Amyloid formation by the intrinsically disordered α-synuclein protein is the hallmark of Parkinson's disease. We present atomistic Molecular Dynamics simulations of the core of α-synuclein using enhanced sampling techniques to describe the conformational and binding free energy landscapes of fragments implicated in fibril stabilization. The theoretical framework is derived to combine the free energy profiles of the fragments into the reaction free energy of a protein binding to a fibril. Our study shows that individual fragments in solution have a propensity toward attaining non-β conformations, indicating that in a fibril β-strands are stabilized by interactions with other strands. We show that most dimers of hydrogen-bonded fragments are unstable in solution, while hydrogen bonding stabilizes the collective binding of five fragments to the end of a fibril. Hydrophobic effects make further contributions to the stability of fibrils. This study is the first of its kind where structural and binding preferences of the five major fragments of the hydrophobic core of α-synuclein have been investigated. This approach improves sampling of intrinsically disordered proteins, provides information on the binding mechanism between the core sequences of α-synuclein, and enables the parametrization of coarse grained models.