What is the present tense verb form of apoptosis?
According to Google Scholar, there were ~40000 hits for "apoptose" and ~120k hits for "undergo apoptosis" in published literature, both of which had significant numbers of high-impact articles. 

Therefore, it is clear that both expressions are sufficiently used in literature for either to be used. 

Personally, I would say "undergo apoptosis" being both shorter than your original phrase and not risking coining new word forms.