Background

Zinc(II) ions are commonly bound by proteins, link to nucleic acid recognision and binding. Zn²⁺ has 10 valence electrons, which warrants a tetrahedral coordination with four two-electron donors. Typically, these are (deprotonated) cysteines or histidines, sometimes can be alcohol sidechains or water. These moieties are often called Zn fingers.

MM force fields generally rely on describing ion binding by non-bonding interactions, electrostatics and van der Waals. This often breaks down with Zn fingers, partly because they do not account for the covalent character of the binding and because they ignore the charge transfer from Lewis base to acid. Therefore, keeping the formal 2+ charge on the zinc creates an electrostatic well polling in negative particles, and since the size exclusion allows enough space for six ligands, often results in an octahedral coordination around the metal ion.

ZAFF

Zinc Amber Force Field (ZAFF) was developed to handle these issues, a useful tutorial is available for its usage. It describes 12 different Zn fingers, varied in the type and protonation of the coordinating residues. Further combinations can be created either based on these parameters, or by carrying out QM calculations, especially for getting the (RESP) charges.

Implementation

There are two major changes that are required for using the modified FF, apart from the obvious deprotonation of coordinating cysteins (CYS->CYM). One is the modification of the system topology, including the 2-3-4 atom interactions involving the zinc. The other one is modifying the charges, which, depending on the software environment, may require the definition of one-off residue types, see the amber example.

NAMD

I discuss the usage in NAMD, as our preferred MD engine, especially with the CHARMM36m forcefield shipped from CHARMM-GUI

CHARMM also implemented extra parameters for the Zn fingers, part of the toppar_all36_prot_modify_res.str compilation. Here the bonding, angle and dihedral parameters are set for S and N atoms, assuming CYM and HIS (HSD or HSE) coordination. To use these, the psf file of the system has to be modified: registering the index of the atoms involved, doubles, triples and quadrupoles for bonds, angles and dihedrals are to be added to their respective sections, so the software will invoke these parameters. Although this modification could be scripted, we have not done that as it only has to be done once for a psf.

(Some classical MD software register only the parameters which are used, like amber or gromacs. In NAMD or charmm, one may read in many redundant paremeters, the necessary ones are employed in runtime based on the topology.)

The second modification is swapping the charges to the ones representing the charge transfer. In NAMD, that can be done in the psf as well. I suggest borrowing them from ZAFF, the minor changes are within the errors of the forcefield. For instance, the Zn(CYM)₄ site assigns a partial charge of 0.52437 to the zinc, and the CYM sidechains are modified accordingly to have a net of -2 for the moiety.

D. Berta, Mar 2024