We present a new model to describe DNA interactions with large ligands such as proteins, based on a quenched-disorder equation for ligand binding along the double helix and on Manning's description for the local changes of the persistence length at the binding sites. Such a model allows one to extract the physical chemistry of the interactions from pure mechanical measurements, such as those typically performed with DNA-protein complexes in force spectroscopy assays. We have tested the proposed methodology here to investigate the DNA interaction with the protein lysozyme, determining binding parameters such as the equilibrium association constant, the cooperativity degree of the binding reaction, and the fraction of neutralized charges on the phosphate backbone. The model also allows one to get information on the size and positional conformation of the bound proteins.