A computational model to measure the probability of T-cell activation by DCs. (A) Illustration of a simulation run with the computational model. DCs are represented as green spheres whose apparent size in the figure varies with depth. Trajectories of T cells are shown in red. (B) Probability of T cell-DC encounters as a function of time in the presence of 2 × 10⁴ DCs. ● represents results from the computational model. The theoretical formula (see supplemental Methods) is graphed for T-cell diffusion coefficients of D = 10 (green) and D = 50 μm^2. min⁻¹ (black). Diffusion coefficients of 10 and 50 have been measured for T cells migrating in inflamed and noninflamed lymph nodes, respectively. The rest of the simulation was performed with D = 10. (C) Probability of T cell-DC encounters as a function of DC numbers for a T cell residing 6, 12, or 24 hours in the lymph node. Values from the computational model (circles) and theoretical formula (lines) are graphed. (D) The probability that at least 1 T cell encounters a DC within 24 hours is shown as a function of DC number for distinct T-cell precursor frequencies. (E) The graph shows, for distinct T-cell precursor frequencies, the number of DCs yielding a 50% probability that at least 1 T cell encounters a DC in 24 hours.