  The article analyzes the contribution of stochastic thermal fluctuations in
the attachment times of the immature T-cell receptor TCR:
peptide-major-histocompatibility-complex pMHC immunological synapse bond. The
key question addressed here is the following: how does a synapse bond remain
stabilized in the presence of high frequency thermal noise that potentially
equates to a strong detaching force? Focusing on the average time persistence
of an immature synapse, we show that the high frequency nodes accompanying
large fluctuations are counterbalanced by low frequency nodes that evolve over
longer time periods. Our analysis shows that such a behavior could be easily
explained from the fact that the survival probability distribution is governed
by two distinct phases, for the two different time regimes. The relatively
shorter time scales correspond to the cohesion:adhesion induced immature bond
formation whereas the larger time reciprocates the association:dissociation
regime leading to TCR:pMHC signaling. From an estimation of the bond survival
probability, we show that at shorter time scales, this probability
$P_{\Delta}(\tau)$ scales with time $\tau$ as an universal function of a
rescaled noise amplitude $\frac{D}{\Delta^2}$, such that $P_{\Delta}(\tau)\sim
\tau^{-(\frac{\Delta}{\sqrt{D}}+\frac{1}{2})}$, $\Delta$ being the distance
from the mean inter-membrane (T cell:Antigen Presenting Cell) separation
distance. The crossover from this shorter to a longer time regime leads to an
universality in the dynamics, at which point the survival probability shows a
different power-law scaling compared to the one at shorter time scales. In
biological terms, such a crossover indicates that the TCR:pMHC bond has a
survival probability with a slower decay rate than the longer LFA-1:ICAM-1 bond
justifying its stability.
