Before revision:  We find the expressions for average length of binding  (the number of monomers at the chain ends that form bonds) and the critical tube diameter at which such constrained binding occurs  .
After revision:  We find the expressions for average length of binding (the number of monomers at the chain ends that form bonds) and the critical tube diameter at which such constrained binding occurs . We carry out Brownian dynamics simulations of tightly confined chains, demonstrating their binding over the characteristic length m*, changing in tubes of different diameter .