Using a triangular lattice model to study the designability of protein folding, we overcame the parity problem of previous cubic lattice model and enumerated all the sequences and compact structures on a simple two-dimensional triangular lattice model of size 4+5+6+5+4. We used two types of amino acids, hydrophobic and polar, to make up the sequences, and achieved 223+212 different sequences excluding the reverse symmetry sequences. The total string number of distinct compact structures was 219,093, excluding reflection symmetry in the self-avoiding path of length 24 triangular lattice model. Based on this model, we applied a fast search algorithm by constructing a cluster tree. The algorithm decreased the computation by computing the objective energy of non-leaf nodes. The parallel experiments proved that the fast tree search algorithm yielded an exponential speed-up in the model of size 4+5+6+5+4. Designability analysis was performed to understand the search result.
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