Abstract.: Roughly 3/4 of human genomes are sequestered by nucleosomes, DNA spools with a protein core, dictating a broad range of biological processes, ranging from gene regulation, recombination, and replication, to chromosome condensation. Nucleosomes are dynamical structures and temporarily expose wrapped DNA through spontaneous unspooling from either end, a process called site exposure or nucleosome breathing. Here we ask how this process is influenced by the mechanical properties of the wrapped DNA, which is known to depend on the underlying base pair sequence. Using a coarse-grained nucleosome model we calculate the accessibility profiles for site exposure. We find that the process is very sensitive to sequence effects, so that evolution could potentially tune the accessibility of nucleosomal DNA and would only need a small number of mutations to do so. Graphical abstract: [Figure not available: see fulltext.].