By exact computer enumeration and combinatorial methods, we have calculated the designability of proteins in a simple lattice H-P model for the protein folding problem. We show that if the strength of the non-additive part of the interaction potential becomes larger than a critical value, the degree of designability of structures will depend on the parameters of potential. We also show that the existence of a unique ground state is highly sensitive to mutation in certain sites.
Geometrical properties of protein ground states are studied using an
algebraic approach. It is shown that independent from inter-monomer
interactions, the collection of ground state candidates for any folded protein
is unexpectedly small: For the case of a two-parameter Hydrophobic-Polar
lattice model for $L$-mers, the number of these candidates grows only as $L^2$.
Moreover, the space of the interaction parameters of the model breaks up into
well-defined domains, each corresponding to one ground state candidate, which
are separated by sharp boundaries. In addition, by exact enumeration, we show
there are some sequences which have one absolute unique native state. These
absolute ground states have perfect stability against change of inter-monomer
interaction potential.Comment: 9 page, 4 ps figures are include
The concept of the reduced set of contact maps is introduced. Using this concept we find the ground state candidates for a hydrophobic-polar lattice model on a two-dimensional square lattice. Using these results we exactly enumerate the native states of all proteins for a wide range of energy parameters. In this way, we show that there are some sequences which have an absolute native state. Moreover, we study the scale dependence of the number of members of the reduced set, the number of ground state candidates, and the number of perfectly stable sequences by comparing the results for sequences with lengths of 6 up to 20.
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