There are a number of variations on the classical force field approach described above. One can categorize the different methods by considering the concept of a molecular model. Where a molecular model is defined by the basic elements, such as atoms and bonds, and the nature of the interactions of these elements, described by the force field equation, such as that discussed above, the parameters of the potential and the method used for the representation of solvent. Together these elements form the model. There is a tight connection between a model type and an accompanying force field in the sense that the molecular model and the kinds of behaviors to be modeled determine what needs to be in the force field. However, there can be several force fields, with different parameters and functional forms for the same molecular model type. With this important distinction between the model type and the force field in mind, the most commonly used model types and then the most popular force fields will be discussed, and finally a brief description of current solvent model types. Each of these topics, coupled with the background to classical molecular mechanics described above, deserves a full chapter in itself and so we present only a brief overview of what is most popular and what we believe to be the essential tools in the current state-of-the-art research. For a more in-depth discussion the reader can refer to references Allen and Tildesley (9), Grant and Richards (10), Frenkel and Smit (11), Leach (12), Jensen (13), and Cornell etal. (6).

The most detailed and also most used classical mechanical model for biomolecular sim­ulation is the “All-Atom” model in which the basic element of the model is an atom with properties of mass, partial charge, and an atom type which describes its bonding properties and van der Waals parameters. The energy function of a given arrangement of atoms in an all-atom approach typically conforms to the AMBER force field equation described above which is itself an all-atom model. An all-atom molecular model is created by describing all the atoms and choosing a force field. A full description of atoms includes specifying which atoms are bonded together, what kind of atoms they are, such as an sp2 carbon, and positioning them in space. The “United Atom” model (14-17) is the same as an all-atom model except that aliphatic hydrogen atoms are combined with the carbon to which they are bonded to form a “united” atom with most of the properties of the carbon, but a larger van der Waals radius and a larger mass. This model requires a different force field than the all-atom model.

Reduced models currently in use are the bead (18) or GO (19, 20) models, models used in large-scale normal mode analysis, and large subunit modeling such as is used in virus capsid assembly modeling (21). Bead models use a whole residue as the element of the model in which each residue, such as an amino acid in a protein, is represented by a single sphere with size and interaction properties, and each bead is bonded to other beads. There is a simple force field for this kind of model, which can include attractions, repulsions, and bonding properties such as angles and dihedrals. It is used primarily for studies of folding of biopolymers. For large-scale normal mode analysis, described later, the Hessian matrix can become impossibly large at 9N2 for a system of N atoms. An elastic-network model, in which each alpha carbon of a protein is connected to every other alpha carbon by a spring, reproduces the lowest frequency modes (22-24), which are generally the modes of interest, reducing the size of the problem by at least an order of magnitude. The granularity of the problem has been increased further by combining multiple residues into blocks with only rotational and translational degrees of freedom, bonded together and with an elastic spring network; this model is the RTB model (25). The largest granularity that is worth mentioning is the subunit model used in simulating virus capsid assembly (26), in which each unit represents the basic subunit of a virus, which contains three to nine proteins. Each subunit is a rigid body that interacts with other subunits through interaction points with both attractive and repulsive forces. One could envision using this kind of modeling for interactions between the subunits of the plant cell wall.