Quantitative analysis of interleukin-2-induced proliferation in the presence of inhibitors using a mathematical model

Mathematical model for IL-2-based cancer immunotherapy

A basic mathematical model for IL-2-based cancer immunotherapy is proposed and studied. Our analysis shows that the outcome of therapy is mainly determined by three parameters, the relative death rate of CD4+ T cells, the relative death rate of CD8+ T cells, and the dose of IL-2 treatment. Minimal equilibrium tumor size can be reached with a large dose of IL-2 in the case that CD4+ T cells die out. However, in cases where CD4+ and CD8+ T cells persist, the final tumor size is independent of the IL-2 dose and is given by the relative death rate of CD4+ T cells. Two groups of in silico clinical trials show some short-term behaviors of IL-2 treatment. IL-2 administration can slow the proliferation of CD4+ T cells, while high doses for a short period of time over several days transiently increase the population of CD8+ T cells during treatment before it recedes to its equilibrium. IL-2 administration for a short period of time over many days suppresses the tumor population for a longer time before approaching its steady-state levels. This implies that intermittent administration of IL-2 may be a good strategy for controlling tumor size.

Empirical models of the proliferative response of cytokine-dependent hematopoietic cell lines

There is an expanding need for predictive mathematical models to accelerate the optimization of cell therapy culture processes. Here we demonstrate the ability of simple mathematical models to describe quantitatively the cytokine growth-rate dependence of two human hematopoietic cell lines, TF-1 and MO7e. These cells are immortal but depend on either interleukin-3 (IL-3) or granulocyte-macrophage colony stimulating factor (GM-CSF) for their continued survival and maximal proliferation. They are also responsive to interleukin-6 (IL-6) and exhibit saturation kinetics when these cytokines are limiting. A Monod-type relationship consistently failed to fit measured cytokine dose-proliferation response curves while a Hill-type relationship showed a good fit. Cytokine interactions were first modeled by modifying the Hill-function to include an interaction parameter, gamma. This model did not indicate either synergistic or even additive effects between IL-3 and GM-CSF. Based on the reported competition between IL-3 and GM-CSF for their common receptor (beta(c)) subunit, a competitive model was also developed. This model had no new parameters beyond those obtained from single cytokine cultures and provided improved prediction of the growth rates for both cell lines exposed to combinations of IL-3 and GM-CSF over a wide range of concentrations. As expected, the competitive model failed to fit the data for IL-6 in combination with either IL-3 or GM-CSF, since IL-6 signaling does not involve the beta(c) chain of the IL-3/GM-CSF receptors. Interestingly, the cell-specific rates of GM-CSF uptake and cell proliferation were found to be uncoupled processes. Taken together, these results illustrate the utility of appropriately designed empirical models to describe the proliferative responses of hematopoietic cells to cytokine stimulation.

Computational models in immunological methods: an historical review

The utilization of computational models in immunology dates from the birth of the science. From the description of antibody-antigen binding to the structural models of receptors, models are utilized to bring fundamental understandings of the processes together with laboratory measurements to uncover implications of these data. In this review, an historical view of the role of computational models in the immunology laboratory is presented, and short mathematical descriptions are given of fundamental assays. In addition, the range of current uses of models is explored -- especially as seen through papers which have appeared in the Journal of Immunological Methods from volume 1 (1971/1972) to volume 208 (1997). Each paper which introduced a new mathematical, statistical, or computer simulation model, or introduced an enhancement to an instrument through a model in those volumes is cited and the type of computational model noted.

Effects of retinoids on regulatory cellular interactions in primary mixed lymphocyte reaction (MLR)

The effects of two retinoids, all-trans-retinoic acid and 13-cis-retinoic acid on murine splenic lymphocyte proliferative response in mixed culture were evaluated. In contrast with previously reported absence of retinoic acid (RA) effect on mixed lymphocyte reaction (MLR) the conditions for a strong potentiation of proliferative response of murine lymphocytes with RA were obtained. Stimulatory cells were determined to be the main targets for RA. The data suggest that the RA potentiating effect is the result of an increase in stimulator cell immunogenicity after their pre-treatment with RA before use in MLR. Optimal potentiation by retinoids of proliferative response was found at non-optimal conditions of mixed culture.

Regulatory cellular interactions in the primary mixed lymphocyte reaction

Limiting dilution analysis (LDA) of allogeneic and syngeneic murine mixed lymphocyte reactions was used to study the heterogeneity both of the responding spleen cells and of the stimulating antigen-presenting dendritic cells (DC). In contrast with traditional LDA of single-hit processes, a non-linear dependence of the proportion of negative microcultures on responding spleen cell concentration was obtained. The non-linearity of this LDA plot was interpreted as being the result of a competitive interaction between two types of limiting precursor cells. The regulatory and stimulatory functions of DC were investigated in the same LDA systems by testing various levels of DC from spleen or thymus as limiting cells in the presence of a constant quantity of syngeneic splenic responder T cells. This revealed a functional heterogeneity amongst DC, which were found to suppress proliferation of responder cells at low DC levels but to stimulate proliferation at higher levels. At levels where splenic DC became stimulatory, thymic DC remained suppressive.