Go-or-grow models in biology: a monster on a leash

Journal of Mathematical Biology · 2025-10-16 · 1 citations

Go-or-grow approaches represent a specific class of mathematical models used to describe populations where individuals either migrate or reproduce, but not both simultaneously. These models have a wide range of applications in biology and medicine, chiefly among those the modeling of brain cancer spread. The analysis of go-or-grow models has inspired new mathematics, and it is the purpose of this review to highlight interesting and challenging mathematical properties of reaction-diffusion models of the go-or-grow type. We provide a detailed review of biological and medical applications before focusing on key results concerning solution existence and uniqueness, pattern formation, critical domain size problems, and traveling waves. We present new results related to the critical domain size and traveling wave problems, and we connect these findings to the existing literature. Moreover, we demonstrate the high level of instability inherent in go-or-grow models. We argue that there is currently no accurate numerical solver for these models, and emphasize that special care must be taken when dealing with the "monster on a leash".

An Approximate Bayesian Computation Approach for Embryonic Astrocyte Migration Model Reduction

Bulletin of Mathematical Biology · 2024-09-13

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

Journal of Theoretical Biology · 2024-09-20 · 2 citations

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.

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

bioRxiv (Cold Spring Harbor Laboratory) · 2024-05-02 · 1 citations

Abstract 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.

An Agent-Based Model of Biting Midge Dynamics to Understand Bluetongue Outbreaks

Bulletin of Mathematical Biology · 2023-06-15 · 3 citations

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

Journal of Mathematical Biology · 2023-12-15 · 16 citations

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.

Dynamics of a linearly perturbed May–Leonard competition model

Chaos An Interdisciplinary Journal of Nonlinear Science · 2023-06-01 · 1 citations

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.

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

bioRxiv (Cold Spring Harbor Laboratory) · 2023-05-16 · 1 citations

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.

An ABM of biting midge dynamics to understand Bluetongue outbreaks

bioRxiv (Cold Spring Harbor Laboratory) · 2022-09-27

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.

Spreading mechanics and differentiation of astrocytes during retinal development

Journal of Theoretical Biology · 2022-07-04 · 2 citations