Simple biophysical model of tumor evasion from immune system control

A stochastic individual-based model to explore the role of spatial interactions and antigen recognition in the immune response against solid tumours

Spatial interactions between cancer and immune cells, as well as the recognition of tumour antigens by cells of the immune system, play a key role in the immune response against solid tumours. The existing mathematical models generally focus only on one of these key aspects. We present here a spatial stochastic individual-based model that explicitly captures antigen expression and recognition. In our model, each cancer cell is characterised by an antigen profile which can change over time due to either epimutations or mutations. The immune response against the cancer cells is initiated by the dendritic cells that recognise the tumour antigens and present them to the cytotoxic T cells. Consequently, T cells become activated against the tumour cells expressing such antigens. Moreover, the differences in movement between inactive and active immune cells are explicitly taken into account by the model. Computational simulations of our model clarify the conditions for the emergence of tumour clearance, dormancy or escape, and allow us to assess the impact of antigenic heterogeneity of cancer cells on the efficacy of immune action. Ultimately, our results highlight the complex interplay between spatial interactions and adaptive mechanisms that underpins the immune response against solid tumours, and suggest how this may be exploited to further develop cancer immunotherapies.

Quantitative Mechanistic Modeling in Support of Pharmacological Therapeutics Development in Immuno-Oncology

Following the approval, in recent years, of the first immune checkpoint inhibitor, there has been an explosion in the development of immuno-modulating pharmacological modalities for the treatment of various cancers. From the discovery phase to late-stage clinical testing and regulatory approval, challenges in the development of immuno-oncology (IO) drugs are multi-fold and complex. In the preclinical setting, the multiplicity of potential drug targets around immune checkpoints, the growing list of immuno-modulatory molecular and cellular forces in the tumor microenvironment-with additional opportunities for IO drug targets, the emergence of exploratory biomarkers, and the unleashed potential of modality combinations all have necessitated the development of quantitative, mechanistically-oriented systems models which incorporate key biology and patho-physiology aspects of immuno-oncology and the pharmacokinetics of IO-modulating agents. In the clinical setting, the qualification of surrogate biomarkers predictive of IO treatment efficacy or outcome, and the corresponding optimization of IO trial design have become major challenges. This mini-review focuses on the evolution and state-of-the-art of quantitative systems models describing the tumor vs. immune system interplay, and their merging with quantitative pharmacology models of IO-modulating agents, as companion tools to support the addressing of these challenges.

A nonlinear mathematical model of cell-mediated immune response for tumor phenotypic heterogeneity

Human cancers display intra-tumor heterogeneity in many phenotypic features, such as expression of cell surface receptors, growth, and angiogenic, proliferative, and immunogenic factors, which represent obstacles to a successful immune response. In this paper, we propose a nonlinear mathematical model of cancer immunosurveillance that takes into account some of these features based on cell-mediated immune responses. The model describes phenomena that are seen in vivo, such as tumor dormancy, robustness, immunoselection over tumor heterogeneity (also called "cancer immunoediting") and strong sensitivity to initial conditions in the composition of tumor microenvironment. The results framework has as common element the tumor as an attractor for abnormal cells. Bifurcation analysis give us as tumor attractors fixed-points, limit cycles and chaotic attractors, the latter emerging from period-doubling cascade displaying Feigenbaum's universality. Finally, we simulated both elimination and escape tumor scenarios by means of a stochastic version of the model according to the Doob-Gillespie algorithm.

An Agent-based Model for Investigating the Effect of Myeloid-Derived Suppressor Cells and its Depletion on Tumor Immune Surveillance

BACKGROUND

To predict the behavior of biological systems, mathematical models of biological systems have been shown to be useful. In particular, mathematical models of tumor-immune system interactions have demonstrated promising results in prediction of different behaviors of tumor against the immune system.

