Understanding how cells inherit their epigenetic state is a complex issue. European researchers found the answers in yeast.
Cells possess a mechanism known as transcriptional memory that allows them to remember which genes they must express at any time. This ensures that they respond quickly to their environmental cues. It is now widely accepted that transcriptional memory is part of the epigenetic profile of the cell. This is passed down to its progeny through an unknown mechanism.
Further details: Epigenetics in yeast