  The critical role of energy consumption in biological systems including T
cell discrimination process has been investigated in various ways. The kinetic
proofreading(KPR) in T cell recognition involving different levels of energy
dissipation influences functional outcomes such as error rates and specificity.
In this work, we study quantitatively how the energy cost influences error
fractions, sensitivity, specificity, kinetic speed in terms of Mean First
Passage Time(MFPT) and adaption errors. These provide the background to
adequately understand T cell dynamics. It is found that energy plays a central
role in the system that aims to achieve minimum error fractions and maximum
sensitivity and specificity with the fastest speed under our kinetic scheme for
which numerical values of kinetic parameters are specially chosen, but such a
condition can be broken with varying data. Starting with the application of
steady state approximation(SSA) to the evaluation of the concentration of each
complex produced associated with KPR, which is used to quantify various
observables, we present both analytical and numerical results in detail.
