Protein variability in single cells has been studied extensively in
populations, but little is known about temporal protein fluctuations in a
single cell over extended times. We present here traces of protein copy number
measured in individual bacteria over multiple generations and investigate their
statistical properties, comparing them to previously measured population
snapshots. We find that temporal fluctuations in individual traces exhibit the
same universal features as those previously observed in populations. Scaled
fluctuations around the mean of each trace exhibit the same universal
distribution shape as found in populations measured under a wide range of
conditions and in two distinct microorganisms. Additionally, the mean and
variance of the traces over time obey the same quadratic relation. Analyzing
the temporal features of the protein traces in individual cells, reveals that
within a cell cycle protein content increases as an exponential function with a
rate that varies from cycle to cycle. This leads to a compact description of
the protein trace as a 3-variable stochastic process - the exponential rate,
the cell-cycle duration and the value at the cycle start - sampled once each
cell cycle. This compact description is sufficient to preserve the universal
statistical properties of the protein fluctuations, namely, the protein
distribution shape and the quadratic relationship between variance and mean.
Our results show that the protein distribution shape is insensitive to
sub-cycle intracellular microscopic details and reflects global cellular
properties that fluctuate between generations
