PC-Refinement of the Highest Peaks of the Cross-Rotation Function

The next step is to carry out $PC$-refinement of the highest peaks of the rotation function. PC-refinement (Brünger, 1990) of the overall orientation ($\Omega$) and the individual orientations ($\Omega_i$) and translations ($t_i$) of the four domains of the Fab can be carried out by minimization against a target function defined as

$$E_{TOTAL}(\Omega,\Omega_i,t_i)=(1-PC(\Omega,\Omega_i,t_i))$$ (19.7)

where

$${\it PC}(\Omega,\Omega_i,t_i)=$$ (19.8)

$$\frac {<\vert E_{obs}\vert^2\vert E_{m}(\Omega,\Omega_i,t_... ...i,t_i)\vert^4-<\vert E_{m}(\Omega,\Omega_i,t_i)\vert^2>^2> }}.$$

The angle brackets denote an averaging over the set of observed reflections expanded to $P_1$. $E_{obs}$ denotes the normalized observed structure factors, and $E_{m}(\Omega,\Omega_i,t_i)$ denotes the normalized structure factors of the search model placed in a triclinic unit cell identical in geometry to that of the crystal.

In the following example, PC-refinements of the search model are carried out where the model is oriented according to each of the 240 selected peaks of the rotation function listed in the file ``rotation.rf".

filter.inp

This file produces a new listing stored in the file ``filter.list". It contains the results of the $PC$-refinement. The following shows a few lines of this file:

20.765 70 253.45     20.173 68.125 253.61     1 1.2 1.08E-02 3.03E-02 7.10E-02
35.554 75 68.657     36.231 76.77 70.961      6 1.1 2.29E-02 2.97E-02 6.13E-02
9.555 67.5 257.06     10.617 65.649 254.72    7 1.1 1.13E-02 2.02E-02 5.75E-02
34.519 75 249.69     33.645 72.563 251.84     8 1.1 1.97E-02 2.97E-02 6.51E-02

It lists the orientations before and after $PC$-refinement and the correlation coefficients at various stages of the refinement process. The number in the last column, the most interesting one, can be plotted by using the following Mathematica script:

filter.math The result of the filtering procedure is shown in Fig. 19.3.

Figure 19.3: Rotation function after $PC$-refinement.

A single peak is produced. It corresponds to the orientation ($\theta_1$=274.45, $\theta_2$=35, $\theta_3$=324.68) before and ($\theta_1$=275.06, $\theta_2$=34.905, $\theta_3$=324.7) after $PC$-refinement.