To generate the positions of the backbone atoms, an
extension (*Macromolecules* (1985) **18**, 2767-2773) of the
local chain deformation and chain closure procedure of Go and Scheraga
(*Macromolecules* (1970) **3**, 178-187) is used. Given fixed,
oriented endpoints and a chain of bonded atoms containing six freely
rotatable torsions, their procedure determines a set of values for the
torsion angles that permit the chain to bridge the endpoints. The free
torsions are the phi and psi angles so three is the minimum number of
residues for which a search over an internal polypeptide segment can be
performed (it is presumed that the omega peptide torsion angle is planar
and normally trans, although cis peptides are considered as described
below).

It turned out that the original Go & Scheraga procedure was
overly restrictive, particularly for bridging regular structures like
alpha-helicies. To avoid this problem, we have modified the method to
permit limited alterations in the bond angles and the procedure is named
`CLSCHN`

. The main option controlling bond angle variations is
`MAXDT` which gives the maximum variation from standard bond angles.
Its default value is 5 degrees which improves its performance
significantly while incurring a bond angle energy penalty of at most 1
kT per angle. The number of solutions obtained from the chain closure
method is always even and has not exceeded eight in our experience with
peptides.

The ring in proline creates special problems. The proline ring
constrains the phi torsion to be close to -65 degrees; any deviation
from -65 degrees distorts the ring. Prior to running `CONGEN`, we
determine the minimum energy configuration of the proline ring
(specifically, 1,2 dimethyl pyrrolidine) for a range of phi angles (+/-
90 degrees) about -65 degrees using energy minimization with a
constraint on phi, and we construct a file (`PRO.CNS`) which
contains these energies and the construction parameters necessary to
calculate the position of CB, CG and CD of the proline. All of these
energies are adjusted relative to a minimum ring energy equal to zero.
After a chain closure is performed, we discard any conformations which
have a proline phi angle whose energy exceeds the minimum energy by more
than the parameter, `ERINGPRO`. Generally, we use a large value for
`ERINGPRO`, 50 kcal/mole, so `CLSCHN`

does not overly restrict
proline closures. We handle cis-trans peptide isomerization by trying
all possible combinations of cis and trans configurations. The user has
complete control over which residues can be built in the cis isomer.
Since there are only three residues involved in the chain closure, this
results in no more than eight (2^3) attempts at chain closure.

The backbone search of an N residue segment begins by using
backbone degrees of freedom to sample the free torsions of N-3 residues
and then using the chain closure degree of freedom to close the chain.
As the free torsions are sampled, we can discard any segment if the end
of the constructed chain is too far from the other framework end for
closure to be possible. See Backbone Degree of Freedom, for a
description of the `CLSA` and `CLSD` options which control this
process. The determination is made by calculating the distance between
the last atom constructed and the other fixed endpoint and comparing
that to the distance spanned by m peptides with all torsions being trans
and all bond angles increased by `MAXDT`, where m is the number of
peptides still to be constructed.

The direction of backbone construction is arbitrary, although the endpoints of the search are conserved regardless of the order. The N-terminus of the internal segment is anchored on the peptide nitrogen; the C-terminus is anchored on the alpha carbon. When the construction direction is from the N terminus to the C terminus, the first torsion to be sampled in a residue is the omega angle (which normally is sampled just at 180 degrees, and sampled at 0 degrees and 180 degrees for prolines). It determines the alpha-carbon and the peptide hydrogen positions. The phi angle determines the position of the carbonyl carbon and the beta carbon of the sidechain; and finally, the psi angle determines the carbonyl oxygen and peptide nitrogen of the next residue. When the construction is in the reverse direction; the psi angle determines the peptide nitrogen; the phi angle determines the carbonyl carbon of the preceding residue, the peptide hydrogen, and the beta carbon; and the omega angle determines the position of the preceding residue's alpha carbon and carbonyl oxygen.

Rather than treating each of the three torsion angles in a amino acid residue as three separate degrees of freedom, we combine them into a single degree of freedom. This permits the use of Ramachandran type plots to limit the range of phi, psi values to those that are energetically acceptable and found in known structures.

To determine the allowed phi,psi angles, the `CONGEN`
command uses energy maps. These energy
maps are stored as files, see Backbone Maps, and they are expressed
in tabular form with entries composed of omega, phi, and psi angle
values along with the energy for that angle combination. Thus, any
arbitrary criterion may be used in place of the energy in these maps.
There are three different types of maps, one for glycine, one
for proline, and one for the other amino acids which are modeled by
alanine. Typically, the glycine and alanine maps are computed by
modeling a dipeptide and using the van der Waals energy, whereas the
proline maps is computed using a dipeptide, but the energy in the map is
the sum of the van der Waals energy plus the ring energy. The actual
values for phi and psi in these tabulations are usually multiples of 15
degrees or 30 degrees with all possible combinations of angles present.
Thus, these maps determine the sampling grid. For the alanine and
glycine map, phi and psi both range over -180 degrees to 180 degrees,
and the omega angle can be either 0 or 180 degrees. Normally, the omega
angle of 0 degrees is not used. In the proline map, the range of phi
angles is -150 degrees to 30 degrees; psi goes from 0 degrees to 360
degrees; and omega has values of 0 degrees and 180 degrees.

Each backbone degree of freedom can specify its own map.
However, in most applications, each backbone residue will use the
correct map for its type (proline, glycine, or alanine), and the grid
spacing in all the maps will be the same. Therefore, default maps are
typically specified for each type of amino acid, and the user can
override these maps for individual residues. Fortran unit numbers for
default maps for glycine, proline, and other amino acids are specified
with the global variables; `GLYMAP`, `PROMAP`, and `ALAMAP`;
respectively.

The particular values of torsion angles used for generating
conformations is determined by these maps and the so-called `EMAX` options.
The maps specify all the possible angles.
The `EMAX` options restrict these sets as they specify the maximum
allowed energy relative to the minimum energy value found in each map.
The global options;
`GLYEMAX`, `ALAEMAX`, and `PROEMAX`;
specify the selection of the default backbone maps, see Global Options for Conformational Search.
`GLYEMAX` specifies that for the glycine map; `PROEMAX` for the
proline map; and `ALAEMAX` for the alanine map.
The backbone degree of freedom option, `EMAX`, specifies the
allowed energy for an individual backbone degree of freedom.
For example, when
using the alanine map with a sequence of alanines and a value of
`ALAEMAX` of 2.0 kcal/mole, all the conformations generated will
have phi, psi angles corresponding to only right-handed alpha-helices or
beta-sheets. For a value around 5 kcal/mole, phi, psi angles for
left-handed alpha-helices will also be selected. If values for the
`EMAX` options are set to very large values then the entire phi, psi
space will be sampled.

D amino acids are indicated by the presence of the word, “`D`”,
in the residue attributes. These residues are handled by inverting all torsion
angles for the backbone maps and for the proline constructor files.

For more details on the commands which implement these degrees of freedom, see Backbone Degree of Freedom, and Chain Closure.