Force field methods energy comparisons

The molecular mechanics (MM) or force field method is an empirical method based on classical mechanics and adjustable parameters. It has the disadvantage of being limited in its application to certain kinds of compounds for which the required parameters have been determined (experimentally or by theoretical calculations). Its advantage is a considerably shorter computation time in comparison with other procedures having the same purpose. This method has been shown to be very reliable and efficient in determing molecular geometries, energies, and other properties for a wide variety of compounds. 

MD simulations provide a detailed insight in the behavior of molecular systems in both space and time, with ranges of up to nanometers and nanoseconds attainable for a system of the size of a CYP enzyme in solution. However, MD simulations are based on empirical molecular mechanics (MM) force field descriptions of interactions in the system, and therefore depend directly on the quality of the force field parameters (92). Commonly used MD programs for CYPs are AMBER (93), CHARMM (94), GROMOS (95), and GROMACS (96), and results seem to be comparable between methods (also listed in Table 2). For validation, direct comparisons between measured parameters and parameters calculated from MD simulations are possible, e.g., for fluorescence (97) and NMR (cross-relaxation) (98,99). In many applications where previously only energy minimization would be applied, it is now common to perform one or several MD simulations, as Ludemann et al. and Winn et al. (100-102) performed in studies of substrate entrance and product exit. 

Instead, the comparison of strain energies should be limited to sets of isomers. When the atom connectivities are the same, electronic factors and other omissions and errors in the force field can be assumed to be constant and therefore will cancel when differences between strain energies are considered. The values of the strain energies reveal which isomer is the most stable (has the lowest strain energy) and what percentage of each isomer should be observed in an equilibrated system[65]. The methods for calculating these percentages are described in Chapter 8. 

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. 

In spite of these caveats, there is intense activity in the application of these methods to polymorphic systems and considerable progress has been made. Two general approaches to the use of these methods in the study of polymorphism may be distinguished. In the first, the methods are utilized to compute the energies of the known crystal structures of polymorphs to evaluate lattice energies and determine the relative stabilities of different modifications. By comparison with experimental thermodynamic data, this approach can be used to evaluate the methods and force fields employed. The ofher principal application has been in fhe generation of possible crystal structures for a substance whose crystal structure is not known, or which for experimental reasons has resisted determination. Such a process implies a certain ability to predict the crystal structure of a system. However, the intrinsically approximate energies of different polymorphs, the nature of force fields, and the inherent imprecision and inaccuracy of the computational method still limit the efificacy of such an approach (Lommerse et al. 2000). Nevertheless, in combination with other physical data, in particular the experimental X-ray powder diffraction pattern, these computational methods provide a potentially powerful approach to structure determination. The first approach is the one applicable to the study of conformational polymorphs. The second is discussed in more detail at the end of this chapter. 

Table 5 A comparison between quantum-mechanical and force-field treatment of dispersion and repulsive contributions to the free energy of solvation. The force field is given under method, and for each solvent the first line gives the root mean square deviation (rmsd, in kcal/ mol) and the second line gives the coefficient c that gives the best fit of y = cx with y being the force-field results and x being the quantum-mechanical results. All results are from ref 30...

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