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

Abstract

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.

Appendices

Appendix 1

See Fig. 6.

Fig. 6

Results of the data fitting: predicted tumor growth curves are shown over-laid with the experimental data for both antitumor and pro-tumor parameter set ensembles. Values of the parameters for each set are listed in Table 1 (Color figure online)

Appendix 2

See Fig. 7.

Fig. 7

Box plots showing the variability in the pro-tumor and antitumor parameter ensembles. Parameter values are rescaled for easier comparison by the normalization formula: $x_i \rightarrow \frac{x_i -\mu _x }{\sigma _x }$ where $\mu _x$ is the average, and $\sigma _x$ is the standard deviation, of the set of values for parameter x (Color figure online)

Appendix 3

See Fig. 8.

Fig. 8

Cancer–immune phase portraits demonstrate the variability across the 10 parameter sets in the antitumor (a) and pro-tumor (b) immunity ensembles (values listed in Table 1). Tumors are simulated to grow from an initial injection of $C_0 =10^{4}$ cancer cells and varying numbers of immune cells $(I_0 =\gamma C_0 )$. The ranges (values of $\gamma )$ that divide the behavior between tumor growth (red) or tumor suppression (blue) are listed below the plots. Simulations result from solving the full system of equations (1)–(4) with direct predation through $\varPsi$, Eq. (5). Axes indicate diameter of spherical population in mm (Color figure online)