A Sigmoid Functional Response Emerges When Cytotoxic T Lymphocytes Start Killing Fresh Target Cells

Modeling the Development of Cellular Exhaustion and Tumor-Immune Stalemate

Cellular exhaustion in various immune cells develops in response to prolonged stimulation and overactivation during chronic infections and in cancer. Marked by an upregulation of inhibitory receptors and diminished effector functions, exhausted immune cells are unable to fully eradicate the antigen responsible for the overexposure. In cancer settings, this results in a relatively small but constant tumor burden known as a localized tumor-immune stalemate. In recent years, studies have elucidated key aspects of the development and progression of cellular exhaustion and have re-addressed previous misconceptions. Biological publications have also provided insight into the functional capabilities of exhausted cells. Complementing these findings, the model presented here serves as a mathematical framework for the establishment of cellular exhaustion and the development of the localized stalemate against a solid tumor. Analysis of this model indicates that this stalemate is stable and can handle small perturbations. Additionally, model analysis also provides insight into potential targets of future immunotherapy efforts.

Tumor-mediated immunosuppression and cytokine spreading affects the relation between EMT and PD-L1 status

Epithelial-mesenchymal transition (EMT) and immune resistance mediated by Programmed Death-Ligand 1 (PD-L1) upregulation are established drivers of tumor progression. Their bi-directional crosstalk has been proposed to facilitate tumor immunoevasion, yet the impact of immunosuppression and spatial heterogeneity on the interplay between these processes remains to be characterized. Here we study the role of these factors using mathematical and spatial models. We first designed models incorporating immunosuppressive effects on T cells mediated via PD-L1 and the EMT-inducing cytokine Transforming Growth Factor beta (TGFβ). Our models predict that PD-L1-mediated immunosuppression merely reduces the difference in PD-L1 levels between EMT states, while TGFβ-mediated suppression also causes PD-L1 expression to correlate negatively with TGFβ within each EMT phenotype. We subsequently embedded the models in multi-scale spatial simulations to explicitly describe heterogeneity in cytokine levels and intratumoral heterogeneity. Our multi-scale models show that Interferon gamma (IFNγ)-induced partial EMT of a tumor cell subpopulation can provide some, albeit limited protection to bystander tumor cells. Moreover, our simulations show that the true relationship between EMT status and PD-L1 expression may be hidden at the population level, highlighting the importance of studying EMT and PD-L1 status at the single-cell level. Our findings deepen the understanding of the interactions between EMT and the immune response, which is crucial for developing novel diagnostics and therapeutics for cancer patients.

Cytotoxic T Lymphocytes Control Growth of B16 Tumor Cells in Collagen-Fibrin Gels by Cytolytic and Non-Lytic Mechanisms

Cytotoxic T lymphocytes (CTLs) are important in controlling some viral infections, and therapies involving the transfer of large numbers of cancer-specific CTLs have been successfully used to treat several types of cancers in humans. While the molecular mechanisms of how CTLs kill their targets are relatively well understood, we still lack a solid quantitative understanding of the kinetics and efficiency by which CTLs kill their targets in vivo. Collagen-fibrin-gel-based assays provide a tissue-like environment for the migration of CTLs, making them an attractive system to study T cell cytotoxicity in in vivo-like conditions. Budhu.et al. systematically varied the number of peptide (SIINFEKL)-pulsed B16 melanoma cells and SIINFEKL-specific CTLs (OT-1) and measured the remaining targets at different times after target and CTL co-inoculation into collagen-fibrin gels. The authors proposed that their data were consistent with a simple model in which tumors grow exponentially and are killed by CTLs at a per capita rate proportional to the CTL density in the gel. By fitting several alternative mathematical models to these data, we found that this simple "exponential-growth-mass-action-killing" model did not precisely describe the data. However, determining the best-fit model proved difficult because the best-performing model was dependent on the specific dataset chosen for the analysis. When considering all data that include biologically realistic CTL concentrations (E≤107cell/mL), the model in which tumors grow exponentially and CTLs suppress tumor's growth non-lytically and kill tumors according to the mass-action law (SiGMA model) fit the data with the best quality. A novel power analysis suggested that longer experiments (∼3-4 days) with four measurements of B16 tumor cell concentrations for a range of CTL concentrations would best allow discriminating between alternative models. Taken together, our results suggested that the interactions between tumors and CTLs in collagen-fibrin gels are more complex than a simple exponential-growth-mass-action killing model and provide support for the hypothesis that CTLs' impact on tumors may go beyond direct cytotoxicity.

