The thymus is the primary organ for the generation of naive T cells, a key component of the immune system. Tolerance of T cells to self is achieved primarily in the thymic medulla, where immature T cells (thymocytes) sample self-peptides presented by medullary thymic epithelial cells (mTECs). A sufficiently strong interaction activates the thymocytes leading to negative selection. A key question of current interest is whether there is any structure in the manner in which mTECs present peptides: can any mTEC present any peptide at any time, or are there particular patterns of correlated peptide presentation? We investigate this question using a mathematical model of negative selection. We find that correlated patterns of peptide presentation may be advantageous in negatively selecting low-degeneracy thymocytes (that is, those thymocytes which respond to relatively few peptides). We also quantify the probability that an auto-reactive thymocyte exits the thymus before it encounters a cognate antigen. The results suggest that heterogeneity of gene co-expression in mTECs has an effect on the probability of escape of autoreactive thymocytes.