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12.1.2 Overview of Sidechain Degree of Freedom

Given a set of backbone conformations, it remains to generate a set of side chain atom positions for each of the backbone conformations. Before we explore the problems inherent in side chain generation, we describe the side chain atom placement.

As with the backbone atom placement, the side chain atoms are positioned based on free torsion angles. The side chain torsions are processed from the backbone out as each succeeding atom requires the position of the previous atom for its placement. The sampling interval of each torsion (the option SGRID) can be either some fixed number of degrees or the period of the torsion energy. When the latter is used, the sidechain torsions will be at minima in the torsion angle potential involving the free atom and its antecedents. It is also possible to modify the sampling to avoid van der Waals contacts (VAVOID option). It is common for one free torsion to generate the position of more than one atom because of side chain branching, non-rotatable bonds, and rings. For example, although tryptophan has 11 side chain atoms to be placed, it has only two free torsion angles. Also, certain torsions have symmetry so we can reduce the sampling necessary. Finally, a search of the surrounding space is made for any constructed atom to see if there are any close contacts with a repulsive energy greater than MAXEVDW, and if so, that structure is eliminated.

Although this data structure was designed for amino acids, it can be applied to an arbitrary molecule. The only prerequisite is the presence of a few known atomic position upon which the remaining atoms can be constructed.

The information needed for side chain construction is stored in a side chain topology file, see Sidechain Topology.

Given these specifications for generating side chain atomic positions, we need to introduce a protocol that generates only a limited number of conformers. The procedure analogous to the backbone generation procedure would result in a series of nested iterations over each chi torsion angle with the number of levels being equal to the sum of the free torsions in all the side chains of the peptide segment. The large number of free torsions in the side chains and the absence of a connectivity constraint, such as exists for the backbone, result in an enormous number of possible sidechain conformations. Consequently, such a direct approach is not feasible except in limited cases.

However, the situation is not that bleak. First, the backbone construction process provides the position of CB which gives a strong bias to the side chain orientation. Thus, an acceptable course of action is the generation of only one sidechain conformation for each backbone conformation. We must strive to make this one conformation the lowest energy possible for the given backbone. Second, because the side chains close together in sequence frequently are not close together in space, and therefore, do not interact strongly, it is a reasonable approximation to treat the side chains quasi-independently. Instead of finding all combinations of side chain atomic positions, we can handle the side chains sequentially so the time required for side chain placement increases linearly, rather than exponentially, with the number of residues.

In order not to limit the options for using the program, six possible methods for generating side chain positions have been implemented. These are specified using the SIDEOPT option in the sidechain degree of freedom. All of these methods discard conformations which have any repulsive contacts exceeding MAXEVDW in van der Waals energy. The first two methods described, ALL and FIRST, assume no quasi-independence of the sidechains whereas the others do.

The first method, ALL, generates all possible conformations by a series of nested iterations over every sidechain as described above. The second method, FIRST, uses the same algorithm as ALL except that all the iterations terminate when the first conformation for all the sidechains has been found. This method is useful for determining if a backbone conformation will accommodate the sidechains when details about the sidechain energetics are not required.

The next three methods all depend on a function which evaluates the side chain positions as they are generated so that the best ones can be selected. "Best" is defined as the conformation whose evaluation function is numerically smallest. Two evaluation functions are currently provided, one based on positional deviations, and one based on the CHARMM energy function. The evaluation function based on positional deviations is present for testing CONGEN as it provides a means for determining the limit of CONGEN's ability to generate a known structure. If coordinates are present for the peptide gap, this evaluation function will determine the RMS shift between a generated side chain conformation and the initial coordinates. The second evaluation function computes the CHARMM energy of the sidechain atoms omitting the bond and bond angle energies because the generation procedure does not vary either of these two terms. At present, either the r dependent dielectric or the constant dielectric for the electrostatic energy is used. The other electrostatic calculations, see Non-bonded Interactions, are not available.

The INDEPENDENT method assumes that the side chains in the peptide chain being generated do not interact with one another. The atoms of each side chain are placed independently, with those of the other side chains in the peptide being ignored; interactions with all other atoms in the system are included. The conformation which has the lowest value for the evaluation function is selected for each side chain. When the RMS evaluation function is used, this method gives the optimum conformation, though it may be sterically inappropriate. Thus, it cannot be used when the energy is the evaluation function unless the possibility of large repulsive van der Waals is not important.

The method, COMBINATION, begins by generating a small number of the best side chain conformations for each side chain independently, as above. Then, these side chain conformations are assembled in all possible combinations, and those combinations which do not have bad van der Waals contacts are accepted. The number of conformations saved for each side chain must be small to avoid a combinatorial explosion.

The ITERATIVE method starts with an energetically acceptable side chain conformation for all the side chains. This conformation is generated, if possible, using the FIRST method (see above). Starting with this conformation, we regenerate all the possible positions for the side chain atoms of the first residue, and select the conformation with the lowest energy. We also save the value of the evaluation function. This regeneration is done with all the other side chain atoms present so we can account for their effect. The process is repeated sequentially for the rest of sidechains in the gap. We then return to the first residue and go through the process again until the energies of the side chain atoms do not change or until the number of passes reaches an iteration limit. This method has the virtue that only one conformation is generated per backbone conformation, and it is an energetically reasonable one. However, if there are significant interactions between the sidechain atoms, the first part of the process will bias the iterative process toward the initial side chain arrangement selected, and we may miss the lowest energy side chain conformation.

The FIXED method is used to construct sidechains in a fixed conformation. When this method is specified, the program calculates the construction bond lengths, angles, and torsions for all atoms in the degree of freedom from the starting coordinates, and will generate just one sample using those values. If there are van der Waals overlaps, then no conformation will be generated.

With any of the methods described above, the CONGEN command can apply any of the minimization algorithms to the generated conformations before they are written out for further analysis. Minimization provides an ability to reduce the small van der Waals repulsions that are inevitable with coarse torsion grids used.

See Sidechain Degree of Freedom, for more information on this degree of freedom.