templates, have been developed to recognize dis- 
tantly related proteins or protein domains and to 
carry out model building on the basis of the know^n 
protein structures. Another example is the determi- 
nation of three-dimensional structures of small pro- 
teins and nucleic acids from NMR NOESY (nuclear 
Overhauser enhancement two-dimensional spec- 
^^troscopy) experiments. The search models ob- 
tained by these methods are often approximate. For 
example, the atomic root-mean-square differences 
in the protein core of homologous proteins range 
from 0.76 to 2.3 A. Thus MR could become difificult, 
if not impossible. It is therefore desirable to extend 
the applicability of MR. 
If there is one molecule in the crystallographic 
asymmetric unit, then three positional and three 
angular parameters fully describe the placement of 
the search model in the unit cell of the target crys- 
tal. This six-dimensional search can be reduced to a 
sequence of a three-dimensional angular search 
using a rotation function (RF), follov^^ed by a three- 
dimensional positional search using a translation 
function (TP). This procedure assumes that the 
highest peak of the RF yields the correct orienta- 
tion. Examples are known where this is not true. 
Due to advances in computer technology, multidi- 
mensional search strategies with more than three 
parameters are now possible. 
Even six-dimensional searches may fail to solve 
the crystal structure. In this case. Dr. Briinger pro- 
poses to vary the atomic coordinates of the search 
model in a neighborhood of the initial positions. 
For instance, R factor refinements could be carried 
out with the search model placed in the most likely 
orientations and positions, as determined by a mul- 
tidimensional search. However, this procedure 
would be computationally intensive, since the 
translation searches may not yield a unique solu- 
tion, and one would have to carry out refinements 
for several peaks for the translation search for each 
selected orientation. 
A new method was developed to refine atomic 
coordinates of the search model prior to transla- 
tion searches. The target function for the new re- 
finement method, PC refinement, consists of a 
Patterson energy term combined with an empirical 
energy function. The Patterson energy term is pro- 
portional to the negative correlation coefficient PC 
between the squared amplitudes of the observed 
and the calculated normalized structure factors. 
The normalized structure factors are computed 
with the search model placed in a triclinic unit cell 
identical in geometry to that of the crystal. The em- 
pirical energy function represents information 
about the geometry and nonbonded interactions of 
the macromolecule. PC refinement of individual 
atomic coordinates may be impractical for large 
molecules because of the large computational ex- 
pense. In this case, generalized coordinates, such 
as the orientation and position of rigid groups, can 
be refined against a target function that simply con- 
sists of the Patterson energy term without an em- 
pirical energy function. 
A combined MR and PC-refinement strategy was 
proposed in Dr. Briinger's laboratory. First, a con- 
ventional RF is carried out. All sampled orientations 
are sorted with respect to the RF value, and a large 
number of the highest peaks are selected for PC re- 
finements. Finally the PC-refined search models 
with the highest correlation coefficients are used 
for conventional translation searches. 
Computer studies were carried out that were 
aimed at evaluating the utility of PC refinement. A 
particular search model of crambin with a 2 A back- 
bone atomic root-mean-square difference from the 
crystal structure failed to provide the correct orien- 
tation when using an RF or a six-dimensional 
search. PC refinements of the search model in the 
most likely orientations resulted in the correct ori- 
entation having the lowest value of the target func- 
tion. This enabled Dr. Briinger and his colleagues 
to solve the crambin structure, starting with the PC- 
refined search model. In an application to myoglo- 
bin, it was shown that rigid-group PC refinement of 
the eight a-helices has an approximate radius of 
convergence of 13° for orientation parameters. A 
search model of myoglobin with the a-helices artifi- 
cially tilted by 13° failed to provide the correct ori- 
entation when an RF or a six-dimensional search 
was used. PC refinements uniquely determined the 
correct overall orientation of the myoglobin search 
model by returning the a-helices to their original 
placements. 
Dr. Briinger is also Assistant Professor of Molecu- 
lar Biophysics and Biochemistry at Yale University. 
Continued 
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