Electrostatically Embedded Many-Body Expansion for Neutral and Charged Metalloenzyme Model Systems

Abstract

The electrostatically embedded many-body (EE-MB) method has proven accurate for calculating cohesive and conformational energies in clusters, and it has recently been extended to obtain bond dissociation energies for metal–ligand bonds in positively charged inorganic coordination complexes. In the present paper, we present four key guidelines that maximize the accuracy and efficiency of EE-MB calculations for metal centers. Then, following these guidelines, we show that the EE-MB method can also perform well for bond dissociation energies in a variety of neutral and negatively charged inorganic coordination systems representing metalloenzyme active sites, including a model of the catalytic site of the zinc-bearing anthrax toxin lethal factor, a popular target for drug development. In particular, we find that the electrostatically embedded three-body (EE-3B) method is able to reproduce conventionally calculated bond-breaking energies in a series of pentacoordinate and hexacoordinate zinc-containing systems with an average absolute error (averaged over 25 cases) of only 0.98 kcal/mol.

Analysis of the Errors in the Electrostatically Embedded Many-Body Expansion of the Energy and the Correlation Energy for Zn and Cd Coordination Complexes with Five and Six Ligands and Use of the Analysis to Develop a Generally Successful Fragmentation Strategy

“…Our EE-MB-CE calculations on neutral, negatively, and positively charged Zn and Cd systems demonstrate, consistently with our previous findings, 44,45 that one must choose a fragmentation scheme where one of the monomers is Zn 2+ or Cd 2+ coordinated to at least two ligands. We rationalize this rule in terms of partial atomic charges.…”

“…As discussed previously, 44,45 the instantaneous bond dissociation energy is the sum of the energies of the two products (separated frozen fragments) minus the energy of the reactant, without reoptimization and without including vibrational energy. When calculating the energies of a given dissociation product, the embedding charges of the other product are not included because the other product is considered to be infinitely separated.…”

“…These model structures are the same as those reported in our previously published work. 45,48 System 3 (Figure 2) is a model compound based on the X-ray structure of the matrix metalloproteinase-7 (MMP-7, also known as matrilysin) active site, co-crystallized with sulfodiimine (PDB ID 1MMR). 58 In MMP-7, the catalytic Zn is coordinated by three histidines, and in 1MMR.pdb, the two remaining coordination sites are occupied by imine nitrogens in the co-crystallized inhibitor.…”

“…System 3 is also used to demonstrate the advantage of our newly developed fragmentation strategy over previously published fragmentation guidelines. 45 We also consider three other pentacoordinate systems: Zn(NH 3 ) 5 2+ , Zn(H 2 O) 5 2+ , and Zn(H 2 O) 4 (OH) + (systems 4 , 5 , and 6 , respectively, Figure 3). These are used to test the applicability of the EE-MB-CE method to positively charged systems.…”

“…The EE-3B method is able to predict bond energies obtained by conventional full-system calculations done at the same level of theory to within 1.0 kcal/mol for cationic, neutral, and negatively charged Zn 2+ complexes. 44,45 In EE-MB-CE, one applies the many-body expansion only to the correlation energy, that is, to the post-Hartree–Fock part of the energy calculation. Here we apply the EE-MB-CE method to predict MP2 correlation energies for a variety of pentacoordinate and hexacoordinate Zn 2+ and Cd 2+ systems, and we compare its performance to the EE-MB method.…”