linear manner. We find that for small mutation rates, the perturbed system not only retains some of the dynamics seen in the classical model, such as the three-species equal-population equilibrium bifurcating to a limit cycle, but also exhibits new behavior. For instance, we capture curves of fold bifurcations where pairs of equilibria emerge and then coalesce. As a result, we uncover parameter regimes with new types of stable fixed points that are distinct from the single- and dual-population equilibria characteristic of the original model. On the contrary, the linearly perturbed system fails to maintain heteroclinic connections that exist in the original system. In short, a linear perturbation proves to be significant enough to substantially influence the dynamics, even with small mutation rates.

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 (eFAST). 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.

The May--Leonard model was introduced to examine the behavior of three competing populations where rich dynamics, such as limit cycles and nonperiodic cyclic solutions, arise. In this work, we perturb the system by adding the capability of global mutations, allowing one species to evolve to the other two in a linear manner. We find that for small mutation rates the perturbed system not only retains some of the dynamics seen in the classical model, such as the three-species equal-population equilibrium bifurcating to a limit cycle, but also exhibits new behavior. For instance, we capture curves of fold bifurcations where pairs of equilibria emerge and then coalesce. As a result, we uncover parameter regimes with new types of stable fixed points that are distinct from the single- and dual-population equilibria characteristic of the original model. On the contrary, the linearly-perturbed system fails to maintain heteroclinic connections that exist in the original system. In short, a linear perturbation proves to be significant enough to substantially influence the dynamics, even with small mutation rates.

A bstract: Bluetongue (BT) is a well-known vector-borne disease that infects ruminants such as sheep, cattle, and deer with high mortality rates. Recent outbreaks in Europe highlight the importance of understanding vector-host dynamics and potential courses of action to mitigate the damage that can be done by BT. We present an agent-based model (ABM), entitled MidgePy, that focuses on the movement of individual Culicoides spp. biting midges and their interactions with ruminants to understand their role as vectors in BT outbreaks, especially in regions that do not regularly experience outbreaks. Sensitivity analysis is performed and results indicate that midge survival rate has a significant impact on the probability of a BTV outbreak as well as its severity. Parameter regions where outbreaks are more likely to occur are determined, with an increase in environmental temperature corresponding with an increased probability of outbreak, where midge flight activity is used as a proxy for temperature. This suggests that future methods to control BT spread could combine large-scale vaccination programs with biting midge population control measures such as the use of pesticides. Spatial heterogeneity in the environment is also explored to give insight on optimal farm layouts to reduce the potential for BT outbreaks.