We study the early steps of amyloid formation of the seven residue peptide GNNQQNY from yeast prion-like protein Sup35 by simulating the random coil to beta-sheet and alpha-helix to beta-sheet transition both in the absence and presence of a cross-beta amyloid nucleus. The simulation method at atomic resolution employs a new implementation of a Langevin dynamics "reaction path annealing" algorithm. The results indicate that the presence of amyloid-like cross-beta-sheet strands both facilitates the transition into the cross-beta conformation and substantially lowers the free energy barrier for this transition. This model systems allows us to investigate the energetic and kinetic details of this transition, which is consistent with an auto-catalyzed, nucleation-like mechanism for the formation of beta-amyloid. In particular, we find that electrostatic interactions of peptide backbone dipoles contribute significantly to the stability of the beta-amyloid state. Furthermore, we find water exclusion and interactions of polar side-chains to be driving forces of amyloid formation: the cross-beta conformation is stabilized by burial of polar side-chains and inter-residue hydrogen bonds in the presence of an amyloid-like "seed". These findings are in support of a "dry, polar zipper model" of amyloid formation.