introducing additional parameters or chemical re- 
straints. Perhaps the most striking result is a high 
correlation between the free R value and the 
model's phase accuracy. In other words, the accu- 
racy of the model's phases can be assessed with the 
observed amplitudes. 
This suggests applications of the free R approach 
in the area of ab initio phasing. An example is the 
modeling of diffraction data by a liquid of atomic 
point scatterers, which shows some promise for ei- 
ther very high or very low resolution phasing. Be- 
cause of the simplicity of the liquid, configurational 
space can be searched efficiently. However, at me- 
dium resolution ranges typically obtainable for mac- 
romolecules, there are a large number of configura- 
tions with R values that are equally as good as those 
of the correct solution. There appear to be fewer 
configurations with free R values equally as good as 
those of the correct solution. It is thus conceivable 
that the free /? approach could extend the applicabil- 
ity of the liquid model. 
The project described above was supported in 
part by a grant from the National Science 
Foundation. 
NMR Spectroscopy: Accuracy and Precision 
of Solution Structures 
Parallel to the development of criteria for the ac- 
curacy of crystal structures, Dr. Briinger's group has 
embarked on similar investigations for solution 
NMR-derived structures. The theory that describes 
NMR relaxation processes based on atomic models is 
less well developed than in x-ray crystallography, 
where the atomic model is essentially related to the 
diffraction data by a Fourier transformation. In con- 
trast, NMR relaxation processes depend on atomic 
motions over a wide range of time scales, which are 
difficult to simulate with current methodologies 
and computing power. Furthermore, solution NMR- 
derived structures are usually less well determined 
than x-ray crystal structures; the observed nu- 
clear Overhauser enhancement (NOE) intensities 
show large errors; and efforts to improve the fit of 
the model to the NOE intensity data are prone to 
overfitting. 
The intensity of the observed NOE cross-peaks is a 
function of certain interproton distances, thus pro- 
viding information on the three-dimensional struc- 
ture of the studied molecule. For a rigid spin system 
and short mixing times in a first approximation, the 
NOE intensity between a pair of protons is directly 
proportional to the inverse of the sixth power of the 
distance separating the protons (isolated spin-pair 
approximation). In the case of large molecules, the 
relationship between the cross-peak intensity and 
the distance between the two protons is more com- 
plicated, since indirect magnetization transfer via 
other protons ("spin diffusion") contributes as 
well. This, together with uncertainties in the mo- 
tional behavior of abiomolecule, allows only within 
approximate ranges the determination of interpro- 
ton distances derived with the isolated spin-pair 
approximation. Until very recently structure de- 
termination with NMR data has relied on these ap- 
proximate distance ranges. 
Dr. Briinger's group has begun to apply complete 
matrix relaxation methods to a number of systems 
that, at least in principle, can circumvent the iso- 
lated spin-pair approximation. In this approach the 
differences between the NOE intensities and those 
calculated by the full relaxation matrix approach 
are directly minimized. Chemical restraints are 
added in a fashion similar to crystallographic 
refinement. 
The results can be summarized as follows. Upon 
refinement of the macromolecule, the fit to the 
NMR data improves significantly with relatively 
small shifts (typically 0.5-1 A) in the refined struc- 
tures. For example, in the case of the squash trypsin 
inhibitor CMTI, the refined structures are somewhat 
closer to the x-ray structure of the inhibitor (actu- 
ally, a complex of CMTI with trypsin) than are the 
initial structures. The deviations between observed 
and computed NOEs are significantly improved, ex- 
cept for NOEs that are either misassigned or inappro- 
priately modeled as a result of conformational 
averaging. 
Structure Prediction of Helical Supercoils 
as Applied to Leucine Zippers 
and Membrane Proteins 
While ab initio prediction of protein structure is 
an elusive goal, prediction of tertiary structure from 
secondary structure using "docking" procedures is 
more likely to succeed. Although the general princi- 
ples of protein association seem fairly well under- 
stood, the application of these principles to the pre- 
diction of specific association remains difficult, 
even for a seemingly straightforward case. Simple 
criteria such as buried surface area, solvation free 
energy, electrostatics, or packing are insufficient to 
predict correct association, while empirical energy 
functions are prone to inaccuracies and subject to 
the multiple minima problem. 
Under certain minimal assumptions about helix- 
helix association, it is possible to guide the docking 
process. An automated approach for the modeling of 
helical supercoils through simulated annealing was 
developed previously by Dr. Briinger's group. Ini- 
tially, a model consisting only of C atoms is cre- 
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