Detailed, mechanistic models of immune cell behavior across multiple scales in the context of cancer provide clinically relevant insights needed to understand existing immunotherapies and develop more optimal treatment strategies. We highlight mechanistic models of immune cells and their ability to become activated and promote tumor cell killing. These models capture various aspects of immune cells: (a) single‐cell behavior by predicting the dynamics of intracellular signaling networks in individual immune cells, (b) multicellular interactions between tumor and immune cells, and (c) multiscale dynamics across space and different levels of biological organization. Computational modeling is shown to provide detailed quantitative insight into immune cell behavior and immunotherapeutic strategies. However, there are gaps in the literature, and we suggest areas where additional modeling efforts should be focused to more prominently impact our understanding of the complexities of the immune system in the context of cancer. This article is categorized under: Biological Mechanisms > Cell Signaling Models of Systems Properties and Processes > Mechanistic Models Models of Systems Properties and Processes > Cellular Models

Natural killer (NK) cells are innate immune effector cells that play an immediate role in host defense. NK cells contain a variety of stimulatory pathways that induce the release of cytotoxic chemicals when activated. Mathematical modeling of such pathways can inform us about the magnitude and kinetics of activation. This, in turn, can provide insight for NK cell-based therapies. To quantitatively understand the differences between three main stimulatory pathways in NK cells (CD16, 2B4 and NKG2D), we developed a mathematical model that mechanistically describes their intracellular signaling dynamics. In particular, the model predicts the dynamics of the phosphorylated receptors, pSFK, pErk, pAkt and pPLC , as these species contribute to cell activation. The model was fit to published experimental data and validated with separate experimental measurements. Modeling simulations show that the CD16 pathway exhibits rapid activation kinetics for all species, and co-stimulation of CD16 with either NKG2D or 2B4 induces the greatest magnitude of activation. Moreover, the magnitude of cell activation under co-stimulation is more sensitive to CD16 stimulation than either 2B4 or NKG2D stimulation. Overall, the model predicts CD16 stimulation is more influential in cell activation. These modeling results complement ongoing experimental work that applies CD16 stimulation for therapeutic purposes. IntroductionMathematical modeling of signal transduction pathways provides a framework that enables better cell engineering approaches. Indeed, many models have augmented our understanding of biological processes (Bellouquid and CH-Chaoui, 2014; Eftimie et al., 2016; Pappalardo et al., 2012) by generating quantitative detail and actionable insight. As an example, researchers investigating the EGFR pathway in an in silico cancer cell model demonstrated that inhibition of multiple upstream processes significantly attenuates signal propagation (Araujo et al., 2005). These findings would later support the use of multi-kinase inhibitors as a potential cancer therapeutic (Gridelli et al., 2007;Zhou, 2012). Despite such advances, a few areas of biology provide new opportunities to be explored by quantitative, engineering-based computational models (Baxter and Hodgkin, 2002). Immunology is one example, and in particular, tumor immunology can benefit from robust computational modeling. Recently, the advent of cancer immunotherapy (Bollino and Webb, 2017; Klingemann, 2005) has engendered a new hope for cancer patients and their families. In fact, immunotherapy is meritoriously considered a breakthrough therapeutic approach in the clinic, especially as an effective treatment for hematological cancers (Gattinoni et al., 2006; Mellman et al., 2011;Rosenberg et al., 2004). Ongoing work is aimed at achieving similar success for solid tumors. Mechanistic models of tumor-immune cell interactions can help identify new strategies and potentially enhance the success rate of immunotherapies against solid tumors.

Natural killer (NK) cells are part of the innate immune system and are capable of killing diseased cells. As a result, NK cells are being used for adoptive cell therapies for cancer patients. The activation of NK cell stimulatory receptors leads to a cascade of intracellular phosphorylation reactions, which activates key signaling species that facilitate the secretion of cytolytic molecules required for cell killing. Strategies that maximize the activation of such intracellular species can increase the likelihood of NK cell killing upon contact with a cancer cell and thereby improve efficacy of NK cell-based therapies. However, due to the complexity of intracellular signaling, it is difficult to deduce a priori which strategies can enhance species activation. Therefore, we constructed a mechanistic model of the CD16, 2B4 and NKG2D signaling pathways in NK cells to simulate strategies that enhance signaling. The model predictions were fit to published data and validated with a separate dataset. Model simulations demonstrate strong network activation when the CD16 pathway is stimulated. The magnitude of species activation is most sensitive to the receptor’s initial concentration and the rate at which the receptor is activated. Co-stimulation of CD16 and NKG2D in silico required fewer ligands to achieve half-maximal activation than other combinations, suggesting co-stimulating these pathways is most effective in activating the species. We applied the model to predict the effects of perturbing the signaling network and found two strategies that can potently enhance network activation. When the availability of ligands is low, it is more influential to engineer NK cell receptors that are resistant to proteolytic cleavage. In contrast, for high ligand concentrations, inhibiting phosphatase activity leads to sustained species activation. The work presented here establishes a framework for understanding the complex, nonlinear aspects of NK cell signaling and provides detailed strategies for enhancing NK cell activation.

