# Distance Matrix Predictions and Distance Statistics

**M.G. Reese, O. Lund and J. Bohr**

The Technical University of Denmark

Department of Physics

DK-2800 Lyngby, Denmark.

H. Bohr and S. Brunak

Center of Biological Sequence Analysis

The Technical University of Denmark

DK-2800 Lyngby, Denmark.

E-mail: reese@cbs.dtu.dk

## Abstract:

We present a statistical analysis of protein structures based on
inter atomic "C-alpha"-distances. The overall distance distributions
reflect in detail the contents of sequence specific substructures
maintained by local interactions (such as "alpha"-helices), and longer
range interactions (like disulfide bridges and "beta"-sheets). The
distance distributions are shown to be indicative for a given fold
class. We also show that a volume scaling of the distances, makes
distance distributions for protein chains of different length
superimposeable. Distance distributions were also calculated specifically for
amino acids separated by a given number of residues. Specific features
in these distributions are visible for sequence separation up to 20
amino acid residues. A simple representation, which preserves most of
the information in the distance distributions, was obtained using 6
parameters only. The parameters give rise to canonical distance
intervals, and when predicting coarse grained distance constraints by
methods like data driven artificial neural networks, these
should preferably be selected from these intervals.
We discuss the use of the 6
parameters for determining or reconstructing 3-dimensional
protein structures.

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