Regularization

X-PLOR can regularize coordinates that are obtained by distance geometry embedding by minimizing the coordinates against an effective energy term (DG) that represents all upper and lower bounds in the distance geometry bounds matrix. The bounds matrix has to be stored in memory using the STOREBounds statement prior to invoking the DG energy term. The atoms that should be restrained have to be defined through the SELEction statement. The DG term is defined as

$$E_{DG} = S \sum_{i < j} \left\{ \begin{array}{ll} (R_{ij}-d... ...ij})^e & \mbox{$R_{ij} < d_{ij}^{lower}$} \end{array} \right.$$ (37.1)

where $S$ is the scale factor specified by the SCALe statement, $e$ is the exponent defined by the EXPOnent statement, $d_{ij}^{lower}$ is the upper bounds, $d_{ij}^{lower}$ is the lower bounds generated by the initialization stage of distance geometry, and the sum goes over all atoms $i$, $j$ that are selected by the selection statement.

The DG energy term is turned on by using the flag statement (see Section 4.5). Normally, all other energy terms should be turned off when using the DG term. However, for defining the bounds matrix initially, the other energy terms should be turned on, because bounds are computed only for the activated energy terms. Then, after storing the bounds matrix, all other energy terms should be turned off and the DG energy term turned on. Energy minimization, molecular dynamics, or any other energy calculation can be performed with the DG energy term.