  In this paper we study a simple stochastic version of the Hopfield-Ninio
kinetic proofreading model. The model is characterized by means of two
parameters, the unbinding time, which depends on the binding energy between a
ligand and a receptor, and the number of times $M \geq 1$ that a ligand
attaches to a receptor. We prove that, under suitable assumptions on M, our
model has an extreme specificity, i.e. it is capable to discriminate between
different ligands, and a high sensitivity, i.e. the response of the system does
not change in a significant manner for ranges of ligands varying within several
orders of magnitude. Additional quantities like the amount of energy used by
the network or the time required to yield a response will be also computed. We
also show that our results are robust, i.e., they do not depend on the specific
choice of parameters that we make in this paper.
