Mathematical Modeling of Natural Killer Cell Proliferation in Response to Physiological Stimuli

Date of Award

Spring 5-15-2013

Author's Department

Biomedical Engineering

Degree Name

Doctor of Philosophy (PhD)

Degree Type



Natural killer (NK) cells are innate lymphocytes that provide early defense essential to host response against intracellular pathogens, such as viruses. Interleukin 15 (IL-15), upregulated during viral infection, is a key cytokine that modulates the development and proliferation of NK cells. Many molecules involved in the IL-15 signaling pathway have been identified as crucial components in NK cell response to viral infection in animal models. However, the IL-15 receptor mediated regulation of the stimulatory signal and its impact on NK cell proliferation have not been quantitatively characterized.

We adopted a mathematical model-guided approach to characterize the effects of cytokine and receptor interactions on NK cell proliferation. First, we used a differential equations-based model incorporating experimentally estimated parameters to analyze the kinetics of receptor interactions that modulate IL-15/IL-15 receptor complex signaling. Computational results show that the binding and internalization of the IL-15 receptors are the primary factors impacting receptor occupancy on the cell surface. The number of IL-15/ IL-15 receptor complexes on the cell surface was demonstrated to be the key determinant of the magnitude and duration of the proliferative signal. Furthermore, IL-15 receptor complexes functioned as effective surrogate measure of IL-15 receptor signaling.

After mathematically modeling the effects of IL-15 signaling at the level of individual cells, we expanded the scope of our computational analysis to examine IL-15's stimulatory effect on NK cells at the population level. We developed a series of two-compartment (representing quiescent and dividing NK cell subpopulations) mathematical models, incorporating different assumptions about the kinetic parameters regulating NK cell expansion. Using experimentally derived division and death rates, we tested each model's assumptions by comparing predictions of NK cell numbers with independent experimental results and demonstrated that the kinetic parameters are distinct for non-dividing and dividing NK cell subpopulations. IL-15 influenced NK cell expansion by modulating recruitment and division rates to a greater extent than death rates. The observed time delay to first division could be accounted for by differences in the kinetic parameters of non-dividing and dividing subsets of NK cells. Although the duration of the time delay to first division was not significantly influenced by IL-15, the recruitment of non-dividing NK cells into the replicating subpopulation increased with higher IL-15 concentrations.

We then united the receptor interaction and population expansion models into an integrated and comprehensive model framework that predicted how receptor kinetics regulated IL-15 signaling at the cell level manifests in NK cell population response.

Our modeling work delineated a quantitative cell cycle threshold that regulated NK cell entry and progression within the cell cycle. Model predictions of the threshold requirement for NK cell recruitment to the cell cycle and the subsequent exponential proliferation were verified by comparisons with data obtained from independent experiments.

In summary, our modeling analysis offers novel insight into the regulation of IL-15 driven NK cell proliferation and illustrates the power of combining computational analysis with experimental techniques in studying cell signaling. These findings provide a foundation for modeling in vivo NK cell responses to viral infections and the development of IL-15 based immunotherapy to modulate the proliferation of NK cells.


English (en)


Anthony R French

Committee Members

Kristen Naegle, Rohit Pappu, Heinz Schaettler


Permanent URL:

This document is currently not available here.