Close Contact Fluctuations: Time of Contact

The letter resolves the long standing debate as to the proper time scale ($<\tau>$) of the onset of the immunological synapse (IS) bond, the non-covalent chemical bond defining the immune pathways involving T-cells and antigen presenting cells (APC). Results from our model calculations show $<\tau>$ to be of the order of seconds instead of minutes. Close to the linearly stable regime, we show that in between the two critical spatial thresholds defined by the integrin:ligand pair ($\Delta_2\sim$ 40-45 nm) and the T cell receptor (TCR):pMHC bond ($\Delta_1\sim$ 14-15 nm), $<\tau>$ grows monotonically with increasing co-receptor bond length separation $\delta$ (= $\Delta_2-\Delta_1\sim$ 26-30 nm) while $<\tau>$ decays with $\Delta_1$ for fixed $\Delta_2$. The non-universal $\delta$-dependent power-law structure of the probability density function (PDF) further explains why only the TCR:pMHC bond is a likely candidate to form a stable synapse.