METHODS

This study aimed at the introduction of a new model of tumor-immune system interaction, which includes tumor and immune cells as well as myeloid-derived suppressor cells (MDSCs). MDSCs are immune suppressor cells that help the tumor cells to escape the immune system. The structure of this model is agent-based which makes possible to investigate each component as a separate agent. Moreover, in this model, the effect of low dose 5-fluorouracil (5-FU) on MDSCs depletion was considered.

RESULTS

Based on the findings of this study, MDSCs had suppressive effect on increment of immune cell number which consequently result in tumor cells escape the immune cells. It has also been demonstrated that low-dose 5-FU could help immune system eliminate the tumor cells through MDSCs depletion.

CONCLUSION

Using this new agent-based model, multiple injection of low-dose 5-FU could eliminate MDSCs and therefore might have the potential to be considered in treatment of cancers.

A structural methodology for modeling immune-tumor interactions including pro- and anti-tumor factors for clinical applications

The immune system turns out to have both stimulatory and inhibitory factors influencing on tumor growth. In recent years, the pro-tumor role of immunity factors such as regulatory T cells and TGF-β cytokines has specially been considered in mathematical modeling of tumor-immune interactions. This paper presents a novel structural methodology for reviewing these models and classifies them into five subgroups on the basis of immune factors included. By using our experimental data due to immunotherapy experimentation in mice, these five modeling groups are evaluated and scored. The results show that a model with a small number of variables and coefficients performs efficiently in predicting the tumor-immune system interactions. Though immunology theorems suggest to employ a larger number of variables and coefficients, more complicated models are here shown to be inefficient due to redundant parallel pathways. So, these models are trapped in local minima and restricted in prediction capability. This paper investigates the mathematical models that were previously developed and proposes variables and pathways that are essential for modeling tumor-immune. Using these variables and pathways, a minimal structure for modeling tumor-immune interactions is proposed for future studies.

Modeling the Dichotomy of the Immune Response to Cancer: Cytotoxic Effects and Tumor-Promoting Inflammation

Although the immune response is often regarded as acting to suppress tumor growth, it is now clear that it can be both stimulatory and inhibitory. The interplay between these competing influences has complex implications for tumor development, cancer dormancy, and immunotherapies. In fact, early immunotherapy failures were partly due to a lack in understanding of the nonlinear growth dynamics these competing immune actions may cause. To study this biological phenomenon theoretically, we construct a minimally parameterized framework that incorporates all aspects of the immune response. We combine the effects of all immune cell types, general principles of self-limited logistic growth, and the physical process of inflammation into one quantitative setting. Simulations suggest that while there are pro-tumor or antitumor immunogenic responses characterized by larger or smaller final tumor volumes, respectively, each response involves an initial period where tumor growth is stimulated beyond that of growth without an immune response. The mathematical description is non-identifiable which allows an ensemble of parameter sets to capture inherent biological variability in tumor growth that can significantly alter tumor-immune dynamics and thus treatment success rates. The ability of this model to predict non-intuitive yet clinically observed patterns of immunomodulated tumor growth suggests that it may provide a means to help classify patient response dynamics to aid identification of appropriate treatments exploiting immune response to improve tumor suppression, including the potential attainment of an immune-induced dormant state.

Abscopal Benefits of Localized Radiotherapy Depend on Activated T-cell Trafficking and Distribution between Metastatic Lesions

