A kinetic approach to the immunology of cancer: stationary states properties of effector-target cell reactions.

We present a kinetic model of the onset of a tumor which involves the coupling of three principal phenomena: 1. (1) the transformation of normal into neoplastic cells, 2. (2) the replication of transformed cells, 3. (3) the immunological interaction of the host organism with transformed cells and/or oncogenic viruses. We assume that the immunological component has two opposite (destructing and facilitating) functions, each of which is regulated by activators and inhibitors. In this paper our analysis is devoted to the cell-mediated neoplastic cell destruction and its negative regulation by blocking factors or by other immunosuppressive agents. We assume that the immunological system may reach different stationary states (nonactivated, activated, suppressed, etc.). In each of these immunological stationary states, Michaelian-like kinetics for the cell-mediated cytotoxic reaction allow to describe the homogeneous stationary states of the neoplastic cell population in term of three adimensional parameters: (1) α, which represents the relative rate of cellular transformation; (2) β, which characterizes the relative rate of neoplastic cell destruction, and (3) θ, α parameter whose value determines the presence of a metastable region for the neoplastic transition of the tissue. The application of our model to the kinetic analysis of the immunological rejection of MSV-M induced tumors confirms our kinetic hypotheses and predicts the minimum ratio of aggressor to target cells that must be reached within the tumor mass to obtain a rejection. Since during rejection this level is not attained with the immune T-cells, we suggest additional co-operative mechanisms involving antibodies and other effector cell types. In the framework of our model we propose the following conclusions: 1. (1) Under physiological conditions tissues contain at least, one neoplastic cell to 1014–1018 normal cells, suggesting that they are exempted from neoplastic cells. 2. (2) The cell to cell cytotoxic activity of the different types of effectors seems to increase in the order: activated macrophages < immune T lymphocytes and natural activity of T lymphocytes. 3. (3) Whereas the cytotoxic activity of T lymphocytes is sufficiently high to cope with allogenic tumor rejection, in syngeneic tumor systems a complex interaction between differejnt effector cells and humoral factors must certainly take place in order to obtain a successful surveillance against cancer. 4. (4) The transition of normal to neoplastic tissues may bear some analogy with metastability phenomena.