Double-strand breaks (DSBs) in nuclear DNA represents radiation-induced damage that has been identified as particularly deleterious. Calculating this damage using Monte Carlo track structure modeling could be a suitable indicator to better assess and anticipate the side-effects of radiation therapy. However, as already demonstrated in previous work, the geometrical description of the nucleus and the DNA content used in the simulation significantly influence damage calculations. Therefore, in order to obtain accurate results, this geometry must be as realistic as possible. In this study, a new geometrical model of an endothelial cell nucleus and DNA distribution according to the isochore theory are presented and used in a Monte Carlo simulation chain based on the Geant4-DNA toolkit. In this theory, heterochromatin and euchromatin compaction are distributed along the genome according to five different families (L1, L2, H1, H2, and H3). Each of these families is associated with a different hetero/euchromatin rate related to its compaction level. In order to compare the results with those obtained using a previous nuclear geometry, simulations were performed for protons with linear energy transfers (LETs) of 4.29 keV/µm, 19.51 keV/µm, and 43.25 keV/µm. The organization of the chromatin fibers at different compaction levels linked to isochore families increased the DSB yield by 6-10%, and it allowed the most affected part of the genome to be identified. These new results indicate that the genome core is more radiosensitive than the genome desert, with a 3-8% increase in damage depending on the LET. This work highlights the importance of using realistic distributions of chromatin compaction levels to calculate radio-induced damage using Monte Carlo simulation methods.