Nucleosomes represent the basic building block of chromatin and provide an important mechanism by which cellular processes are controlled. The locations of nucleosomes across the genome are not random but instead depend on both the underlying DNA sequence and the dynamic action of other proteins within the nucleus. These processes are central to cellular function, and the molecular details of the interplay between DNA sequence and nucleosome dynamics remain poorly understood. In this work, we investigate this interplay in detail by relying on a molecular model, which permits development of a comprehensive picture of the underlying free energy surfaces and the corresponding dynamics of nucleosome repositioning. The mechanism of nucleosome repositioning is shown to be strongly linked to DNA sequence and directly related to the binding energy of a given DNA sequence to the histone core. It is also demonstrated that chromatin remodelers can override DNA-sequence preferences by exerting torque, and the histone H4 tail is then identified as a key component by which DNA-sequence, histone modifications, and chromatin remodelers could in fact be coupled.