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

Treatment of melanoma with dendritic cell vaccines and immune checkpoint inhibitors: A mathematical modeling study

Dendritic cell (DC) vaccines and immune checkpoint inhibitors (ICIs) play critical roles in shaping the immune responses of tumor cells (TCs) and are widely used in cancer immunotherapies. Quantitatively evaluating the effectiveness of these therapies are essential for the optimization of treatment strategies. Here, based on the combined therapy of melanoma with DC vaccines and ICIs, we formulated a mathematical model to investigate the dynamic interactions between TCs and the immune system and understand the underlying mechanisms of immunotherapy. First, we obtained a threshold parameter for the growth of TCs, which is given by the ratio of spontaneous proliferation to immune inhibition. Next, we proved the existence and locally asymptotic stability of steady states of tumor-free, tumor-dominant, and tumor-immune coexistent equilibrium, and identified the existence of Hopf bifurcation of the proposed model. Furthermore, global sensitivity analysis showed that the growth of TCs strongly correlates with the injection rate of DC vaccines, the activation rate of CTLs, and the killing rate of TCs. Finally, we tested the efficacy of multiple monotherapies and combined therapies with model simulations. Our results indicate that DC vaccines can decelerate the growth of TCs, and ICIs can inhibit the growth of TCs. Besides, both therapies can prolong the lifetime of patients, and the combined therapy of DC vaccines and ICIs can effectively eradicate TCs.

ZNF92, an unexplored transcription factor with remarkably distinct breast cancer over-expression associated with prognosis and cell-of-origin

Tumor phenotype is shaped both by transforming genomic alterations and the normal cell-of-origin. We identified a cell-of-origin associated prognostic gene expression signature, ET-9, that correlates with remarkably shorter overall and relapse free breast cancer survival, 8.7 and 6.2 years respectively. The genes associated with the ET-9 signature are regulated by histone deacetylase 7 (HDAC7) partly through ZNF92, a previously unexplored transcription factor with a single PubMed citation since its cloning in 1990s. Remarkably, ZNF92 is distinctively over-expressed in breast cancer compared to other tumor types, on a par with the breast cancer specificity of the estrogen receptor. Importantly, ET-9 signature appears to be independent of proliferation, and correlates with outcome in lymph-node positive, HER2+, post-chemotherapy and triple-negative breast cancers. These features distinguish ET-9 from existing breast cancer prognostic signatures that are generally related to proliferation and correlate with outcome in lymph-node negative, ER-positive, HER2-negative breast cancers. Our results suggest that ET-9 could be also utilized as a predictive signature to select patients for HDAC inhibitor treatment.

A Mathematical Model of the Dynamics of Cytokine Expression and Human Immune Cell Activation in Response to the Pathogen Staphylococcus aureus

Cell-based mathematical models have previously been developed to simulate the immune system in response to pathogens. Mathematical modeling papers which study the human immune response to pathogens have predicted concentrations of a variety of cells, including activated and resting macrophages, plasma cells, and antibodies. This study aims to create a comprehensive mathematical model that can predict cytokine levels in response to a gram-positive bacterium, S. aureus by coupling previous models. To accomplish this, the cytokines Tumor Necrosis Factor Alpha (TNF-α), Interleukin 6 (IL-6), Interleukin 8 (IL-8), and Interleukin 10 (IL-10) are included to quantify the relationship between cytokine release from macrophages and the concentration of the pathogen, S. aureus, ex vivo. Partial differential equations (PDEs) are used to model cellular response and ordinary differential equations (ODEs) are used to model cytokine response, and interactions between both components produce a more robust and more complete systems-level understanding of immune activation. In the coupled cellular and cytokine model outlined in this paper, a low concentration of S. aureus is used to stimulate the measured cellular response and cytokine expression. Results show that our cellular activation and cytokine expression model characterizing septic conditions can predict ex vivo mechanisms in response to gram-negative and gram-positive bacteria. Our simulations provide new insights into how the human immune system responds to infections from different pathogens. Novel applications of these insights help in the development of more powerful tools and protocols in infection biology.

Space-velocity thermostatted kinetic theory model of tumor growth

The competition between cancer cells and immune system cells in inhomogeneous conditions is described at cell scale within the framework of the thermostatted kinetic theory. Cell learning is reproduced by increased cell activity during favorable interactions. The cell activity fluctuations are controlled by a thermostat. The direction of cell velocity is changed according to stochastic rules mimicking a dense fluid. We develop a kinetic Monte Carlo algorithm inspired from the direct simulation Monte Carlo (DSMC) method initially used for dilute gases. The simulations generate stochastic trajectories sampling the kinetic equations for the distributions of the different cell types. The evolution of an initially localized tumor is analyzed. Qualitatively different behaviors are observed as the field regulating activity fluctuations decreases. For high field values, i.e. efficient thermalization, cancer is controlled. For small field values, cancer rapidly and monotonously escapes from immunosurveillance. For the critical field value separating these two domains, the 3E's of immunotherapy are reproduced, with an apparent initial elimination of cancer, a long quasi-equilibrium period followed by large fluctuations, and the final escape of cancer, even for a favored production of immune system cells. For field values slightly smaller than the critical value, more regular oscillations of the number of immune system cells are spontaneously observed in agreement with clinical observations. The antagonistic effects that the stimulation of the immune system may have on oncogenesis are reproduced in the model by activity-weighted rate constants for the autocatalytic productions of immune system cells and cancer cells. Local favorable conditions for the launching of the oscillations are met in the fluctuating inhomogeneous system, able to generate a small cluster of immune system cells with larger activities than those of the surrounding cancer cells.

Breast cancer dormancy: need for clinically relevant models to address current gaps in knowledge

Breast cancer is the most commonly diagnosed cancer in the USA. Although advances in treatment over the past several decades have significantly improved the outlook for this disease, most women who are diagnosed with estrogen receptor positive disease remain at risk of metastatic relapse for the remainder of their life. The cellular source of late relapse in these patients is thought to be disseminated tumor cells that reactivate after a long period of dormancy. The biology of these dormant cells and their natural history over a patient's lifetime is largely unclear. We posit that research on tumor dormancy has been significantly limited by the lack of clinically relevant models. This review will discuss existing dormancy models, gaps in biological understanding, and propose criteria for future models to enhance their clinical relevance.

Spatio-temporal aspects of the interplay of cancer and the immune system

The conventional mean-field kinetic models describing the interplay of cancer and the immune system are temporal and predict exponential growth or elimination of the population of tumour cells provided their number is small and their effect on the immune system is negligible. More complex kinetics are associated with non-linear features of the response of the immune system. The generic model presented in this communication takes into account that the rates of the birth and death of tumour cells inside a tumour spheroid can significantly depend on the radial coordinate due to diffusion limitations in the supply of nutrients and/or transport of the species (cells and proteins) belonging to the immune system. In this case, non-trivial kinetic regimes are shown to be possible even without appreciable perturbation of the immune system.