We explore the HP model not only on the square lattice as originally proposed by Ken Dill, but we also use the triangular lattice. We find upper and lower bounds on the number of self-avoiding walks. In the square lattice, we get O(b^n) for some b in [2.414, 3]. We count the number of all self-avoiding walks of length up to 16 in the square and triangular lattices by exhaustively listing them. We use these lists of self-avoiding walks to study two HP sequences, one of length 11, and the other of length 16. We show that the diameter of the convex hull of a conformation can be used as an estimate of the energy of the conformation. Our examples demonstrate that the same holds true for the area of the convex hull. Both of these measures can be easily computed for a given conformation.
Worcester Polytechnic Institute
Major Qualifying Project
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