It remains unclear how localized radiotherapy for cancer metastases can occasionally elicit a systemic antitumor effect, known as the abscopal effect, but historically, it has been speculated to reflect the generation of a host immunotherapeutic response. The ability to purposefully and reliably induce abscopal effects in metastatic tumors could meet many unmet clinical needs. Here, we describe a mathematical model that incorporates physiologic information about T-cell trafficking to estimate the distribution of focal therapy-activated T cells between metastatic lesions. We integrated a dynamic model of tumor-immune interactions with systemic T-cell trafficking patterns to simulate the development of metastases. In virtual case studies, we found that the dissemination of activated T cells among multiple metastatic sites is complex and not intuitively predictable. Furthermore, we show that not all metastatic sites participate in systemic immune surveillance equally, and therefore the success in triggering the abscopal effect depends, at least in part, on which metastatic site is selected for localized therapy. Moreover, simulations revealed that seeding new metastatic sites may accelerate the growth of the primary tumor, because T-cell responses are partially diverted to the developing metastases, but the removal of the primary tumor can also favor the rapid growth of preexisting metastatic lesions. Collectively, our work provides the framework to prospectively identify anatomically defined focal therapy targets that are most likely to trigger an immune-mediated abscopal response and therefore may inform personalized treatment strategies in patients with metastatic disease.

A model for effects of adaptive immunity on tumor response to chemotherapy and chemoimmunotherapy

Complete clinical regressions of solid tumors in response to chemotherapy are difficult to explain by direct cytotoxicity alone, because of low growth fractions and obstacles to drug delivery. A plausible indirect mechanism that might reconcile this is the action of the immune system. A model for interaction between tumors and the adaptive immune system is presented here, and used to examine controllability of tumors through the interplay of cytotoxic, cytostatic and immunogenic effects of chemotherapy and the adaptive immune response. The model includes cytotoxic and helper T cells, T regulatory cells (Tregs), dendritic cells, memory cells, and several key cytokines. Nearly all parameter estimates are derived from experimental and clinical data. Individual tumors are characterized by two parameters: growth rate and antigenicity, and regions of tumor control are identified in this parameter space. The model predicts that inclusion of the immune response significantly expands the region of tumor control for both cytostatic and cytotoxic chemotherapies. Moreover, outside the control zone, tumor growth is delayed significantly. An optimal fractionation schedule is predicted, for a fixed cumulative dose. The model further predicts expanded regions of tumor control when several forms of immunotherapy (adoptive T cell transfer, Treg depletion, and dendritic cell vaccination) are combined with chemotherapy. Outcomes depend greatly on tumor characteristics, the schedule of administration, and the type of immunotherapy chosen, suggesting promising opportunities for personalized medicine. Overall, the model provides insight into the role of the adaptive immune system in chemotherapy, and how scheduling and immunotherapeutic interventions might improve efficacy.

Mathematical models of immune-induced cancer dormancy and the emergence of immune evasion

Cancer dormancy, a state in which cancer cells persist in a host without significant growth, is a natural forestallment of progression to manifest disease and is thus of great clinical interest. Experimental work in mice suggests that in immune-induced dormancy, the longer a cancer remains dormant in a host, the more resistant the cancer cells become to cytotoxic T-cell-mediated killing. In this work, mathematical models are used to analyse the possible causative mechanisms of cancer escape from immune-induced dormancy. Using a data-driven approach, both decaying efficacy in immune predation and immune recruitment are analysed with results suggesting that decline in recruitment is a stronger determinant of escape than increased resistance to predation. Using a mechanistic approach, the existence of an immune-resistant cancer cell subpopulation is considered, and the effects on cancer dormancy and potential immunoediting mechanisms of cancer escape are analysed and discussed. The immunoediting mechanism assumes that the immune system selectively prunes the cancer of immune-sensitive cells, which is shown to cause an initially heterogeneous population to become a more homogeneous, and more resistant, population. The fact that this selection may result in the appearance of decreasing efficacy in T-cell cytotoxic effect with time in dormancy is also demonstrated. This work suggests that through actions that temporarily delay cancer growth through the targeted removal of immune-sensitive subpopulations, the immune response may actually progress the cancer to a more aggressive state.

