Methods for molecular mechanics modeling of coordination compounds

Parmscan is an automatic engine for force-field parameterization. In this work, we applied both systematic search (SS) and a genetic algorithm (GA) to optimize the force-field parameters (bond length, bond angle, as well as torsional angle terms) to reproduce the relative energies of conformational pairs as well as other molecular properties such as vibrational frequencies. We present an example of how to apply Parmscan to reproduce the relative energies of 11 hydrocarbons by optimizing the torsional parameter of C–C–C–C using both systematic search and the genetic algorithm. Both of the two methods successfully found the lowest RMS error, which is 0.51 kcal/mol (the unsigned mean error is 0.37 kcal/mol). The Cornell et al. model (Parm94, ref. 21) achieves an RMS error of 0.78 kcal/mol. A second example is the application of the genetic algorithm to optimize the torsional parameter C–O–C–O and bond angle parameter O–C–O simultaneously for 11 dioxanes, to reproduce the experimental relative energies. After 300–400 iterations of GA optimizations, the RMS deviation is reduced to 0.56–0.57 kcal/mol, slightly better than that of Parm99 (ref. 22) and much better than that of the Cornell et al. model. In further applications, the bond length and bond angle parameters of hydrocarbons and benzene were optimized to reproduce the experimental vibrational frequencies. Encouraging results were obtained compared to the Cornell et al. force field: for the low vibrational frequencies of ethane, propane, and butane, the new model achieves an unsigned mean error of 19 cm−1, compared to 30 cm−1 of the Cornell et al. model; for 20 vibrational frequencies of benzene, the new model can also give much smaller unsigned mean error (29 vs. 53 cm−1). It seems that after appropriate parameterizations, a simple harmonic molecular model, such as employed in AMBER, can also reproduce lower vibrational frequencies of molecules quite well. © 2001 John Wiley & Sons, Inc. J Comput Chem 22: 1219–1228, 2001

Automatic parameterization of force field by systematic search and genetic algorithms

We carried out an extensive series of ab initio quantum mechanical (QM) calculations using pure effective core potential (ECP) and hybrid Hartree–Fock (HF)/ECP basis sets, including various electron correlation treatments up to the MP4 level on cis-diamminedichloroplatinum(II), cisplatin, an important anticancer drug. The optimized geometric parameters and vibrational frequencies of cisplatin were compared with the experimental values, and the effects of varying basis sets and correlation (MP level) treatments on the geometric parameters and vibrational frequencies were analyzed. We also present a detailed description of the bonding in cisplatin using qualitative MO analysis to characterize the key intramolecular interactions in cisplatin. The calculated molecular electrostatic potential (MEP), and the electrostatic potential (ESP) charges for cisplatin were used to identify regions of electrophilic and nucleophilic character. The charge density and the Laplacian of charge density of cisplatin were calculated to determine its bonding relationships. Using basis set performance, we identified two hybrid basis sets (HF/6-311G* and MP2/6-311G*) as basis sets of choice for studying cisplatin's molecular properties. Furthermore, we recommend a hybrid ECP/HF approach with electron correlation for the most accurate physicochemical and electronic description of cisplatin and related compounds. ©1999 John Wiley & Sons, Inc. J Comput Chem 20: 365–382, 1999

Comprehensive ab initio quantum mechanical and molecular orbital (MO) analysis of cisplatin: Structure, bonding, charge density, and vibrational frequencies†

The structure of the general classical trajectory FORTRAN code is discussed for use in molecular dynamics simulations of polymer processes. Substantial reductions in the number of mathematical operations in the code are achieved by using statement functions, modifying the ususal chain rule derivatives, applying appropriate vector identities, and using closure relationships among the required derivatives of the potential.

Molecular dynamics simulations of polymers: methods for optimal FORTRAN programming

A new set of formulae is developed for the derivatives of torsion angle energy terms and is introduced into the program CHARMM. These formulae, which are based on derivatives of the torsion angle itself, avoid the singularities introduced by use of the derivatives of the torsion angle cosine. The potential energy can include any differentiable function of the torsion angle and there is no need for a special treatment for cases where planar conformations are not extrema. The resulting code is simpler than the original version and yields correct derivatives in all practical situations. Because the minimum of the torsion energy can be at any angle, the functionality of the existing energy routines is generalized. © 1996 by John Wiley & Sons, Inc.

