  We describe and solve a discrete persistent chain model of protein binding on
DNA, involving an extra sigma_i s at a site i of the DNA. This variable takes
the value 1 or 0 depending on whether the site is occupied by a protein or not.
In addition, if the site is occupied by a protein, there is an extra energy
cost epsilon. For small force, we obtain analytic expressions for the
force-extension curve and the fraction of bound protein on the DNA.For higher
forces, the model can be solved numerically to obtain force extension curves
and the average fraction of bound proteins as a function of applied force. Our
model can be used to analyze experimental force extension curves of protein
binding on DNA, and hence deduce the number of bound proteins in the case of
non-specific binding.