Tumor-immune dynamics regulated in the microenvironment inform the transient nature of immune-induced tumor dormancy

Cancer in a host induces responses that increase the ability of the microenvironment to sustain the growing mass, for example, angiogenesis, but cancer cells can have varying sensitivities to these sustainability signals. Here, we show that these sensitivities are significant determinants of ultimate tumor fate, especially in response to treatments and immune interactions. We present a mathematical model of cancer-immune interactions that modifies generalized logistic growth with both immune-predation and immune-recruitment. The role of a growing environmental carrying capacity is discussed as a possible regulatory mechanism for tumor growth, and this regulation is shown to modify cancer-immune interactions and the possibility of achieving immune-induced tumor dormancy. This mathematical model qualitatively matches experimental observations of immune-induced tumor dormancy as it predicts dormancy as a transient period of growth that necessarily ends in either tumor elimination or tumor escape. As dormant tumors may exist asymptomatically and may be easier to treat with conventional therapy, an understanding of the mechanisms behind tumor dormancy may lead to new treatments aimed at prolonging the dormant state or converting an aggressive cancer to the dormant state.

Immunoediting: evidence of the multifaceted role of the immune system in self-metastatic tumor growth

Background

The role of the immune system in tumor progression has been a subject for discussion for many decades. Numerous studies suggest that a low immune response might be beneficial, if not necessary, for tumor growth, and only a strong immune response can counter tumor growth and thus inhibit progression.

Methods

We implement a cellular automaton model previously described that captures the dynamical interactions between the cancer stem and non-stem cell populations of a tumor through a process of self-metastasis. By overlaying on this model the diffusion of immune reactants into the tumor from a peripheral source to target cells, we simulate the process of immune-system-induced cell kill on tumor progression.

Results

A low cytotoxic immune reaction continuously kills cancer cells and, although at a low rate, thereby causes the liberation of space-constrained cancer stem cells to drive self-metastatic progression and continued tumor growth. With increasing immune system strength, however, tumor growth peaks, and then eventually falls below the intrinsic tumor sizes observed without an immune response. With this increasing immune response the number and proportion of cancer stem cells monotonically increases, implicating an additional unexpected consequence, that of cancer stem cell selection, to the immune response.

Conclusions

Cancer stem cells and immune cytotoxicity alone are sufficient to explain the three-step “immunoediting” concept – the modulation of tumor growth through inhibition, selection and promotion.

Fine-tuning anti-tumor immunotherapies via stochastic simulations

BACKGROUND

Anti-tumor therapies aim at reducing to zero the number of tumor cells in a host within their end or, at least, aim at leaving the patient with a sufficiently small number of tumor cells so that the residual tumor can be eradicated by the immune system. Besides severe side-effects, a key problem of such therapies is finding a suitable scheduling of their administration to the patients. In this paper we study the effect of varying therapy-related parameters on the final outcome of the interplay between a tumor and the immune system.

RESULTS

This work generalizes our previous study on hybrid models of such an interplay where interleukins are modeled as a continuous variable, and the tumor and the immune system as a discrete-state continuous-time stochastic process. The hybrid model we use is obtained by modifying the corresponding deterministic model, originally proposed by Kirschner and Panetta. We consider Adoptive Cellular Immunotherapies and Interleukin-based therapies, as well as their combination. By asymptotic and transitory analyses of the corresponding deterministic model we find conditions guaranteeing tumor eradication, and we tune the parameters of the hybrid model accordingly. We then perform stochastic simulations of the hybrid model under various therapeutic settings: constant, piece-wise constant or impulsive infusion and daily or weekly delivery schedules.

CONCLUSIONS

Results suggest that, in some cases, the delivery schedule may deeply impact on the therapy-induced tumor eradication time. Indeed, our model suggests that Interleukin-based therapies may not be effective for every patient, and that the piece-wise constant is the most effective delivery to stimulate the immune-response. For Adoptive Cellular Immunotherapies a metronomic delivery seems more effective, as it happens for other anti-angiogenesis therapies and chemotherapies, and the impulsive delivery seems more effective than the piece-wise constant. The expected synergistic effects have been observed when the therapies are combined.