Competition for antigenic sites during T cell proliferation: a mathematical interpretation of in vitro data

Abstract

By fitting different mathematical T cell proliferation functions to in vitro T cell proliferation data, we studied T cell competition for stimulatory signals. In our lymphocyte proliferation assays both the antigen (Ag) availability and the concentration of T cells were varied. We show that proliferation functions involving T cell competition describe the data significantly better than classical proliferation functions without competition, thus providing direct evidence for T cell competition in vitro. Our mathematical approach allowed us to study the nature of T cell competition by comparing different proliferation functions involving (i) direct inhibitory T-T interactions, (ii) Ag-specific resource competition, or (iii) resource competition for nonspecific factors such as growth factors, and access to the surface of Ag-presenting cells (APCs). We show that resource competition is an essential ingredient of T cell proliferation. To discriminate between Ag-specific and nonspecific resource competition, the Ag availability was varied in two manners. In a first approach we varied the concentration of APCs, displaying equal ligand densities; in a second approach we varied the Ag density on the surface of the APCs, while keeping the APC concentration constant. We found that both resource competition functions described the data equally well when the Ag availability was increased by adding APCs. When the APC concentration was kept constant, the nonspecific resource competition function yielded the best description of the data. Our interpretation is that T cells were competing for "antigenic sites" on the APCs.

Figure 1

Proliferative responses of different concentrations of Z1a T cells in response to different concentrations of equally prepulsed APCs. Graphs compare experimental results (in symbols) and best theoretical fits (curves). The experimental data were fitted to the conventional saturation function without T cell competition (Eq. 1; a), the proliferation function involving inhibitory T–T interactions (Eq. 2; b), the Ag-specific resource competition function (Eq. 4; c), and the nonspecific resource competition function (Eq. 5; d). On the Left the data are expressed as total proliferative responses, whereas on the Right the same data are expressed as proliferative responses per T cell. Parameters of the theoretical curves are listed in Table 1.

Figure 2

Statistical comparison of the SSRs of the different proliferation functions of the first experimental approach, with SSRs in parentheses. Arrows represent different model extensions and are accompanied by the corresponding F values. Solid arrows denote model extensions that significantly improved the fit to the experimental data (F test, P < 0.001); dashed arrows denote extensions that did not lead to significantly better fits (P > 0.001). C represents the conventional saturation function without competition (Eq. 1), T the inhibitory T–T interaction function (Eq. 2), A the Ag-specific resource competition function (Eq. 4), and N the nonspecific resource competition function (Eq. 5). The proliferation function denoted by NA combines both forms of resource competition, AT combines Ag-specific competition and inhibitory T–T interactions, and NT combines nonspecific resource competition and inhibitory T–T interactions.

Figure 3

Proliferative responses of different concentrations of Z1a T cells in response to a standard concentration of APCs prepulsed with different concentrations of MBP 72–85_S79A. For details see the legend of Fig. 1.

Figure 4

Statistical comparison of the SSRs of the different proliferation functions of the second experimental approach. For details see the legend of Fig. 2.