1 The eukaryotic DNA is organized in one or more linear molecules, called chromosomes, which are associated with histone proteins. 2  All chromosomal DNA is stored in the cell nucleus, separated from the cytoplasm by a membrane. 3  Some eukaryotic organelles such as mitochondria also contain some DNA. Some eukaryotic cells (plant cells and fungal cells) also have a cell wall. 2  Inside the cell is the cytoplasmic region that contains the genome (DNA), ribosomes and various sorts of inclusions. 3  The genetic material is freely found in the cytoplasm.