CHARMM energy functions

Of the biomolecular force fields, AMBER [21] is considered to be transferable, whereas academic CHARMM [20] is not transferable. Considering the simplistic form of the potential energy functions used in these force fields, the extent of transferability should be considered to be minimal, as has been shown recently [52]. As stated above, the user should perform suitable tests on any novel compounds to ensure that the force field is treating the systems of interest with sufficient accuracy. 

The energy functions for folding simulations include atom-based potentials from molecular mechanics packages [164] such as CHARMM [81], AMBER [165], and ECEPP... 

AD MacKerell Jr, B Brooks, CL Brooks III, L Nilsson, B Roux, Y Won, M Karplus. CHARMM The energy function and its paramerization with an overview of the program. In PvR Schleyer, NL Alhnger, T Clark, J Gasteiger, PA Kollman, HP Schaefer III, PR Schreiner, eds. Encyclopedia of Computational Chemistry, Vol 1. Chichester, UK Wiley, 1998, pp 271-277. 

MacKerell AD Jr., Brooks B, Brooks CL III, et al., eds. CHARMM The Energy Function and Its Parameterization with an Overview of the Program. Chichester, U.K. John Wiley Sons 1998. 

Force-field-based scoring functions use arbitrary empirical estimates of interaction energies obtained by molecular mechanics energy functions. This simple approximation, which takes into account only enthalpic contribution often correlates well with the experiment. Solvent effects are described by atom-based solvation parameters, which are computed for the surface of both ligand and receptor which is buried upon complexation. DOCK-chemical27 and CHARMm scoring functions represent this class. 

MacKerell AD, Brooks B et al (1998) CHARMM the energy function and its parameterization with an overview of the program in The Encyclopedia of Computational Chemistry, Wiley, Chichester... 

Some formulations of the potential energy function (e.g., References 27 and 79, and AMBER, CHARMM, and DISCOVER, as well as most force fields used in small-molecule studies) include terms that allow for bond stretching and bond angle bending, that is, for flexible geometry. Hence, the terms in Eq. [1] are augmented by the expression27... 

A wide variety of energy functions have been used as part of the various GA-based protein structure prediction protocols. These range from the hydrophobic potential in the simple HP lattice model [19] to energy models such as CHARMM, based on full fledged, detailed molecular mechanics [9]. Apparently, the ease by which various energy functions can be incorporated within the framework of GAs as fitness functions encouraged researchers to modify the energy function in very creative ways to include terms that are not used with the traditional methods for protein structure prediction. 

Another set of early studies came from the work of Judson and coworkers [35, 36], which emphasized using GAs for search problems on small molecules and peptides, especially cyclic peptides. A dihedral angle representation was used for the peptides with values encoded as binary strings, and the energy function used the standard CHARMM force field. Mutations were implemented as bit flips and crossovers were introduced by a cut-and-paste of the strings. The small size of the system enabled a detailed investigation of the various parameters and policies chosen. In Ref. [37], a comparison between a GA and a direct search minimization was performed and showed the advantages and weaknesses of each method. As many concepts are shared between search problems on small peptides and complete proteins, these studies have contributed to subsequent attempts on full proteins. 

King et al. (292)used an empirical binding Ifee-energy function when docking MVT-101 to HIV protease. Forty-nine translation/rota-tions were examined with the Ponder/Richard rotamer library. Only a limited number of retainers for each amino acid were examined Thr(2), Ile(3), Nle(3), Nle(3), Gln(6), and Arg(5). According to the authors, 2.24 x 10 ° discrete states were examined. Sixty-four low ener structures with an average rmsd of 1.36 A were found. If the CHARMM potential was used with the same protocol, then the av-eragQ rmsd was increased to 1.68 A. 

The CHARMM code, version c25bl, was chosen for integration with the metal potential. CHARMM is a multi-purpose molecular dynamics program [35], which uses empirical potential energy functions to simulate a variety of systems, including proteins, nucleic acids, lipids, sugars and water. The availability of periodic boundary conditions of various lattice types (for example cubic and orthorhombic) makes it possible to treat solids as well as liquids. 

The success of any molecular simulation method relies on the potential energy function for the system of interest, also known as force fields [27]. In case of proteins, several (semi)empirical atomistic force fields have been developed over the years, of which ENCAD [28,29], AMBER [30], CHARMM [31], GRO-MOS [32], and OPLSAA [33] are the most well known. In principle, the force field should include the electronic structure, but for most except the smallest systems the calculation of the electronic structure is prohibitively expensive, even when using approximations such as density functional theory. Instead, most potential energy functions are (semi)empirical classical approximations of the Born-Oppenheimer energy surface. 

In this work, a recently developed semi-empirical method, SCC-DFTB method, is employed to account for the electronic structure of QM part. The details of this method and its implementation to CHARMM have been summarized elsewhere [6, 22-24]. Here we just give a short description. This method is derived by a second order expansion of the DFT total energy functional with respect to the charge density fluctuation around a given reference density. The total energy can be expressed as following [22] ... 

---