This paper couples a general d-dimensional (d arbitrary) model for the intr
acellular biochemistry of a generic cell with a probabilistic division hypo
thesis and examines the consequence of division for stability of cell funct
ion and structure. We show rather surprisingly that cell division is capabl
e bf giving rise to a stable population of cells with respect to function a
nd structure even if, in the absence of cell division, the underlying bioch
emical dynamics are unstable. In the context of a simple example, our stabi
lity condition suggests that rapid cell proliferation plays a stabilizing r
ole for cellular populations.