We report the reproducible first-principles folding of the 40 amino acid, three-helix headpiece of the HIV accessory protein in a recently developed all-atom free-energy forcefield. Six of twenty simulations using an adapted basin-hopping method converged to better than 3Å backbone RMS deviation to the experimental structure. Using over 60,000 low-energy conformations of this protein, we constructed a decoy tree that completely characterizes its folding funnel.PACS numbers: 87.15. Cc,02.70.Ns,02.60.Pn Available genomic and sequence information for proteins contains a wealth of biomedical information that becomes accessible when translated into three-dimensional structure [1]. While theoretical models for protein structure prediction [2,3] that partially rely on experimental information have shown consistent progress [4], the assessment of de-novo strategies that rely on sequence information alone has been much less favorable [5]. The development of such techniques, in particular of transferable first-principle all-atom folding methods, would significantly benefit the understanding of protein families where little experimental information is available, the prediction of novel folds as well as the investigation of protein association and dynamics which are presently difficult to probe experimentally. Recent progress for small peptides [3,6,7,8] documents both the feasibility of this approach as well as its limitations [9,10], in particualr those associated with the direct simulation of the folding process through molecular dynamics [11].Overwhelming experimental evidence supports the thermodynamic hypothesis [12] that many proteins are in thermodynamic equilibrium with their environment: their native state thus corresponds to the global minimum of their free energy landscape [13]. The free energy of the system is accessible either indirectly by explicit ensemble averaging of the combined internal energy of protein and solvent, or directly in a free-energy forcefield where an implicit solvation model approximates direct interactions with the solvent as well as most of the entropic contributions. We developed an all-atom protein forcefield (PFF01) [8,14,15] with an area-based implicit solvent model that approximates the free energy of peptide conformations in the natural solvent. Using a rational decoy approach this forcefield was optimized to correctly predict the native structure of the 36-amino acid headgroup of villin [9,10,11]. Without further parameter adjustment we then simulated the structurally conserved 40 amino-acid headpiece of the autonomously folding HIV accessory protein (1F4I-40) [16] with a modified basin hopping technique [17,18]. Out of twenty simulations the five energetically lowest correctly reproduced the NMR structure of this three-helix protein with a backbone RMS deviation of less than 3Å. The combination of decoy based model development for the free energy with efficient stochastic optimization methods suggests a viable route for protein structure prediction at the all atom level with p...