Deficiencies
All force fields are based on numerous approximations and derived from different types of experimental data. Therefore they are called empirical. Some existing force fields do not account for electronic polarization of the environment, an effect that can significantly reduce electrostatic interactions of partial atomic charges. This problem was addressed by developing “polarizable force fields” or using macroscopic dielectric constant. However, application of a single value of dielectric constant is questionable in the highly heterogeneous environments of proteins or biological membranes, and the nature of the dielectric depends on the model used.
All types of van der Waals forces are also strongly environment-dependent, because these forces originate from interactions of induced and “instantaneous” dipoles (see Intermolecular force). The original Fritz London theory of these forces can only be applied in vacuum. A more general theory of van der Waals forces in condensed media was developed by A. D. McLachlan in 1963 (this theory includes the original London’s approach as a special case). The McLachlan theory predicts that van der Waals attractions in media are weaker than in vacuum and follow the "like dissolves like" rule, which means that different types of atoms interact more weakly than identical types of atoms. This is in contrast to “combinatorial rules” or Slater-Kirkwood equation applied for development of the classical force fields. The “combinatorial rules” state that interaction energy of two dissimilar atoms (e.g. C…N) is an average of the interaction energies of corresponding identical atom pairs (i.e. C…C and N…N). According to McLachlan theory, the interactions of particles in a media can even be completely repulsive, as observed for liquid helium. The conclusions of McLachlan theory are supported by direct measurements of attraction forces between different materials (Hamaker constant), as explained by Jacob Israelachvili in his book "Intermolecular and surface forces". It was concluded that "the interaction between hydrocarbons across water is about 10% of that across vacuum". Such effects are unaccounted in the standard molecular mechanics.
Another round of criticism came from practical applications, such as protein structure refinement. It was noted that CASP participants did not try to refine their models to avoid "a central embarrassment of molecular mechanics, namely that energy minimization or molecular dynamics generally leads to a model that is less like the experimental structure". Actually, the force fields have been successfully applied for protein structure refinement in different X-ray crystallography and NMR spectroscopy applications, especially using program XPLOR. However, such refinement is driven primarily by a set of experimental constraints, whereas the force fields serve merely to remove interatomic hindrances. The results of calculations are practically the same with rigid sphere potentials implemented in program DYANA (calculations from NMR data), or with programs for crystallographic refinement that do not use any energy functions. The deficiencies of the force fields remain a major bottleneck in homology modeling of proteins. Such situation gave rise to development of alternative empirical scoring functions specifically for ligand docking, protein folding, homology model refinement, computational protein design, and modeling of proteins in membranes.
There is also an opinion that molecular mechanics may operate with energy which is irrelevant to protein folding or ligand binding. The parameters of typical force fields reproduce enthalpy of sublimation, i.e. energy of evaporation of molecular crystals. However, it was recognized that protein folding and ligand binding are thermodynamically very similar to crystallization, or liquid-solid transitions, because all these processes represent “freezing” of mobile molecules in condensed media. Therefore, free energy changes during protein folding or ligand binding are expected to represent a combination of an energy similar to heat of fusion (energy absorbed during melting of molecular crystals), a conformational entropy contribution, and solvation free energy. The heat of fusion is significantly smaller than enthalpy of sublimation. Hence, the potentials describing protein folding or ligand binding must be weaker than potentials in molecular mechanics. Indeed, the energies of H-bonds in proteins are ~ -1.5 kcal/mol when estimated from protein engineering or alpha helix to coil transition data, but the same energies estimated from sublimation enthalpy of molecular crystals were -4 to -6 kcal/mol. The depths of modified Lennard-Jones potentials derived from protein engineering data were also smaller than in typical force fields and followed the “like dissolves like” rule, as predicted by McLachlan theory.
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