New formulation for derivatives of torsion angles and improper torsion angles in molecular mechanics: Elimination of singularities

Matrix elements for the first and second derivatives of the internal coordinates with respect to Cartesian coordinates are reported for stretching, linear, nonlinear, and out-of-plane bending and torsional motion. Derivatives of the energy with respect to the Cartesian coordinates are calculated with the chain rule. Derivatives of the energy with respect to the internal coordinates are straightforward, but the calculation of the derivatives of the internal coordinates with respect to the Cartesian coordinates can be simplified by the following two steps outlined in this article. First, the number of terms in the analytical functions can be reduced or will vanish when the derivatives of the bond length, bond angle, and torsion angle are reported in a local coordinate system in which one bond lies on an axis and an adjacent bond lies in the plane of two axes or is projected onto perpendicular planes for linear and out-of-plane bending motion. Second, a simple rotation transforms these derivatives to the appropriate orientation in the space-fixed molecular coordinate system. Functions of the internal coordinates are invariant with respect to translation and rotation. The translational invariance and the symmetry of the second derivatives for a system with L atoms are used to select L-1- and L(L-1)/2-independent first and second derivatives, respectively, of which approximately half of the latter vanish in the local coordinate system. The rotational invariance permits the transformation of the simplified derivatives in the local coordinate system to any orientation in space. The approach outlined in this article simplifies the formulas by expressing them in a local coordinate system, identifies the most convenient independent elements to compute, from which the dependent ones are calculated, and defines a transformation to the space-fixed molecular coordinate system.

First and second derivative matrix elements for the stretching, bending, and torsional energy

The binding of cis-Pt(II) diammine (cis-DP) to double-stranded DNA was studied with several kinked conformations that can accommodate the formation of a square planar complex. Molecular mechanics (MM) calculations were performed to optimize the molecular fit. These results were combined with quantum mechanical (QM) calculations to ascertain the relative energetics of ligand binding through water vs direct binding of the phosphate to the ammine and platinum, and to guide the selection of DNA conformations to model complex formation. Based on QM and MM calculations, models are proposed that may be characterized by several general features. A structure involving hydrogen bonding between each ammine and distinct adjacent phosphate groups, referred to as closed conformation (CC), has already been reported. This is also found in the crystal structure of small dimers. We report alternative conformations that may be important in platination of duplex DNA. They are characterized by an intermediate conformation (IC), involving hydrogen bonding between one ammine and phosphate group, and an open conformation (OC), without ammine phosphate hydrogen bonding. The IC and OC can be stabilized by water bridges in the space between the ammine and the phosphate groups. Sugar puckers alternate from the type C(2')-endo or C(1')-exo (S), to the type C(3')-endo or C(2')-exo (N), with intermediate types near O(1')-endo (O). In general, the sugar puckers alternate from S to N to S through the platinated region (3'-TpG*pG*p-5'), with the complexed strand exhibiting, (3')-S*-N*-S-(5') alternation, while the complementary strand shows either (3')-S*-N*-S-(5') or (3')-S*-N*-O-(5') alternation. In both the OC and IC, a hydrogen bond is found between the ammine and O4(T) on thymine (T) at the (3') end, adjacent to the complex site. There is a continuous range of backbone conformations through the platinated region which relate the OC to the IC. The models presented suggest that the dynamics of the binding of the cis-Pt(II)-diammines to adjacent N7(G) in double-stranded DNA may encompass several conformational possibilities, and that water bridges may play a roll in supporting open and intermediate conformations. Proton-proton distances are reported to assist in the experimental determination of conformations.

Theoretical studies of cis‐Pt(II)‐diammine binding to duplex DNA

The results of a study of the binding to DNA of substituted cis-Pt(II) diammines, (cis-DP) are presented. Computer modeling of a series of cis-Pt(NH2R)2(+2)--where R = H, CH3, cyclopropyl, cyclobutyl, and cyclopentyl--to N7(G) atoms of two adjacent intrastrand guanine bases in a square planar complex in a pentamer duplex of DNA were performed. The stability of the complexes is studied by calculating the relative conformational energy of the cis-DP-DNA complexes with molecular mechanics (MM) and the intrinsic binding energy, which is the relative binding energy for ligand replacement in the presence of the substituents R with quantum mechanics. In the model, the receptor site geometry and the conformation of the DNA is changed little in the accommodation of the series of monosubstituted diammines. These diammines bind to one family of DNA conformations, denoted as IC in a previous study, and this suggests that a common conformational feature in the DNA may exist to explain the smooth trend in activity. The slight increase in van der Waals energy resulting from an increasing number of atoms in the substituents is countered by a larger decrease in the ligand replacement energy as the substituent increases in size. This overall decrease in relative energy is consistent with the slight decrease in activity as the substituent size increases.

Robert J. Hinde

Papers

First and second derivative matrix elements for the stretching, bending, and torsional energy

Theoretical studies of cis‐Pt(II)‐diammine binding to duplex DNA

The binding of substituted cis‐Pt(II)‐diammines to duplex DNA