  In order to produce specific complex structures from a large set of similar
biochemical building blocks, many biochemical systems require high sensitivity
to small molecular differences. The first and most common model used to explain
this high specificity is kinetic proofreading, which has been extended to a
variety of systems from detection of DNA mismatch to cell signaling processes.
While the specification properties of the kinetic proofreading model are well
known and were studied in various contexts, very little is known about its
temporal behavior. In this work, we study the dynamical properties of discrete
stochastic two branch kinetic proofreading schemes. Using the Laplace transform
of the corresponding chemical master equation, we obtain an analytical solution
for the completion time distribution. In particular we provide expressions for
the specificity and the mean and the variance of the process completion times.
We also show that, for a wide range of parameters a process distinguishing
between two different products can be reduced to a much simpler three point
process. Our results allow for the systematic study of the interplay between
specificity and completion times as well as testing the validity of the kinetic
proofreading model in biological systems.
