  Uncovering the quantitative laws that govern the growth and division of
single cells remains a major challenge. Using a unique combination of
technologies that yields unprecedented statistical precision, we find that the
sizes of individual Caulobacter crescentus cells increase exponentially in
time. We also establish that they divide upon reaching a critical multiple
($\approx$1.8) of their initial sizes, rather than an absolute size. We show
that when the temperature is varied, the growth and division timescales scale
proportionally with each other over the physiological temperature range.
Strikingly, the cell-size and division-time distributions can both be rescaled
by their mean values such that the condition-specific distributions collapse to
universal curves. We account for these observations with a minimal stochastic
model that is based on an autocatalytic cycle. It predicts the scalings, as
well as specific functional forms for the universal curves. Our experimental
and theoretical analysis reveals a simple physical principle governing these
complex biological processes: a single temperature-dependent scale of cellular
time governs the stochastic dynamics of growth and division in balanced growth
conditions.
