On the kinetics and optimal specificity of cytotoxic reactions mediated by T-lymphocyte clones

ROLE OF CYTOTOXIC T-LYMPHOCYTES IN TUMOR STABILITY: A PREY-PREDATOR MODELING APPROACH

We present and analyze a three-species mathematical model of tumor progression and regression using prey-predator dynamics. The tumor cell population is supposed to be the prey species and the cytotoxic T-lymphocytes (CTL) and macrophages (which are killer cells of the immune system) as their predator. Using a ratio-dependent predation functional form, the ODE model is analyzed for stability criteria. A discrete time delay required for destruction of tumor cells is then incorporated into the basic model and the resulting delayed model is studied to explore the significance of various system parameters controlling the stability of the system. The active killer cells are shown to be the key population species controlling the system dynamics. A range of the delay parameter is estimated that ensures stability of different system components. Numerical simulations are performed to support analytical findings.

Kinetics of T lymphocyte responses to persistent antigens

Long term sequential study of immune responses in the same individuals is difficult from the time commitment required and the problem of maintaining enough subjects to provide for comparative analysis. We closely studied one hundred women with silicone mammary devices through cross sectional analysis up to 26 years post implantation and a similar sample of women to 6 years post explantation. The T cell index, calculated from tritiated thymidine incorporation during lymphoblast transformation, rose to a post implant peak at 10.5-12.0 years, falling progressively over the next 14.0-15.5 years to values indicative of probable immune quiescence. Post explantation, the index rose over the first 3 years and then sharply declined to within the range for unexposed controls. The shape of these time curves contains considerable information referent cell dynamics for both stimulatory and inhibitory factors and for demonstrating net group effects, appropriate to analysis in the cross sectional perspective. When a subset of four women was studied frequently and sequentially up to 8 years, an internal oscillatory pattern emerged, focusing attention on both the stimulatory and the inhibitory aspects of long term clonal expansion. IL-2 has stimulatory and inhibitory properties at different levels of production and is considered a prime candidate as the essential cytokine. The equations have details, however, which require exploration beyond any such provisional conclusion. The analytic process was aided by normalization of oscillatory data to eliminate subject variability and by Pareto optimization to assess the trend shown by normalization. Pareto analysis revealed two minimally coordinated oscillations, one over time and the other along net clonal expansion or decline of the siloxane specific T lymphocyte clone. The segments of the time related oscillation greatly exceeded the reaction times of cytokines currently known to be active in T cell regulation. Although the ultimate controlling factor(s) may be cytokine or chemokine combinations, the data are compatible with some more basic regulatory factor(s) of cell integrity, including limits on the number of cell divisions which can be sustained in long term immunopathic lesions, among other processes.

Nonlinear dynamics of immunogenic tumors: parameter estimation and global bifurcation analysis

We present a mathematical model of the cytotoxic T lymphocyte response to the growth of an immunogenic tumor. The model exhibits a number of phenomena that are seen in vivo, including immunostimulation of tumor growth, "sneaking through" of the tumor, and formation of a tumor "dormant state". The model is used to describe the kinetics of growth and regression of the B-lymphoma BCL1 in the spleen of mice. By comparing the model with experimental data, numerical estimates of parameters describing processes that cannot be measured in vivo are derived. Local and global bifurcations are calculated for realistic values of the parameters. For a large set of parameters we predict that the course of tumor growth and its clinical manifestation have a recurrent profile with a 3- to 4-month cycle, similar to patterns seen in certain leukemias.