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Natural killer (NK) cells are immune effector cells that can detect and lyse cancer cells. However, NK cell exhaustion, a phenotype characterized by reduced secretion of cytolytic models upon serial stimulation, limits the NK cell's ability to lyse cells. In this work, we investigated in silico strategies that counteract the NK cell's reduced secretion of cytolytic molecules. To accomplish this goal, we constructed a mathematical model that describes the dynamics of the cytolytic molecules granzyme B (GZMB) and perforin-1 (PRF1) and calibrated the model predictions to published experimental data using a Bayesian parameter estimation approach. We applied an information-theoretic approach to perform a global sensitivity analysis, from which we found that the suppression of phosphatase activity maximizes the secretion of GZMB and PRF1. However, simply reducing the phosphatase activity is shown to deplete the cell's intracellular pools of GZMB and PRF1. Thus, we added a synthetic Notch (synNotch) signaling circuit to our baseline model as a method for controlling the secretion of GZMB and PRF1 by inhibiting phosphatase activity and increasing production of GZMB and PRF1. We found that the optimal synNotch system depends on the frequency of NK cell stimulation. For only a few rounds of stimulation, the model predicts that inhibition of phosphatase activity leads to more secreted GZMB and PRF1; however, for many rounds of stimulation, the model reveals that increasing production of the cytolytic molecules is the optimal strategy. In total, we developed a mathematical framework that provides actionable insight into engineering robust NK cells for clinical applications.

Natural killer (NK) cells are immune effector cells that can detect and lyse cancer cells. However, NK cell exhaustion, a phenotype characterized by reduced secretion of cytolytic models upon serial stimulation, limits the NK cell’s ability to lyse cells. In this work, we investigated in silico strategies that counteract the NK cell’s reduced secretion of cytolytic molecules. To accomplish this goal, we constructed a mathematical model that describes the dynamics of the cytolytic molecules granzyme B (GZMB) and perforin-1 (PRF1) and calibrated the model predictions to published, experimental data using a Bayesian parameter estimation approach. We applied an information-theoretic approach to perform a global sensitivity analysis, from which we found the suppression of phosphatase activity maximizes the secretion of GZMB and PRF1. However, simply reducing the phosphatase activity is shown to deplete the cell’s intracellular pools of GZMB and PRF1. Thus, we added a synthetic Notch (synNotch) signaling circuit to our baseline model as a method for controlling the secretion of GZMB and PRF1 by inhibiting phosphatase activity and increasing production of GZMB and PRF1. We found the optimal synNotch system depends on the frequency of NK cell stimulation. For only a few rounds of stimulation, the model predicts inhibition of phosphatase activity leads to more secreted GZMB and PRF1; however, for many rounds of stimulation, the model reveals that increasing production of the cytolytic molecules is the optimal strategy. In total, we developed a mathematical framework that provides actionable insight into engineering robust NK cells for clinical applications.

Natural killer (NK) cells are innate immune effector cells that play an immediate role in host defense by releasing cytotoxic chemicals upon activation. A better understanding of the mechanisms regulating NK cell activation can improve NK cell-based therapies. However, due to the diversity of stimulatory pathways, each with a complex network of signaling species, a systems biology approach is required to understand NK cell activation. We constructed a mathematical model that mechanistically describes the signaling network of CD16, 2B4 and NKG2D. The model was fit to published experimental data and validated with a separate dataset. Baseline model predictions demonstrate that CD16 and NKG2D are qualitatively similar in that they activate the downstream species to a greater degree and at a faster rate when compared to 2B4. Contrastingly, 2B4 activates the signaling species over a longer time interval. In silico pairwise co-stimulation of the receptors, using various ligand concentrations, preferentially impacts the kinetics of species activation: the species are activated faster but the time interval of species activation becomes shorter as more ligands are introduced. Perturbing the stimulatory pathways by altering kinase (activator) and phosphatase (inhibitor) activity, highlights the phosphatases’ predominant control of the network and shows that decreasing their level of activity greatly improves the rate of species activation. Thus, the model predicts (1) qualitative differences between the pathways, (2) increasing receptor stimulation impacts the kinetics of species activation and (3) inhibiting the inhibitor significantly augments signal transduction. This insight can help design NK cell immunotherapies.