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Here, we combine the two approaches to extend the size of systems for which free energies can be calculated. We study a series of all\u2010atom poly\u2010alanine systems in a simple dielectric solvent and find that precise free energies can be obtained rapidly. For instance, for 12 residues, less than an hour of single\u2010processor time is required. The combined approach is formally equivalent to the annealed importance sampling algorithm; instead of annealing by decreasing temperature, however, interactions among fragments are gradually added as the molecule is grown. We discuss implications for future binding affinity calculations in which a ligand is grown into a binding site. \u00a9 2010 Wiley Periodicals, Inc. 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