  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 semi-empirical Hamiltonian. For configurations sampled
from this simulation, we study the free energy of replacing Zn(II) with Fe(II),
Co(II), and Ni(II) using density functional theory. The calculated
selectivities are in fair agreement with experimental results.
