  How cells regulate the number of organelles is a fundamental question in cell
biology. While decades of experimental work have uncovered four fundamental
processes that regulate organelle biogenesis, namely, de novo synthesis,
fission, fusion and decay, a comprehensive understanding of how these processes
together control organelle abundance remains elusive. Recent fluorescence
microscopy experiments allow for the counting of organelles at the single-cell
level. These measurements provide information about the cell-to-cell
variability in organelle abundance in addition to the mean level. Motivated by
such measurements, we build upon a recent study and analyze a general
stochastic model of organelle biogenesis. We compute the exact analytical
expressions for the probability distribution of organelle numbers, their mean,
and variance across a population of single cells. It is shown that different
mechanisms of organelle biogenesis lead to distinct signatures in the
distribution of organelle numbers which allows us to discriminate between these
various mechanisms. By comparing our theory against published data for
peroxisome abundance measurements in yeast, we show that a widely believed
model of peroxisome biogenesis that involves de novo synthesis, fission, and
decay is inadequate in explaining the data. Also, our theory predicts
bimodality in certain limits of the model. Overall, the framework developed
here can be harnessed to gain mechanistic insights into the process of
organelle biogenesis.
