  Microbial growth and division are fundamental processes relevant to many
areas of life science. Of particular interest are homeostasis mechanisms, which
buffer growth and division from accumulating fluctuations over multiple cycles.
These mechanisms operate within single cells, possibly extending over several
division cycles. However, all experimental studies to date have relied on
measurements pooled from many distinct cells. Here, we disentangle long-term
measured traces of individual cells from one another, revealing subtle
differences between temporal and pooled statistics. By analyzing correlations
along up to hundreds of generations, we find that the parameter describing
effective cell-size homeostasis strength varies significantly among cells. At
the same time, we find an invariant cell size which acts as an attractor to all
individual traces, albeit with different effective attractive forces. Despite
the common attractor, each cell maintains a distinct average size over its
finite lifetime with suppressed temporal fluctuations around it, and
equilibration to the global average size is surprisingly slow (> 150 cell
cycles). To demonstrate a possible source of variable homeostasis strength, we
construct a mathematical model relying on intracellular interactions, which
integrates measured properties of cell size with those of highly expressed
proteins. Effective homeostasis strength is then influenced by interactions and
by noise levels, and generally varies among cells. A predictable and measurable
consequence of variable homeostasis strength appears as distinct oscillatory
patterns in cell size and protein content over many generations. We discuss the
implications of our results to understanding mechanisms controlling division in
single cells and their characteristic timescales
