A lattice chain model is extended to investigate the preferential position of a sticky sphere bound to a polymer chain, motivated by wrapping one nanosize core-histone with DNA to form a nucleosome structure. It was shown that the single bound histone is populated in DNA chain ends from the experiment by T. Sakaue et al [Phys. Rev. Lett.87, 078105 (2001)]. Here, the possible mechanisms are examined to elucidate such behavior. For neutral chains or ionic chains in high salt concentrations, spheres bound on the middle of chain may trigger conformational constraints to reduce conformational entropy. For ionic chains, the bound sphere can be driven to chain ends if its effective charge and the charge of chain monomers are of like charge. The two-dimensional chain is further studied to mimic the chromosome strongly adsorbed onto surfaces, of which behavior is similar to the three-dimensional case with minor difference due to surface confinement.

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