Molecular dynamics simulations and free energy calculations of the wild-type EcoRI-DNA complex and several variants have been performed in aqueous solvent. In general, he theoretical estimations of the free energy differences (DeltaDeltaA) qualitatively agree well with the corresponding experimental data. The modifications which were experimentally found unfavorable compared to the wild-type complex were also found to be so in theoretical estimates. The mutant where the amino group of the base Ade(6) was replaced by a hydrogen atom eliminating one H-bond between the DNA and the protein, was experimentally found to be more stable than the wild-type complex. It was speculated that the modification also caused a structural relaxation in the DNA making DeltaDeltaA favorable. Our theoretical estimate yields a positive DeltaDeltaA in this case, but the difference is small, and no significant local structural relaxation was observed. The major H-bonds between the DNA and the protein in the wild-type complex are found to be maintained in the different mutants although the specific and non-specific interaction energies between the interacting the DNA bases and the protein residues are different in different mutants. The interaction pattern of the other nearby nucleotides are significantly influenced by each modification. Thus, the alteration of the non-specific interactions may also play an indirect role in determining the specificity of the complex. The interaction of the Gua(4) of the DNA with the protein is found to be most sensitive to any alteration in the recognition site. Because Gua(4) is the nucleotide closest to the scissile bond, this extra sensitivity seems to play an important role in altering the functional activity of the complex.