Mathematical modeling suggests cytotoxic T lymphocytes control growth of B16 tumor cells in collagin-fibrin gels by cytolytic and non-lytic mechanisms

Cytotoxic T lymphocytes (CTLs) are important in controlling some viral infections, and therapies involving transfer of large numbers of cancer-specific CTLs have been successfully used to treat several types of cancers in humans. While molecular mechanisms of how CTLs kill their targets are relatively well understood we still lack solid quantitative understanding of the kinetics and efficiency at which CTLs kill their targets in different conditions. Collagen-fibrin gel-based assays provide a tissue-like environment for the migration of CTLs, making them an attractive system to study the cytotoxicity in vitro. Budhu et al. [1] systematically varied the number of peptide (SIINFEKL)- pulsed B16 melanoma cells and SIINFEKL-specific CTLs (OT-1) and measured remaining targets at different times after target and CTL co-inoculation into collagen-fibrin gels. The authors proposed that their data were consistent with a simple model in which tumors grow exponentially and are killed by CTLs at a per capita rate proportional to the CTL density in the gel. By fitting several alternative mathematical models to these data we found that this simple "exponential-growth-mass-action-killing" model does not precisely fit the data. However, determining the best fit model proved difficult because the best performing model was dependent on the specific dataset chosen for the analysis. When considering all data that include biologically realistic CTL concentrations ( E ≤ 10 ⁷ cell/ml) the model in which tumors grow exponentially and CTLs suppress tumor's growth non-lytically and kill tumors according to the mass-action law (SiGMA model) fitted the data with best quality. Results of power analysis suggested that longer experiments (∼ 3 - 4 days) with 4 measurements of B16 tumor cell concentrations for a range of CTL concentrations would best allow to discriminate between alternative models. Taken together, our results suggest that interactions between tumors and CTLs in collagen-fibrin gels are more complex than a simple exponential-growth- mass-action killing model and provide support for the hypothesis that CTLs impact on tumors may go beyond direct cytotoxicity.

Modeling LSD1-Mediated Tumor Stagnation

LSD1 (KDMA1) has gained attention in the last decade as a cancer biomarker and drug target. In particular, recent work suggests that LSD1 inhibition alone reduces tumor growth, increases T cell tumor infiltration, and complements PD1/PDL1 checkpoint inhibitor therapy. In order to elucidate the immunogenic effects of LSD1 inhibition, we develop a mathematical model of tumor growth under the influence of the adaptive immune response. In particular, we investigate the anti-tumor cytotoxicity of LSD1-mediated T cell dynamics, in order to better understand the synergistic potential of LSD1 inhibition in combination immunotherapies, including checkpoint inhibitors. To that end, we formulate a non-spatial delay differential equation model and fit to the B16 mouse model data from Sheng et al. (Cell 174(3):549-563, 2018. https://doi.org/10.1016/j.cell.2018.05.052 ). Our results suggest that the immunogenic effect of LSD1 inhibition accelerates anti-tumor cytotoxicity. However, cytotoxicity does not seem to account for the slower growth observed in LSD1-inhibited tumors, despite evidence suggesting immune-mediation of this effect.

Evaluation of CD8 T cell killing models with computer simulations of 2-photon imaging experiments

In vivo imaging of cytotoxic T lymphocyte (CTL) killing activity revealed that infected cells have a higher observed probability of dying after multiple contacts with CTLs. We developed a three-dimensional agent-based model to discriminate different hypotheses about how infected cells get killed based on quantitative 2-photon in vivo observations. We compared a constant CTL killing probability with mechanisms of signal integration in CTL or infected cells. The most likely scenario implied increased susceptibility of infected cells with increasing number of CTL contacts where the total number of contacts was a critical factor. However, when allowing in silico T cells to initiate new interactions with apoptotic target cells (zombie contacts), a contact history independent killing mechanism was also in agreement with experimental datasets. The comparison of observed datasets to simulation results, revealed limitations in interpreting 2-photon data, and provided readouts to distinguish CTL killing models.

Heterogeneous, delayed-onset killing by multiple-hitting T cells: Stochastic simulations to assess methods for analysis of imaging data

Although quantitative insights into the killing behaviour of Cytotoxic T Lymphocytes (CTLs) are necessary for the rational design of immune-based therapies, CTL killing function remains insufficiently characterised. One established model of CTL killing treats CTL cytotoxicity as a Poisson process, based on the assumption that CTLs serially kill antigen-presenting target cells via delivery of lethal hits, each lethal hit corresponding to a single injection of cytotoxic proteins into the target cell cytoplasm. Contradicting this model, a recent in vitro study of individual CTLs killing targets over a 12-hour period found significantly greater heterogeneity in CTL killing performance than predicted by Poisson-based killing. The observed killing process was dynamic and varied between CTLs, with the best performing CTLs exhibiting a marked increase in killing during the final hours of the experiments, along with a "burst killing" kinetic. Despite a search for potential differences between CTLs, no mechanistic explanation for the heterogeneous killing kinetics was found. Here we have used stochastic simulations to assess whether target cells might require multiple hits from CTLs before undergoing apoptosis, in order to verify whether multiple-hitting could explain the late onset, burst killing dynamics observed in vitro. We found that multiple-hitting from CTLs was entirely consistent with the observed killing kinetics. Moreover, the number of available targets and the spatiotemporal kinetics of CTL:target interactions influenced the realised CTL killing rate. We subsequently used realistic, spatial simulations to assess methods for estimating the hitting rate and the number of hits required for target death, to be applied to microscopy data of individual CTLs killing targets. We found that measuring the cumulative duration of individual contacts that targets have with CTLs would substantially improve accuracy when estimating the killing kinetics of CTLs.

