An elastic-network-based local molecular field analysis of zinc finger proteins

We study two designed and one natural zinc finger peptide each with the Cys₂His₂ (CCHH) type of metal binding motif. In the approach we have developed, we describe the role of the protein and solvent outside the Zn(II)-CCHH metal-residue cluster by a molecular field represented by generalized harmonic restraints. The strength of the field is adjusted to reproduce the binding energy distribution of the metal with the cluster obtained in a reference all-atom simulation with empirical potentials. The quadratic field allows us to investigate analytically the protein restraints on the binding site in terms of its eigenmodes. Examining these eigenmodes suggests, consistent with experimental observations, the importance of the first histidine (H) in the CCHH cluster in metal binding. Further, the eigenvalues corresponding to these modes also indicate that the designed proteins form a tighter complex with the metal. We find that the bulk protein and solvent response tends to destabilize metal binding, emphasizing that the favorable energetics of metal-residue interaction is necessary to drive folding in this system. The representation of the bulk protein and solvent response by a local field allows us to perform Monte Carlo simulations of the metal-residue cluster using quantum-chemical approaches, here using a semiempirical Hamiltonian. For configurations sampled from this simulation, we study the free energy of replacing Zn²⁺ with Fe²⁺, Co²⁺, and Ni ²⁺ using density functional theory. The calculated selectivities are in fair agreement with experimental results.