title: Cluster formation in a symmetrical network: a dynamical system for the description of the suppression among non-immune T lymphocytes and its application to the effects of immunization.
abstract: A mathematical model has been developed for the description of the suppressive regulation between polyclonally activated normal and immune T cells. The model assumes reversible cell-cell interactions to interpret results from limiting dilution experiments performed to determine the frequencies of precursor cells for antigen-specific T effector lymphocytes and to analyse mechanisms regulating the maturation of precursor into effector T cells. In particular, the model deals with the changes induced in the T lymphocytes population following immunization with antigens. In these limiting dilution experiments, T cells are placed in cultures at varying cell numbers with all other essential culture constituents kept in excess. After polyclonal activation of the T cells in culture they are supplied with growth and maturation factors so that they form daughter clones of functionally active T effector cells. The typical result observed was that effector T cells develop in cultures at low cell input but that this development is totally suppressed at high cell numbers. This result suggested that, at high cell numbers, the effector T cells are exposed to a sufficient number of other T cells of appropriate specificity to permit suppressive interactions. Whereas this is the case for non-immune T cells, T cells after immunization develop into effector cells both at high as well as at low cell concentrations, though with efficiencies less than proportional to their number of precursors. Our mathematical model is made up of a set of first order autonomous ordinary differential equations in many variables permitting the calculations of numbers of free cells and of cells engaged in cellular clusters of varying sizes. Free cells can develop into effector cells whereas cells engaged in clusters cannot. We calculate the consequences of several reasonable hypotheses concerning the effects of immunization. We consider the possibility that immunization modifies the growth behavior of the antigen-specific cells to permit an increased or accelerated clonal expansion in culture. Alternatively, we consider the possibility that immunization changes the interaction strength between cells specific for the immunizing antigen and other cells. Thirdly, we have connected both behaviors by calculating the case of an inverse relationship between growth rates and intensities of interaction between cells. Our model has been inspired by the symmetrical network model and can be interpreted in this framework. It proposes that immune regulation is a consequence of idiotype-anti-idiotype interactions.(ABSTRACT TRUNCATED AT 400 WORDS)
mesh_terms: D000818:Animals; D002455:Cell Division; D002478:Cells, Cultured; D007114:Immunization; D007165:Immunosuppression Therapy; D051379:Mice; D008954:Models, Biological; D013601:T-Lymphocytes / Q000276:immunology*