(1) Center for Biological Sequence Analysis,
Department of Physical Chemistry, DTU,
The Technical University of Denmark, DK-2800, Lyngby, Denmark
(2) Department of Condensed Matter Physics
Risoe National Laboratory, DK-4000 Roskilde, Denmark
Structural fold classes for proteins are being represented on a three dimensional lattice and a model Hamiltonian[1] is suggested that can explain the division into fold classes during the compactification stage of the folding process. Proteins are described by chains of secondary structure elements with hinges in between, being the important degree of freedom. In such a chain representation protein structures can be represented uniquely by a 1-dimensional string of physical coupling constants describing scalar and vectorial spin interactions. An automated procedure is constructed in which any 3-dimensional protein structure in the usual $PDB$ coordinate format can be transformed into the proposed chain representation. From more general statistical mechanics arguments one can estimate the upper limit of the total number of possible fold classes to be around 4000[1,2]. This number is confirmed through an explicit calculation of the possible chain configurations that are tightly packed on a small 3-dim. regular lattice. Taking into account hydrophobic forces we have found a mechanism for formation of domains containing magic numbers of secondary structures and multiple of these domains[3]. We have performed a statistical analysis of available protein structures and found agreement with the predicted preferred abundances of proteins with a magic number of secondary structures.
REFERENCES
[1] P. A. Lindgaard and H. Bohr, Protein Folds, Eds.
H. Bohr and S. Brunak, CRC Press, New York, p. 98 (1995).
[2] C. Chothia, Nature, 357, p.543 (1992).
[3] P. A. Lindgaard and H. Bohr, "Magic
numbers in protein structurs", To appear in Phys. Rev. Lett. (1996).