Modulation of T cell activation by localized K⁺ accumulation at the immunological synapse--a mathematical model

The response of T cells to antigens (T cell activation) is marked by an increase in intracellular Ca²⁺ levels. Voltage-gated and Ca²⁺-dependent K⁺ channels control the membrane potential of human T cells and regulate Ca²⁺ influx. This regulation is dependent on proper accumulation of K⁺ channels at the immunological synapse (IS) a signaling zone that forms between a T cell and antigen presenting cell. It is believed that the IS provides a site for regulation of the activation response and that K⁺ channel inhibition occurs at the IS, but the underlying mechanisms are unknown. A mathematical model was developed to test whether K⁺ efflux through K⁺ channels leads to an accumulation of K⁺ in the IS cleft, ultimately reducing K⁺ channel function and intracellular Ca²⁺ concentration ([Ca²⁺](i)). Simulations were conducted in models of resting and activated T cell subsets, which express different levels of K⁺ channels, by varying the K⁺ diffusion constant and the spatial localization of K⁺ channels at the IS. K⁺ accumulation in the IS cleft was calculated to increase K⁺ concentration ([K⁺]) from its normal value of 5.0 mM to 5.2-10.0 mM. Including K⁺ accumulation in the model of the IS reduced calculated K⁺ current by 1-12% and consequently, reduced calculated [Ca²⁺](i) by 1-28%. Significant reductions in K⁺ current and [Ca²⁺](i) only occurred in activated T cell simulations when most K⁺ channels were centrally clustered at the IS. The results presented show that the localization of K⁺ channels at the IS can produce a rise in [K⁺] in the IS cleft and lead to a substantial decrease in K⁺ currents and [Ca²⁺](i) in activated T cells thus providing a feedback inhibitory mechanism during T cell activation.