The Functional Form of Angular Forces around Transition Metal Ions in Biomolecules

Abstract

A method for generating angular forces around sigma-bonded transition metal ions is generalized to treat pi-bonded configurations. The theoretical approach is based on an analysis of ligand-field and small-cluster Hamiltonians based on the moments of the electron state distribution. The functional forms that are obtained involve a modification of the usual expression of the binding energy as a sum of ligand-ligand interactions, which, however, requires very little increase in CPU time. The angular interactions have simple forms involving sin and cos functions, whose relative weights depend on whether the ligands are sigma- or pi-bonded. They describe the ligand-field stabilization energy to an accuracy of about 10%, and the interaction energy of covalently bonded systems to an accuracy of better than 4%. The resulting functional forms for the force field are used to model the structure of small clusters, including fragments of the copper blue protein structure. Large deviations from the typical square copper coordination are found when pi-bonded ligands are present.

A valence bond model for aqueous Cu(II) and Zn(II) ions in the AMOEBA polarizable force field

“…A small amount of s hybridization is modeled to take into account the effect of d–s mixing. Figure 3 shows the overall shape of the VB angular potential, which is similar to the corresponding function derived by Carlsson and Zapata[29, 63] from AOM considerations. The main features of the potential function are the two local minima at ligand–metal–ligand angles of 180 and 90°, allowing tetra‐aqua Cu 2+ complexes to adopt the preferred square‐planar geometry.…”

“…TM ions are described as resonance centers, and angular terms are developed from geometrical overlap between sd n hybridized bonding metal–ligand orbitals. On the other hand, DommiMOE developed by Deeth et al[28] and previous work by Carlsson and Zapata[29] are based on AOM in which the metal–ligand angular term arises from the explicit diagonalization of a ligand‐field potential matrix. Both approaches avoid the use of reference ligation geometries in their angular potentials and have shown to provide favorable results when compared to experimental data and QM‐based calculations across a range of different coordination geometries and ligation states.…”

c-di-GMP heterogeneity is generated by the chemotaxis machinery to regulate flagellar motility

“…This was calculated for these exposure conditions for the cells expressing mCyPet alone to be 0.46. The original nFret equation subtracts bleedthrough from Yfp into the Fret channel as well ( Xia and Liu, 2001 ). Because imaging mYPet significantly increases photobleaching over time, our calculation of nFret does not include subtracting Yfp from the Fret signal.…”

Tinker 8: Software Tools for Molecular Design

“…Three ligand field models for describing the coordination geometry at transition metal sites within the Tinker package have also been described. 61–63…”