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Lattice models, for their coarse-grained nature, are best suited for thestudy of the ``designability problem'', the phenomenon in which most of theabout 16,000 proteins of known structure have their native conformationsconcentrated in a relatively small number of about 500 topological classes ofconformations. Here it is shown that on a lattice the most highly designablesimulated protein structures are those that have the largest number ofsurface-core switchbacks. A combination of physical, mathematical andbiological reasons that causes the phenomenon is given. By comparing the mostfoldable model peptides with protein sequences in the Protein Data Bank, it isshown that whereas different models may yield similar designabilities,predicted foldable peptides will simulate natural proteins only when the modelincorporates the correct physics and biology, in this case if the main foldingforce arises from the differing hydrophobicity of the residues, but does notoriginate, say, from the steric hindrance effect caused by the differing sizesof the residues.Comment: 12 pages, 10 figure

Geometric and statistical properties of the mean-field hydrophobic-polar model, the large-small model, and real protein sequences