Endocrine Autoimmune Disease as a Fragility of Immune Surveillance against Hypersecreting Mutants

Some endocrine organs are frequent targets of autoimmune attack. Here, we addressed the origin of autoimmune disease from the viewpoint of feedback control. Endocrine tissues maintain mass through feedback loops that balance cell proliferation and removal according to hormone-driven regulatory signals. We hypothesized the existence of a dedicated mechanism that detects and removes mutant cells that missense the signal and therefore hyperproliferate and hypersecrete with potential to disrupt organismal homeostasis. In this mechanism, hypersecreting cells are preferentially eliminated by autoreactive T cells at the cost of a fragility to autoimmune disease. The "autoimmune surveillance of hypersecreting mutants" (ASHM) hypothesis predicts the presence of autoreactive T cells in healthy individuals and the nature of self-antigens as peptides from hormone secretion pathway. It explains why some tissues get prevalent autoimmune disease, whereas others do not and instead show prevalent mutant-expansion disease (e.g., hyperparathyroidism). The ASHM hypothesis is testable, and we discuss experimental follow-up.

Recognition of Apoptotic Cells by Viruses and Cytolytic Lymphocytes: Target Selection in the Fog of War

Viruses and cytolytic lymphocytes operate in an environment filled with dying and dead cells, and cell fragments. For viruses, irreversible fusion with doomed cells is suicide. For cytotoxic T lymphocyte and natural killer cells, time and limited lytic resources spent on apoptotic targets is wasteful and may result in death of the host. We make the case that the target membrane cytoskeleton is the best source of information regarding the suitability of potential targets for engagement for both viruses and lytic effector cells, and we present experimental evidence for detection of apoptotic cells by HIV, without loss of infectivity.

Contact-Dependent Killing by Cytotoxic T Lymphocytes Is Insufficient for EL4 Tumor Regression In Vivo

Immunotherapies are an emerging strategy for treatment of solid tumors. Improved understanding of the mechanisms employed by cytotoxic T lymphocytes (CTL) to control tumors will aid in the development of immunotherapies. CTLs can directly kill tumor cells in a contact-dependent manner or may exert indirect effects on tumor cells via secretion of cytokines. Here, we aim to quantify the importance of these mechanisms in murine thymoma EL4/EG7 cells. We developed an agent-based model (ABM) and an ordinary differential equation model of tumor regression after adoptive transfer of a population of CTLs. Models were parameterized based on in vivo measurements of CTL infiltration and killing rates applied to EL4/EG7 tumors and OTI T cells. We quantified whether infiltrating CTLs are capable of controlling tumors through only direct, contact-dependent killing. Both models agreed that the low measured killing rate of CTLs in vivo was insufficient to cause tumor regression. In our ABM, we also simulated CTL production of the cytokine IFNγ in order to explore how an antiproliferative effect of IFNγ might aid CTLs in tumor control. In this model, IFNγ substantially reduced tumor growth compared with direct killing alone. Collectively, these data demonstrate that contact-dependent killing is insufficient for EL4 regression in vivo and highlight the potential importance of cytokine-induced antiproliferative effects in T-cell-mediated tumor control. SIGNIFICANCE: Computational modeling highlights the importance of cytokine-induced antiproliferative effects in T-cell-mediated control of tumor progression.

Towards multiscale modeling of the CD8+ T cell response to viral infections

The CD8⁺ T cell response is critical to the control of viral infections. Yet, defining the CD8⁺ T cell response to viral infections quantitatively has been a challenge. Following antigen recognition, which triggers an intracellular signaling cascade, CD8⁺ T cells can differentiate into effector cells, which proliferate rapidly and destroy infected cells. When the infection is cleared, they leave behind memory cells for quick recall following a second challenge. If the infection persists, the cells may become exhausted, retaining minimal control of the infection while preventing severe immunopathology. These activation, proliferation and differentiation processes as well as the mounting of the effector response are intrinsically multiscale and collective phenomena. Remarkable experimental advances in the recent years, especially at the single cell level, have enabled a quantitative characterization of several underlying processes. Simultaneously, sophisticated mathematical models have begun to be constructed that describe these multiscale phenomena, bringing us closer to a comprehensive description of the CD8⁺ T cell response to viral infections. Here, we review the advances made and summarize the challenges and opportunities ahead. This article is categorized under: Analytical and Computational Methods > Computational Methods Biological Mechanisms > Cell Fates Biological Mechanisms > Cell Signaling Models of Systems Properties and Processes > Mechanistic Models.