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On the study of protein folding, our understanding about the proteinstructures is limited. In this paper we find one way to characterize thecompact structures of lattice protein model. A quantity called Partnum is givento each compact structure. The Partnum is compared with the conceptDesignability of protein structures emerged recently. It is shown that thehighly designable structures have, on average, an atypical number of localdegree of freedom. The statistical property of Partnum and its dependence onsequence length is also studied.Comment: 10 pages, 5 figure

One way to characterize the compact structures of lattice protein model